Book: Magnetobiology: Underlying Physical Problems



Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Magnetobiology: Underlying Physical Problems

Foreword

The book is meant primarily for physicists, but it will also appeal to workers in chemistry, biology, medicine, and related fields. It is written by Vladimir N. Binhi, a well-known expert in magnetobiology and a member ofthe American Bioelectromagnetics Society.

Electromagnetobiology is a fast-developing field of research, its practical and environmental aspects being a topic ofever-increasing number ofbooks. At the same time, physically, the biological effects ofweak magnetic fields are still regarded as a paradox. The book comes to grips with that problem and fills in a theoretical gap. It reviews and analyzes the experimental evidence that yields some insights into the primary physical processes ofmagnetoreception and the f

requency and

amplitude spectra ofthe action ofweak magnetic fields. Also, the book reviews the available hypothetical mechanisms for that action.

The methodology used in the book enables any physical idea to be quickly ix

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assessed in terms ofits value for magnetobiology. The author proposes a unified foundation to account for the biological effects of magnetic fields. Of especial interest is his hypothesis ofthe interference ofquantum states ofions and molecules put forth to explain the paradoxes ofthe non-thermal action ofelectromagnetic fields.

Binhi draws on fundamental physical principles to derive a reasonable model for the interaction ofelectromagnetic fields with biological systems. The model agrees well with experiment and is essentially a thorough formulation of this interaction problem. The theory awaits elaboration, a fact that is bound to attract to that field new workers to whom the book could be recommended as a proper introduction.

The subject ofthe book could also be referred to as magnetobiological spectroscopy, in which data on physical processes in biophysical structures are derived by physical as well as biological means. It is safe to say that a new field, magnetobiology, has made its appearance in theoretical biophysics. This field still continues to cause much discussion, but it calls for more sophisticated studies to be carried out using rigorous mathematical and physical tools.

A. M. Prokhorov

member ofthe Russian Academy ofSciences

winner ofthe Nobel Prize for Physics

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Acknowledgements

It is a pleasure to express my deep sense ofobligation to A. M. Prokhorov who has found time to go over the book and make valuable comments. I am grateful to E. E. Fesenko. His support oforiginal studies and discussions ofthe issue influenced the structure ofthe book and the interplay ofits parts. I also thank V. A. Milyaev for useful discussions and for making my cooperation with the Institute of General Physics possible.

I thank H. Berg, F. Bersani, C. Blackman, R. Fitzsimmons, R. Goldman, B. Greenebaum, Yu. G. Grigoriev, A. Liboff, V. P. Makarov, S. D. Zakharov, and A. V. Zolotaryuk for their reviews, comments, and assistance.

Discussions with colleagues and friends have always been an invaluable source ofnew insights. I record my thanks to A. E. Akimov, I. Ya. Belyaev, O. V. Betskii, L. A. Blumenfeld, M. Fillion-Robin, R. Goldman, Yu. I. Gurfinkel, A. P. Dubrov, A. A. Konradov, V. K. Konyukhov, A. N. Kozlov, V. V. Lednev, V. I. Lobyshev, A. V. Savin, S. E. Shnoll, I. M. Shvedov, and E. V. Stepanov.

Translators A. Repiev and M. Edelev, two bilingual physicists, deserve particular credit for the fact that the English version of the book is more readable than its Russian original.

At various times I received much assistance from my parents and relatives.

Their generous encouragement made the book possible. Special thanks are due to E. Tourantaeva, who has taken immense pains in the production ofthis work and whose skill and forbearance have greatly eased my task.

Vladimir Binhi

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Physical notation

m e, m p

masses ofthe electron and proton, respectively

M, q

mass and electric charge ofa particle

S, µ

spin in units of and magnetic moment ofa particle

γ = µ/ S

gyromagnetic ratio

I

moment ofinertia

χ

magnetic susceptibility

A , A 0

vector and scalar potentials ofan EM field

H , B

strength and induction ofa magnetic field

E , D

strength and displacement ofan electric field

H DC, H AC

strength ofDC and AC magnetic fields

h = H AC /H DC

relative amplitude ofa magnetic field

circular frequency of an external field

Ωc = qH DC /M c

cyclotron frequency

f = Ω / Ωc

relative frequency of a magnetic field

ΩN = γH DC

NMR frequency

ΩR = γH AC

Rabi frequency

Γ = ΩN / Ωc = γM c/q

ion–isotope constant

ω 0 = Ωc / 2

Larmor frequency

ω 1 = qH AC / 2 M c

Larmor frequency in terms ofthe amplitude ofa magnetic

field

L, H

Lagrange and Hamilton functions

H

Hamiltonian operator

P , P, p, L, L, l

vector and scalar operators ofthe momentum and angular

momentum and their eigenvalues

S = σσ/ 2, S

vector and scalar spin operators

I , I

same for the nuclear spin

M = µS /S

magnetic moment operator

σ = ( σ 1 , σ 2 , σ 3)

Pauli matrices

Ψ

wave function

ψi, εi

eigenfunctions and eigenvalues of the Hamiltonian

m

magnetic quantum number

T

absolute temperature

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Mathematical notation

ab

scalar product ofvectors

a × b

vector product

..

quantum-mechanical averaging

{ , }

commutation operator

E[ .. ]

mathematical expectation

equal in order ofmagnitude

,

real and imaginary parts

δ

delta function

Fundamental constants

e = 4 . 803 · 10 10

electron charge (CGS system)

= 1 . 055 · 10 27 erg s

Planck constant

c = 2 . 998 · 1010 cm s 1

velocity oflight in a vacuum

m e = 9 . 109 · 10 28 g

electron mass

m p = 1 . 673 · 10 24 g

proton mass

µ = e / 2 m

B

e c = 9 . 274 · 10 21 erg G 1

Bohr magneton

µ = e / 2 m

N

p c = 5 . 051 · 10 24 erg G 1

nuclear magneton

µ p = 2 . 7928 µ

proton magnetic moment

N

κ = 1 . 3807 · 10 16 erg K 1

Boltzmann constant

N = 6 . 022 · 1023 mol 1

Avogadro number

A

Some physical quantities

κT ≈ 4 . 6 · 10 14 erg

thermal energy at T = 300 K

1 amu = 1 . 661 · 10 24 g

atomic mass

1 A/m = 1 . 26 · 10 2 Oe

magnetic field strength

1 V/m = 0 . 333 · 10 4 CGS units

electric field strength

o

1 D = e · 1 A = 3.336 · 10 30 C m

electric dipole moment

= 10 18 CGS units

1 ohm = 1 . 11 · 10 12 CGS units

electric resistance

1 mW/cm2 = 104 erg/(m2s)

energy flux

1 cm 1 = 30 GHz

frequency ( f /c = λ− 1)

1 eV = 1.602 · 10 12 erg

energy

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INTRODUCTION

There were also two choruses, one of which

somehow managed to represent the de Broglie’s

waves and the logic of history, while the other

chorus, the good one, argued with it.

V. Nabokov, The Gift

Magnetobiology is a new multidisciplinary domain with contributions coming from fields as diverse as physics and medicine. Its mainstay, however, is biophysics. Magnetobiology has only received a remarkable impetus in the recent two decades. At the same time magnetobiology is a subject matter that during the above relatively long time span failed to receive a satisfactory explanation. There is still no magnetobiological theory, or rather its general physical treatments, or predictive theoretical models. This is all due to the paradoxical nature ofthe biological action ofweak low-frequency magnetic fields, whose energy is incomparable by far with the characteristic energy ofbiochemical transformations. This all makes the very existence ofthe domain quite dubious with most ofthe scientific community, despite a wealth ofexperimental evidence.

A large body ofobservational evidence gleaned over years strongly suggests that some electromagnetic fields pose a potential hazard to human health and are a climatic factor that is of no less significance than temperature, pressure, and humidity. As more and more scientists become aware ofthat fact, studies ofthe mechanisms ofthe biological action ofelectromagnetic fields become an increasingly more topical issue.

There being no biological magnetoreceptors in nature, it is important to perceive the way in which the signal ofa magnetic field is transformed into a response ofa biological system. A low-frequency magnetic field permeates a living matter without any apparent hindrances. It affects all the particles ofthe tissue, but not all ofthe particles are involved in the process ofthe transferring ofinformation about the magnetic field to the biological level. Primary processes ofthe interaction ofa magnetic field with matter particles, such as electrons, atoms, and molecules, are purely physical processes. Charged particles ofliving matter, ions, that take part in biophysical and biochemical processes seem to be intermediaries in the transfer of magnetic field signals to the next biochemical level. Such a subtle regulation ofthe activity ofproteins ofenzyme type, affected via biophysical mechanisms involving 1

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INTRODUCTION

interim ions, shifts the metabolic processes. Beginning with that level one can gauge the action ofa magnetic field from the changes in metabolic product densities.

The biological effects of a magnetic field are often observed from the life-support parameters and the behavior ofindividuals and populations. Experiments, as a rule, boil down to the observation ofrelations between an external magnetic field and the biological effects it causes. Intermediary levels ofthe organization ofa living system, such as biophysical, biochemical, and physiological ones, appear to lie outside the experimental range, but anyway they affect the experimental results. We thus end up having a kind ofa cause-and-effect black box with properties beyond our control.

This does not allow any cause–effect relations to be worked out completely. At the same time, there is no practical way to observe the result ofthe action of weak magnetic fields at the level ofindividual biochemical reactions or biophysical structures using physical or chemical methods. Magnetobiology is thus fraught with practical difficulties caused by the fact that it necessarily combines issues of physics, biophysics, biochemistry, and biology.

In addition to an analytical review ofmagnetobiological studies, the book also provides the first detailed description ofthe effect ofthe interference ofquantum ion states within protein cavities. Using the Schrödinger and Pauli equations, a treatment is given of ion dynamics for idealized conditions and for parallel magnetic fields, as well as for a series ofother combinations ofmagnetic and electric fields. The treatment takes into consideration the ion nuclear spin and the non-linear response ofa protein to the redistribution ofion probability density. Formulas are obtained for the magnetic-field-dependent component of the dissociation probability for an ion–protein complex. The principal formula that gives possible magnetobiological effects in parallel DC H DC and AC H AC magnetic fields has the form1


sin2 A

m h

1

P =

|amm| 2

J2

, A =

m + nf Ξ .

A 2

n

2 f

2

m= m; n

Here m is the magnetic quantum number, m = m − m, Ξ = T Ωc is a dimensionless parameter that depends on the properties ofan ion–protein complex, Ωc = qH DC /M c is the cyclotron frequency of an ion, f = Ω / Ωs and h = H AC /H DC

are the dimensionless frequency and amplitude ofthe variable components ofa magnetic field, and J n is the n th order Bessel function. The elements amm are constant coefficients that define the initial conditions for an ion to stay in a cavity. The natural frequency and amplitude interference spectra are worked out for a wide variety ofmagnetic conditions, including those ofpulsed magnetic fields (MFs), for a “magnetic vacuum”, subjected to natural rotations ofmacromolecules, etc. They show a high level ofagreement with available experimental data.

1The book provides formulas to compute probable biologically active regimes of exposure to an EMF. We note that their practical application is fraught with unpredictable consequences, specifically with risks to human health.

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AN OVERVIEW OF MAGNETOBIOLOGICAL ISSUES

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The interference ofquantum states ofthe molecules rotating inside protein cavities, i.e., the interference of molecular gyroscopes, is considered. The properties of molecular gyroscopes are a consistent basis for explaining the physical mechanism ofthe non-thermal resonance-like biological effects ofEMFs, and for solving the so-called “kT problem”.

1.1 AN OVERVIEW OF MAGNETOBIOLOGICAL ISSUES

Unlike biomagnetism, which studies the MFs produced by various biological systems (Vvedenskii and Ozhogin, 1986; Kholodov et al. , 1990; Hämäläinen et al. , 1993; Baumgartner et al. , 1995), magnetobiology addresses the biological reactions and mechanisms ofthe action ofprimarily weak, lower than 1 mT, magnetic fields.

Recent years have seen a growing interest in the biological actions ofweak magnetic and electromagnetic fields. “Microwave News”, published in the USA, provides a catalogue ofhundreds ofInternet links to organizations that are directly concerned with electromagnetobiological studies, http: // www.microwavenews.com/www.html.

Electromagnetobiology is a part ofa more general issue ofthe biological effectiveness ofweak and hyperweak physico-chemical factors. It is believed that the action of such factors lies below the trigger threshold for protective biological mechanisms and is therefore prone to accumulating at the subcellular level and is likely at the level ofgenetic processes.

Electromagnetobiological research received an impetus in the 1960s when Devyatkov’s school developed and produced generators ofmicrowave EM radiations.

Almost immediately it was found that microwaves caused noticeable biological effects (Devyatkov, 1973). Those works were reproduced elsewhere. Ofmuch interest was the fact that more often than not the radiations concerned had a power too low to cause any significant heating oftissues. At the same time, the radiation energy quantum was two orders ofmagnitude lower than the characteristic energy ofchemical transformations κT . Also, the effects were only observed at some, not all, frequencies, which pointed to a non-thermal nature of the effects. The action of microwaves was also dependent on the frequency of low-frequency modulation.

Therefore, as early as the 1980s reliable observations ofbioeffects oflow-frequency 10–100 Hz magnetic fields themselves were obtained. This is important, since that frequency range covers frequencies of industrial and household electric appliances.

Interest in magnetobiology stems predominantly from ecological considerations.

The intrusion ofman into natural processes has reached a dangerous level. The environment is polluted with the wastes ofindustrial and household activities. We are also witnessing a fast buildup of electromagnetic pollution. In addition, there is still no clear understanding ofthe physico-chemical mechanisms for the biological action ofhyperweak natural and artificial agents. We have thus a paradox on our hands. That is to say, these phenomena are not just unaccountable, they seem to be at variance with the current scientific picture ofthe world. At the same time, a wealth ofobservational and experimental data has been accumulated, thus

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INTRODUCTION

I S Q P

N

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(OHFWURQ0)DWDWRPLFVFDOH

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Figure 1.1. Levels of various natural and man-made sources; approximate boundaries are indicated.

pointing to the real nature ofthe phenomenon. It follows that the biological action ofhyperweak agents is a fundamental scientific problem with a host ofapplications.

What factors can be called hyperweak? An intuitively acceptable threshold is dictated by common sense. Ifan effect, or rather a correlation, observed when exposed to some small signal is inconsistent with current views, i.e., we have a that-is-impossible situation, then the signal can be referred to as hyperweak. For electromagnetic fields (EMFs) within a low-frequency range it is a background level, which is engendered by industrial or even household electric devices (Grigoriev, 1994). The diagram in Fig. 1.1 shows the relative level ofmagnetic fields that characterize their sources and application fields. Figure 1.2 contains information on the spectral composition ofa low-frequency MF ofnatural origins. The spectrum, especially its part below 1 kHz, is strongly dependent on the place ofmeasurement, weather, season, etc.; therefore it is only conventional in nature. Municipal magnetic noise in the same spectral range, except for its discrete components 50 Hz and harmonics, is one or two orders ofmagnitude higher than the natural background.

Earlier on it had been believed that weak low-frequency MFs and EMFs of nonthermal intensity were safe for humans, and a biological action of such fields had seemed to be impossible in terms ofphysics. With time, experimental evidence has been gleaned that pointed to a potential danger ofthose fields and radiations (Pool, 1990a; Nakagawa, 1997), and the often-concealed nature of their action. Consequences may show themselves months or even years later. The ecological pertinence ofmagnetic fields becomes a subject ofinvestigations. Sanitary norms, prognosti-cation, and control ofand protection against electromagnetic smog are important

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AN OVERVIEW OF MAGNETOBIOLOGICAL ISSUES

5


7+]µ

+


I+]

Figure 1.2. Spectral density of fluctuations of low-frequency MFs fromnatural sources; adapted fromVladimirskii (1971).

aspects ofelectromagnetic ecology. Standards ofelectromagnetic safety are worked out by various national and international organizations, such as Comite Europeen de Normalisation Electrotechnique (CENELEC), Deutsche Institut fur Normung (DIN), American National Standards Institute (ANSI), International Non-Ionising Radiation Committee ofInternational Radiation Protection Association (INIRC

IRPA), and Occupational Health Institute ofthe Russian Academy ofSciences.

The World Health Organization (WHO) coordinates that activity with a view to achieve unified world standards. At present, safety norms for various ranges may differ tens or even hundreds oftimes, which strongly suggests that this domain awaits in-depth scientific studies.

The biological action ofinterest is that produced by systems and devices whose

“services” are hard to do without: power transmission lines, cars, TV sets, background radiations of dwellings, and manufacturing facilities. Special culprits of late are computers and radio telephones (Carlo, 2000). A quantitative indication of the power-frequency EMF level coming from power transmission lines is given in Fig. 1.3, which provides the theoretical distribution ofelectric and magnetic fields with the distance from a line.

Radiations produced by household appliances have been measured many times.

For instance, measurements ofthe 50-Hz MF conducted by Conti et al. (1997) within half a meter from household appliances yielded the following roughly averaged data: a washing machine — 5 µ T, a refrigerator — 0.1 µ T, a conditioner —

1 µ T, an electric meat grinder — 2 µ T , a vacuum cleaner — 2 µ T . The range of 0 . 1–1 µ T is characteristic ofthe majority ofoffice and public premises and vehicles, although peak values may be three orders ofmagnitude higher.

Intensity distributions ofbackground magnetic fields in the range of30–

2000 Hz in town (Göteborg City, Sweden) were studied by Lindgren et al. (2001).

It appeared that up to 50 % ofthe population were exposed to MFs higher than

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INTRODUCTION


µ7%

(.9P


'LVWDQFHP

Figure 1.3. Mean EMF profiles 1 m fromthe ground for a standard 380-kV, 50-Hz line at 400 A, according to Conti et al. (1997).

0.2 µ T, and around 5 % were exposed to 1 µ T.

The biological significance ofsuch electric and magnetic fields has been revealed in many epidemiological studies (e.g., Tenforde, 1992) initiated by the work of Milham, Jr (1982) on the mortality ofworkers with higher EMF exposures. One of the last reviews on the subject (Nakagawa, 1997) contains an analysis of31 positive and 13 negative results pointing to doubled cancer risks for populations living near electric transmission lines and workers in energy-intensive industries. In all the cases, the mean MF level lay in the interval 0.1–10 µ T. Grigoriev (1994) pointed out that it is necessary to continually monitor background ambient electromagnetic fields.

“Electromagnetic weather”, i.e., exposure to space and geophysical electromagnetic factors, such as magnetic storms (0.1–1 µ T), has long become an indispensable topic at International Biometeorology Congresses.

The EMF ofelectric household appliances can also inflict its harmful action in an indirect manner. It is common knowledge that under normal conditions the ambient air inside dwellings contains some natural aeroions due to the ionization of the air by decay products ofradioactive radon. Its concentration is about several thousand ions per cubic centimeter. That fact of nature is not indifferent for the vital activity (Andreeva et al. , 1989). The screen ofa standard monitor, which normally possesses a high positive potential, attracts negative aeroions and repulses positive ones.2 Aeroions are thus totally removed from the area around the computer operator (Akimenko and Voznesenskii, 1997). WHO experts regard work with a computer monitor, which in addition to its indirect actions emits EMFs within a wide frequency range, as a stress factor.

2Modern monitors have applied onto their screens special-purpose layers that reduce the electrostatic potential.

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AN OVERVIEW OF MAGNETOBIOLOGICAL ISSUES

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The correlation ofEMFs with cardio-vascular incidences is a subject ofmany studies. In that respect, also ofsignificance are EMFs ofnatural origins, specifically the geomagnetic field (GMF).

The most extensively studied issue is cancer risks (Wilson et al. , 1990; Pool, 1990b; Goodman and Henderson, 1990; Stevens et al. , 1997), a topic ofhundreds of publications (Nakagawa, 1997). The American Journal ofEpidemiology has recently devoted a collection ofmaterials just to one concern — EMFs and brain tumors in children (Preston-Martin et al. , 1996). Some works maintain that findings do not support the hypothesis ofcarcinogenic effects ofthe magnetic fields ofhigh-voltage lines, electric heaters, and other household appliances (Verreault et al. , 1990). Others stress the primitive nature ofthe techniques used to gauge the results ofexposure to magnetic fields, the possible systematic control errors and the preliminary nature of those works, and the need for further discussions (Gurney et al. , 1995; Lacy-Hulbert et al. , 1995).

Long-term exposures to even weak fields are believed to be able to suppress the activity ofsome clones ofthe cells ofthe immune system, thereby impairing the defences ofthe organism against the multiplication of“foreign” cells (Adey, 1988; Lyle et al. , 1988). Another possible mechanism is related to genetic changes induced by an MF (Goodman et al. , 1989). There is also evidence that low-frequency MFs are able to affect the synthesis ofsome peptides that in the organism play the role of some internal biological signals (Goodman and Henderson, 1988; Novikov, 1994).

Coghill (1996) indicated that levels ofpower-frequency EMFs (both electric and magnetic) near beds of children are 1.3–2 times higher for leukemia cases than for healthy children. Recent studies in the UK (documents3 ofthe National Radiological Protection Board, 12(1), 2001) provided evidence that relatively heavy average exposures of0.4 µ T or more are associated with a doubling ofthe risk ofleukemia in children under 15 years ofage. Novikov et al. (1996) report that under certain conditions weak MFs, in contrast, retard the cancer-producing process.

The European Journal of Cancer published a paper by Feychting et al. (1995) with the results ofextensive long-term studies ofcancer in children ofSweden and Denmark. The authors came to the conclusion that their data support the hypothesis ofa correlation between the magnetic fields ofhigh-voltage lines and leukemia in children. One ofthe interested consulting companies has recently issued a compre-hensive analysis ofthe literature on epidemiological investigations concerned with the level ofelectromagnetic pollution. Their manual, (Sage and Sampson, 1996), contains more than 500 (!) observations and risk assessments related to cancers and pregnancy disorders as a result ofexposures to EMFs under household and professional conditions.

Twenty percent ofthe works at the III Congress ofthe European Bioelectromagnetics Association in 1996 addressed, to some degree or other, the interrelation between cancer incidence and electromagnetic radiations. On the one hand, it is well established that EMFs in certain cases enhance the carcinogenic effect ofsome detri-3http://www.nrpb.org.uk/publications/documents of nrpb/abstracts/absd12-1.htm

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INTRODUCTION

mental chemical substances and other factors (Wilson et al. , 1990). For instance, Juutilainen et al. (1996) found that a 50-Hz MF accelerates the development of skin cancer on exposure to UV radiation. It is well known that an MF changes the activity ofmelatonin enzyme, which is responsible for the fine regulation of the immune system (Wilson et al. , 1981; Cremer-Bartels et al. , 1984; Lerchl et al. , 1991; Kato et al. , 1993, 1994; Loscher et al. , 1994; Kato and Shigemitsu, 1996; Stevens et al. , 1997; Harland and Liburdy, 1997; Blackman et al. , 2001). On the other hand, there is no hard correlation with exposure to an MF, and no correlation between a 60-Hz MF and the melatonin level has been found by Lee et al. (1995).

Juutilainen et al. (2000) believe that the effects manifest themselves especially distinctly with long-term exposures to both an EM radiation and chemical carcinogens.

Much remains unclear so far, and further studies are in order (Reiter and Robinson, 1993; Taubes, 1993).

We note that such investigations, especially epidemiological ones, are quite active (Aldrich et al. , 1992; Theriault et al. , 1994). Scientific societies that enjoy governmental support have been established. Also, electromagnetobiological projects have attracted the interest and financial support ofmanuf

acturers of

radiotelephones and computers. Even realtor brokers have begun to take into consideration the electromagnetic factor in their financial estimations of real estate objects (Lathrop, 1996). At the same time, the American Cancer Society has published in its journal a paper by Heath (1996) with an overview ofthe findings ofepidemiological studies over the past 20 years, which pronounces the epidemiological evidence on the correlation ofEMFs with cancer incidence to be “weak, inconsistent, and inconclusive”. Note also the special issue of Bioelectromagnetics, Supplement 5, 2001, which summarizes the state ofthe art ofstudies on the cancer hazard ofbackground EMFs.

Despite the still negative attitude ofphysicists to the issues under consideration, the last issue ofthe Physical Encyclopedia contains the following statement (Golovkov, 1990): “Some variations ofthe geomagnetic field can affect living organisms.” Although this statement is not quite correct,4 the fact that this phenomenon has been recognized is ofimportance. Fairly recently, in 1981, M. V. Volkenstein in his monograph Biofizika wrote: “there are almost no sound data to date on the action ofa DC magnetic field on biological phenomena.” Ten to fifteen years later we have a large body ofdata on magnetobiology. We should note, by the way, that some works on magnetobiology were published at the turn ofthe 20th century, see, e.g., a concise overview by Warnke and Popp (1979).

The controversy is fuelled by negative statements made by some members of the international scientific community. So, in the leading American physical journal Physical Review A 43, 1039, 1991, one reads “any biological effects ofweak low-frequency fields at the cellular level must be outside of the framework of traditional 4In the absence of a large body of direct experimental evidence that would provide a reliable confirmation of the biological action of a weakly fluctuating component of an MF, we should speak about a correlation of the variation of the GMF and the vital activity of some organisms.

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9

physics.” The American Physical Society has issued a resume (APS Statement, 1995) that doubts the expediency ofgovernmental financing ofthese investigations. The US National Academy striving to arrive at some final conclusion on this question established an ad hoc commission. A report ofthe commission (NRC, 1997), which is basically an overview ofa voluminous literature on the topic, has instead given rise to a host ofquestions. Even the members ofthat commission had different opinions on the report’s conclusions. A year later, on completion ofits 5-year research program RAPID5 concerned with EMFs, the US National Institute ofEnvironmental and Health Studies (NIEHS) published an extensive report to the US Congress (Portier and Wolfe, 1998) that covered about a dozen aspects of the problem. Reading the section on biophysical mechanisms for magnetoreception leaves one in no doubt that professional physicists were largely excluded from the implementation ofthe program. According to the report, low-frequency MFs can cause cancer in men; there is also another conclusion that animal studies do not support cancer risks (Boorman et al. , 2000).



One reason behind such a confounding situation is that the physical mechanisms for the biochemical action of hyperweak EMFs are yet unclear.

The current status ofelectromagnetobiology, its “nerve”, so to speak, was appropriately addressed in a memorandum ofthe 1996–1998 presidents R. A. Luben, K. H.

Mild, and M. Blank ofthe American Bioelectromagnetics Society6 to officers ofthe House ofRepresentatives and the Senate responsible for budgeting and scientific and technological policy making (Luben et al. , 1996). Specifically, the presidents wrote

A wealth of published, peer-reviewed scientific evidence indicates that exposure to different combinations of electric and magnetic fields consistently affects biological systems in living body as well as in laboratories. . . . There is a potential for benefits from these fields as well as the possibility of adverse public health consequences. Understanding their biological effects may allow us to increase the benefits as well as mitigate the possible hazards. (page 4) The number ofoverviews ofexperimental work, all sorts ofguidelines,

reports, and books in the field ofmagnetobiology is large and continues to grow. The following is just a short and incomplete list: Presman (1970); Piruzyan and Kuznetsov (1983); Wilson et al. (1990); Luben (1991); Polk

(1991);

Simon

(1992);

Berg and Zhang

(1993);

Adey

(1993);

Bates

(1994); Blank (1995); Hitchcock and Patterson (1995); Goodman et al. (1995); Hafemeister (1996); Hughes (1996); Sagan (1996); Ueno (1996); Adey (1997); Gandhi (1997); Lin and Chou (1997); Mahlum (1997); Stevens et al. (1997), and Repacholi and Greenebaum (1999). Even academic reviews make their appearance (Carpenter and Ayrapetyan, 1994).

A good introduction to electromagnetobiology is a huge tome ofthe proceedings ofthe Second World Congress for Electricity and Magnetism in Biology and 5Research and Public Information Dissemination Program (e.g., Moulder, 2000).

6The society has more than 700 members from more than 30 countries.

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Medicine edited by Bersani (1999). This book contains more than 230 papers covering a wide variety of aspects, from fundamental physical and biological to socio-political ones. There exists a data base, http: // infoventures.com, on all the aspects ofelectromagnetobiology, scientific, medical, and social, which includes as much as 30,000 bibliographic units. Addresses ofopen bibliographic data bases on individual domains ofmagnetobiology can be found at http: // www.biomagneti.com. An interesting assay ofthe history ofelectromagnetobiology is given in a monograph by Kholodov (1982). As early as 1986 there was an analysis ofmore than 6000

literature sources (Kholodov, 1986). Now several thousand papers on electromagnetobiology are published each year, see Fig. 5.19. A historical overview ofRussian, mostly experimental, works is contained in a recent publication by Zhadin (2001).

At the same time, there are almost no critical reviews oftheoretical work, if only because there are no theoretical works as such. Some papers contain critical reviews in terms ofphysics ofwell-known ideas on the mechanisms ofexposure to an MF (Kuznetsov and Vanag, 1987; Vanag and Kuznetsov, 1988; Adair, 1991; Binhi, 2001). The available reviews for the most part are concerned with recording ideas (Adey and Sheppard, 1987; Polk, 1991; Grundler et al. , 1992; Berg and Zhang, 1993). Several provocative works are attempts at a physical substantiation of some reliably reproducible experiments with weak MFs (Moggia et al. , 1997; Binhi, 1997c). These models, at least on the surface of it, contradict neither orthodox physics nor common sense.

Investigations into how to protect against harmful EMF actions are exploding.

The most complete protection is only possible under natural conditions, in the country, where the level of“electromagnetic smog” is about three orders ofmagnitude smaller than in town, Fig. 1.4. Maximal magnetic variations ofa technogenic nature are observed on the z-component ofan MF within trams, trains, and near other power-intensive rigs (Tyasto et al. , 1995). These variations within the range of0.05–0.2 Hz can exceed the amplitude ofa strong magnetic storm thousandfold.

General measures are known to reduce the risks ofdiseases due to EMF over-exposures. They boil down to reducing the level ofelectromagnetic pollution. One snag here is that biological systems themselves are sources ofelectromagnetic fields (Kholodov et al. , 1990); for millennia they have evolved against a background of the Earth’s natural electromagnetic field. Certain fields ofnatural levels and spectra are useful and even necessary for normal vital activity. Furthermore, there are many efficient therapeutic techniques using EM radiations (Congress WRBM, 1997). Purely practical and perceived uses ofelectricity and magnetism can be traced down to 1270 (Stillings, 1997). Fundamental works by Devyatkov and Betskii (1994) on microwave technologies paved the way for remedial applications of these electromagnetic radiations. In Russia alone, more than a thousand medical establishments employ about one hundred modifications ofEHF devices. For several decades more than a million cases for up to 50 disorders have been successfully treated.

There has been an extensive growth in magnetotherapy worldwide (Bassett, 1984; Congress EMBM, 1997). Low-frequency EM fields are known, e.g., to promote

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11


7RZQ

=FRPSRI0)Q7


'LVWDQFHNP

Figure 1.4. Mean intensity of the variations of the z-component of a 10 3–10 Hz magnetic field at St.Petersburg and its environs along the NW–SE line. According to Tyasto et al. (1995).

fracture healing in difficult cases (Ryaby, 1998). In a number of cases, a pre-exposure of an organism to a weak low-frequency MF enables its resistance to unfavorable external factors to be drastically improved (Kopylov and Troitskii, 1982). At the same time, the high curative efficiency ofEMFs also points to their potential hazard.

Here we have an analogy with the uses ofchemical preparations. While useful in certain quantities, medicinal preparations may become dangerous ifused without control for a long time. Therefore, reducing the risks of diseases due to EM pollution is a complicated scientific and technological problem. The sanitary safety norms for electromagnetic radiations are regulated in Russia by GOST 50949-96 and SNiP

2.2.2.542-96. Internationally known standards are MPR-II, MPR-III, TCO 95-96, and some others.

One promising area ofresearch, in addition to the general reduction in the pollution level, is the use of. . . electromagnetic fields! That is no mistake. Just as very small homeopathic doses ofdrugs are able to compensate for a biological action ofthe same substances in normal doses, so the action ofweak deleterious EMFs can be offset by similar fields, only much weaker ones. Devices based on that principle were shown at the 1996 Congress ofthe European Bioelectromagnetics Association at Nancy. Works ofsome scientific groups coordinated by M. Fillion-Robin have shown that these devices reduce the risk ofdiseases in users ofcomputer monitors and mobile phones (Hyland et al. , 1999).

There is some direct evidence suggesting that special-purpose experimental MFs are able to retard the growth and even cause a dissolution ofcancer tumors (Muzalevskaya and Uritskii, 1997). Garkavi et al. (1990) report a retardation of sarcoma growth in rats exposed to a low-frequency MF, Fig. 1.5.

Hopefully, it will soon become possible to account for the action of low-frequency EMFs at a geomagnetic level, although we are not any closer to an understanding ofthe biological effects ofthe geomagnetic field fluctuations, to put it mildly.

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INTRODUCTION

itsn

Chem

l.u

Chem and EMF

e

EMF

, r 20

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meluo

r v

0

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0

10

20

Days

Figure 1.5. Sarcoma growth in rat males exposed separately and jointly to cyclophosphamide and a 1-mT MF. According to Garkavi et al. (1990).

1.2 STATISTICS

The statistics ofinvestigations into magnetobiology, and its integral part electromagnetobiology, is quite interesting. Throughout the decades ofthe development ofthe science, the body ofpublications has grown manifold and its annual vintage now amounts to thousands ofpapers and reports. To gain an understanding ofthe world spread ofthose works, and also ofthe intrinsic structure ofthe studies, an analysis is in order ofproceedings ofmajor symposia, congresses, and conferences devoted to electromagnetobiology.

The Third International Congress ofthe EBEA, held in the spring of1996

at Nancy, France, enjoyed an attendance from 27 countries. Presented were more than two hundred works. Contributions from various nations varied widely, such that Fig. 1.6 gives an indication ofthe intensity ofwork in electromagnetobiology throughout the world. The figures are absolute, i.e., numbers ofpapers presented, and relative, in relation to a country’s population in millions. An average input was one report per two million ofpopulation. It is noteworthy that the relative figures are roughly similar. This is indicative ofthe fact that the potential dangers of“electromagnetic smog”, the interaction ofEMFs with the biosphere as a whole, are concerns ofglobal proportions.

Shown in Fig. 1.7 is the percentage ofworks on respective topics in electromagnetobiology. Experiments were conducted in fairly equal proportions on prepared living tissues, cells, proteins, and whole biological and social cohorts, including humans. Theoretical works are clearly dominated by engineering calculations of distributions ofEMFs in man-made and natural environments. Especially prolific are studies ofemissions ofmobile phones near the user’s head.

The absence of

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13

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Figure 1.6. Absolute numbers of reports and relative contributions of nations to the proceedings of the III EBEA Congress, 1996.

Figure 1.7. The structure of the reports presented at the III EBEA Congress. Percentages of the number of works presented: (a) the range of electromagnetic fields; (b) the nature of the works.

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INTRODUCTION

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Figure 1.8. Distribution of reports at the Second World Congress for Electricity and Mag-netismin Biology and Medicine, Bologna, 1997.

productive physical ideas on the primary magnetoreception mechanisms7 explains the small number ofworks on the nature ofbiomagnetic reception, which is a matter ofprinciple for magnetobiology. This was said to be due to the paradoxical nature ofmagnetobiological effects. The paradox stands out with especial clarity in experiments with low-frequency EMFs, where the field energy quantum is approximately ten orders ofmagnitude smaller than the characteristic energy ofchemical bonds.8

We have no universally accepted mechanism to date for the biological actions of such fields. It is obvious that this, along with the relative ease ofgeneration ofartificial low-frequency fields, accounts for the relatively large number of experiments in this area.

Since 1983 at Pushchino, Russia, symposia for the correlation of a variety of physico-chemical and biological processes with space-physical processes have been held (Shnoll, 1995a). It is to be noted that out ofthe 57 papers published as proceedings ofthe 1990 symposium (Pushchino, 1992), 40 % contain discussions of the relation between biospheric processes with geomagnetic perturbations. Out of the 65 contributions to the 1993 symposium, the percentage ofsuch works grew to 55 % (Pushchino, 1995).

7The term magnetoreception is used throughout the book in a wide sense as the ability of living systems to respond to changes in magnetic conditions.

8 Such a comparison however is only of limited use as the interaction of low-frequency EMFs with biophysical targets may be a multiquantum process, see Section 3.12.

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Table 1.1. Reports of the international congress in St.Petersburg, 1997

hyperlow field intensities

3

DC fields

13

electric fields

3

ELF EMFs

41

combined AC–DC fields

5

extreme dose dependences

3

MHz

4

UHF–EHF, microwaves

41

IR, optical and UV

20

EMF target indicated

1

computer models

3

analytical models and estimates

9

water systems

10

engineering R&D

38

general ideas, hypotheses

19

reports with deviations from scientific methodology 59

The Second World Congress for Electricity and Magnetism in Biology and Medicine was attended by researchers drawn from 35 countries and had more than 600 contributions, Fig. 1.8. The Congress covered the issues ofbiology, medicine, technologies, and physics concerned with a variety ofmanifestations ofelectromagnetobiology. Discussions centered around several topics: biophysical mechanisms, bioenergetics and electron transport, transfer of biological signals, sensor physiology, microwave effects, electromagnetic epidemiology, radiation level gauges, mobile phone bioeffects, bioelectron devices and biocomputers, EMF treatment ofbones and cartilages, electroinjuries and electrotreatments, electroinduced transport of drugs and genes, thermal effects ofEMFs, melatonin secretion and EMF action on immune and nerve systems, electric transmission lines and permissible radiation doses, effects ofa DC magnetic field, and learning and memory for electromagnetic exposures. Among the co-sponsors ofthe Congress, in addition to governmental institutions ofthe USA and Italy, were some industrial corporations concerned with the production and distribution ofelectric power and well-known manufacturers of mobile phones.

Another remarkable event was the International Congress for “Weak and Hyperweak Fields and Radiations in Biology and Medicine” that took place in the summer of1997 in St.Petersburg, Russia (Congress WRBM, 1997). Among the 352 reports presented at the congress, 223 were concerned with electromagnetobiology. Table 1.1

is a breakdown ofthe reports by topics.

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Some reports (about 2-3 %) were classed fairly arbitrarily, and there were relatively few analytical studies of EMF action mechanisms. This seems to be due to the uncertainty oftargets ofthat action — only one paper discussed a possible MF target in a living tissue. There were almost no reports wherein static MF was under control, with the natural exception ofpapers on the bioaction ofDC fields themselves. At the same time, there were works galore that contained just speculations unsupported by any factual evidence or statements that could not be proven in principle.

Significantly, there were virtually no reports under the heading ofanalytical reviews provided in Chapters 2 and 3. Most ofthe experimental works were not concerned with testing any hypothesis, although nearly always they stressed the unclear nature ofthe mechanisms involved. As a result, there were many, often similar, works that defied any comments in terms ofphysics. In substance, they only confirmed the existence ofEMF-induced biological effects. Admittedly, it is important to amass a body offactual evidence, especially medical, but the wealth ofmaterial available in the world already enables one to plan special-purpose experiments to reveal the primary mechanisms ofelectro- and magnetoreception.

1.3 METHODOLOGICAL NOTES AND TERMS

In order to describe real quantum physical processes they employ the well-established tool kit ofquantum mechanics (QM) and quantum electrodynamics (QED). Different processes call for QM and QED mathematical tools of different caliber. Phenomena considered in this work do not require any special mathematical techniques. This is because the subject under study — primary mechanisms for biomagnetic reception — is a relatively new domain ofphysics, which awaits further elaboration. Therefore, at the first stage of the investigation into magnetobiological effects it is sufficient to employ QM mathematical tools at the level ofcomplexity ofmost university QM courses, such as laid down in the well-known monographs by Landau and Lifshitz (1977), Blokhintsev (1983), and Davydov (1973).

Discourses on the physical nature ofthe biological efficiency ofan MF use the terms “mechanism” and “model”, the meanings ofwhich are close but still slightly different. The term “mechanism” is used to describe a concept, physical processes, or their progression that may underlie a phenomenon. Ifit is stressed that a given mechanism is realized via some equations or mathematical relationships that feature a predictive power, the term “model” is used. Cases are possible where there are no models at all, or in contrast, several mathematical models for the same mechanism ofbiological effectiveness ofan MF.

In certain cases, the term “atom” is used for short to designate a charged particle in a central potential, rather than electrons in the field ofa nucleus. An analogy is apparent here.

Graphs with reference to earlier works were constructed or adapted from the results ofthose works and are no direct reproduction ofthe graphs published previously.

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1.3.1 Notation and terms for magnetic fields

In the literature, the conditions ofmagnetobiological experiments are described using both the MF strength H, and the MF induction B. The latter quantity is related to H by the relationship B = µH. Here the permeability µ ofthe medium, generally speaking, is essentially averaged over a physically small volume ofthe medium. That is so because B, in addition to H, contains a contribution ofthe medium’s magnetization induced by H. The magnetization is only referred to as an average over a sufficiently large volume, when the local inhomogeneities ofMFs of atomic sources are largely ironed out, i.e., those due to orbital magnetic moments ofatomic electrons, and also ofunpaired electron and nuclear spins.

Clearly, when considering the primary magnetoreception mechanisms involving the motion ofparticles precisely on an atomic scale, it is more correct to use H, rather than B. Considering that in the Gaussian system the permeability ofbiological tissues is close to unity (Pavlovich, 1985), the atomic field H averaged over a physically small volume is nearly coincident with the exogenous field — with given external sources: permanent magnets, Helmholz coils, etc.

Some authors, however, make use ofthe MKS system, in which vacuum possesses a permeability. Therefore, even to describe the motion of particles in a vacuum, e.g., on interatomic scales, one has to apply the magnetic induction B. In that system, the unit of B is Tesla (T), related to the unit of B in the Gauss system (G) by the relationship 1 G = 10 4 T. In the Gaussian system the MF strength H is measured in Oersteds (Oe). Since in that system µ is unity and, moreover, dimensionless, the units Oe and G in fact coincide: 1 Oe = 1 G = 1 cm 1 / 2 g1 / 2 s 1.

In this connection, throughout the book we will characterize an MF using both H and B. It is to be stressed that in the latter case we do not imply the presence of some macroscopic magnetization in a living tissue, but rather our desire to make use ofMKS units, T and µ T, which are convenient for a number of reasons. In actual fact, more often than not we deal with a magnetic field engendered by external sources in a vacuum. Relationships between physical quantities in the book are given in the Gauss system.

Some organisms are not indifferent to the compensation ofa natural local DC

MF down to the level of 1 G. To deal with a situation where a DC MF takes on values that are sufficiently small to cause a biological response and that have no distinct boundary, we will utilize terms that are current in the literature, such as

“magnetic vacuum” and “zero field”, and use them without inverted commas. We will take the formal definitions of a magnetic vacuum in biological terms to be the inequalities

H AC H DC H geo ,

where H geo is a natural magnetic biological reference, i.e., the local geomagnetic field.

One ofthe MF configurations most popular in experiment is a superposition of collinear DC and AC magnetic fields. The MF vector axis being time-independent, such a configuration is conditionally referred to as a “uniaxial MF”. In the more

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general case ofthe superposition ofarbitrarily oriented DC and AC magnetic fields we will talk about a “combined MF”.

In the literature, for frequency ranges of fields they employ the following nomenclature: low frequency (LF) 30–300 kHz, very low frequencies (VLF) 3–30 kHz, ultralow frequencies (ULF) 0.3–3 kHz , superlow frequencies (SLF) 30–300 Hz, and extremely low frequencies (ELF) 3–30 Hz. Since there are no significant differences between these ranges in terms ofprimary physical mechanisms, the book uses for convenience one general term “low-frequency MFs”.

The values ofmagnetic fields are defined below in relation to the biologically natural level ofthe geomagnetic field 50 µ T. There being no clear-cut boundaries, for such fields in the literature they use the term “weak MFs”. Fields higher than 1 mT will be defined as “strong MFs”. Correspondingly, fields under 1 µ T are called “superweak MFs”. In the magnetobiological literature they often use the term “amplitude” in relation to a sinusoidal signal at large, always pointing out what specifically is meant: the peak value, the rms (root-mean-square) value, or the peak-to-peak value. In the book the term is taken to mean strictly the peak value.

In certain cases the term “power” is utilized to mean the relative energetic characteristic ofelectromagnetic radiation, which will become apparent from the context.

1.4 MAGNETOBIOLOGICAL EFFECT

The term “magnetobiological effect”, or MBE for short, used in the book has the following meanings.

On the one hand, the term implies any change in any variables ofa biological system caused by a change in the magnetic conditions ofits occurrence. Those may be biological properties ofan organism in vivo or biochemical parameters ofa living system in vitro.

At the microscopic level, biological structures are common for most of the living systems — these are proteins, membranes, etc. Clearly, the primary mechanism of magnetoreception realized at the level ofbiophysical structures displays the same level ofgenerality, but one and the same primary mechanism in various biological systems can manifest itselfthrough changes in a wide variety ofproperties.

For a researcher ofthe primary mechanism, biological systems are just special tools. In a sense, all the biological systems that display a measure ofmagnetosensitivity are the same. It is important that the way some property varies with change-able magnetic conditions would enable one to derive information on the nature of primary magnetoreception. Also which variable in particular in a biological system is being changed is immaterial. Therefore, it would be convenient to view a

“magnetobiological effect” just as a dependence ofthe system’s behaviour on MF

variables, whatever the biological nature ofthat dependence.

On the other hand, physically, that term singles out magnetic conditions from a general electromagnetic situation. Some comments are in order. Electromagnetic

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fields are known to cause biological effects within a wide range ofamplitudes, frequencies, etc. For instance, sufficiently intensive EMFs engender conduction currents, heat biological tissues, and cause rotations ofmolecular dipoles. They give rise to noticeable shifts in many reactions and spectacular biological effects. Thermal and electrochemical effects are widely used in practice, including in medicine: UVF treatments, electrophoresis, and so on. These phenomena are no paradox. In contrast, paradoxical are the bioaction ofDC MFs, low-frequency AC MFs, and centimeter and millimeter waves ofnonthermal intensities. At the same time, both AC low-frequency MFs and microwave radiations may have a meaningful electric component. The question ofits role in the biological effects ofan EMF in those ranges is not that simple. In experiment and theoretical treatments ofeffects of weak low-frequency MFs, an electric component is normally ignored.

As the frequency of a low-frequency MF is increased, sooner or later one will have to take into consideration the induced electric component, because it varies with the field frequency. Whether it is possible to ignore the electric component is also dependent on the specific experimental realizations ofan EMF source, and the presence ofthe configuration ofthe “near” zone or “far” zone in relation to the source. As the EMF intensity is decreased or the frequency increased, a moment comes when it can only be described in QED terms. The language ofelectromagnetic waves is replaced by that offield quanta. It becomes impossible to break down an EMF into magnetic and electric components. The criteria ofthe “magnetism” of an electromagnetic field define the confines ofmagnetobiology as such, and are therefore in need of clarification.

1.4.1 Evaluation of the thermal action of eddy currents

Temporal variations ofan MF induce an electric field. Ifwe expose to an MF an electroconductive medium, e.g., a biological system, it develops macroscopic currents. Their electrochemical effects, — i.e., those on a phase boundary and involving charge carriers, — can cause a biological reaction. A reaction can also occur owing to the Joule heating oftissues. In the latter case, the biological response has nothing to do with magnetobiology, since an MF here is just one ofthe possible heating factors or sources of electromotive force (e.m.f.) On the other hand, it is clear that such a response is a biological effect ofan MF. What is thus ofimportance here is the difference between MF biological effects in general and magnetobiological effects, the latter appealing to special non-thermal and non-electrochemical mechanisms for the interaction of an MF and living matter.

Let us identify the boundary between magnetobiological and thermal effects of an MF. Biological tissues being macroscopically neutral, the Maxwell equations for an electric field look like

rotE = 1

B ,

divD = 0 ,

D = εE

c ∂t

4 π

rotH =

j ,

divB = 0 ,

B = µH ,

j = σE .

c

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20

INTRODUCTION

We re-write them as

rotE = 1

(B + Bind) ,

divE = 0

c ∂t

µ 4 π

rot (B + Bind) =

j ,

j = σE ,

c

where B is an external homogeneous MF, and Bind is an MF induced by eddy currents.

It is seen from the equations that the electric field induced by a sinusoidal field B is about rB/c. The electric field produces a current density of σrB/c, which in turn engenders an MF equal to

B ind 4 πr 2 µσB .

c 2

The proportionality coefficient for “biological” values of the parameters r ∼ 1 cm and σ ∼ 9 · 109 CGS units is much smaller than unity up to megahertz frequencies.

Therefore, we will later use the equations

rotE = 1

B ,

divE = 0

c ∂t

and ignore the effects, e.g., the skin-effect, concerned with MF induction by eddy currents. The last equation suggests that the field E is solenoidal. It can then be represented as the rotor ofa certain vector field (Korn and Korn, 1961), 1

rotE(r )

E(r) =

rot

4 π

|r r | dv ,

integrating over all the points r . The relationship defines the induced field E from its rotor in an arbitrary coordinate system up to the gradient ofsome potential ϕ, which meets the condition div(grad ϕ) = 0. It is easier, however, to work out the field E from symmetry considerations and suitable potentials of an EMF.

Let a homogeneous MF B be aligned along the z-axis and limited by the dimensions ofan infinitely long solenoid — an idealization that is often used in calculations. The field E then possesses only an angular (tangential) component. The potentials can be taken to be

1

A(r) =

B × r ,

A 0 = 0 .

2

It is easily seen that B = rotA, as the case should be. Since E(r) = grad A 0

1 A(r), then, in a cylindrical coordinate system, we find9

c ∂t

= − r

B( t) .

2 c ∂t

Note that for the chosen potential gauge E(0) = 0. That is to say that such gauging is only possible in the coordinate system ofthe symmetry center ofMF sources, 9In convenient units this relationship can be written (Misakian and Kaune, 1990) as E peak[ µ V/m] = 0 . 01 π r[cm] f[Hz] B peak[ µ T].

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MAGNETOBIOLOGICAL EFFECT

21

and that the MF homogeneity condition alone is insufficient to arrive at . Here r is the distance to the solenoid center.

On the other hand, the Joule thermal energy ofthe current with density j = σE, emitted per unit time per unit volume is

w = σE 2 ,

where σ is the specific electric conductivity ofthe medium. Hence we can readily arrive at the mean energy per unit time within a macroscopic volume ofradius R

and height a, which is placed at the center ofthe solenoid. That will be a model of a biological body. We write


2

π aσR 4

π aσR 4

w dv = a

σE 2 2 πr dr =

B( t)

=

B 2Ω2 .

ϕ

8

c 2

∂t

16

c 2

The last equality is derived considering that the MF is sinusoidal, B( t) = B cos(Ω t), and we have sin2(Ω t) = 1 . It follows that on average, per unit body volume ( V =



2

aπR 2), we get the power

σR 2

P =

B 2Ω2 .

16 c 2

It is conditioned by the body dimensions, a corollary of being proportional to the distance r to the solenoid center.

The increase in the temperature T ofthe body due to heat Q will be 1

dT =

dQ ,

c Q

where c Q is the heat capacity ofa volume unit. Taking the time derivative we get 1

T =

P ,

t

c Q

which, after the substitution of the expression for P , yields the frequency dependence ofthe MF amplitude, which defines the boundary ofthermal effects on the amplitude–frequency plane, Fig. 3.1.


4 c

T

1

B =

t c Q

.

(1.4.1)

R

σ

We note that for bodies with a fairly complicated geometry and inhomogeneous distributions ofconductivities and heat capacities over the volume, which is nearly always the case in experiments, the appropriate computations are more complicated by far and require special numerical techniques (e.g., Gandhi et al. , 2001). Therefore, rough estimations of the orders of magnitude in this case are quite justified.

We will apply the following values ofthe variables ofa biological tissue and the specimen dimensions: σ ∼ 1 S/m

= 9 · 109 CGS units (Mazzoleni et al. ,

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INTRODUCTION

1986; Foster and Schwan, 1996; Gabriel et al. , 1996), c Q 1 cal/(cm3 o C)

4 . 2 · 107 erg/(cm3 o C), R ∼ 1 cm. We take a tissue-heating criterion ofbiological significance to be the temperature growth at a rate of T ∼

t

0 . 1 o C/min (in the

absence ofa heat sink). Then the proportionality between B and f − 1 = 2 π/ Ω in Gaussian units will be

B ∼ 108 /f .

(1.4.2)

The relationship holds well until the conductivity can be regarded as frequency independent. As the frequency is increased, we have a contribution to conductivity and Joule heat owing to the imaginary component ofthe complex permittivity of the medium, i.e., to polarization currents. The conductivity grows; therefore the boundary ofthermal values ofthe amplitude B declines in comparison with the predictions (1.4.2). This drop can set in at frequencies 1 kHz. Since the static permittivity ofa biological tissue is under 100, the above drop is below one or two orders and on the scale ofFig. 3.1 is nearly imperceptible. Note that the dependence (1.4.2) yields only an approximate indication ofthe boundary ofthermal effects, to within two or three orders ofmagnitude. Therefore, in each specific case it may be required to be estimated individually.

Sometimes for a ofbiological significance criterion ofeddy currents they take the current density 1 mA/m2 (Nakagawa, 1997), ofthe order ofnatural biological electric currents, above which electrochemical reactions in a living tissue set in. The MF amplitude vs frequency dependence, worked out similarly to (1.4.2), will then have the form

1

B ∼ 6 · 102

,

(1.4.3)

f

i.e., five orders below the specified thermal threshold. That dependence, a section ofthe broken curve in Fig. 3.1, is accepted by the American Conference ofGovernmental Industrial Hygienists as the safety boundary for a low-frequency MF.

Specifically, at 50 Hz it gives the threshold level about 12 G. It is to be noted that this value is one or two orders higher than the levels ofa number ofmagnetobiological effects established with certainty in laboratory assays. Similar values ofnorms have also been established by other organizations (Suvorov et al. , 1998).

1.4.2 Criterion for classical EMF

Berestetskii et al. (1982) gives a criterion for the applicability of the classical treatment ofan EMF. It relies on the large-numbers requirement for the filling ofthe levels ofelementary EMF oscillators in a quantum treatment. The criterion relates the frequency f to the amplitude ofan AC field,10


2 π 2

H

c

f 2 10 30 f 2 ,

(1.4.4)

c

10The estimate holds well for the electric field E as well. In the Gaussian system physical dimensions of E and H are the same g1 / 2cm 1 / 2s 1.

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MAGNETOBIOLOGICAL EFFECT

23

where the numerical coefficient is in the CGS system. That can be readily perceived from general considerations. The energy flux of an EMF plane wave is related to the MF strength as (1.4.8) S = cH 2 / 4 π. Hence the volume λ 3, where λ = c/f is the wavelength, contains about 2 λ ofenergy. At the same time, λ 3 is the c

characteristic volume ofa quantum ofEM radiation with the wavelength λ. The classical description is clearly valid ifthe number ofquanta ofthe field 2 π f in the volume λ 3 is much larger than unity. That is, 3 /c 2 π f . From this we can easily derive the inequality, which will, up to a numerical factor of about unity, repeat (1.4.4).

It is seen that in the range oflow-frequency magnetic fields down to infinitesimal amplitudes the classical treatment ofan electromagnetic field is applicable. Dependence (1.4.4), which defines the ranges for the classical and quantum descriptions of an EMF in the amplitude–frequency plane, is also shown in Fig. 3.1. Together with the curve (1.4.2), it identifies the area ofmagnetobiology that by definition must be the area ofnon-thermal effects and, at the same time, the area ofthe classical treatment ofan EMF, where it is possible to single out the magnetic component of the field.

The quantum dynamics ofparticles in a classical EMF constitutes the so-called semiclassical approximation. In that approximation, the dynamic equation ofa particle has the form of the Schrödinger equation, in a broad sense, and the EMF enters into the equation as a vector A and a scalar A 0 potentials ofthe field. The potentials are defined accurate to the gauge transformation: for the important special cases ofan external homogeneous AC MF and a plane electromagnetic wave, the fields H and E can be defined just in terms ofthe vector potential, by putting A 0 = 0.

Then the question ofwhich field, magnetic or electric, determines the motion of a particle no longer makes sense. From the general point ofview, the governing factor here is the vector potential of an EMF, and there are no constraints on the frequency or amplitude of the field, besides the specified QED one. If, however, we take into consideration some mechanisms defined below, they will define on the frequency–amplitude plane some areas of their possible effectiveness.

For a non-plane wave, in the vicinity ofan emitter, it is sometimes possible to create a purely electric or purely magnetic AC field, to within some accuracy.

So, Broers et al. (1992) employed a cavity for 150 MHz of cylindrical shape about halfa meter in size. In such a cavity, standing electric and magnetic waves form nodes and crests. To place the cellular culture of M. africana fungus in the cavity, locations were chosen either with a purely magnetic wave (1.2 nT at maximum), within experimental accuracy, or with a purely electric (0.91 V/m) wave. The findings, shown in Fig. 1.9, indicate that, unlike the electric field, the magnetic field produced a statistically significant biological effect.

It would be ofinterest to plot on the graph ofFig. 3.1 areas ofthe variation ofEMF parameters as a classical wave that correspond to some processes and experiments.

The human eye is known to have a sensitivity threshold ofabout N = 10 photons during the eye response time τ ∼ 0 . 1 s (Aho et al. , 1988). We take it that the photon

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INTRODUCTION

PDJQHWLFILHOG


HOHFWULFILHOG

FRQWURO


5DWHRIJHUPLQDWLRQ

7LPHRIH[SRVXUHK

Figure 1.9. Germination of fungus cells in the magnetic and electric fields of an EMF that is frequency-modulated (10 Hz) 150 MHz depending on exposure time.

energy or frequency corresponds to a maximum of eye spectral sensitivity; i.e., the wavelength is λ = 55 . 5 · 10 6 cm. We can then readily work out the energy quantum to be 2 π s/λ, and the energy flux through the pupil ofarea 1 ∼ 1 cm2 will be 1

1

N 2 π c

.

τ

λ 1

On the other hand, the energy flux ofa plane wave is related to the amplitude ofits magnetic component by the relationship (1.4.8). Equating these quantities gives the MF amplitude H ofthe EMF classical wave, which corresponds to the eye sensitivity. Its order ofmagnitude is


2 N

H = 2 π

4 · 10 10 G .

τ λ1

As is seen in Fig. 3.1, the EMF ofthis, optical, section ofthe spectrum at such a low intensity is in fact a quantum object.

We now find the equivalent amplitude ofan optical range MF produced by a household light source, e.g., by a 100-W incandescent lamp. The optical part of the spectrum only makes up several percents ofpower, i.e., about P ∼ 5 W. At a distance of R ∼ 1 m the optical radiation flux will be P/ 4 πR 2; hence we get H ∼ 0 . 3 · 10 2 G. Obviously, there are more grounds to regard such as radiation as a classical wave. It falls somewhere between a classical and a quantum description. In fact, the optical radiation ofthat power displays properties both ofwaves (interference) and of quanta (photoelectric phenomena).

1.4.3 Some limitations on an electric field

Interaction ofan EMF with bound charged particles seems to be the only criterion in the search for primary magnetoreception mechanisms. When a quantum particle

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25

is exposed to a field with some binding highly symmetric, e.g., central, potential, its initially degenerate energy levels split. It is natural, therefore, to compare splitting amounts caused by magnetic and electric fields. This gives a smallness criterion for an electric field in relation to an atomic system exposed to a magnetic field. This does not exhaust, ofcourse, all the possible situations, but still gives some estimates ofvalue for magnetobiology.

To arrive at proper estimates we assume that a particle is exposed to some central potential. A charge q ofmass M exposed to a magnetic field H has its levels split (Zeeman effect) as follows:


E ∼

q H .

(1.4.5)

2 M c

In an electric field E, a system acquires a dipole moment d ∼ αE, where α is a polarizability ofthe system. The moment energy −dE = −αE 2 varies with the squared electric field. A perturbation operator in the field E is V = dE , where d = qr is the operator ofthe ion dipole moment. We take the z-axis to be in the E

direction, then

V = −qrE = −qzE .

In the first order of perturbation theory, the energy shift for a non-degenerate level, e.g., where H = 0, in a homogeneous field E is (in terms ofthe notation of (Landau and Lifshitz, 1977))

E(1) = V

n

nn = ψn|V |ψn = −qE ψn|r |ψn = 0 , where ψn is an unperturbed wave function of the n th level, and n is a set ofquantum numbers. The splitting ofa degenerate level, in the absence ofan MF, is dictated by the solution to the secular equation

Vnn − E(1) δ

n

nn = 0 ,

where n and n refer to the states of a degenerate level, and have the same parity. It follows that irrespective of an MF, corrections to energy are dependent on matrix elements ofthe vector r or pseudoscalar z, between functions of like parity.11 But such matrix elements are zero. Therefore, the level splitting is determined by second-approximation corrections (quadratic Stark effect)

|

|

E

(dE)

( z)

(2)

nm| 2

nm| 2

n

=

= q 2 E 2

,

m = n ,

ε

ε

m

n − εm

m

n − εm

where the denominator contains the difference ofenergies ofunperturbed states.

The main contribution to E(2)

n

is made by terms with the smallest values ofenergy

difference. States ofa Zeeman multiplet in a central potential have the same parity, 11Except for cases of Coulomb and harmonic potentials, where the functions of stationary states may have no parities.

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INTRODUCTION

and appropriate matrix elements are zero. Therefore, the smallest energy difference values correspond to various values ofthe radial or azimuthal quantum numbers.

The splitting is around

|

E

( z)

(2)

10 | 2

= q 2 E 2

.

n

ε 10

Considering that the transition energy is ε 10 2 / M R 2, where R is the size of the area where a particle stays, and subject to ( z) nm ∼ R, we obtain the following relationship for the corrections to energies in an electric field:

E ∼ q 2 MR 4


E 2 .

(1.4.6)

2

We can estimate, for instance, the true order of polarizability of α ∼ ∂ 2 E/∂E 2

q 2 M R 4 / 2 ofthe ground state ofthe hydrogen atom.

Equating the splittings (1.4.5) and (1.4.6) yields an estimate ofthe electric field, where perturbations introduced into an atom-like system in a magnetic field become significant


H

E ∼

.

M R 2

2 cq

The following sections provide evidence that the biologically significant ions of calcium, magnesium, etc., are primary targets for an MF in biological systems.

Considering that a typical laboratory level ofan MF is about 0.5 G and substituting approximate values for the 40Ca2+ calcium ion in a capsule with an effective radius o

potential of0.7 A give E ∼ 10 3 CGS units or 30 V/m.

A biological tissue is 60–95 % water. It possesses a relatively high permittivity for quasi-static electric fields ε ≈ 80. Therefore, in an external electric field, an ion in a biological tissue has acting on it a field that is ε times smaller. Thus, the estimate

E ∼ 100–1000 V/m

is acceptable for the highest permissible electric fields in the above sense. Note that for dwellings the standard level is 5–20 V/m at frequency 50 Hz. The estimate is valid for quasi-static fields, when the field frequency is much lower than that oftransitions / M R 2 with a change in the radial quantum number. For the specified system, that equals 1010 Hz.

Note that here we deal with electric fields produced by external sources. Electric fields induced by an AC MF are said to be included in the dynamic equation alongside the MF via the vector potential.

1.4.4 Limitations on plane waves

We have considered so far mainly homogeneous MFs and the electric fields they engender. That is to say we have dealt with fields in the so-called near zone, where the distance to an emitter is comparable with its size. To be more exact, if d is

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the emitter size and λ is the EM wavelength, then the near zone occurs within a distance r to the emitter, approximately not father than

d 2 /λ , d λ

r 0

(1.4.7)

λ , d < λ .

For the near zone, the EMF configuration is mainly determined by the distribution ofcurrents and charges on the emitter. Ifthe distance to the emitter is much larger than r 0, we have the far zone. In the latter case, an EMF, with small scales, is close to the plane wave, and the field strengths are related by

H = n × E ,

where n is the unit vector in the direction ofwave propagation. From this we can readily find the energy flux in the plane wave

c

c

S =

E × H =

H 2n .

(1.4.8)

4 π

4 π

For instance, the far zone conditions are met by an EMF acting on some areas ofthe human body when using a mobile phone. Also, far zone situations are staged specially when conducting experiments with microwave radiations. In such cases the plane wave idealization is quite justified and mathematically convenient.

Relationships (1.4.5) and (1.4.6), which determine the splitting ofatomic levels in magnetic and electric fields, for a plane EM wave, yield estimates of radiation power levels, where either electric or magnetic effects prevail.

We derive the ratio of(1.4.5) and (1.4.6), considering that for the plane wave E = H,

E mag

3

E

=

.

el

2 M 2 R 4 cqH

We introduce the convenient quantities

4 a = 2 /M R 2 ,

4 p = m p c 2 ,

which are the characteristic scale ofthe vibrational energy ofan ion in the cavity with the effective potential ofradius R and the rest energy ofa proton, respectively.

The desired relationship will then assume the convenient form

E mag

4 2a

E

=

,

el

4 q4 p µ H

N

where q = q/e is the ion relative change. We can rewrite that relationship in a still more convenient form, subject to the definition (1.4.8) ofthe energy flux ofa plane wave:


E

2

mag

S 0

c

4 2a

E

=

,

S 0 =

.

(1.4.9)

el

S

π

8 q4 p µ N

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INTRODUCTION

It is clear that the quantity S 0 defines the same threshold level ofthe radiation power density, where magnetic and electric effects are potentially identical. We can readily arrive at

S 0 8 . 8 · 10 10 W/cm2

o

for calcium in the binding cavity of calmodulin with potential radius R ∼ 0 . 7 A.

As follows from (1.4.8), corresponding to that quantity is the amplitude of the magnetic component H 0 2 πS 0 /s ∼ 2 · 10 6 G.

In the diagram in Fig. 3.1 that level separates the lower part in the high-frequency range, i.e., in the range where the plane wave approximation is valid and where the EMF electric component can be ignored. As is seen in the diagram, the power range ofmicrowaves effective in relation to E. coli cells studied by Belyaev et al. (1996) nearly wholly lies within the range ofthe action ofthe magnetic component.

The power ofmicrowave radiation, e.g., ofmobile phones, falls off exponentially penetrating biological tissues. Therefore, there is always a tissue layer where magnetic effects are more probable. As will become clear later in the book, magnetic fields in comparison with electric ones feature definite advantages from the point ofview ofthe probability ofthe biological effects they will produce.

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OVERVIEW OF EXPERIMENTAL

FINDINGS

Some law of logic should fix the number of

coincidences, in a given domain, after which

they cease to be coincidences, and form,

instead, the living organism of a new truth.

V. Nabokov, Ada or Ardor: A Family Chronicle

This overview encompasses just a small part ofthe published work on magnetobiology. It does not cover many remarkable results because they are not concerned with the physical nature ofmagnetobiological effects, although they may be unique in their own right and be ofsignificant scientific value. One example is works ofan epidemiological nature, which look into correlations between the intensity ofpower-frequency electromagnetic noise and incidences for some diseases. It is clear that the presence ofa correlation between these factors does not suggest their cause–effect links and can hardly give us any helpful insights into the nature of the effect. At the same time, these findings are an important social and political factor.

The scope ofthis book warrants our concern only with those ideas that lie within the mainstream oftraditional physics and raise no doubts as to their validation.

This gives some indication ofcriteria followed in selecting experimental evidence.

So, the selection was guided by a possibility ofcommenting in terms ofphysics.

Findings had to contain dependences, functions, and correlations that could be coupled with various physical mechanisms that were likely to underlie the effects observed. We have focused on experimental observations of multipeak dependences ofMBEs with magnetic conditions properly described. Such observations are especially paradoxical and, at the same time, they are on a par with mechanisms of MF non-thermal effects, in particular, with ion interference, which is a focus of the book. We generally overlooked work on actions ofAC MFs that did not indicate the amount and orientation ofa DC MF on samples. The yardstick ofcompleteness ofinformation on the magnetic situation comes also to be employed by specialized journals when reviewing submissions.

MF exposure time is an important parameter dictating the amount and sometimes the direction ofa biological response. Studies ofMBE temporal variations are the core ofa halfofthe works on electromagnetobiology. These data are impor-29

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OVERVIEW OF EXPERIMENTAL FINDINGS

tant in yielding a wider understanding ofthe biochemistry and physiology ofEMF

reception by living systems. At the same time, temporal variations, which as a rule are relatively slow, with characteristic times of10 minutes or longer, carry virtually no information on the primary physical process of the transformation of an EMF

signal into a biochemical response. This book concentrates primarily on magnetoreception processes. Therefore, a wealth of results involving temporal dependences are outside the scope ofthis review.

We only note that in the majority ofcases exposure times from several minutes to several months were used. Typical here are two types ofdependences ofthe measurable variables on exposure times: a s-shaped curve with a saturation and a bell-type dependence (e.g., Byus et al. , 1984; Lin et al. , 1996). The first type is defined by the balance ofprocesses ofaccumulation and decay ofproducts ofbiochemical reactions that accompany primary reception processes. The bell-shaped-type dependence reflects the additional involvement ofadaptive mechanisms that hinder the shift ofhomeostasis and enhance the stability ofliving systems under changed external conditions. At the same time, in the organism there is a whole spectrum oftopical time scales ofbiochemical and physiological processes, including natural biorhythms. Therefore, measurable temporal dependences are often curves that are more complex than the aforementioned ones.

Nearly 5–10 % ofpapers on magnetobiology report failures to observe any MBEs.

These works are also excluded from the overview because these data are impossible to analyze. The chain ofprocesses involved in the transformation ofan MF signal into an observable biological parameter is very long and beyond control, and so the fact that many experiments show no effect is quite normal. As is shown in Ho et al.

(1992); McLeod et al. (1992a); Berg and Zhang (1993); Ružič et al. (1998), reproducible MBEs can only be obtained when “electromagnetic” windows coincide with

“physiological” windows. For instance, Blank and Soo (1996) observed that sign of the EMF response changed when Na,K-ATPase enzyme initial activity was varied.

That implies that within some range ofinitial activities there was no EMF effect, whatever the kind ofEMF stimulation, magnetic or electric, and its variables.

Also observed are temporal windows, i.e., time intervals where a biological system is able to be sensitive to an MF. Such windows have been found for various time scales, from minutes and hours (Ho et al. , 1992) to seasons (Ružič et al. , 1992, 1998). Importantly, reasons for magnetobiological assays being not quite reproducible may be quite exotic. So, Simko et al. (1998) report that whether a biological reaction appeared in human amnion cells was dictated by which magnetic system —

Helmholtz or Merritt rings — was used to produce an AC MF, the field amplitude in both cases being the same. In experiments on biological effects ofmicrowaves the result may be significantly dependent on the distance to an emitter, the energy flux density being equal (Gapeyev et al. , 1996).

Researchers often took pains seeking relatively rare successful combinations of electromagnetic and physiological conditions. Nevertheless, biological systems were found to be influenced by weak MFs in a host of experimental configurations. The following is a concise catalogue of them.

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Some important experimental works are described or commented on later in the book when comparing findings with theory.

This author could not find in the libraries accessible to him some important works dating from the turn of the 20th century to the late 1970s. However, there are reviews ofsuch works (Kholodov, 1975; Warnke and Popp, 1979) that point to the therapeutic uses ofMFs and discuss investigations into physiological and tissue responses to weak DC, AC and pulsed MFs, magnetic vacuum, and geomagnetic fluctuations. The main “set” ofmagnetic configurations studied remained essentially the same.

It would be ofinterest to point to some “pioneer” works on magnetobiology from the turn of the 20th century and earlier.12

E.K. O’Jasti (1798). Magic Magnet Mystery. “Hibernia”, Dublin.

W. Waldmann (1878). Der Magnetismus in der Heilkunde. Deutsch. Arch. Geschichte Med. Med. Geographie 1, 320.

N.I. Grigoriev (1881). Metalloscopy and Metallotherapy. St. Petersburg, (in Russian).

V.Ya. Danilevsky (1900–1901). Research into the Physiological Action of Electricity at a Distance. V.1–2. Kharkov, (in Russian).

B. Beer (1901). Über das Auftreten einer subjektiven Licht-empfindung im magnetischen Feld. Wiener klin. Wochenschr. 4.

C. Lilienfeld (1902). Der Elektromagnetismus als Heilfaktor. Therapie Gegenwart Sept., 390.

P. Rodari (1903). Die Physikalischen unf physiologisch-therapeutischen Einflusse des magnetischen Feldes auf den menschlichen Organismus. Correspond. Schweiz. Arzte 4, 114.

S.P. Thompson (1910). A physiological effect of an alternating magnetic field. R. Soc.

82, 396.

G. Durvil (1913). Treatment of Diseases by Magnets. Kiev, (in Russian).

C.E. Magnussen and H.C. Stevens (1914). Visual sensations caused by a magnetic field.

Philos. Mag. 28, 188.

H.B. Barlow, H.J. Kohn and G. Walsh (1917). Visual sensations aroused by magnetic fields. Am. J. Physiol. 148, 372.

Many magnetobiological assays still await confirmations by other laboratories.

It might appear that there is no evidence reliable enough for theoretical models to be constructed. However, when pooled (e.g., Bersani, 1999), these findings show a measure ofcommonness in what concerns manifestations ofMBEs under various conditions and on various biological objects. It is these common elements that serve as a foundation for our further theorizing.

12This author is grateful to S.N. Uferom of Leeds University who introduced him to a curiosity by O’Jasti. Other publications are borrowed from bibliographies available in Warnke and Popp (1979) and Kholodov and Lebedeva (1992).

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2.1 A POTPOURRI OF EXPERIMENTAL WORK

The following is a summary of experimental findings that are primarily discussed in the book. For convenience, works are grouped by (1) research objects, (2) parameters observable in experiment, (3) frequency ranges, and (4) configurations of electromagnetic fields to which organisms were subjected.

2.1.1 Objects studied

Among the commonest objects studied are:

biochemical

reactions

(Jafary-Asl et al. ,

1983;

Litovitz et al. ,

1991;

Shuvalova et al. , 1991; Markov et al. , 1992; Novikov, 1994; Markov et al. , 1998; Blank and Soo, 1998; Ramundo-Orlando et al. , 2000),13

DNA damage and repair processes (Whitson et al. , 1986; Nordensen et al. , 1994),

DNA–RNA

synthesis

(Liboff et al. ,

1984;

Takahashi et al. ,

1986;

Goodman and Henderson, 1991; Phillips et al. , 1992; Goodman et al. , 1993a; Lin and Goodman, 1995; Blank and Goodman, 1997),

enzymes — membrane ion pumps (Blank and Soo, 1996),

cells (Spadinger et al. , 1995; Alipov and Belyaev, 1996; Sisken et al. , 1996):

amoeba cells (Berk et al. , 1997),

bacterial cells (Moore, 1979; Alexander, 1996),

∗ E. coli (Aarholt et al. , 1982; Dutta et al. , 1994; Alipov et al. , 1994; Nazar et al. , 1996),

yeast cells (Jafary-Asl et al. , 1983),

∗ Candida (Moore, 1979),

cells ofplants (Fomicheva et al. , 1992a,b; Belyavskaya et al. , 1992),

fungi (Broers et al. , 1992),

algae (Smith et al. , 1987; Reese et al. , 1991) and

insects (Goodman and Henderson, 1991).

animal cells (Takahashi et al. , 1986):

fibroplasts (Whitson et al. , 1986; Ross, 1990; Matronchik et al. , 1996b; Katsir et al. , 1998),

mouse epidermis (West et al. , 1996),

erythrocytes (Serpersu and Tsong, 1983; Mooney et al. , 1986; Shiga et al. , 1996),

lymphocytes (Conti et al. , 1985; Rozek et al. , 1987; Lyle et al. , 1988; Goodman and Henderson,

1991;

Lyle et al. ,

1991;

Walleczek,

1992;

Yost and Liburdy, 1992; Coulton and Barker, 1993; Lindstrom et al. , 1995; Tofani et al. , 1995),

13Evidence is scarce. Actions of a low-frequency MF on biochemical reactions in vitro have been comparatively little studied.

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leucocytes (Barnothy, 1956; Goodman et al. , 1989; Picazo et al. , 1994; Sontag, 2000),

osteoblasts (Luben et al. , 1982),

neoblasts (Lednev et al. , 1996b,a),

endothelia (Yen-Patton et al. , 1988),

ofsalivary glands (Goodman et al. , 1983; Goodman and Henderson, 1988),

thymocytes (Walleczek and Budinger, 1992; Matronchik et al. , 1996b),

amniotic (Simko et al. , 1998),

bone cells (Fitzsimmons et al. , 1989).

tumor cells (Phillips et al. , 1986b; Wilson et al. , 1990; Lyle et al. , 1991):

Ehrlich carcinoma (Garcia-Sancho et al. , 1994; Muzalevskaya and Uritskii, 1997),

breast cancer MCF-7 (Harland and Liburdy, 1997; Blackman et al. , 2001),

pheochromocytoma (Blackman et al. , 1993),

leukemia in humans U937 (Smith et al. , 1991; Garcia-Sancho et al. , 1994; Eremenko et al. , 1997),

E6.1 (Galvanovskis et al. , 1999),

carcinoma ofmouse embryo F9 (Akimine et al. , 1985),

glioma N6 (Ruhenstroth-Bauer et al. , 1994),

human osteosarcoma TE-85 (Fitzsimmons et al. , 1995).

tissues ofthe brain (Bawin and Adey, 1976; Blackman et al. , 1979; Dutta et al. ,

1984;

Blackman et al. ,

1988,

1990;

Martynyuk,

1992;

Agadzhanyan and Vlasova,

1992;

Espinar et al. ,

1997;

Lai and Carino,

1999),

nerve (Semm and Beason, 1990),

intestine (Liboff and Parkinson, 1991),

bone (Reinbold and Pollack, 1997).

organs:

brain (Kholodov, 1982; Richards et al. , 1996),

heart (Kuznetsov et al. , 1990).

physiological systems:

central nervous (Bawin et al. , 1975; Kholodov, 1982; Lerchl et al. , 1990),

neuroendocrine (Reiter, 1992),

immune (Lyle et al. , 1988).

organisms:

plants (Pittman and Ormrod, 1970; Kato, 1988; Kato et al. , 1989; Govorun et al. , 1992; Sapogov, 1992; Smith et al. , 1995),

plant seeds (Ružič and Jerman, 1998; Ružič et al. , 1998),

kidneys (Ružič et al. , 1992),

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OVERVIEW OF EXPERIMENTAL FINDINGS

insects (Ho et al. , 1992),

rats (Wilson et al. , 1981; Ossenkopp and Ossenkopp, 1983; Thomas et al. , 1986; Sidyakin, 1992; Temuriyants et al. , 1992a; Pestryaev, 1994; Kato et al. , 1994; Kato and Shigemitsu, 1996; Deryugina et al. , 1996; Nikollskaya et al. , 1996) and

embryos ofrats (Delgado et al. , 1982; McGivern et al. , 1990),

mice (Barnothy, 1956; Kavaliers and Ossenkopp, 1985, 1986; Picazo et al. , 1994),

newts (Asashima et al. , 1991),

worms (Jenrow et al. , 1995; Lednev et al. , 1996a,b),

pigeons (Sidyakin, 1992),

chickens (Saali et al. , 1986),

snails (Prato et al. , 1993, 1995),

human organism (Akerstedt et al. , 1997; Sastre et al. , 1998).

ecosystems and bio-geocenosis (Uffen, 1963; Opdyke et al. , 1966; Hays, 1971; Valet and Meynadier, 1993; Feychting et al. , 1995; Belyaev et al. , 1997),

solutions ofamino acids — although they are no biological objects, they display MF effects that are very close in essence to those discussed —

(Novikov and Zhadin, 1994; Novikov, 1994, 1996).

2.1.2 Observables

The observable parameters were:

physical:

dimensions and weight ofan object (Saali et al. , 1986; Kato, 1988; Kato et al. , 1989; Sapogov, 1992; Smith et al. , 1995),

viscosity ofcell suspension (Alipov et al. , 1994; Alipov and Belyaev, 1996),

rheological properties ofcells (Shiga et al. , 1996),

number ofcells (Broers et al. , 1992; Picazo et al. , 1994; Tofani et al. , 1995; Alexander, 1996; West et al. , 1996; Eremenko et al. , 1997; Berk et al. , 1997) and

subcellular structures (Simko et al. , 1998),

surface electric change (Smith et al. , 1991; Muzalevskaya and Uritskii, 1997),

transmembrane potential (Liboff and Parkinson, 1991),

structure ofimages ofelectron and other microscopies (Goodman et al. , 1983; Belyavskaya et al. , 1992; Blackman et al. , 1993; Espinar et al. , 1997),

current through electrochemical cell with an object (Novikov and Zhadin, 1994; Novikov, 1994, 1996),

photoprotein luminescence (Sisken et al. , 1996),

intensity ofradioactive tracer emission (Liboff et al. , 1984; Fitzsimmons et al. , 1989; Markov et al. , 1992; Fitzsimmons et al. , 1995; Markov et al. , 1998; Katsir et al. , 1998),

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DNA mobility (Lai and Singh, 1997a),

parameters analyzed:

chromatographic (Novikov and Zhadin, 1994; Novikov, 1994),

fluorescent (Fitzsimmons et al. , 1989; Katsir et al. , 1998)

microfluorescent

(Walleczek,

1992;

Walleczek and Budinger,

1992;

Lindstrom et al. ,

1995;

Muzalevskaya and Uritskii,

1997;

Reinbold and Pollack, 1997),

spectrophotometric (Blank and Soo, 1998; Ramundo-Orlando et al. , 2000),

gel-electrophoresis (Goodman and Henderson, 1988; Lin and Goodman, 1995),

radiographic

(Goodman et al. ,

1983;

Mooney et al. ,

1986;

Goodman and Henderson, 1991),

ECG, EEG, ECoG (Kholodov and Lebedeva, 1992; Pestryaev, 1994; Sastre et al. , 1998).

biochemical:

activity and level ofan enzyme in the transcription ofa β-galactosidase gene (Aarholt et al. , 1982),

adenylate cyclase (Luben et al. , 1982),

lysozyme (Jafary-Asl et al. , 1983),

protein-kinase (Byus et al. , 1984),

Na,K-ATPase (Serpersu and Tsong, 1983; Blank and Soo, 1990, 1996),

acetylcholinesterase (Dutta et al. , 1992),

enolase (Dutta et al. , 1994; Nazar et al. , 1996),

melatonin (Wilson et al. , 1981; Lerchl et al. , 1991; Reiter, 1992; Kato et al. , 1993, 1994; Loscher et al. , 1994; Lee et al. , 1995; Kato and Shigemitsu, 1996),

noradrenaline and adrenaline (Temuriyants et al. , 1992a),

phosphorylation oflight myosin chains (Markov et al. , 1992),

choline (Lai and Carino, 1999),

ornithine-decarboxylase (Litovitz et al. , 1991, 1997b),

cytochrome-oxidase (Blank and Soo, 1998),

N-acetyl-serotonin transferase (Cremer-Bartels et al. , 1984).

Calcium efflux (Bawin et al. , 1975; Dutta et al. , 1984; Smith et al. , 1987; Blackman et al. , 1988, 1990; Schwartz et al. , 1990; Blackman et al. , 1991; Adey, 1992; Dutta et al. , 1992),

intra- and extracellular ion concentration (Liboff, 1985; Galvanovskis et al. , 1999),

concentration ofperoxide lipid oxygenation products and oftotal thiol groups (Martynyuk, 1992),

uptake ofradioactive tracers (Serpersu and Tsong, 1983; Takahashi et al. , 1986; Lyle et al. , 1991; Fomicheva et al. , 1992a; Garcia-Sancho et al. , 1994),

level ofribonucleic acids (mRNA) (Goodman et al. , 1989; Fomicheva et al. , 1992b).

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OVERVIEW OF EXPERIMENTAL FINDINGS

biological:

pulsed

activity

ofneurons

(Semm and Beason,

1990;

Agadzhanyan and Vlasova, 1992),

stability ofbiological rhythm (Kuznetsov et al. , 1990),

parameters ofmorphogenesis and development (Asashima et al. , 1991; Ho et al. , 1992; Ružič et al. , 1992, 1998),

seed germination rate (Ružič and Jerman, 1998),

mobility and morphology ofcells (Smith et al. , 1987; Spadinger et al. , 1995; Reese et al. , 1991),

proliferation of cells (Akimine et al. , 1985; Whitson et al. , 1986; Ross, 1990; Fomicheva et al. , 1992a; Ruhenstroth-Bauer et al. , 1994; Lednev et al. , 1996b; Muzalevskaya and Uritskii, 1997; Harland and Liburdy, 1997; Katsir et al. , 1998; Blackman et al. , 2001),

expression ofgenes (Goodman and Henderson, 1988; Phillips et al. , 1992),

behavior ofindividuals and cohorts:

conditional-reflex activity (Kholodov, 1982; Ossenkopp and Ossenkopp, 1983; Thomas et al. , 1986; Sidyakin, 1992),

time ofreaction (Kavaliers and Ossenkopp, 1986; Prato et al. , 1995) and regeneration (Jenrow et al. , 1995),

motive and exploratory activity (Deryugina et al. , 1996; Nikollskaya et al. , 1996),

memory (Richards et al. , 1996),

physiological parameters ofsleep (Akerstedt et al. , 1997).

2.1.3 EMF ranges

Observed is the behavior ofbiological systems in electromagnetic fields ofvarious ranges:

DC fields (Barnothy, 1956; Ramirez et al. , 1983; Strand et al. , 1983; Cremer-Bartels et al. ,

1984;

Persson and Stahlberg,

1989;

Kato,

1988;

Kato et al. , 1989; Semm and Beason, 1990; Luben, 1991; Ho et al. , 1992; Ružič et al. , 1992; Malko et al. , 1994; Nikollskaya et al. , 1996; Shiga et al. , 1996; Espinar et al. , 1997; Berk et al. , 1997; Markov et al. , 1998),

geomagnetic fields (Yeagley, 1947; Lindauer and Martin, 1968; Blakemore, 1975; Bookman, 1977; Martin and Lindauer, 1977; Kalmijn, 1978; Gould et al. , 1980; Frankel et al. , 1981; Mather and Baker, 1981; Quinn et al. , 1981; Bingman, 1983; Ossenkopp et al. , 1983; Chew and Brown, 1989),

range < 1 Hz (Kavaliers and Ossenkopp, 1986; Semm and Beason, 1990; Muzalevskaya and Uritskii, 1997),

range 1–100 Hz (Delgado et al. , 1982; Goodman et al. , 1983; Akimine et al. , 1985;

Whitson et al. ,

1986;

Saali et al. ,

1986;

Takahashi et al. ,

1986;

Smith et al. , 1987; Lyle et al. , 1988; Fitzsimmons et al. , 1989; Kuznetsov et al. ,

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1990;

Ross,

1990;

Wilson et al. ,

1990;

Lyle et al. ,

1991;

Reese et al. ,

1991; Agadzhanyan and Vlasova, 1992; Martynyuk, 1992; Sidyakin, 1992; Reiter,

1992;

Temuriyants et al. ,

1992a;

Walleczek and Budinger,

1992;

Coulton and Barker,

1993;

Blackman et al. ,

1993;

Alipov et al. ,

1994;

Kato et al. , 1994; Novikov and Zhadin, 1994; Novikov, 1994; Dutta et al. , 1994; Fitzsimmons et al. , 1995; Jenrow et al. , 1995; Lindstrom et al. , 1995; Prato et al. , 1995; Smith et al. , 1995; Spadinger et al. , 1995; Tofani et al. , 1995;

Blank and Soo,

1996;

Kato and Shigemitsu,

1996;

Novikov,

1996;

Alipov and Belyaev, 1996; Nazar et al. , 1996; West et al. , 1996; Akerstedt et al. , 1997; Harland and Liburdy, 1997; Reinbold and Pollack, 1997; Litovitz et al. , 1997b;

Katsir et al. ,

1998;

Ružič and Jerman,

1998;

Ružič et al. ,

1998;

Sastre et al. , 1998; Simko et al. , 1998; Galvanovskis et al. , 1999; Lai and Carino, 1999; Ramundo-Orlando et al. , 2000; Blackman et al. , 2001),

range 102–103 Hz (Saali et al. , 1986; Blackman et al. , 1988, 1990; Blank and Soo, 1990; Liboff and Parkinson, 1991; Deryugina et al. , 1996; Blank and Soo, 1998),

range 1–103 kHz (Serpersu and Tsong, 1983; Liboff et al. , 1984; Blank and Soo, 1990; Ruhenstroth-Bauer et al. , 1994; Lednev et al. , 1996b; Blank and Soo, 1998; Sontag, 2000),

range 1–100 MHz (Aarholt et al. , 1988; Alexander, 1996),

range 102–103 MHz (Bawin et al. , 1975; Byus et al. , 1984; Dutta et al. , 1984; Broers et al. , 1992; Dutta et al. , 1994),

more than 1 GHz (Smolyanskaya et al. , 1979; Webb, 1979; Adey, 1980; Bannikov and Ryzhov, 1980; Grundler and Keilmann, 1983; Dutta et al. , 1984; Andreev et al. , 1985; Aarholt et al. , 1988; Didenko et al. , 1989; Grundler et al. , 1992; Grundler and Kaiser, 1992; Belyaev et al. , 1993; Kataev et al. , 1993; Gapeyev et al. , 1994; Belyaev et al. , 1996),

narrow-band noise and broad-band MFs (Smith et al. , 1991; Pestryaev, 1994; Ruhenstroth-Bauer et al. , 1994; Lin and Goodman, 1995; Litovitz et al. , 1997b; Muzalevskaya and Uritskii, 1997).

2.1.4 Field configurations

They use various combinations and orientations offields:

parallel DC and AC MFs (Thomas et al. , 1986; Smith et al. , 1987; Liboff et al. , 1987a; Liboff and Parkinson, 1991; Reese et al. , 1991; Prato et al. , 1995; Smith et al. , 1995; Tofani et al. , 1995; Lednev et al. , 1996a,b; Deryugina et al. , 1996; Reinbold and Pollack, 1997; Ramundo-Orlando et al. , 2000),

perpendicular DC and AC MFs (Thomas et al. , 1986; Blackman et al. , 1990; Picazo et al. , 1994; Blackman et al. , 1996; Ružič et al. , 1998),

tilted fields (Ross, 1990; Kuznetsov et al. , 1990; Lyle et al. , 1991; Blackman et al. ,

1993;

Alipov et al. ,

1994;

Fitzsimmons et al. ,

1995;

Lindstrom et al. ,

1995;

Alipov and Belyaev,

1996;

Blackman et al. ,

1996;

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OVERVIEW OF EXPERIMENTAL FINDINGS

West et al. , 1996;

Litovitz et al. , 1997b; Muzalevskaya and Uritskii, 1997;

Ružič and Jerman, 1998; Galvanovskis et al. , 1999),

rotating MFs (Ossenkopp and Ossenkopp, 1983; Kavaliers and Ossenkopp, 1985, 1986; Kato et al. , 1994; Sastre et al. , 1998),

near-zero MFs (Becker, 1965; Beischer, 1965; Halpern and Van Dyke, 1966; Busby, 1968; Lindauer and Martin, 1968; Conley, 1969; Dubrov, 1969; Beischer, 1971;

Gleizer and Khodorkovskii,

1971;

Khodorkovskii and Polonnikov,

1971;

Wever,

1973;

Edmiston,

1975;

Pavlovich and Sluvko,

1975;

Semikin and Golubeva, 1975; Sluvko, 1975; Chew and Brown, 1989; Kato et al. , 1989; Asashima et al. , 1991; Kashulin and Pershakov, 1995; Eremenko et al. , 1997),

electric fields, also in combination with MFs (Wilson et al. , 1981; Jafary-Asl et al. ,

1983;

Serpersu and Tsong,

1983;

Whitson et al. ,

1986;

Phillips et al. ,

1986b;

Blackman et al. ,

1988;

Lyle et al. ,

1988;

Fitzsimmons et al. ,

1989;

Blackman et al. ,

1990;

Blank and Soo,

1990;

Nazar et al. , 1996; Huang et al. , 1997; Schimmelpfeng and Dertinger, 1997; Sontag, 1998, 2000),

parallel MF and a perpendicular electric field (Novikov and Zhadin, 1994; Novikov, 1994, 1996),

pulses and pulse bursts ofMFs ofvarious shapes (Aarholt et al. , 1982; Goodman et al. , 1983; Mooney et al. , 1986; Takahashi et al. , 1986; Goodman and Henderson,

1988;

Semm and Beason,

1990;

Luben,

1991;

Smith et al. , 1991; Walleczek and Budinger, 1992; Ruhenstroth-Bauer et al. , 1994; Pestryaev, 1994; Richards et al. , 1996),

with low-frequency EMF modulation (Bawin et al. , 1975; Lin and Goodman, 1995; Litovitz et al. , 1997b),

motion ofbiosystems in a modulated MF (Sapogov, 1992; Nikollskaya et al. , 1996),

low-frequency MFs of super-low <

1 µ T

intensity

(Delgado et al. ,

1982;

Takahashi et al. ,

1986;

Berman et al. ,

1990;

Kato et al. ,

1993;

Ruhenstroth-Bauer et al. ,

1994;

Kato et al. ,

1994;

Loscher et al. ,

1994;

Feychting et al. , 1995; Blank and Soo, 1996; Novikov, 1996; Richards et al. , 1996; West et al. , 1996; Akerstedt et al. , 1997; Harland and Liburdy, 1997; Farrell et al. , 1997),

millimeter-wavelength radiation ofsuper-low intensity (Aarholt et al. , 1988; Grundler and Kaiser,

1992;

Belyaev et al. ,

1996;

Gapeyev et al. ,

1996;

Kuznetsov et al. , 1997).

Unfortunately, a number of interesting works are fairly difficult to be classed with any ofthe above combinations, since, as is very often the case, no indication is given in them ofthe DC MF level involved. That variable is as important as the frequency and amplitude of an AC field.

The works cited above are only provided here by way ofexample to illustrate the variety, completeness, and generality ofmagnetobiological effects. These quali-

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ties alone strongly suggest that biological actions ofelectromagnetic fields are not exotic highly specialized effects, but rather common phenomena, refined regulatory mechanisms, perhaps used by nature on a global scale. Anyway, not all share that point ofview (Garcia-Sancho et al. , 1994; Gustavsson et al. , 1999). The last work concludes, by the way, that there is perhaps no common cellular effect for low-frequency MFs. That inference was prompted by low reproducibility of findings in various laboratories, except for melatonin assays (e.g., Reiter, 1998). However whether uses ofstatistical tools are legitimate here is questionable. We might as well believe that science as a whole does not exist because only a small proportion ofpeople are involved in scientific activities. Low reproducibility ofresults on various cohorts, with high reproducibility in each cohort, for more than a decade is indicative ofthe fact that it is just the experimental conditions that have not been adequately reproducible.

Information on the plausible physical nature of observed magnetobiological effects is primarily contained in the “physical part” ofexperiments, i.e., in the details ofeffective MFs. Emphasis, therefore, has been placed on MF configuration details, which are crucial for the outcome of an experiment. The “biological part”, the preparation ofbiological systems, supporting preparations and adequate conditions, as well as procedures for measuring the final variable — which are often sophisticated and artful experimental techniques — lie outside the scope of the discussion. Selection ofan appropriate low-frequency MF range is dictated, as stated above, by the possibility ofignoring an induced electric field, which varies with the frequency, and mainly by the fact that in that range EMF biological effects are especially paradoxical. Uses ofDC MFs and combined DC and low-frequency fields are detailed below.

In our descriptions ofexperiments we will make use ofa unified scheme, or formula, of an experiment. It will contain controllable MF parameters, intervals of their variations, and some statistical data. Units ofmeasurement are those often employed in experiments ofthat nature: for MF induction B µ T, for frequency f — Hz, for time intervals T, τ — s. For instance, the formula B(45 ± 5) b(0 12 / 1) f (50 , 60) B p(!) n(5 8) g(?) (2.1.1)

implies that the DC MF B (we will also denote it B DC or H DC depending on the context) is 45 µ T to within 5 µ T; a parallel field with an amplitude, i.e., peak value, b (or B AC) varied from 0 to 12 µ T with an increment of 1 µ T. Various trials used two fixed frequencies, either 50 or 60 Hz, the value of the perpendicular component ofDC MF B p was not controlled (!), and the number ofrepeats n (experimental points) for each set of MF variables was from 5 to 8, the MF gradient being unknown (?). With pulsed MFs, b meant the pulse height. The order ofparameter listing is arbitrary.

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2.2 BIOLOGICAL EFFECTS OF DC MAGNETIC FIELDS

The behavior ofliving systems exposed to DC MFs has been discussed for quite a long time. The biological effect ofDC MFs, unlike that oflow-frequency ones, does not seem to be paradoxical on the face of it, since there are no EMF quanta whose energy could be compared with the energy ofbiochemical transformations.

It seems plausible that a DC MF acts following another mechanism and is able to accumulate at some biological level, bypassing the state ofprimary physical oscillators. However, in this case as well, there are no reliably established mechanisms ofprimary reception ofweak fields, except for those connected with the so-called biogenic magnetite (Simon, 1992).

Malko et al. (1994) deem it generally accepted that DC MFs exert no marked adverse biological action, which is confirmed by a rich experience ofmagnetic resonance tomography (Persson and Stahlberg, 1989). They addressed the multiplication of S. cerevisiae yeast cells exposed to a static MF of1.5 T, produced by a clinical NMR tomograph. Exposed and control cells were allowed to multiply in a broth for 15 hours, which corresponded to seven cell divisions cycles. The DC

and AC 60-Hz fields were under 50 and 3 µ T (rms), respectively. Data processing unearthed no statistically reliable effect.

The authors thus assumed that a given MF would not affect mammal cells as well, since most ofthe chemical reactions involving these cells and those ofunicellular organisms are identical. They challenged reports ofadverse actions ofa DC MF

on the blood in mice (Barnothy, 1956), Drosophila larvae (Ramirez et al. , 1983), and trout (Strand et al. , 1983). However, that inference is hard to accept considering a wealth ofdata on biological efficiency ofboth strong and weak static MFs, including changes in enzyme activity (e.g., Wiltschko et al. , 1986; Polk and Postow, 1997; Moses and Basak, 1996).

Constant exposure to a 20-mT field in Espinar et al. (1997) produced a 25 %

change in the histological parameters ofchicken cerebellum tissue. Fields ofabout 71 and 107 mT, investigated in Berk et al. (1997), retarded the growth ofan amoeba population by 9–72 %. Also, stimulation was observed (Moore, 1979) at 15 mT and inhibition at 30–60 mT in various bacteria and fungi. Furthermore, from the viewpoint ofthe most likely interference MBE mechanisms, in certain cases strong MFs are less effective than weak fields, comparable with the geomagnetic field.

With the exception ofrelatively strong MFs, more than 1 mT, the question ofpossible adverse consequences ofexposure to an MF different from the Earth’s also awaits its solution. The issue is important because the level ofa DC MF of technogenic origin and its gradient strongly vary from place to place. In given production premises a DC MF may be as low as several percent ofthe geomagnetic field, or as high as tens ofoersteds near massive iron structures, and it may take on those extreme values within meters. The action ofDC MFs on the human health and international programs in that field were discussed in a review by Repacholi and Greenebaum (1999).

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2.2.1 Biological effects of weak magnetic fields

Leucht (1987) investigated the dissipation ofmelanophore pigments in tadpole skin samples subjected to a stimulating hormone and their aggregation under light.

These processes appeared to have different rates, depending on the value ofa DC

MF. Doubling the field, from 42 to 84 µ T, reduced the dissipation rate by 22–24 %.

In these assays, the MBE was largely independent ofthe hormone density and illumination intensity, a fact that, according to the author, points to modulation of secondary signaling processes involving calcium by a magnetic field.

Belyaev et al. (1994) and Matronchik et al. (1996a) studied the influence ofa 15-min exposure of E. coli cells to an MF, modified in comparison with the Earth’s field, on the viscosity ofcell suspension. The MF varied within 0–110 µ T. The absolute maximum ofthe MBE was about 25 ± 2 % in a near-zero MF. The dependence of the MBE on H DC displayed several extrema with their sign alternating, Fig. 4.48.

Markov et al. (1998) found that the rate of Ca2+-calmodulin-dependent phosphorylation ofmyosin light chains in a cell-free reaction mixture was strongly dependent on the DC MF level. The rate, worked out using the 32P radioactive tracer, grew monotonously from 80 to 280 % as the MF was varied from 0 ± 0 . 1 to 200 µ T.

2.2.2 Orientation in the Earth’s magnetic field

Worthy ofspecial attention are effects involving the orientation ofliving organisms in a weak MF, specifically in the geomagnetic field (GMF). Many biological systems have been found to “see” magnetic lines of force and employ this faculty for navigation (Kirschvink et al. , 1985; Beason, 1989). Biosystems can thus respond not only to the value ofan MF, but also to changes in its direction. In this case, however, magnetosensitivity is no paradox. Kirschvink et al. (1985) came up with more or less satisfactory insights into the nature of that phenomenon. The magazines Nature and Science publish editorials on that topic with amazing constancy, overlooking at the same time to give to the general physical issues ofthe paradoxical biological action ofEMFs a positive treatment.

Some navigational capabilities in a weak MF are displayed by bacteria (Blakemore, 1975; Frankel et al. , 1981), birds (Yeagley, 1947; Bookman, 1977; Bingman, 1983; Wiltschko et al. , 1986; Beason, 1989), fishes (Kalmijn, 1978; Quinn et al. , 1981; Chew and Brown, 1989), insects (Lindauer and Martin, 1968; Martin and Lindauer, 1977; Gould et al. , 1980), and mammals (Mather and Baker, 1981; Zoeger et al. , 1981).

Large-scale orientation using a “compass” requires a conjunction ofa magnetic chart to a geographic chart. To us humans such a conjunction is our knowledge that the magnetic meridian is approximately aligned along the geographic one. Birds have no such knowledge, and so they have to adjust or to learn by coordinating their magnetic “feel” with their innate navigational means, e.g., those relying on the polarization distribution ofdaylight. After some learning, birds do not need daylight anymore, and so some ofthem are able to perform seasonal migrations

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OVERVIEW OF EXPERIMENTAL FINDINGS

6HPPDQG%HDVRQ


1XPEHURIVSLNHV


0)FKDQJHµ7

Figure 2.1. Changes in the vertical component of a local MF within 0.2 s bring about some heightened spike activity of the trigeminal ganglion cells, according to Semm and Beason (1990).

by night. Able and Able (1995) exposed sparrows in open cages for four days to a local MF oriented at 90 o relative to the natural geomagnetic field. This tended to change the predominant direction, also by 90 o, ofnight flights both in young and adult individuals.

Collett and Baron (1994) found that bees remember and then recognize the visual picture ofsome place, taking bearings using the lines offorce ofthe geomagnetic field, i.e., using them as a reference. This markedly simplifies the retention and retrieval of information from memory.

Compass-type magnetic orientation is also inherent in newts in the daylight, but not by night. Orientation nature varies depending on the spectral composition of the light. It is believed therefore that photoreceptors of the retina can be suitable targets for a DC MF since their orientation is linked with the body stance. At the same time, Lohmann (1993) has shown that there exists light-independent compass-type orientation in some invertebrates, fishes, and mammals.

Semm and Beason (1990) studied the optic nerve and trigeminal ganglion in bobolinks exposed to short-term variations ofa local DC MF. Their goal was to identify field-sensitive fibers of the nerve and to find out whether their sensitivity is high enough for a kind of “magnetic map” to be realized. The spontaneous activity ofsome areas or cells ofthe nerve (studied were 182 cells in 23 birds) was registered using micropipets–electrodes 1–5 µ m in diameter. An inclinable couple ofHelmholtz rings was used.

Only 14 % ofcells with a spontaneous activity appeared to be sensitive to MF

variations. These cells did not respond to vibrations and mechanical stimulation ofa bird’s body. Different cells responded differently. Some only responded to an increase, others to a decrease in the MF. Some cells appeared to be sensitive to hyperweak, 200 nT, variations within an interval from 0.2 to 4 s, the pulse front

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being 6 ms. The variation ofthe number ofactivity spikes with the stimulus intensity for one of the cells is given in Fig. 2.1. Biological systems’ sensitivity to stimulus typically shows a logarithmic dependence. This suggests that this dependence reflects secondary biochemical processes, rather than primary biophysical reception ofan MF. Another evidence ofthat is the relatively large time, 10–20 s, ofthe recovery ofinitial cell activity after the removal ofa weak magnetic stimulus. The authors believe that the “magnetic map” in birds, which responds to variations about 100 nT (Wiltschko et al. , 1986), could be due to the magnetic sensitivity of neurons.

2.2.3 Effects of a near-zero magnetic field

It has long been noticed that living organisms are not indifferent to changes in a DC

MF level. Life on Earth has always existed under a weak (but not zero) geomagnetic field. It is widely believed that during the many millennia biological systems have somehow adjusted to the natural level ofthe magnetic field. Therefore, any MF changes can cause some infirmities and disorders. Some researchers maintain that an inversion ofthe Earth’s magnetic poles could bring about changes ofglobal proportions (Uffen, 1963; Opdyke et al. , 1966; Hays, 1971; Valet and Meynadier, 1993; Belyaev et al. , 1997). Specifically, a correlation ofthe emergence and disappearance ofbiological species with the average frequency ofGMF inversions was found, Fig. 2.2.

The Earth’s magnetic field changes its orientation approximately every 200 thousand years (ranging from 10 to 730 thousand years) and lasts for about 4–5 thousand years, with the result that living organisms find themselves for a long time in changed magnetic conditions, specifically exposed to a markedly reduced (to 10 %) geomagnetic field (e.g., Skiles, 1985). Skiles provides arguments that we now witness a GMF inversion. Since during an inversion the geomagnetic field is different from a dipole field, local magnetic conditions may include values that are yet closer to zero (Valet and Meynadier, 1993).

Liboff (1997) believes that perturbations in biological species in a changing geomagnetic field are rather associated with cyclotron resonance conditions for some ions in the GMF and in the endogenous electric field oforganisms. Unlike the already established fact ofbiological activity ofa zero field, this hypothesis does not lend itselfto easy verification, unfortunately. What is more, the very idea of cyclotron resonance in biology has not yet received any physical substantiation.

The relative simplicity ofthe realization ofconditions ofa near-zero MF, the presence ofsuch a field in the working conditions ofsome professions, e.g., astro-nauts and submariners, predicated scientific research ofbiological effects ofa magnetic vacuum, or a zero MF. A review ofsuch works till 1976 is given in a monograph by Dubrov (1978) and till 1985 in a monograph by Kopanev and Shakula (1986). It is generally possible to reduce the value ofan MF within an experimental space by two or three orders ofmagnitude as compared to that ofthe GMF.

There are also sophisticated magnetic vacuum systems with a passive or active

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OVERVIEW OF EXPERIMENTAL FINDINGS

U


DQFH


DSSHDU

'LV


)UHTXHQF\

Figure 2.2. Correlation diagram: the x-axis, index of GMF inversion frequency; y-axis, index of the vanishing of biological species. Processing of data in Fig.24 fromDubrov (1978).

compensation to reduce the field 105–106 times (Govorun et al. , 1992) and more (Vvedenskii and Ozhogin, 1986).

Biological effects ofa magnetic vacuum are displayed by plants (Dubrov, 1969; Edmiston, 1975; Semikin and Golubeva, 1975; Kato et al. , 1989; Govorun et al. , 1992; Fomicheva et al. , 1992a,b; Belyavskaya et al. , 1992; Kashulin and Pershakov, 1995), microorganisms (Pavlovich and Sluvko,

1975; Sluvko, 1975),

insects

(Becker,

1965;

Lindauer and Martin,

1968),

worms

(Lednev et al. ,

1996a),

newts

(Asashima et al. ,

1991),

fishes

(Gleizer and Khodorkovskii,

1971;

Khodorkovskii and Polonnikov,

1971;

Chew and Brown,

1989),

mammals

(Halpern and Van Dyke, 1966; Busby, 1968; Conley, 1969; Beischer, 1971), various cells (Belyaev et al. , 1997), and the human organism (Beischer, 1965, 1971; Wever, 1973).

No response ofplants to a zero MF was f

ound in Dyke and Halpern (1965).

Different responses were observed (Shrager, 1975) in right and left isomer forms of onion seeds.

Kato et al. (1989) studied in a magnetic vacuum 5 nT the growth of“pilose roots” on carrot and belladonna induced by some genetic methods. The growth of roots on belladonna in the field 50 µ T was enhanced by 40–56 % as compared with controls. The carrot root growth remained nearly unchanged. At the same time a DC field 0 . 5 T, strong as compared with the control field 10 3 T, caused a

25 % enhancement ofroot growth in both plants. It was shown that a changed DC MF in those assays acts precisely on plant roots, since a pre-treatment ofthe medium where the plants grew under similar magnetic conditions did not result in any changes. It was concluded that a strong MF and a magnetic vacuum might have different targets in plants, i.e., different mechanisms ofbiological action. The authors also refer to a work where identical conditions, H DC 5 nT, resulted in the death ofnewt embryos within several days.

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*0)

QXOO0)


7K


*

6

*

0

7RWDO


Figure 2.3. Influence of an MF on reproduction cycle phases of pea root meristema cells.

Phase G1, RNA and protein synthesis; S, DNA synthesis; G2, post-synthesis; M, mitosis phase; Total, entire cycle; according to data (Fomicheva et al. , 1992a).

Many hours ofexposure ofoats plants at the early stages ofontogenesis under hypomagnetic conditions, with the GMF compensated down to 1 % ofits local value, stimulated plant growth (Kashulin and Pershakov, 1995).

Bacterial cultures respond to screening from the GMF in a wide variety of ways, by changes at the phenotype and genotype levels, which manifest themselves both in metabolic and physiological processes (Dubrov, 1978). Hypomagnetic conditions, up to 0.1 µ T, brought about an increase in cellular nuclei size and a marked reduction in mitosis intensity in mouse and hamster cells in vitro (Sushkov, 1975). At the same time, hypomagnetic conditions (Green and Halpern, 1966) have not produced any changes in isolated cells ofsome mammals.

GMF screening is often performed using protective boxes from non-retentive, magnetically soft materials. Such a screening always leaves one wondering whether an effect observed could be due to changed levels ofAC MFs and electric fields.

Therefore, the findings were compared with a control group of biological objects held in metal non-magnetic containers (Halpern and Van Dyke, 1966; Busby, 1968; Govorun et al. , 1992; Fomicheva et al. , 1992a,b; Belyavskaya et al. , 1992).

In a series ofworks Govorun et al. (1992), Fomicheva et al. (1992a,b), and Belyavskaya et al. (1992) addressed the vital activity ofgerminating pea, lentil, and flax seeds. A multilayer permalloy screen box was used to produce a magnetic vacuum ofabout 10 5–10 6 GMF. It was shown that the predominant response to a magnetic vacuum was a decline in seed germination rate by 30-50 % (Govorun et al. , 1992). The proliferative pool of root meristem cells dropped from 90-96 % to 68-75 % with consistent statistics (Fomicheva et al. , 1992a); the evidence for changes in activities ofvarious phases ofthe reproduction cycle is shown in Fig. 2.3. Radioactive tracing here was done using a 3H hydrogen isotope. The authors assumed that responses to a zero MF in these plants are associated with the synthesis of

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OVERVIEW OF EXPERIMENTAL FINDINGS

+aQ7

+aµ7


]+

G

KROHV

WKU


ULWLFDO&


Figure 2.4. A response of one of the rhythms in men to a zero MF on four human volunteers.

Averaging: on the left, during the exposure; on the right, 3 days before and 3 days after it.

According to Beischer (1965).

RNA and proteins, rather than with the synthesis ofDNA or mitosis. RNA synthesis dynamics in some proteins ofmeristem cells was studied (Fomicheva et al. , 1992b) by fluorescent spectroscopy to reveal some details oftranscription processes in cells ofa variety ofplants. Electron microscopy ofsections ofroot meristem cells revealed some structural functional changes in the state of the cells, primarily Ca-homeostasis (Belyavskaya et al. , 1992). Under a zero MF, free and weakly bound calcium made its appearance in cellular hyaloplasm, whereas it was absent during the growth in the GMF.

Also, many experiments in Becker (1965), Beischer (1965), Lindauer and Martin (1968),

Conley

(1969),

Dubrov

(1969),

Gleizer and Khodorkovskii

(1971),

Khodorkovskii and Polonnikov (1971), including the relatively recent work by Kashulin and Pershakov (1995), were conducted with the GMF compensated by man-made MF sources, such as Helmholtz rings. Beischer (1965) used an 8-m ring system to cope with four volunteers at the same time. Figure 2.4 shows the response ofa functional characteristic ofthe central nervous system after a 10-day exposure to a magnetic vacuum measured under these conditions. It is well seen that the mean frequency of the rhythm drops markedly for three out of four volunteers.

Unfortunately, with very few exceptions, the literature on biological effects of a zero MF contains no dependences ofan effect on the field magnitude. Such dependences are ofinterest, because they carry information on magnetoreception primary processes.

Asashima et al. (1991) exposed Japanese newt larvae in development phase to a magnetic vacuum 5 nT for five days. On the 20th day of their development the authors observed distorted spines, irregular eye formation, general retardation of development, and even the appearance oftwo-headed individuals. Vacuum exposure turned out to be effective in the early phases oflarvae development, including the

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gastrula phase, the effect being 100–200 %.

Belyaev et al. (1997) measured the abnormal viscosity ofa suspension of E. coli cells after a 15-min exposure to an MF changed in relation to the geomagnetic field.

As the field was decreased from 2 to 0 ± 0 . 1 µ T a 5 % MBE growth was observed.

Similar effects under these conditions have also been found in other cells, e.g., in rat thymocytes and human fibroblasts.

Lednev et al. (1996a) observed a zero MF effect in the mitosis ofneoblast cells ofregenerating planaria. A DC field was varied from 200 to 0 µ T to within 0.06 µ T.

The mitotic index increased by 37 ± 12 % in going over from a field of 0 . 2 µ T to zero, Fig. 4.47.

Measurements ofsome parameters ofbiological systems indicate that not all of those systems show evidence ofeffective influences ofmagnetic vacuum conditions.

Proliferation of leukemia cells was studied (Eremenko et al. , 1997) in a residual (after magnetic screening) field of 20 nT. Although some statistically significant difference from control samples, outside of the chamber, was registered, the effect was fairly small, < 5 %.

We note that biological effects ofa magnetic vacuum are circumstantial evidence for the quantum nature ofMBEs. In terms ofthe classical dynamics ofrelatively free charges, e.g., of ions in a solution, an MF decrease is not accompanied by any qualitative changes. The geomagnetic field, let alone yet lower fields, exerts virtually no influence on a particle’s trajectory within its mean free path. So, a relative deviation ofan ion with charge q and mass M in an MF H ∼ H geo during the time ofa mean-free path at room temperature, t ∼ 10 11 s, will be Ωc t ∼ 10 9, where Ωc = qH/M c is an ion cyclotron frequency. However, bound particles, such as ions and electrons, oscillating in an MF are subject to the so-called Zeeman splitting ofenergy levels — a quantum phenomenon at the microscopic scale ofoscillations.

In the absence ofan MF, the splitting vanishes, and the levels become degenerated.

It is immaterial that the splitting amount had the same order ofsmallness 10 9 as compared with κT . It is important that the symmetry ofthe particle wave function changes, which is a qualitative change. Other qualitative changes that accompany the deprivation ofan MF are not observed, which is an indirect indication to the quantum nature ofMBEs.

2.2.4 Biological effects of gradient magnetic fields

During the past decade some companies were manufacturing all sorts of magnetic bracelets, necklaces, pads, etc. They sell well but have no adequate scientific underpinnings. In this case, MF sources lie outside ofbiological receptors, and so it is not to be excluded that any possible action ofsuch devices is due to spatial inhomogeneity ofan MF. Descriptions ofsuch devices used in magnetotherapy and popular publications on the topic are available on the Internet, see, e.g., www.biomagnetics.com, www.painreliever.com, and www.magnetease.com.

Medical practitioners also use so-called magnetophores (Fefer, 1967). These are basically flexible rubber applications several millimeters thick, which are cut out

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OVERVIEW OF EXPERIMENTAL FINDINGS

to size from a roll. The rubber incorporates some magnetically rigid filler magnetized following a definite pattern with alternating magnetic poles on the sheet surface. Such an MF source produces an MF that is strongly inhomogeneous near the surface.

Very few research works are known that address the biological action of such devices.

Therapeutic actions ofmagnetophores, in particular the enhanced repair oftissues after skin plastic surgery, is discussed in the monograph by Usacheva (1981).

That evidence is confirmed by Shilov et al. (1983), who investigated into the influence ofa magnetophore applicator on the rate oflipid peroxide oxidation in human skin. The induction and gradient ofan MF on the applicator surface were 30 mT and 5 mT/mm, respectively. An index ofoxidation rate was the behavior ofthe hyperweak chemiluminescence ofskin homogenates. An MF ofspecified configuration would totally remove the effect ofa 20 % activation oflipid free-radical oxidation due to hypoxia.

Clinical data ofLin et al. (1985) show that matrices of0.3-T permanent magnets have some neurological action on humans, but do not remove inflammations and do not abate pain.

Krylov and Tarakanova (1960) report their findings ofdifferent biological actions caused by the opposite poles ofpermanent magnets, with the south pole MF exerting a stimulating action on plant growth. Davis and Rawls (1987) reported that plants were growing faster in the field of a magnet’s north pole. The evidence was confirmed by Ružič et al. (1993), although stimulation here was provided by the south pole.

Kogan and Tikhonova (1965) addressed the motion of Paramecium caudatum infusoria in a 0.5-mm dia capillary 50–70 mm long with a nutrient solution. The motion of Paramecia in the control was fairly regular in nature. An infusorium periodically moved from one edge of a capillary to the other; the mean residence time at some halfofthe capillary ranged from 17 to 50 s, depending on the individual properties ofan animal. The capillary was then brought to a pole ofa permanent magnet of160 Oe or, in another experiment, about 700 Oe. It appeared that Paramecia are quite pole-sensitive. They stayed for a long time near the south pole and avoided the north pole, as ifthey contained a Dirac monopole. The asymmetry attained 300 % and was on the whole proportional to the magnet force.

Cavopol et al. (1995) observed the reaction ofsensory neurons in a cell culture to the MF gradient. Such an MF affected the probability of“firing” ofthe neuron action potential (AP). A gradient of1 mT/mm blocked 70 % ofthe AP; 1.5 mT/mm, 80 %. At the same time, a DC field of0.2 mT with a gradient of0.02 mT/mm caused no changes.

It is to be noted that the physical mechanism for the detection of MF orientation by biological systems is yet unclear. What we need here is a reference vector in relation to which we could discriminate MF direction. One such vector is the gradient ofthe MF absolute value, Fig. 2.5. The figure shows that the MF and its gradient are oriented in the same direction near the magnet’s south pole, and in

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4H

H

H 4H

Figure 2.5. Magnetic lines of force of a permanent magnet and the relative orientations of MFs and their gradients near magnet poles.

opposite directions near the north pole. No data are yet available on similar effects in cellular cultures with randomly oriented cells. For plants, a vector that orients cells and can therefore be taken to be a reference for MF orientation detection is the gravity vector. We note that in the experimental works just described it is maintained that a magnet’s poles have different actions. That would be so ifthe authors had shown that an MF with a specified direction and magnitude, produced in two different manners, say, by putting the north pole ofa bar magnet to the right ofa symmetrical object, or the south pole to the left, would produce different biological effects.

It is interesting that Yano et al. (2001) described exactly such an experiment.

They placed tubes with radish seedlings in a gel horizontally on a platform. By slowly rotating the platform around a horizontal axis they eliminated the action ofgravitation on the seedlings. Illuminating the tubes along their axes would set the direction for root growth. In the middle of each tube a disk-shaped axially magnetized permanent magnet was attached. Some magnets had their north poles pointing to the tube axis, others in the opposite direction. For controls, they used brass disks ofthe same shape and size. With such an arrangement, a root grew in a permanent MF gradient pointing to the magnet at all times, and also in a DC MF whose sense was conditioned by the magnet orientations. It appeared that magnetotropism is dictated by magnet orientation. The seedling root deflected away from the magnet if the latter had its south pole pointing at the plant. Approximate mean daily deflections are as follows: controls, 0 . 01 ± 0 . 09 mm; the north pole, 0 . 05 ± 0 . 08 mm; the south pole, 0 . 14 ± 0 . 1 mm. At the tube center, where it intersects the magnet axis, the MF was about 40 mT for a gradient of 10 mT/mm. That experiment shows that it makes sense to talk about biosystems that detect the direction ofan MF relative to its gradient.

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OVERVIEW OF EXPERIMENTAL FINDINGS

Rai et al. (1996) and Pandey et al. (1996) observed different actions on water samples ofMFs produced by the north and south poles ofpermanent magnets.

The samples were tested using different biological reactions. However, in that case no reliable conclusions were made, since the experiments were staged with other objectives in mind.

It is shown later in the book that biological actions oflow-frequency MFs and microwaves have a measure ofsimilarity and, probably, in certain cases the physical processes underlying such actions have a general nature. It would be ofinterest, therefore, to cite the work Gapeyev et al. (1996) concerned with frequency spectra ofthe action ofmicrowave radiation on cells ofthe immune system in mice. Both near and far zone radiation conditions, see Section 1.4.4, were utilized to obtain equal energy flux densities at samples. It appeared that the far-zone radiation had a pronounced resonance-like action on cells; i.e., the spectrum had a maximum.

At the same time, the far-zone radiation had only a frequency-independent action.

Note that the far-zone radiation had relatively small field gradients, suggesting that the plane waves approximation often appears to be insufficient. At the same time, in the near zone, in the immediate vicinity ofthe emitter, field gradients are large.

We also note a work by Makarevich (1999), which focuses on the influence on microorganism growth ofmagnetoplasts — ferrite-containing magnetized polymer composites. On the surface of magnetoplast samples the residual induction was 0.1–

1 mT. Microbial strains were incubated in Petri dishes that also contained cylindrical magnetoplast samples. After two days of incubation, around the samples they observed ring areas ofenhanced and retarded growth, depending on the magnetization ofthe samples. In some assays, growth enhancement was observed near the north pole ofa magnetoplast magnetized along its axis. In contrast, near the south pole, the microbial growth was retarded. The possible role ofMF gradients was not discussed in that work.

No special studies to separate the effects ofa homogeneous and a gradient MF are known. Also, in the literature there are no discussions ofpossible physical mechanisms for the biological reception ofthe aligning ofan MF relative to its gradient — i.e., ofmechanisms ofbiological sensitivity to the sign ofthe scalar product B ∇B.

2.3 BIOLOGICAL EFFECTS OF AC MAGNETIC FIELDS

Biological effects ofAC MFs have for a long time been studied ignoring the DC

MF level at site. It was supposed that the amplitude and frequency of an AC MF, or the shape and frequency of pulses for pulsed action, are in themselves sufficient to completely characterize the magnetic conditions involved. Studies ofamplitude dependences were in turn restrained by our intuitive understanding ofthe resonance mechanism for MF reception by biological objects where the main parameter is the field frequency, although amplitude–frequency windows in EMF biological effects were observed by Bawin et al. (1975), Bawin and Adey (1976), and Blackman et al.

(1979). Plekhanov (1990), who has reviewed the impressive body ofexperimental

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51

evidence due to the Tomsk group ofmagnetobiologists, also points to the existence ofMF effectiveness windows.

This section focuses primarily on experiments that reveal complex frequency and amplitude MBE spectra (Adey, 1980). It is spectral curves that bear especially much information on the physics of magnetoreception primary processes.

2.3.1 Effects of combined AC–DC fields

A series offundamental works by Blackman et al. and Liboff et al. revealed in the 1980s that in certain biological systems the DC MF level would define the position ofmaxima in MBE f

requency spectra (Blackman et al. , 1985; Liboff, 1985;

McLeod et al. , 1987a; Liboff et al. , 1987a,b). The importance oftaking into consideration the permanent geomagnetic field in experiments with biosystems exposed to an EMF was also noted by Cremer-Bartels et al. (1984) and Blackman et al.

(1985). A dependence ofAC MF effects on the magnitude ofthe DC component was pointed out by Lednev (1991) and Lyskov et al. (1996). The DC MF level was a significant parameter also in early theoretical MBE models ofChiabrera and Bianco (1987). Bowman et al. (1995) noted a correlation between definite “resonant” DC

MF magnitudes and the childhood leukemia risk in an epidemiological study.

It has taken more than a decade for the involvement of DC fields in the shaping ofexperimental conditions to become a criterion ofscientific value in magnetobiology. It is now clear why magnetobiological experiments used to exhibit such a low reproducibility, a fact that has been continually stressed by opponents. Special-purpose studies have been undertaken to reveal biologically meaningful elements in the organization ofthe electromagnetic environment (Valberg, 1995). It has gradually become clear that the AC MF amplitude, which may not necessarily be large, may also play a decisive role in observing the effect. That sets the behavior of biological systems in an MF apart from that of oscillators in the standard spectroscopy ofphysical systems. It is this involved behavior ofbiosystems, which was one of the reasons for the poor reproducibility, that supplies ample information on the physical nature ofthe primary processes ofMF reception.

14 The action ofan MF on the weight ofa chicken on the 10th day ofits development was studied by Saali et al. (1986) under the conditions B(?) B p(?) b(0 125) f (50 , 1000) n(14 28) , and also under pulsed MF conditions. They found that both pulsed and sinusoidal MFs cause some MBEs. In the latter case, an MBE was observed with statistical confidence at various AC MF amplitudes. Figure 2.6 shows results depending on the field amplitude variations relative to a local DC MF, whose magnitude is taken to be 50 µ T. It is seen that at 50 Hz an MBE occurs when the field amplitude becomes 14In what follows this symbol marks works or groups of works that are arranged in chronological order.

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OVERVIEW OF EXPERIMENTAL FINDINGS


+]

+]


0%(DUEXQLWV

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+ +

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Figure 2.6. Dependence of the weight of a 10-day chicken embryo on the amplitude of a 60-min exposure to an AC MF at the early development stage for various field frequencies, according to Saali et al. (1986).

comparable with a local field. At 1 kHz, the MBE shows no definite dependence and, on the whole, remains unchanged within a wide amplitude range.

Smith et al. (1987) measured the mobility ofdiatomic algae cells in agar with a low content of 40Ca as a function of the frequency of an AC MF with an amplitude of 20 µ T, a parallel DC field being 21 µ T. They found a resonance-like mobility growth by 35 ± 4 % at 16 Hz, which corresponded to a cyclotron frequency of 40Ca2+ ions, Fig. 2.21.

A detailed study ofthe mobility ofdiatomic algae subjected to an MF under various conditions corresponding to a cyclotron resonance (CR) frequency and its harmonics was conducted in McLeod et al. (1987a). The diagram ofthe experiment B( kf ) B p(?) b(15) f (8 , 12 , 16 , 23 , 31 , 32 , 46 , 64) n( > 500) was selected so that the magnetic conditions corresponded to a cyclotron resonance ofCa2+ ions: k = 1 . 31 µ T/Hz. Under all conditions, a statistically significant MBE

was found that was similar to that in a control exposed to a B(55 . 7 ± 0 . 1) DC field.

For conditions f (8 , 12 , 16 , 23 , 31), bell-shaped frequency spectra were found near respective central frequencies.

Kuznetsov et al. (1990) studied the probability ofarrhythmia in frog auricle preparations as a function of the MF frequency and amplitude. Experiments were conducted following the scheme

B(?) B p(?) b(0 750) f (0 100) t(30 min) n(7) .

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53

0%(UHOXQLWV


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+ µ7

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Figure 2.7. Myocardiumarrhythmia incidence in frogs as a function of the AC MF frequency and amplitude, according to Kuznetsov et al. (1990).

The effect appeared to have a quasi-resonance behavior in both frequency and amplitude. It had a maximum at H AC = 15 µ T, f = 40 Hz, Fig. 2.7. A relatively large increment ofchanges ofMF variables, and also the absence ofinformation on the magnitude and direction ofa local DC MF, hinders the interpretation of data, although the general nature ofthe window structure ofthe response is quite obvious. It is supposed that the effect is produced by AC MF-induced electric fields.

Reese et al. (1991) reproduced and confirmed the assays ofSmith et al. (1987).

They measured the mobility ofunicellular algae Amphora coffeaformis in agar enriched by calcium ions in concentrations 0.0, 0.25, and 2.5 mM. The experimental setup was like that in Smith et al. (1987)

B(21) b(21) B p( 0) f (16) n(19) B sham(43) b sham( < 0 . 2) .

A wide spread ofdata did not enable the frequency spectrum ofthe effect to be measured. The results (Smith et al. , 1987; Reese et al. , 1991), as is seen in Fig. 2.8, agree quite well. These experiments show that for effects to be observed requires a measure ofnon-equilibrium in calcium. At the same time, in the intercellular medium a large calcium density, 5 mM, “switched off” the calcium-related MBE, but caused an MBE to occur under other magnetic conditions, concerned perhaps with potassium (McLeod et al. , 1987a).

Goodman and Henderson (1991) also observed frequency, amplitude, and temporal windows when transcription processes in human lymphocytes and Drosophila

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OVERVIEW OF EXPERIMENTAL FINDINGS

6KDP

)LHOG


RI'LDWRPV


0RELOLW\


Figure 2.8. The variation of the algae cell mobility in parallel MFs at concentrations (mM) of calciumions in agar 0.0, A,D; 0.25, B,E; 2.5, C,F. According to Smith et al. (1987) (A,B,C) and Reese et al. (1991) (D,E,F).


V


FRXQW


FRQWUROOHYHO


%SHDNµ7

Figure 2.9. Influence of a 20-min exposure to a 60-Hz magnetic field of various amplitudes on the transcription process in HL-60 cells, according to Goodman and Henderson (1991).

saliva glands were exposed to low-frequency MFs. One experiment with amplitude variations was performed using the formula

b(0 . 8 800) B(?) B p(?) f (60 , 72) t(10 , 20 , 40 min) .

The level ofsome transcripts in chromosomes was measured using the radioactive tracer 35S.

Figure 2.9 displays the variation ofthe tracer reference level with the MF amplitude. The effect is seen to be especially significant where the AC MF amplitude compares with the geomagnetic field. Maximal values occurred at a 20-min exposure.

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55


+]µ7

VKDPH[SRVHG

H


XSWDN

&D


Figure 2.10. Influence of inclined low-frequency and DC MFs on 45Ca2+ uptake by lymphocytes of various types — 1,2,3, according to Lyle et al. (1991).

Lyle et al. (1991) investigated the calcium radioactive tracer uptake by lymphocytes exposed to an AC field at an angle to a DC one. Cells ofvarious lines were used, including cancer ones. The magnetic field had the configuration B(16 . 5 ± 0 . 5) b(20) b sham( 0) f (13 . 6) B p(? > 20) .

The authors observed a significant effect, Fig. 2.10, on exposure to a parallel AC

field against the background ofan inclined geomagnetic one. Somewhat smaller, but also statistically significant, changes were observed at 60 Hz. Data on DC field values are contradictory. Its magnitude was reported to be 384 µ T, its slope to the horizontal being 57 ± 2 o. Even ifwe take account ofthe probable error in the indication ofthe field value, there is still no computing the true angle between the fields. It is interesting that ifa 30-min MF exposure was conducted before a tracer was introduced, rather than immediately after it, no effect was observed. This may be due to the fact that a combination of MF variables corresponded exactly to the 45Ca isotope. The authors believed that the frequency they used corresponded to a cyclotron one for calcium in a 16.5- µ T field, although they did not cite the isotope number. By the same token, it hardly makes sense to work out the frequency using only one MF component along some axis, because in the general case the other MF

component also affects the dynamics ofa particle.

Experiments ofPrato et al. (1993) addressed the dependence ofMBEs on the amplitude ofthe AC MF component. They placed Cepaea nemoralis snails on a warm surface and measured the time it took a snail to raise its leg. Before the assay, the snails were treated with an inhibitor to increase the response time. Exposure to an MF reduced the inhibition effect. The arrangement ofthe experiment B(78) b(18 547) f (60) B p( ± 0 . 8)

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OVERVIEW OF EXPERIMENTAL FINDINGS

was chosen to correspond to a cyclotron frequency of 40Ca2+ ions. The magnetic effect appeared to be as high as 80 % ofthe relative amount ofinhibition by a bioactive preparation, the data spread being 10-20 %. The behavior ofthe amplitude B AC displayed several extrema, Fig. 4.39. The data were then confirmed and refined in later works ofthe group (Prato et al. , 1995, 1996) using a double-blind technique.

The procedures of(1) preparation, placement, and transportation ofthe animals, (2) exposure to an MF, and (3) taking the reaction time were conducted by mutually uninitiated workers. In Prato et al. (1995) a multipeak frequency spectrum of an MBE is provided, Fig. 4.36, along with a dependence on DC MF with the frequency and amplitude ofthe DC MF component fixed.

Blackman et al. (1994) carried out some assays to capture the dependence of biological response on the ratio ofthe DC MF amplitude to the magnitude ofDC

collinear MFs. The quantity measured was the inhibition degree ofneurite outgrowth in PC-12 cells. The outgrowth was induced by a biological stimulator. The temperature was sustained to within 0.1 o C. Control was performed in the same thermostat in a passively screened section, which reduced the MF level by two orders of magnitude. There were two types ofcontrols, with and without the outgrowth stimulator. Experimental data were normalized using a technique commonly employed for two different exposure factors; in this case these factors were the outgrowth stimulator and the MF. The relative MF effect was worked out by

R − Z

%NO =

100 % ,

N − Z

where Z is the relative number ofneurite-containing cells in an assay without MF

and stimulator (control 1), N is the same with an MF but without a stimulator (control 2), and R is the same with an MF and a stimulator. The results 0 and 100 %

thus corresponded to the effect value when the cells were treated in the absence ofan MF, with or without stimulator. Exposure to an MF yielded intermediate values. For the formula of the experiment

B(36 . 6) b(10 . 8 66 . 2 /∼ 5) f (45) B p( < 0 . 2) n(3 4) g(!) (2.3.1)

results were obtained that are depicted in Fig. 2.1115 by open circles, the quantity 100 % %NO is shown. Maximal effect was confidently observed with intermediary AC MF amplitudes. Magnetic layout

B(2) b(1 . 1 2 . 9 /∼ 0 . 4) f (45) B p( < 0 . 2) n(3) g(!) (2.3.2)

yielded points that grouped closely around 100 %, i.e., a zero effect.

Studies ofamplitude spectra ofneurite outgrowth inhibition for large relative MF amplitudes were continued in Blackman et al. (1995b). These data, shown in Fig. 2.11 by solid circles, attest to the multipeak nature ofthe amplitude spectra.

15This author is grateful to C. Blackman for the file of data.

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%ODFNPDQHWDO

%ODFNPDQHWDOE


%(0


+ +

$&

'&

Figure 2.11. Variation of MBE in PC–12 cells with the amplitude of the AC component in a uniaxial MF, according to Blackman et al. (1994, 1995b). The line depicts the function

| J1(2 H AC /H DC) |.

Plotted in the figure is also the magnitude ofthe function J1 (2 H AC /H DC). It is a fairly good approximation of the findings; therefore the authors carry on their search for a physical substantiation of that dependence (Machlup and Blackman, 1997).

The authors assumed that Mn(4), V(4), and Mg(2) ions16 and also, with a smaller probability, Li(1) and H(1) ions can be responsible for magnetoreception in PC-12 cells. It is precisely with these ions that, for the DC MF B DC and AC field frequency f specified by the experiment formula (2.3.1), the cyclotron frequencies Ωc = qB DC /M c approximately obey the relation Ωc = n, Ω = 2 πf .

The group also researched the MBE frequency spectra of neurite outgrowth inhibition in the same cells (Blackman et al. , 1995a). The main departure was the presence ofthe DC MF perpendicular component

B(37) b(5 . 3 12 . 5 /∼ 1 . 5) B p(19) f (15 70 / 5) .

MBE frequency windows were found near 40 and 60 Hz and higher, Fig. 2.12; i.e., the MBE frequency spectra had several extrema.

In parallel fields no effects were captured at 45 Hz, and the authors concluded therefore that a DC MF component normal to the AC field was an essential factor.

It is interesting that an opposite conclusion was reached after an investigation 16Shown in parentheses is the ion valence.

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OVERVIEW OF EXPERIMENTAL FINDINGS

% SHDNµ7

$&


%(


0


I+]

Figure 2.12. Inhibition of stimulated neurite outgrowths in PC–12 cells with DC and AC

fields oriented at an angle; points for different AC MF amplitudes are shown, according to Blackman et al. (1995a).

(Belyaev et al. , 1994) into the role ofa perpendicular DC field in another biological system, E. coli cells. McLeod et al. (1987a) also reported that the perpendicular component was insignificant in experiments on the mobility ofdiatomic algae in an MF. On the other hand, it was shown (Blackman et al. , 1996) that parallel and perpendicular orientations offields result in opposite effects, and that MBEs may vanish at some oftheir combinations. It will be shown in what follows that such complicated dependences on field orientations are characteristic ofthe interference ofions bound in macromolecular capsules.

We note that Blackman et al. (1994, 1995a) used a horizontal ring coil for an AC MF source. At various separations from the ring, they could thus get a number ofAC MF amplitudes at the same time. Such an arrangement ofa field source produced relatively strong MF gradients in the vicinity ofbiological samples. There is evidence ofbiological activity in certain cases precisely due to MF gradients. It would be difficult to comment on the findings ifit were not for good agreement in these works ofthe effect for similar MF amplitude values with different gradients.

That is indicative ofan insignificant role played by MF gradients in assays under considerations. Overall, in the absence ofwell-established MF exposure mechanisms, the question ofwhether it is admissible to employ gradient fields in such experiments is open.

Lindstrom et al. (1995) found that a sinusoidal MF induced cytosol calcium density variations in human leukemia T-cell line. The experimental setup was

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B(50) B p(53)[ B(60) B p(22)] b(40 , 80 , 150 , 300) f (5 , 25 , 50 , 75 , 100) .

The variations looked like records ofa random process, but some processing of those curves suggested that the maximal response to fields belonging to the set in the diagram was a concentration growth by a factor of 5–8, which was observed for a 50-Hz, 150- µ T exposure in a parallel field of50–60 µ T. Unfortunately, the authors did not indicate which ofthe AC MF characteristics, root-mean-square or peak ones, they employed; also the parameters’ increment was fairly large. It was therefore fairly hard to identity an MF target, although assays revealed a distinct amplitude–frequency window.

Tofani et al. (1995) undertook to evaluate the oncogenic potential oflow-frequency fields. They visually found the rate of intracellular nuclei formation in human peripheral lymphocytes. The formation of such nuclei under special conditions is a marker ofchromosomal damages. Experimental setups

B( ± 0 . 1) b(150rms) f (50)[ b(75rms) f (32)]

B(42) B p( ± 0 . 1) b(75rms , 150rms) f (32) made it possible to single out the permanent MF component that is parallel to the variable component. Adapted data are given in Fig. 2.13. The authors noticed a statistically significant MBE in the presence ofa parallel DC MF, namely points in the middle ofthe plot. At the same time, overall, the findings are hard to interpret, since experimental points are few. The fact that these results are not as remarkable as those obtained in other cases can be attributed to the fact that the second of the MF diagrams provided here did not meet the condition that the interference has a maximum at H AC /H DC 1 . 8. Indeed, that quantity was 2.5 and 5, since the authors erroneously used the root-mean-square value H AC, rather than the peak one.

A cycle ofworks (Alipov et al. , 1994; Belyaev et al. , 1995; Alipov and Belyaev, 1996) is devoted to effects ofa combined MF on the conformational state ofthe genome of E. coli K12 AB1157 cells under various magnetic conditions. Specially treated cell suspensions were subjected to lysis after exposure to an MF. A rotational viscosimeter was used to measure viscosity ofthe suspensions. The observable here was the rotation period ofthe viscosimeter rotor. That variable is connected with the conformational state of the cell genome prior to lysis. The MBE in cells was thus determined from the relative rotation period for exposed and intact cells.

Measurements were conducted 1 h after a 15-min cell exposure, when the effect was especially robust.

Alipov et al. (1994) observed at 8.6–8.9 Hz a distinct 25 % peak on the MBE

curve with a width ofaround 1.6 Hz for the arrangement

B(43 . 6) B p(19 . 7) b(30) f (7 12) .

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WKHRU\

+]

+]


3DUEXQLWV

0%(UHOXQLWV


+ +

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Figure 2.13. Occurrences of markers of chromosomal damages in HPL cells in parallel low-frequency MFs. The curve is a typical curve fromthe theory of ion interference.


+]

IPD[


&FHOOPO

Figure 2.14. The shift of an MBE maximum in E. coli cells depending on the cell density, according to Belyaev et al. (1995).

A DC field here was the Earth’s field. Under these magnetic conditions, less pronounced changes in the bacterial titer and intensity ofDNA and protein synthesis were obtained using other techniques.

It was also shown that varying the orthogonal component in the range B p(0 148 / 4) changed the peak height only by ± 5 %, and that those changes as a function of B p were sporadic (Belyaev et al. , 1994). In those trials, the orthogonal field did not play any noticeable role. At the same time, varying the parallel field within the range B(126 133 / 1) removed the peak, MBE being at a level of99 ± 4 % within the entire range. The observed frequency of peak at 8.9 Hz was around the fourth subharmonic of the cyclotron frequency of 40Ca ions, ifwe ignore the orthogonal MF component.

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Belyaev et al. (1995) studied the variation ofMBEs with cell density in the range 107–109 ml 1 following the scheme

B(44 ± 1) B p(20 ± 1) b(30) f (7 . 4 10 . 4) and found that MBE peaks shift positively with cell concentration, Fig. 2.14. The authors account for that by the fact that intercellular interactions, whose role grows with cell density, encourage the formation of a cell population response to a combined MF.

Alipov and Belyaev (1996) showed several well-defined MBE frequency windows in the range 6–69 Hz for the same MF strengths as above, Fig. 4.32. Importantly, MBE frequency spectra for standard and mutant lines of E. coli cells appeared to be different. A 16-Hz peak was only observed for mutant cells. The authors suppose that the genome structure and DNA-involving processes are involved in the magnetoreception ofthose cells.

Garcia-Sancho et al. (1994) studied the action oflow-frequency MFs on ion transport in several mammal cell types. The effect was assessed via uptake ofa 42K radioactive tracer at a cyclotron resonance frequency (15.5 Hz for an ion of a given potassium isotope in a field of41 µ T) only by cancer Ehrlich cells and human leukemia cells U937. The 45Ca tracer uptake was observed at an appropriate MF

frequency, but it was not statistically significant and was never observed for 22Na tracers. The experimental setup was

B(41) b(25 1000 ± 5 %) B p( 0) f (13 . 5 16 . 5 / 1) n(8 24) .

The findings are plotted in Fig. 2.15. The plot displays a non-monotonous dependence on the frequency and amplitude of the AC MF component, which makes the results suitable for comparison with computations.

Note that the non-monotonous amplitude dependence ofthe effect poorly agrees with the generally recognized hypothesis on the excitation by AC MFs ofquantum transitions against the background ofa DC field. It is common for transition excitation to be accompanied by a saturation oftransition intensity with the MF

amplitude.

Perpendicular MF combinations were employed by Picazo et al. (1994) when observing MBEs in chronically, for 3 months, irradiated mice

B(40) B p(141) f (50) .

The leukocyte count in the blood ofexposed, 9 . 3+6 . 2

thousand/mm3, and control

2 . 8

( B p = 0), 13 . 3+5 . 7

thousand/mm3, groups differed with a statistical significance.

3 . 3

Both qualitative and quantitative changes in the leukocyte compositions were associated with MF-induced leukemia.

Spadinger et al. (1995) took into account the fact that the cytoskeleton responsible for the shape and mobility of cells contains molecules changed by a Ca2+

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OVERVIEW OF EXPERIMENTAL FINDINGS

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Figure 2.15. The influence of a 1-h exposure of cancer cells to magnetic fields of various amplitudes and frequencies on the uptake of radioactive 42K ions, according to Garcia-Sancho et al.

(1994).

mediator. Since an MF acts on calcium transport in vitro, the field can also change the cell mobility. The authors studied the mobility and morphology offibroblasts before, during, and after a 4-h exposure to a low-frequency MF. The measurements were performed using a computerized microscope equipped to produce an MF by a ring coil that fitted around a Petri dish. Experimental setup was as follows: B(28 . 3) b(141 ± 21) B p(6 . 4) f (10 63 / 2) n( 80) g( < 10 µ T/cm) .

No statistically significant differences between exposed and sham cells were found for those frequencies.

The authors believe that underlying this negative result could be unaccounted parameters ofambient humidity and ofuneven illuminations ofcells by the microscope lamp, as well as the fact that the metabolic state of cells was inadequate.

Observation ofsuch effects does require that MF parameters be fine-tuned or that different parameters form specific combinations concurrently, these parameters being the value ofa DC MF, the amplitude ofa uniaxial AC field, the perpendicular component, the frequency, and also the smallness of background variations of the field and its gradients. Therefore, the absence of an effect here could also be accounted for by a relatively large DC MF gradient, so that the field difference in one cell sampling was consistently as high as 30 %.

Novikov and Zhadin (1994) reported to have found an effect caused by parallel fields at a frequency scanning of 0.1 Hz/s on L-forms ofsolutions ofasparagine,

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arginine, glutamine acid, and tyrosine in a redistillate. They observed the current in an electrochemical cell. The effect consisted in the appearance on the current vs frequency plot of a single 30-50 % maximum near cyclotron frequencies for appropriate molecules. The results are given in Table 2.1, where MF values are in µ T.

The authors underscore the unclear nature ofthe physical mechanism for current growth at cyclotron frequencies corresponding to appropriate molecules of given amino acids containing ionizing amino groups. Note that resonance-like responses in a similar “electrochemical” configuration have been observed in yeast cell suspension in the geomagnetic field as the electric field frequency (Jafary-Asl et al. , 1983; Aarholt et al. , 1988) was scanned. In the latter case, the frequencies of maxima corresponded not to cyclotron frequencies, but to NMR ones.

A more thorough research was conducted (Novikov, 1994) in the Glu solution.

Some Glu molecules were ionized by adding some hydrochloric acid to the solution.

For controls, they used a solution without Glu and a solution at an acid concentration, such that it provided a zero electrokinetic Glu potential, i.e., their immobility.

They used slow frequency scanning 0.01 Hz/s at

B(30) b(0 . 025) B p( < 1) E p(8 V/m) f (1 10) .

A current maximum was observed near a cyclotron frequency of 3.11 Hz, for Glu in a field of B = 30 µ T. The maximum had a width ofabout 0.05–0.1 Hz. The author also performed a gel-chromatographic measurement on a solution exposed to an MF with effective parameters to notice the formation of Glu polymeric molecules.

Chromatographic results obviously suggested that the effects observed were governed by the behavior ofGlu molecules in a solution, rather than on the surface of electrodes. To account for the effect, it was assumed that a target for an MF were clusters or polymeric ions ofamino acids with a cyclotron frequency like that ofan individual molecule.

Solutions of L-asparagine Asn 7 . 57 · 10 3 M/l in acidified redistillate at pH 3.2, T = 18 ± 0 . 1 o C were studied in Novikov (1996) following the scheme B(30 . 34 ± 0 . 16) b((20 ± 2) · 10 3) E p(5 mV/cm) f (3 . 38 3 . 62 / 0 . 01) .

Table 2.1. The action of an MF on the conductivity of amino acid solutions Frequency

b

B

B p

Solution Frequency max., Hz

0.1–40

0.05

25

0

Asn

2 . 9 ± 0 . 1

Arg

4 . 4 ± 0 . 1

Glu

2 . 5 ± 0 . 1

Tyr

4 . 4 ± 0 . 1

H2O

no effect

0

25

no effect

0

no effect

5

25

0

no effect

According to Novikov and Zhadin (1994).

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OVERVIEW OF EXPERIMENTAL FINDINGS

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Figure 2.16. Current pulses in an electrochemical cell with asparagine solution in a DC MF

of 30.34 µ T induced by switching on a parallel AC MF with an amplitude of 20 nT, according to Novikov (1996).

When an AC MF was switched on, a current pulse in the cell was observed, which took 50 s to relax. The field was then switched off, the frequency readjusted to 0.01 Hz, and the field switched again. The findings are plotted in Fig. 2.16 using the data ofNovikov (1996). We note the smallness ofthe AC MF, around 20 nT, and the non-steady-state nature ofthe response, thus suggesting that the molecular structure ofthe solution changed. In that experiment the electric field was an order ofmagnitude smaller than that in Novikov and Zhadin (1994) and Novikov (1994), without any noticeable consequences for the effect observed. That shows that in these experiments an electric field is only ofsignificance for the measurement of an effect. As the solution temperature was increased to 36 o C, the value ofcurrent pulse decreased.

The works do not answer some questions that are important for gaining insights into the physical nature ofthe phenomenon. In particular, it was ofinterest to find out (a) whether an electric field was applied to a solution when the formation of polymer molecules was studied, and (b) whether the frequency of a maximum of the effect was dependent on the solution pH. The charge ofan amino acid zwitterion varies, depending on the medium acidity.

The influence ofa pulsed MF on an enzyme system of lac operon NCTC9001 line E. coli was studied by Aarholt et al. (1982). They measured the gene transcription rate for the β-galactosidase suppressed by a repressor protein, which hinders the approach ofpolymerase to an appropriate DNA section. Control cells were held in a container made of soft-magnetic metal. Experimental cells were exposed for 2 h to square 50-Hz MF pulses. Recorded was the synthesis rate vs pulse height dependence in the range of200–660 µ T.

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The exposed cell synthesis rate deviated from controls in the following manner: for pulse magnitudes around 300 µ T it dropped fourfold; at 550 µ T it increased 2.5 times, Fig. 4.46. The MBE variation with the cell density in suspension had an extremum. MBE observations were performed in the range 2.5–5.5 · 107 ml 1; i.e., the separation between bacteria was about 30 µ m, which is more than 15 times larger than their size. The authors stressed the importance ofintercellular interaction and supposed that the observed MBE is concerned with a change in the activity ofa repressor protein.

Reinbold and Pollack (1997) used modulated MFs, B(20) b(20) f(76 . 6) with a frequency close to a double cyclotron frequency for 39K and a treble one for Mg, and also an MF with a calcium cyclotron frequency, B(130) b(250 , 500) f (100). For bone cells in rats, these fields increased calcium density peaks 2–2.5 times ( P < 0 . 05), as measured using fluorescent microscopy techniques. It is interesting that the effect was conditioned by MF orientation, horizontal or vertical, and by the presence of calcium serum in a cell culture.

Litovitz et al. (1997b) considered the role ofthe invariability ofMF signal parameters in a cell response. They observed ornithine decarboxylase activity in a L929 cell culture. They did not measure the DC field, but conducted assays in a mu-metallic box that reduced an external MF fivefold, so that an approximate value could be around 10 µ T. Magnetic fields with frequencies of 55, 60, and 65 Hz (10 µ T) produced approximately similar effects ofdoubling the activity. However, a regime with 55/65 Hz frequency switching appeared to be effective only if the retention time for each of the frequencies was longer than 10 s. Amplitude switching from 0/10 to 5/15 µ T was also effective, beginning with 10 s within the switching interval.

On the other hand, ifa 60-Hz, 10- µ T MF signal was interrupted each second for more than 0.1 s, no biological effect was revealed. The dependence ofthe enzyme activity on the pause duration and the MF switching interval is shown in Fig. 2.17

and Fig. 2.18.

The authors thus conclude that in a cellular system there are two time scales, 10

and 0.1 s, which characterize the cell memory ofthe invariability ofaction conditions and the MF signal detection time respectively.

A 2-h exposure to an MF with a 1 /f spectrum in the range of10 3–10 Hz definitely reduced the cell adhesion index, which was proportional to the surface negative cell charge, by 30 % as compared with controls (Muzalevskaya and Uritskii, 1997). That also enhanced cell sedimentation and increased the density ofnuclear DNA super-spiral packing. At the same time, MFs ofsimilar intensity, but different spectral composition (white noise, 0.8 Hz meander, and sine field 50 Hz), caused no biological effects.

The authors assumed that the 1 /f spectrum shape ofan MF is a significant asset, because it was responsible for the emergence of an effect. They meant a

“resonance” with a natural 1 /f -type process in cells, e.g., with ion currents. They did not discuss the primary biophysical processes ofmagnetoreception. As it will

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OVERVIEW OF EXPERIMENTAL FINDINGS

Figure 2.17. Activity of ornithine decarboxylase in a L929 cell culture as a function of parameters of an interrupted sinusoidal MF, according to Litovitz et al. (1997b).

%

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Figure 2.18. Parameters of the interrupted 60-Hz, 10- µ T magnetic field: pause duration and MF switching interval.

become clear from the results of Chapter 4, these findings could be described using an ion interference mechanism.

Variation ofthe mobility ofDNA brain cells in rats with the MF amplitude B(?) B p(?) b(100 , 250 , 500) f (60) for a 2-h exposure against a background of uncontrolled local static MF was observed in Lai and Singh (1997a).

Katsir et al. (1998) researched the proliferation of fibroblast embryo cells in chickens under the magnetic conditions

B(?) B p(?) b(60 700) f (50 , 60 , 100) n( 100)

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Figure 2.19. Amplitude dependence of fibroblast cell proliferation in MFs of various frequencies.


5HODWLYHUDWH


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Figure 2.20. The frequency spectrumof the activity of liver cytochrome oxidase in rats in an MF of 10 µ T. Averaged results of Blank and Soo (1998).

and found the multipeak dependence of the response to a 24-h exposure, Fig. 2.19.

Various proliferation measurement techniques, using a hemocytometer, spectrophotometer, or radioactive tracer, have led to similar results. The growth of the effect at large amplitudes and frequencies seems to be associated with induced currents, since the product bf exceeds the established limit (1.4.3). Data on the magnitude and direction of a DC MF are not provided; therefore it would be fairly difficult to comment ofthe possible ion target for an MF, but an extremum at about 200 µ T is largely in sympathy with an ion interference mechanism.

The frequency spectrum for the action of a 10- µ T MF on the activity of cytochrome oxidase, a membrane enzyme, was measured by Blank and Soo (1998).

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OVERVIEW OF EXPERIMENTAL FINDINGS

The activity was measured spectrophotometrically from the density of an oxidized form of C cytochrome. Local DC MF data are not provided. The frequency dependence ofthe effect exhibited a maximum at around 500–1000 Hz, Fig. 2.20. That spectrum seems to be at variance with natural ion frequencies. It is assumed that an MF acts on a traveling charge within an enzyme, the position ofa maximum on the frequency spectrum corresponding to the unit cycle time of the enzyme reaction.

2.3.2 Participation of some ions in magnetoreception

It has been established ever since that biologically effective MF frequencies approximately correspond to cyclotron frequencies of various ions, their harmonics and subharmonics, and they move proportionally to the magnitude ofa DC magnetic field (Liboff, 1985; Liboff et al. , 1987b). The participation ofions in the formation ofthe response ofa biological system is discussed in many works on magnetobiology. The wealth ofexperimental evidence makes the important role ofCa2+ ions as good as universally recognized.

The contribution ofother ions is not that clear and gives rise to a discussion, since one effective frequency can at the same time correspond to various harmonics/subharmonics of different ions. It is then impossible to identify an ion from the shift of a frequency maximum depending on a DC MF, since both hypotheses yield similar predictions. It is clear that an isotopic shift of maxima is a regular way to identify ions; however such experiments are expensive and not always possible. Only some works are known where a calcium ion was identified as a target for an MF

from a shift of MBE peaks with 40Ca (Smith et al. , 1987) and 45Ca (Liboff et al. , 1987b) isotopes, Fig. 2.21. The ratio ofmaxima frequencies 16/14.3 is close to the ratio 44.95/40.08 of 45Ca and 40Ca isotope masses. The value ofthat result was somewhat reduced by the fact that MBE spectra of different biological systems were compared.

Generally they use radioactive isotopes as tracers to take account ofthe intensity ofexchange processes involving substances marked by that tracer. The isotopes used were 3H (Liboff et al. , 1984; Fomicheva et al. , 1992a; Alipov et al. , 1994; Ruhenstroth-Bauer et al. , 1994; Fitzsimmons et al. , 1995), 32P (Markov et al. , 1992), 35S (Goodman and Henderson, 1991), 45Ca (Bawin et al. , 1975, 1978; Conti et al. , 1985; Rozek et al. , 1987; Blackman et al. , 1988; Yost and Liburdy, 1992), 22Na and 86Rb (Serpersu and Tsong, 1984), and 125I (Phillips et al. , 1986a).

Unfortunately, even if some MBE is observed in the processes, the fact in itself does not prove that given isotopes are targets for a magnetic field. To indirectly identify the ions, attempts have been made to observe changes in the conductivity ofappropriate ion channels in an MF (Serpersu and Tsong, 1984; Blank and Soo, 1996).

2.3.2.1 Calcium

Calcium ions are known to contribute to many biological processes, such as synaptic transmission, secretion, ciliary motility, enzyme activation, muscular contraction

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Figure 2.21. 1, incorporation of 45Ca tracer in human lymphocytes (Liboff et al. , 1987a); 2, motility of diatomic cells in agar low in 40Ca (Smith et al. , 1987), as a function of the AC MF

frequency at an amplitude of 20 µ T, the parallel DC field being 21 µ T.

processes, multiplication, growth, and development. Intracellular calcium density

10 8–10 6 M is four orders of magnitude smaller than in the environment and is sustained by membrane mechanisms. This takes care ofthe workings offast signal mechanisms for response to external conditions. Especially sensitive to intercellular calcium density is calmodulin protein that affects the activity ofmany enzymes.

Kislovsky (1971) supposed that calcium plays an important role in biological effects ofEMFs. The works ofBawin et al. (1975) and Bawin and Adey (1976) seem to have been the first assays to reveal a connection between EMF biological effects and calcium ions. They studied the rate ofcalcium ions efflux from brain tissues under low-frequency, RF, and microwave EMFs. Later on these data have been independently confirmed. Calcium binding with calmodulin as a primary target for the biological action ofmicrowaves and the biochemical analysis ofthe hypothesis were discussed by Arber (1985).

Höjerik et al. (1995) performed experiments to test the hypothesis that an MF

interacts with the organism via calcium ion channels. They measured the total Ca2+

flux through micropatches ofcellular membranes where clonal insulin-producing β-cells were subjected to combined AC–DC magnetic fields within the frequency range 10–60 Hz, including the cyclotron frequency 16 Hz (for Ca2+ in a field of B DC = 20 . 9 µ T, H ACpeak = H DC, H DC H AC z). This field was chosen because it was found to be effective. A 50-Hz background field was not higher than 70 nT; the geomagnetic field was compensated. The transport ofCa2+ ions through protein channels exhibited no resonance behavior within the frequency range at hand. This suggests that with magnetosensitive calcium processes an MF does not affect ion channels, but rather other biophysical systems.

Jenrow et al. (1995) found a further biological system that could be successfully

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OVERVIEW OF EXPERIMENTAL FINDINGS

employed to observe a magnetobiological effect. They studied the regeneration of the severed head ofthe Planarian Dugesia tigrina. Underlying the regeneration are many cell signaling processes involving Ca2+ ions, a fact that makes them, according to the authors, a convenient experimental model. The observable was the regeneration time recorded when pigmentation patches appeared at sites where eyes would later develop. Exposure to an MF sometimes increased regeneration time from 140 to 180 h. The experiments were staged to test the hypothesis that electric currents induced by an AC MF was a physical reason for MBEs, see Liboff et al.

(1987b) and Tenforde and Kaune (1987).

The first experiment was performed simultaneously using the two schemes (A1)

B(78 . 42 ± 0 . 18) b(10) f (60) B p(10 2 ± 10 1) N (69) (A2)

B(10 2 ± 5 · 10 2) b(10) f (60) B p(10 2 ± 10 1) N (70) .

The second experiment followed two other schemes

(B1)

B(51 . 13 ± 0 . 12) b(51 . 1) f (60) B p(5 · 10 2 ± 5 · 10 1) N (92) (B2)

B(10 2 ± 2 · 10 2) b(51 . 1) f (60) B p(10 2 ± 5 · 10 2) N (91) .

The third experiment involved exposure to a local geomagnetic field with the power frequency background controlled

(C)

B(18 . 2 ± 10 2) b(5 · 10 3) f (60) B p(53 . 5 ± 10 2) .

In these experiments, the MF gradient did not exceed 10 2 µ T/cm.

Schemes A1 and B1 corresponded to CR conditions for Ca2+ and K+ ions, respectively. The temperature was maintained to within 0 . 05 o C. The findings for all the schemes are given in Fig. 2.22.

It was concluded that there is, probably, a delay in the early regeneration stage, before proliferation and differentiation processes set in, and it is due to Ca2+ ions.

It was shown that an induced electric field and eddy currents are not responsible for the observed MBE. This follows from the fact that (1) the MBEs found in schemes A1 and A2 had different levels, whereas the level ofthe induced electric field is the same, (2) the MBEs for schemes A2 and C were identical, whereas the electric field levels were different, (3) the MBE for A1 was larger than that for B1, whereas the electric fields involved had opposite relations, and (4) direct computations ofthe induced electric field in oriented planaria yielded a value three orders ofmagnitude smaller than the known threshold value.

Smith et al. (1995) tested the hypothesis that various cations, such as Ca, Mg, and K, are responsible for changes in the growth of Raphanus sativus var. Cherry Belle garden radish when continuously exposed to parallel MFs. Exposure by the scheme

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Figure 2.22. Mean regeneration time in planaria exposed to parallel magnetic fields at various temperatures: A, 22 o C; B, 20 o C; C, 22 o C. According to Jenrow et al. (1995).

Ca

N = 1 , 2 , 3 B(78 . 4 , 39 . 2 , 26 . 1) b(20) f (60) (2.3.3)

K

N = 1 , 2 , 3 B(153 . 3 , 76 . 6 , 51 . 1) b(20) f (60) Mg

N = 1 , 5

B(47 . 5 , 9 . 5) b(20) f (60) controls

B(0) b(20) f (60) , B(geo) b(0) , where N is the number ofa cyclotron frequency harmonic, enabled inputs ofions to growth variables to be identified. The strongest, 70–80 %, changes in comparison with the controls were displayed by the weight ofthe root on a 21-day exposure.

Other parameters displayed lesser, although statistically significant, changes. Fine-tuning to a cyclotron frequency and its harmonics appeared to be efficient for all the above-mentioned ions, the most pronounced effect being observed on fine-tuning to calcium. Fine-tunings to odd harmonics appeared to be more effective in comparison with the second harmonic.

The sign ofthe effect, i.e., increase or decrease, depended both on the type of the exposed ion and on the variable selected (stem length, leafwidth, etc.). No pattern was found here, however.

The authors believe that these experiments provide supporting evidence for the cyclotron resonance mechanism in magnetobiology. Unfortunately, these experiments are hard to interpret in terms ofan ion interference mechanism, to be discussed later, since the variable b/B, which was important for that mechanism, changed significantly in the experiments just described.

Sisken et al. (1996) measured the luminescence ofphotoprotein introduced to cells before, during, and after 2 or 3 h of exposure to an MF

B(?) B p(?) b(300 71700) f (16 180) .

Intercellular calcium density and other calcium-dependent processes in ROS 17/2.8

cells remained unchanged when subjected to an MF. The absence ofan MBE seems

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OVERVIEW OF EXPERIMENTAL FINDINGS

to be due to the fact that the variable field was large: its lower value was six times larger than that ofthe geomagnetic one. Nothing was said about DC MF variables, which were important indeed. Moreover, AC MFs were obtained using ferromagnetic concentrators, which normally produce large MF gradients.

The role ofcalcium processes was also discussed in several works (Conti et al. , 1985; Kavaliers and Ossenkopp, 1986; McLeod et al. , 1987a; Lyle et al. , 1991; Reese et al. , 1991; Belyavskaya et al. , 1992; Walleczek, 1992; Yost and Liburdy, 1992; Coulton and Barker, 1993; Garcia-Sancho et al. , 1994; Spadinger et al. , 1995; Deryugina et al. , 1996; Reinbold and Pollack, 1997; Ružič and Jerman, 1998). It was reported (Grundler et al. , 1992) that by 1992 at least 11 research centers observed calcium regulatory processes influenced by low-frequency MFs.

2.3.2.2 Magnesium

Some calcium-binding proteins are also able to bind magnesium, see for example Lester and Blumfeld (1991), and calcium and magnesium can have the same binding sites (Wolff et al. , 1977). Therefore, in addition to calcium ions, Mg2+ ions are regarded as potential targets for an MF.

A long exposure to parallel MFs tuned to a magnesium cyclotron frequency and its fifth harmonic resulted in 10–70 % changes in garden radish growth variables (Smith et al. , 1995), see (2.3.3).

Deryugina et al. (1996) studied the motive and exploratory activities in rats exposed to an “open field”. The animals were subjected to parallel DC and AC

fields. AC MF frequency was chosen from among cyclotron and Larmor frequencies for magnesium, calcium, sodium, potassium, chlorine, lithium, and zinc ions B(500) b(250) f (380 , 630) B p( < 50) .

The effect was only found at magnesium’s and calcium’s cyclotron frequencies.

A magnetobiological effect on Planarian worms at the cyclotron frequency of magnesium ions was observed by Lednev et al. (1996a) using the scheme B(20 . 9 ± 0 . 1) b(38 . 4 ± 0 . 1) f (20 . 4 32 . 4)) .

A characteristic bell-shaped MBE spectrum is given in Fig. 4.35.

2.3.2.3 Sodium

Liboff and Parkinson (1991) made an attempt at observing an MBE in intestine tissue ofa Pseudemys scripta tortoise for a parallel arrangement of DC and AC fields at cyclotron frequencies of 23Na and other ions. They measured the transepithelium potential at fixed MF values in a wide range offrequencies and fields: B(10 220) b(1 20) f (3 770) .

No changes in the potential were found. The authors explained that by a number ofreasons including the absence ofartificial misbalance in ion density, which was a condition for a reliable observation of an MBE involving calcium.

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2.3.2.4 Potassium and rubidium

Obviously, the first observation ofan extremal MBE at a potassium cyclotron frequency was made by McLeod et al. (1987a). In the experiment

B(41) B p(?) b(15) f (16) n( > 300) they observed a reduction in the mobility ofdiatomic algae cells in agar with a high calcium density, which provided for initially maximal mobility. Controls were exposed to a 55.7- µ T DC MF. Some responses were also found at 3, 5, and 15

harmonics of a cyclotron frequency and were not found for the remaining harmonics with numbers from 1 to 17.

Later on that group ofauthors confirmed the efficiency ofexposure ofradish seeds to parallel MFs fine-tuned to 1 and 3 harmonics ofthe potassium cyclotron frequency (Smith et al. , 1995), see (2.3.3).

Statistically significant changes in the trapping of 42K isotope ions in mammal cells both for parallel and for perpendicular orientations of magnetic fields were observed (Garcia-Sancho et al. , 1994) for a certain value of the field amplitude, Fig. 4.42. The frequency of a maximum corresponded to a cyclotron frequency for a given ion, which betokens possible involvement ofpotassium processes in certain magnetobiological effects.

Experiment (Jenrow et al. , 1995) has not confirmed the input ofK+ ions as targets for an MF in the regeneration of Planarian worms, although their probable involvement in MBEs with regenerating planaria is discussed (Lednev et al. , 1996b).

Kavaliers et al. (1996) studied the variation ofopioid-induced analgesia in land snails on a 15-min exposure to parallel MFs at a cyclotron frequency of K+ ions B(76 . 1) f (30) b(0 ± 0 . 2 , 38 . 1 , 114 . 2 , 190 . 3 , 213 . 1) n(23 46) .

The effect attained 27 ± 4 . 2 %. At b(190 . 3), the MBE vanished when the snails were treated with glibenclamidum, an antagonist ofpotassium channels. The authors note that a potassium cyclotron frequency was very close to the second subharmonic ofthe calcium cyclotron frequency, which makes it difficult to differentiate effects between those ions.

In some experiments the 86Rb radioactive isotope is used. The properties ofthe Rb+ rubidium ion are close to those ofthe K+ ion. Their ion radii are equal to 1.49

o

o

and 1.33 A respectively, and differ noticeably from that of Na+, 0.98 A. Theref ore, when investigating into the behavior ofa membrane ion pump, Na,K-ATPase protein, in an AC electric field (Serpersu and Tsong, 1984) some K+ ions were replaced for Rb+. That made it possible to show that in an AC electric field only the K+

part ofthe pump is activated and the protein can work as two independent pumps.

The authors employed an electric field of e(20 V/cm) f (1000). It would be of interest to assume that in such tests a combined MF could affect ions and rubidium isotopes, since potassium ions as targets for an MF were an object of experimental studies.

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OVERVIEW OF EXPERIMENTAL FINDINGS

Ramundo-Orlando et al. (2000) observed a non-living system exposed to a low-frequency MF using a suspension of liposomes, artificial cells that model erythrocytes. The diffusion rate of p-nitrophenyl acetate ( p-NPA) was measured spectrophotometrically. The diffusion rate was connected with the enzyme activity of carbonic anhydrase trapped by liposomes as they were prepared. The liposomes also contained stearylamine, a lipid interacting with other proteins ofthe system.

The exposure scheme included parallel DC and AC MFs:

B(50 ± 0 . 5) b(25 75) f (4 16) n(15) g( < 1 %) .

Control measurements were performed in a geomagnetic field B(22 . 4) b( < 0 . 5). The experiments were repeated using two sets ofequipment in two different premises.

A 60-min exposure to a 7-Hz, B(50) b(50) field caused the p-NPA diffusion rate to rise from the control level of 17 ± 3 to 80 ± 9 % (100 % for destroyed liposomes).

The frequency spectrum of the effect contained pronounced maxima at 7 (main) and 14 Hz. The effect disappeared on exposure to either a DC or an AC MF.

The authors believe that targets for an external MF here are positive charges of stearylamine on the surface of liposomes. The effect disappeared when the medium was alkalinized from pH 7.55 to 8.95 to bind the charges.

Note that in a 50- µ T DC MF the frequency of 7 Hz is close to the rubidium cyclotron frequency and the potassium Larmor frequency; the frequency 14 Hz is close to the potassium cyclotron frequency.

It was shown (Miyamoto et al. , 1996) that the trapping ofpotassium and rubidium tracers changes when subjected to electromagnetic fields. Possible MBEs involving potassium were also discussed (Lednev, 1996).

2.3.2.5 Lithium

Thomas et al. (1986) used mutually perpendicular DC and AC MFs. Five rats were pretreated for several months to develop a conditional reflex. The assay consisted ofthe rats being made to perform that standard procedure immediately upon a 30-min MF exposure. The MF variables were selected assuming that they had been adjusted to a cyclotron frequency of Li+ ions

B(26 . 1) b p( 70) b(?) f (60) .

A small B AC component parallel to the DC field was found. Some aspect of the rats’ behavior, which was connected with the conditional reflex being developed, changed when exposed to an MF; Fig. 2.23 depicts data averaged over five rats. It is seen that significant changes only occur when the DC and AC fields act jointly.

Blackman et al. (1996) observed an MBE by the formula b(18 . 7 48 . 6) B p(36 . 6) B( < 0 . 2) f (45) .

In terms ofresonance interf

erence ofbound ions (interf

erence in perpendicular

fields), the effect is possible at a Larmor frequency. In the specified DC MF it is

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75

&RPELQHG

6WDWLF


2VFLOODWLQJ

6KDP


Figure 2.23. Index of response to a 30-min exposure to an MF in rats, according to Thomas et al. (1986). Levels: control — GMF; only B AC 60 Hz; only B DC = 27 . 1 µ T; joint action of B AC + B DC.

only the Larmor frequency of lithium ions, 40.5 Hz, that is close to the one used in experiments.

Ružič et al. (1998) addressed the effect ofphysiological stress factors (lack of water) on the spruce seed germination sensitivity to a combined perpendicularly oriented MF

B(46 ± 4) b p(26 ± 4 , 105 ± 10) f (50) .

They observed a 10–50 % drop in germination rate due to an MF under stress or the absence or a minor enhancement ofthe effect without stress. We note that the MF frequency used equaled the Larmor frequency of lithium ions at a given level ofDC MF.

It is also possible to account for the form of MBE amplitude spectra obtained in Blackman et al. (1994, 1995b) with the first amplitude maximum near H AC /H DC

0 . 9, assuming that lithium ions are involved in the magnetoreception ofPC–12 cells (Binhi, 2000), see Section 4.5.

The possible role oflithium ions in MBE was discussed in Smith (1988) and Blackman et al. (1990).

2.3.2.6Hydrogen

Trillo et al. (1996) observed the variation ofneurite outgrowth rate in PC–12 cells with magnetic conditions corresponding to a CR ofa proton or 1H+ ions. MBE

amplitude spectra were studied for various DC field values and AC frequencies (1)

B(2 . 96) f (45) b(0 . 41 5 . 81) B p( < 0 . 2) (2)

B(1 . 97) f (30) b(1 . 12 2 . 9) (3)

B(1 . 97) f (45) b(1 . 12 2 . 9) .

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OVERVIEW OF EXPERIMENTAL FINDINGS

+


0%(


%$&%'&

Figure 2.24. Magnetobiological effect at the cyclotron resonance conditions of hydrogen ions: in PC-12 cells, 1, 2 (out of resonance conditions, 3), according to Trillo et al. (1996); in regenerating planaria, 4, according to Lednev et al. (1997).

For comparison a spectrum was also measured under conditions that did not correspond to cyclotron resonance.

The measurement results are provided in Fig. 2.24. It is seen that the cells really respond when the frequency is fine-tuned to Ωc. A good agreement ofpoints 1 and 2, obtained at different levels ofa DC MF that were “in resonance”, indicated that the MF gradients, which were varied both from group to group, 1 and 2, and for different points within one group, were not a biotropic factor here.

On the curve there are three points for mitoses intensity measured in regenerating planaria cells under CR conditions in significantly larger MFs, B(44) (Lednev et al. , 1997).

It is assumed (Trillo et al. , 1996) that the location ofthe points attests to the presence oftwo different MBE mechanisms. One is responsible for the relatively slow rise and fall of the MBE with the relative MF amplitude from 0 to 2, and it can largely be approximated by the Bessel function J1(2 B AC /B DC). The other is responsible for the sharp “drop” in the MBE at the center of the graph. Adey and Bowin (1982) believe that at binding sites hydrogen ions could be substituted for by calcium.

Action ofparallel MFs at a proton magnetic resonance frequency on the proliferation of neoblast cells in regenerating planaria was observed by Lednev et al.

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(1996b). Planaria with their head sections severed were exposed for 24 h to an MF, whereas controls were exposed to an MF that contained no variable components.

Thereupon the number ofmitoses in cells removed from the regenerating tissue was measured. To clarify the variation of the magnetobiological effect with the amplitude and frequency of the variable MF component the assays were performed by the schemes

B(20 . 87 ± 0 . 01) b(0 80 /∼ 20) f (889) , B(42 . 74 ± 0 . 01) b(78 . 6 ± 0 . 8) f (1808 1830 /∼ 3) .

The frequency dependence had a resonance shape with a 10-Hz-wide maximum at a proton NMR frequency. The amplitude dependence also had a maximum at an AC-to-DC field ratio of1.8. The effect at maximum was about 47 ± 10 %, Figs. 4.33 and 4.43. The authors took pains to take account ofthe daily course ofthe geomagnetic field. Note that the magnetic conditions in that experiment excluded an NMR, since the variable and DC fields were coaxial.

It was assumed that MF targets in those experiments were spins ofhydrogen nuclei that enter into the composition ofintra-protein hydrogen bonds. The earlier assumption that hydrogen atoms played an important role in magnetodependent biological reactions in yeast cells was made in Jafary-Asl et al. (1983) and Aarholt et al. (1988), where they observed biological effects at frequencies corresponding to the NMR of 1H in the geomagnetic field. A theoretical treatment of such effects is given in Polk (1989) and Binhi (1995b).

Blackman et al. (1999) reproduced the data ofTrillo et al. (1996) and also determined the frequency dependence near an MBE maximum (neurite outgrowth on PC-12 cells) at a proton cyclotron frequency. The experiment formula was b(1 . 67 4 . 36) B(2 . 97) f (40 50) .

The findings are represented in Fig. 2.25 as amplitude dependences at various frequencies. The window structure ofthe response is clearly apparent in both the frequency and the amplitude ofan MF. A sharp “drop” at the center, exactly where a maximum effect is expected, supports the data ofTrillo et al. (1996), although there is no reliable accounting for that so far.

The proton seems to be the only more or less reliably established target for an MF, since the proton cyclotron frequency is a couple oforders ofmagnitude different from frequencies of other ions of biological significance.

2.3.2.7 Zinc

Thomas et al. (1986) supposed that zinc ions can contribute to the behavioral response ofrats to perpendicular DC and AC MFs. Blackman et al. (1990) discussed the involvement ofzinc ions in the removal ofcalcium from brain tissues exposed to combined MFs.

Binhi et al. (2001) studied processes concerned with conformational restructuring of E. coli genome exposed for 1 h to a changed DC MF B(0 110 ± 1 / 1). The

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OVERVIEW OF EXPERIMENTAL FINDINGS

12


+$&+'&


I+]


Figure 2.25. The influence of a 24-h exposure to a uniaxial MF on the neurite outgrowth in a nerve cell culture at a proton cyclotron frequency. According to Blackman et al. (1999).

dependence ofthe viscosity oflysed cell suspension on the magnitude ofa DC field to which they were exposed is quite complicated and has several extrema, Fig. 4.48.

To account for the dependence they used the ion interference mechanism involving calcium and zinc that respond in a cymbate manner and magnesium that responds oppositely. Such a combination was unique; i.e., no biologically important ions or their combination yielded such a good agreement ofexperimental and theoretical curves. That points to a possible input ofzinc ions to magnetoreception by E. coli cells.

2.3.2.8 Other elements

It was assumed (Blackman et al. , 1988) that responsible for a statically significant MBE caused by combined magnetic and electric fields and observed at a frequency of405 Hz at a DC MF B DC = 38 µ T were 13C atoms. The NMR frequency of this isotope in this field is 406.9 Hz, which is close to the specified value. The natural content ofthat isotope in a biological system, 1.1 %, is sufficient f or it to be a

potential target for an MF.

Smith et al. (1992) studied the multiplication ofN-18 neuroblastoma cells exposed to parallel AC–DC MFs

B(15 40 / 5) b(20) f (16) .

They observed in a B(30) DC field the proliferation stimulated by 60 %. These conditions were noted by the authors as being close to cyclotron ones for Co ions, 30.7 µ T, and Fe2+, 29.1 µ T, Fig. 2.26.

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CORRELATION OF BIOLOGICAL PROCESSES WITH GMF VARIATIONS

79

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&D

0%(


1D

.


% µ7

'&

Figure 2.26. Variation of the rate of neuroblastoma cell proliferation at B AC = 20 µ T, f = 16 Hz, and a comparison with cyclotron ion regimes; according to Smith et al. (1992).

Piruzyan et al. (1984) demonstrated the action ofa variable MF on the sodium current in myocardium cells.

Manganese, zinc, cobalt, vanadium, cesium, selenium, iodine, molybdenum, and copper trace elements are present in the most important proteins, which control the biochemical equilibrium oforganisms. They are scant, on average 10 3 to 10 6 %.

Nevertheless, a shortage ofthose trace elements causes serious maladies. Therefore, generally speaking, these atoms may also be targets for weak EMFs.

2.4 CORRELATION OF BIOLOGICAL PROCESSES WITH GMF

VARIATIONS

One feature of the geomagnetic field (GMF) is the fact that both DC and variable components are important. On the one hand, the magnitude ofa local GMF to within a good accuracy, 10 2, is constant within time spans up to several days.

In some experiments involving those times, the DC component is ofimportance. For larger times, several months or years, the GMF varies widely. Since the course of various biological processes and the slow variation ofthe GMF are often correlated, the very fact of GMF variation is important. In this case, however, the GMF can be regarded to be quasi-static in the sense that MBE physical models may ignore the time derivative ofthe GMF. It is to be noted that so far there are no physically justified frequency criteria for a varying MF to be viewed as constant in relation to biological effects. That is because there are no workable MBE models whose analysis could give such a criterion.

On the other hand, with shorter time intervals, under 24 h, as well, the GMF

vector undergoes insignificant variations that correlate with the course ofsome biological processes. The GMF variation times are here shorter than the characteristic times ofbioprocesses that correlated with them. In that case, the variable

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OVERVIEW OF EXPERIMENTAL FINDINGS

GMF component should be regarded as more significant than the level ofthe DC

component.

The characteristics ofthe geomagnetic field and their correlation with processes on the Sun have been described many times (e.g., Akasofu and Chapman, 1972; Guliyellmi and Troitskaya, 1973; Stern, 1996), and so we here just summarize them.

The GMF shape is close to that ofa dipole field whose axis is oriented at an angle of 11 . 5 o to the Earth’s rotation axis. The GMF strength declines from the magnetic poles to the magnetic equator from about 0.7 to 0.4 Oe, the GMF vector in the north hemisphere pointing down. It is widely believed that the GMF is a result of hydrodynamic flow within the Earth’s liquid core.

Along with the solar wind — a supersonic flux ofhydrogen ions that envelops the Earth — the GMF forms the magnetosphere, i.e., a complicated system of electromagnetic fields and charged particle fluxes. The magnetosphere is compressed by the solar wind on the diurnal side and strongly extended on the nocturnal side.

The electric processes in the magnetosphere produce a variable GMF component ofunder 10 2 Oe during times ofseconds and longer, except f or paleomagnetic

periods. The Sun’s own electromagnetic emission is nearly totally absorbed by the ionosphere, the ionized layer ofthe Earth’s atmosphere, except for the narrow band from near ultraviolet to near IR range. The corpuscular solar emission that shapes the solar wind is subject to random fluctuations due to flares in the Sun’s active regions.

The Sun possesses its own MF, which, unlike the Earth’s field, does not look like a dipole one. Solar wind fluxes capture the MF from the Sun’s surface and carry it to the Earth. In the Earth’s orbit that field, referred to as the interplanetary MF, is only several nT and points either to or away from the Sun, thus breaking down the interplanetary MF into sectors. Since the Sun’s equator area, with which its MF is associated, rotates with a period ofabout 27 days, during that time on Earth we can observe several alternations ofthe sectors ofthe interplanetary MF, i.e., alternations ofthe field direction. Normally, the number ofsectors, which is even ofcourse, is not higher than 4.

It takes the Earth several minutes to cross a sector boundary. Thereafter, marked changes in the magnetosphere may occur. Ifthe component ofthe interplanetary MF is aligned along the Earth’s axis from north to south ( Bz < 0), then the interplanetary and geomagnetic fields in most ofthe magnetosphere compensate for each other. As a result, penetration ofthe solar wind into the magnetosphere becomes deeper and more inhomogeneous, a fact which causes heightened electromagnetic perturbations on Earth.

GMF variations are conventionally divided into quiet and perturbed ones. Quiet variations are due to the daily and seasonal motion ofthe Earth, and also to the motion ofthe Moon; they also include effects ofthe sectoring ofthe interplanetary MF. Quiet daily GMF variations do not exceed 60–70 nT. Perturbed variations —

quasi-periodic and irregular pulsations from split seconds to minutes, or magnetic storms — are caused by random processes on the Sun, which affect the magnetosphere via the solar wind. Therefore, perturbed variations occur approximately

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CORRELATION OF BIOLOGICAL PROCESSES WITH GMF VARIATIONS

81

-DQ


DUG


Z


(DVW


'RZQZDUG

*03YDULDWLRQVQ7


KZDUG


1RUW

7LPHK

Figure 2.27. Variations of GMF components according to the data supplied by a geostationary satellite, 10–13.01.1994. Measurements were taken at 1-min intervals. Daily variations of the components and the geomagnetic perturbations from 6 a.m. of January 11 are clearly seen.

four days after solar “cataclysms”. This is the time taken by solar hydrogen ions to reach the Earth. Perturbed variations attain 1 µ T and last from hours to days.

Figure 2.27 shows variations ofGMF components recorded by a geostationary satellite, http://spidr.ngdc.noaa.gov. The satellite revolved together with the Earth at a height ofseveral Earth’s radii above a meridian, so that its terrestrial coordinates remained almost unchanged during a long time. The figure shows both quiet and perturbed variations. It is these latter that correlate with the state ofthe biosphere. In order to get an insight into the nature ofthose perturbations, i.e., to single out a “useful signal”, such data are processed.

Figure 2.28 provides the result ofthe consecutive procedure ofdifferentiating, squaring, and sliding (15 min) averaging ofsimilar data for the GMF vector module within several days, including the interval in Fig. 2.27. Shown is the absolute rate ofthe GMF variation, or rather the course ofits root-mean-square deviation. The curve is made up ofpoints


1

n+ N

2

∂B

1


=

( Bi − Bi+1)2

,

t = 1 min , N = 15 .

∂t

t N

n

i= n

It is seen that relatively quiet days alternate with days with pronounced perturbations ofthe GMF variation rate. It is not clear yet which ofthe two perturbations, that ofthe field or that ofthe field variation rate, is more concerned with the course ofbiological processes.

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OVERVIEW OF EXPERIMENTAL FINDINGS

-DQ


*0)GLVWXUEDQFHVQ7PLQ


'D\V

Figure 2.28. Perturbations in the GMF magnitude variation rate during a geomagnetic storm.

Processed 1-min measurements of GMF Bn, 8–14.01.1994.

Thus, the GMF may be in various states that are characterized by the presence or absence ofsome variations and the distribution oftheir intensities.

2.4.1 Parameters and indices of the GMF

In order to describe the behavior ofthe variable GMF component they use various local and global indices ofgeomagnetic activity. Also to determine the indices the GMF parameters are ofimportance, because they define the magnitude and direction ofthe GMF vector at a point ofobservation. We note the following parameters: H — the horizontal component ofthe GMF vector,

Z — the vertical component ofthe GMF vector,

I — the magnetic inclination, i.e., the angle between H and the GMF vector at a given point,

D — the declination, i.e., the angle between the H vector and the direction ofthe geographic meridian at a given point, from north to south.

Various indices of geomagnetic activity are found from the behavior of the temporal variation ofthese quantities. The meaning ofsome ofthe commonest indices is explained below.

• C-index. Determined during 24 h. Takes on values 0, 1, or 2 depending on whether the day was quiet, perturbed, or strongly perturbed in terms ofmagnetic

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CORRELATION OF BIOLOGICAL PROCESSES WITH GMF VARIATIONS

83


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Figure 2.29. Correlation diagram. Variation of the GMF horizontal component and the change in the chromosome aberration frequency in rat liver cells. Processed data of Fig. 34 (Dubrov, 1978).

activity.17

• u-index. Determined as a difference ofmean values ofH modulus during the current and previous day.

• K-index. Estimated every 3 h as the mean perturbation in a ten-point scale.

• Ci C-index averaged over several major observatories scattered all over the globe.

• Kp — special-purpose averaging of K-indices from various observatories. The sum of Kp-indices over a day reflects the mean perturbation intensity ofthe solar wind.

• Ap — the daily mean amplitude ofGMF strength oscillations in the middle latitudes.

• AE — a measure ofgeomagnetic activity in high latitudes; and Dst, in low latitudes. Determined during various time intervals.

There are also many other indices that reflect various frequency-temporal, space, and power characteristics ofan intricate process ofGMF variation (Akasofu and Chapman, 1972; Stern, 1996).

2.4.2 Characteristic experimental data

The temporal correlation ofvarious indices ofgeomagnetic activity with a wide variety ofbiological characteristics and processes was observed. Such correlations set in at the cellular level or even at the level ofchemical reactions in vitro, e.g., 17There exist many criteria for such an estimate, but their exact description is of no consequence for our treatment.

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OVERVIEW OF EXPERIMENTAL FINDINGS

0D\


0LWRVLV

,QFOLQDWLRQGHJ


7LPHKP

Figure 2.30. The daily rhythm behavior of cancer cell mitoses and the variation of geomagnetic field inclination, according to Fig. 32 in the monograph (Dubrov, 1978).

in the Piccardi reaction. It is difficult, therefore, to find a process in the biosphere that would not correlate with some parameters ofthe helio-geosphere.

In many frequency ranges under about 0.1 Hz a correlation of GMF variations with some biological processes has been found. The pioneering works were those by Chizhevskii and Piccardi. Some oftheir papers (e.g., Piccardi, 1962; Chizhevskii, 1976) have laid a dramatic foundation for the further development ofheliobiology. It has taken nearly halfa century for investigations into helio-geo-biocorrelations to be promoted from the status of a “pseudo-science” to, at first, an exotic (Gnevyshev and Oll, 1971) and then to a common domain ofscientific research (Shnoll, 1995a). It is quickly becoming one ofthe hottest fields now.

A voluminous monograph by Dubrov (1978) addresses the studies ofcorrelation ofbiospheric processes in objects ranging from plant and microorganism cells to higher animals, humans, and ecological systems, with variations ofthe geomagnetic field within a wide range oftimes scales, from hours to decades. The book contains more than 1200 references to original works of Russian and international researchers. Juxtaposing geophysical and biomedical data, the author has shown quite convincingly for the first time that the bio-GMF correlations are not an exotic phenomenon, but rather a common fact that warrants careful investigation. In what follows the correlations contained in that book are provided between geomagnetic correlations and some processes ofvital activity, mutations, cancer, and so on.

Figure 2.29 shows regression analysis data for an approximately synchronous course oftwo processes. One ofthem is the variation ofthe density ofchromosome

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CORRELATION OF BIOLOGICAL PROCESSES WITH GMF VARIATIONS

85


GHJ

LRQ

LRQ

DWXW


LQDW

P

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)HE

$SU

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Figure 2.31. The behavior of the natural seasonal mutation process and the variation of the GMF parameter, according to Fig. 65 from the monograph (Dubrov, 1978).

structural defects in rat liver cells upon an injection of dipine, an antitumor preparation. The other process is the variation ofthe magnitude ofthe GMF horizontal component at the experiment site. Figure 2.30 provides the circadian rhythm of the mitosis ofhuman carcinoma cells and the GMF inclination value within appropriate time spans. Figure 2.31 is a plot ofthe seasonal variation ofchromosome inversions ofthe ST gene in Drosophila under natural conditions and the mean monthly variations ofinclination.

Correlation diagrams for these graphs are given in Fig. 2.32 and Fig. 2.33. These graphs are seen to show correlation connections for various time scales, which is evidence for the hypothesis ofthe direct influence ofGMF variations on the behavior ofbiological processes.

In some plants, enhancements and retardations oftheir development was observed (Kamenir and Kirillov, 1995) when the Earth passed through sectors with positive and negative polarity ofthe interplanetary MF, respectively. It was shown (Alexandrov, 1995) that the activity biorhythms in aquatic organisms vary with the regional MF. The bioluminescence of Photobacterium bacteria changes markedly during magnetic storms (Berzhanskaya et al. , 1995), so that changes occur a day or two before the onset of a storm and last for two or three days after the storm has ebb.

Gurfinkell et al. (1995) conducted regular measurements ofcapillary blood flow in 80 heart ischemia cases. On the day ofa magnetic storm 60-70 % patients showed impaired capillary blood flows. At the same time, only 20-30 % ofpatients responded

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OVERVIEW OF EXPERIMENTAL FINDINGS


U

0LWRVLV


,QFOLQDWLRQGHJ

Figure 2.32. Correlation diagramof the biological and geomagnetic processes in Fig. 2.30.


0XWDWLRQ

U


,QFOLQDWLRQGHJ

Figure 2.33. Correlation diagramof biological and geomagnetic processes in Fig. 2.31.

to changes in the atmospheric pressure.

Oraevskii et al. (1995) found that even short-term variations of the interplanetary MF polarity within 24 h correlate with serious medical maladies. Shown in Fig. 2.34 is the regression analysis oftheir data. There is a significant correlation between the number ofemergency calls in connection with myocardium infarction (on days with anomalously large or anomalously small number ofcalls) and the index ofinterplanetary MF variations. The index was approximately equal to the daily integral Bz, i.e., to the z-component ofthe interplanetary MF. It was worked out as a sum ofhourly values of

0 , B

B

z ≥ 0

s =

−Bz, Bz < 0

during the 24-h interval shifted 6 h back in relation to the 24 h under consideration.

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&DOOV


,QWHUSODQHWDU\0)LQGH[

Figure 2.34. Correlation diagram: the abscissa axis is the interplanetary MF index, the ordinate axis is the daily number of emergency calls in connection with myocardium infarction; data of Oraevskii et al. (1995) processed, the confidence interval at a level of 0.95.

The authors obtained a similar statistics for emergency calls in connection with insult, hypertonic crisis, bronchial asthma, epilepsy, and various injuries.

Villoresi et al. (1995) conducted a thorough statistical analysis ofthe relation ofthe incidence ofacute cardiovascular pathologies in the years 1979–1981 with the GMF variations. The authors showed that strong planetary-scale geomagnetic storms are related to the growth in the number ofmyocardium infarction cases by 13 % to within a statistical confidence of9 σ, and the number ofbrain insults, by 7 % with a statistical confidence of4.5 σ. It was found that such pathologies as myocardium infarction, stenocardia, and cardiac rhythm violations correlate in a similar manner with the onset ofgeomagnetic storms (Gurfinkell et al. , 1998).

Figure 2.35 provides those findings.

According to observational evidence gleaned over nine years (Zillberman, 1992) a correlation was revealed ofgeomagnetic activity, Ap-index, with a density oftrue predictions in mass-number lotteries, R = 0 . 125 for significance 99.74 %. The density correlated with Ap precisely on the day ofissue and did not correlate with that index on previous or later days.

Also, correlations were found of the geomagnetic perturbations with the decrease in morphine analgesic effect in mice (Ossenkopp et al. , 1983); ofthe index ofshort-period oscillations ofthe H-component ofthe GMF with the brain functional status (Belisheva et al. , 1995); ofa change in the direction ofthe interplanetary MF with leucocyte and hemoglobin content in mouse blood (Ryabyh and Mansurova, 1992); ofthe daily sum of K-indices with the suicide frequency (Ashkaliev et al. , 1995); of the Ap-index with the criminal activity in Moscow (Chibrikin et al. , 1995b); ofthe Ap-index with the amount ofcash circulating in Russia (Chibrikin et al. , 1995a); of the occurrences ofmagnetic storms with the probability ofair crashes (Sizov et al. , 1997).

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OVERVIEW OF EXPERIMENTAL FINDINGS


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Figure 2.35. Relative incidence of cardiovascular pathologies before, during, and after magnetic storms, according to Gurfinkell et al. (1998).

For more information on a variety of biospheric processes that correlate with the geomagnetic activity see some special issues ofthe Biophysics journal (Pushchino, 1992, 1995, 1998), and collections ofworks (Gnevyshev and Oll, 1971, 1982; Krasnogorskaya, 1984, 1992).

2.4.3 Physical aspects of bio-GMF correlations

The mechanisms responsible for a correlation ofthe behavior ofbiological processes with GMF variations are unclear as yet. There are several points ofview on the possible nature ofthat phenomenon.

2.4.3.1 Direct action of a magnetic field

The commonest view is that GMF variations affect biological or biochemical in vivo processes (Vladimirskii, 1971; Dubrov, 1978; Zillberman, 1992; Temuriyants et al. , 1992b; Gurfinkell et al. , 1995; Breus et al. , 1995; Alexandrov, 1995). Specifically, this gives rise to the question (Vladimirskii, 1995) ofwhether heliobiology could be referred to as a part of electromagnetic biology.

Experimental evidence for the idea consists of both “pros” and “cons”. Works by Opalinskaya and Agulova (1984) on the action ofman-made variable MFs larger than GMF fluctuations suggest that the idea is well grounded. At the same time, not all the data provided by the group are confirmed by independent studies (Piruzyan and Kuznetsov, 1983).

Agadzhanyan and Vlasova (1992) modeled short-period GMF pulsations at frequencies of0.05–5 Hz and intensities ofabout 100 nT. They found that such MFs activated spontaneous rhythmic activity in the nerve cells ofthe mouse cerebellum.

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89


6+$0


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Figure 2.36. Proliferative activity of glioma cells in an EMF that simulates natural atmospherics as a function of the pulse amplitude, according to Ruhenstroth-Bauer et al. (1994).

Artificial magnetic pulsations that imitate the level and temporal behavior oflocal magnetospheric pulsations stimulated the growth ofsome grassy plants (Kashulin and Pershakov, 1995). At the same time, stronger field variations caused no biological response, which supports the hypothesis for biosystems being directly affected by GMF variations.

Tyasto et al. (1995) report that during weekends and holidays they observed a 40-50 % reduction in magnetic fluctuations ofa technogenic origin in the frequency range of 10 3–10 1 Hz and, concurrently, a 70 % reduction ofmyocardium infarction cases. The authors believe that this suggests that magnetic fluctuations may play the role ofa trigger mechanism for acute disorders in humans with cardiovascular maladies.

Ruhenstroth-Bauer et al. (1994) addressed the proliferative activity of N6-gliome cells in vitro exposed to an EMF that imitated naturally occurring atmospherics — short, weak quickly decaying EMF pulses. The often observed MF shape ofan atmospheric, that ofa wave packet oflength 400 µ s, frequency 10 kHz, band 5–20 kHz, and amplitude 0 . 01 µ T, was digitized and stored. They generated then, using a computer, a series ofsuch pulses separated by a random interval of50–

150 ms, amplified them, and fed them to single-turn Helmholtz coils. The DC MF

level, it seems, corresponded to a local GMF. Exposure to a field produced using that scheme changes the proliferative activity, Fig. 2.36, measured from radioactivity per unit ofDNA with 3H-thymidine. Biological activity is thus inherent in combined MFs with a noise-like variable component. Here too for relatively small amplitudes the dependence is non-monotonous in nature. These findings also support the hypothesis that GMF perturbations affect the biosphere directly.

There is no clear understanding as yet ofthe possible biophysical mechanisms for the direct action of so small MF disturbances. Biophysical mechanisms for fields similar to the Earth’s seem to be clearer — those fields are three or four orders of

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OVERVIEW OF EXPERIMENTAL FINDINGS

magnitude larger, but even for them appropriate mechanisms should be regarded as suppositions that need further study.

2.4.3.2 The radon hypothesis

An alternative view on the nature ofbio-GMF correlations involves the dependence or correlation ofradon density in the lower atmosphere and the electromagnetic activity on the Earth’s surface (Shemii-Zade, 1992).

Radon isotopes, mostly 222Rn, are constantly emanated by the ground via a chain ofalpha-decays ofsmall amounts of238U, 235U, and 232Th naturally occurring in the lithosphere. Radon is a chemically neutral heavy atomic gas with a half-life of 1600 years. The natural radiation level in the biosphere is partly due to radon decay and its short-lived derivatives 218 , 216 , 214Po, 214Bi, and 214 , 212Pb. The radiation level is subject to strong changes, by tens oftimes, owing to mechanical processes in the lithosphere and the “locking” ofradon in the ground by aquifers.

The marked correlation ofradiation near the ground with the geomagnetic activity enabled Shemii-Zade (1992) to come up with a mechanism for bio-GMF correlation. The author hypothesized that the flares ofgeomagnetic perturbations cause a magnetostrictional deformation of minerals and rocks that include ferromagnetic compounds. That increases radon diffusion from the ground and its density in the lower atmosphere. Through breathing and metabolism radon finds its way into living systems, causing various biological effects as it accumulates. Note that so far no experiments with artificial MFs are known that would confirm the strictional mechanism in the lithosphere for MF perturbations as small as geomagnetic storms.

This issue is being discussed not only in connection with geomagnetic perturbations. It has been established that radon is a risk factor for lung cancer. Radon decay products, specifically the unstable polonium, are transferred by particles of various aerosols, which are always available in the air. Since they carry an electric charge, they are drawn into areas with a heightened electric field strength.

Henshaw et al. (1996) used an alpha counter to measure radioactive aerosol density near household electric cables and found it to be higher several fold. The authors looked at cases where in dwellings and production premises there is a power-frequency electric field from a nearby transmission line and enquired whether that exposure might cause radon products to settle on the surface of lungs and lead then to cancer cases. Despite the small volume ofexperimental evidence, insufficient statistics, lack ofspecial-purpose epidemiological, and even biological studies, the authors believe to have found the missing link in the physical mechanism for the connection ofweak electromagnetic fields with cancer risk. According to their hypothesis, which causes some dispute and is not shared by all, electromagnetic fields act on living matter in an indirect manner, via the growth ofradon product density.

At the same time, for computer terminals with their much higher electric fields of up to 30–50 kV/m at a distance of10 cm, it was found (Akimenko and Voznesenskii, 1997) that the fields do not affect the density ofdaughter radon decay products. In both exposed and control samples it was about 91 . 5 ± 2 . 5 Bq/m3.

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2.4.3.3 Common synchronizing factor

Lastly, a third view ofthe physical nature ofbio-GMF correlations takes account ofthe f

ollowing circumstance. It is well known that the intensity ofnearly all biological and biochemical in vivo processes undergoes to some degree or other some cyclic oscillations. Most ofsuch biological rhythms — an obvious example being the circadian rhythm — occur somewhat in sympathy with geophysical and even space-physical processes (Piccardi, 1962; Chizhevskii, 1976; Dubrov, 1978; Shnoll, 1995a; Klochek et al. , 1995). Infradian rhythms (nearly 3.5, 7, 27 days) are a corollary ofthe periodic activity and rotation ofthe Sun. The same rhythms are to be found in many biological systems (Breus et al. , 1995), including unicellular ones.

The Earth’s rotation and revolution around the Sun, and the Moon’s motion jointly drive some biological rhythms and cause variations ofsome GMF variables.

For instance, found in the power spectrum of geomagnetic aa-index variations are groups ofspectral peaks near 27, 14, 9, and 7 days. On the one hand, these rhythms are conditioned by variations ofsolar wind parameters; on the other hand, they appear in biospheric processes. Therefore, a correlation of the temporal behavior ofbioprocesses and the GMF does not necessarily imply any cause–effect relations, a fact that has repeatedly been stressed in the literature. It is not to be excluded that GMF variations cause no biological response. They may be a corollary ofa yet unknown true reason ofa common synchronizing natural factor.

Environment parameters often vary in sympathy with one another, since they are to a large degree dictated by solar universal rhythms (Vladimirskii et al. , 1995).

Electromagnetic perturbations are accompanied by elevated infrasound noises and microseisms, by a drop in the intensity ofgalactic space rays, and by a rise in the atmosphere radioactivity. Vladimirskii et al. note that those background develop-ments do not make it any easier to answer the question ofwhich physical factor underlies the biorhythms.

Shnoll (1995b) reported that the mean amplitude offluctuations ofprocesses of various nature changes markedly already 1–2 days prior to the Earth’s crossing the boundaries ofinterplanetary MF sectors. That rather suggests the presence ofan unknown influencing factor, perhaps connected with some processes on the Sun. It was assumed (Akimov et al. , 1995) that this factor is the fields engendered by the torsion of space bodies. This factor was found (Klochek et al. , 1995) to feature a high penetrability, and to correlate with biological and geomagnetic activities and with solar RF fluxes in the meter–centimeter ranges. That also corroborates the hypotheses that the bio-GMF correlation has a non-magnetic nature.

The issue ofthe influence ofweak low-frequency electric fields on living organisms against the background ofa DC MF is still not clearly understood. A concise overview ofrelevant work was performed by Binhi and Goldman (2000). The vertical electric component ofgeomagnetic pulsations is known to attain 10 V/m and be rigidly correlated ( r ∼ 0 . 8) with variations ofthe meridian projection ofthe horizontal GMF component (Chetaev and Yudovich, 1970). Therefore, it is not to be

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excluded that biological effects are due not to geomagnetic variations themselves, but to the geoelectric fields that are synchronous with the former.

There may well exist several mechanisms ofsimilar significance that are responsible for the correlation in question. Their competition is dependent on many nearly unaccountable factors, so that correlation values are not too large and the results are not properly reproducible. At the same time the very variety and spectrum of manifestations ofbio-GMF correlations is indicative oftheir non-random nature.

2.5 SPIN EFFECTS IN MAGNETOBIOLOGY

Evidence for the manifestation of spin degrees of freedom in magnetobiological experiments is fairly scarce. There are no assays that have been reproduced by various research groups. This situation may well be due to traditionally large intensities ofMFs used to observe spin effects. In such experiments the signal-to-noise ratio largely grows with the MF. Another reason behind the lack ofprogress with the idea on spin effects in magnetobiology is the smallness ofthe energy ofelectron magnetic spin moment, let alone that ofnuclear magnetic moments, in an MF similar to the geomagnetic one. It is as low as 10 7 κT ; therefore many believe that physically an MBE through spin magnetic resonance mechanism is impossible.

At first sight, it looks highly unlikely that atomic nuclear spins ofmolecules in a living tissue can influence life processes. After all, nuclear spins interact with the ambient environment via interaction ofmagnetic spin moment with internal inhomogeneous electric and magnetic fields. These magnetic interactions are proportional to the nuclear magnetic moment, which is two orders ofmagnitude smaller than that ofthe electron. Nevertheless nuclear spins are somehow involved in biochemical reactions. A circumstantial testimony ofthat is the fact that various substrates ofbiological systems, such as cells and tissues, feature different carbon isotope compositions (Jacobson et al. , 1970).

It was reported (Ivlev, 1985) that the pyruvate decarboxylizing reaction involved separation of 12C and 13C carbon isotopes, the mechanism for isotope inhomogeneity in amino acids being not quite clear. This reaction affects the carbon isotope composition ofcarbon dioxide exhaled by man and animals. This composition undergoes daily variations (Lacroix et al. , 1973) and reflects hormone-metabolic status (Ivlev et al. , 1994). The carbon isotope ratio in exhaled air may change within minutes ofthe administration ofsome preparations. This is convenient for express diagnostics. In laser orthomolecular medical diagnostics (Stepanov et al. , 2000), the 13C/12C ratio is thought to give a clue to the presence ofsome disorders ofthe digestive system.

The two isotopes differ in mass by 8 %, while 13C, unlike 12C, has a spin; i.e., it possesses a different dimension. It is quite possible that it is the spin of 13C, rather than the mass difference, that is a factor responsible for isotope separation in relevant biochemical reactions. Especially attractive in that respect is observation ofan isotope effect for relatively heavy ions, such as Ca, Zn, and Cu, with a mass difference ofonly 1–2 %.

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It appears that MBEs are really unlikely ifthey occur through a spin resonance mechanism in its conventional sense, i.e., as a resonance change in the EMF energy absorption rate by a relaxing spin system. Also unlikely are MBE mechanisms concerned with energy accumulation due to a spin magnetic moment. One can and must, however, dispute the thesis that magnetic interactions ofelectron and nuclear spins have nothing to do with magnetobiology. The role ofspins, including nuclear ones, as go-betweens in the transfer of information signals of an MF is not yet understood (Binhi, 1995b).

It is believed that underlying the mechanism for the biological action of low-frequency MFs is a magnetosensitive process ofa recombination offree radicals that occur in a biological tissue. That process is influenced by the state ofelectron spins ofradicals that enter into the reaction. The state ofspins, in turn, is determined by an MF. However, there is no reliable experimental evidence to date to support such a mechanism for magnetoreception. It is primarily because it does not possess frequency selectivity and is only sensitive to the magnitude of an MF. The fact of magnetoreception in itselfthus does not suggest that there must be a contribution ofspins — there are also other explanations for an MBE that are not necessarily concerned with spins. Therefore, the following is an overview of experiments where spins manifest themselves in frequency-selective biological responses to an EMF, with effective frequencies in the regions of spin resonance. Those assays, if they are not to be taken to be artifacts, point to direct involvement of spin processes in magnetoreception.

Jafary-Asl et al. (1983) performed one of the early works to juxtapose biological effects with spin magnetic resonance conditions. They studied yeast cells using dielectrophoresis, i.e., a method relying on a shift of cells owing to their polarization in an inhomogeneous electric field. Pre-processed S. cerevisiae cells were placed in an electrochemical cell and viewed under microscope. When a field was applied, the cells would begin to move towards the electrodes to form on them some chains along field lines. The electric field was turned off 3 min later, and the mean chain length was measured. The assays were conducted in a controlled DC MF B(50 500) and a variable electric field f (200 5 · 104), such that the potential difference across the electrodes was 40 V. Since the authors provided no information on cell design, it is hard to estimate the value ofthe electric field and its gradient. There were also no data on the mutual orientation ofthe electric and magnetic fields.

Shown in Fig. 2.37 is an experimental curve produced by the processing offive frequency spectra obtained in 50-, 100-, 150-, 300-, and 500- µ T MFs. The plot displays a clear dip in the region of4.26 kHz/G. Also shown is the variation ofthe probability amplitude ofa spin state ofa Zeeman duplet, computed from the NMR

mechanism for the proton for b p /B = 0 . 1.

Since the experiment used a variable electric, rather than a magnetic, field, the results ofFig. 2.37 are just a circumstantial indication ofthe possible role ofnuclear spins ofprotons in those experiments.

The work also contained spectra ofthe complex permittivity 4( f ) = 4( f )+ i4( f )

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3UREDELOLW\


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Figure 2.37. Comparison of experimental evidence (Jafary-Asl et al. , 1983) for dielectrophoresis of yeast cells in a weak MF with a 1H NMR curve.

in the range of f (90 105), and in the region offrequencies that correspond to a spin resonance ofan electron in an MF 50 µ T for a cell culture with a density of 1 . 9 · 106 ml 1. At some fixed frequency values they observed narrow, 1 Hz, flares of 3–15 %. Provided below are (i) frequencies (Hz) found in experiment, (ii) nuclei that, according to the authors, correspond to them, and (iii) NMR frequencies of those nuclei in a field of50 µ T:

2130

1H

2128 . 2

861

31P

862 . 6

563

23Na

563 . 4

208

35Cl

208 . 8

99

39K

99 . 4

To within the experiment accuracy ( 1 Hz) there is a nearly complete agreement.

Also shown is the growth ofdielectric losses at a frequency ofelectron spin resonance

2 . 79 MHz/G.

That work also describes studies ofother cells under NMR conditions. Earth bacteria cultures were exposed to an MF at an NMR of 1H

B(25 · 103) B p(85) f (1 . 064 · 106) .

In the experiment, cell concentration doubled during a 10-h exposure in comparison with controls, while the size ofthe smallest cells reduced by half. It was possible to stop the enzyme reaction oflysozyme with its substrate under near-NMR conditions for 1H

B(2 · 105) f (7 · 106 107) .

Similar data were supplied by Shaya and Smith (1977). It was concluded by Jafary-Asl et al. (1983) that their data point to the ability of 1H NMR conditions to encourage the DNA replication process.

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95

,SURWRQ

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Figure 2.38. Para- and ortho-states of water molecules. Ortho-states feature wave functions that are symmetrical in spin transmutations.

Aarholt et al. (1988) report that in a proton magnetic resonance (perpendicular fields) the mean lifetime of a generation of E. coli cells decreases. The authors also reported that a 55-MHz EMF with a bandwidth of50 Hz caused eye pupil cataracts in animals in vitro, ifthe frequency modulation corresponded to an NMR at 1H, i.e., at 2.13 kHz in a geomagnetic field of50 µ T.

Works by Konyukhov and Tikhonov (1995), Konyukhov et al. (1995), and Belov et al. (1996) contain circumstantial evidence that proton nuclear spins can contribute to the primary reception ofan MF by biosystems. The authors also report that they managed to reveal the existence ofliquid water with metastable deviations from the equilibrium ratio 3:1 ofthe amounts ofwater ortho- and para-molecules H2O. In a singlet para-state the molecular spin I = 0 is f ormed by oppositely directed proton spins and has the only projection Iz = 0 on an arbitrary quantization axis, Fig. 2.38.

For ortho-states, proton spins are unidirectional, and the molecular spin I = 1

has three possible components Iz = 1 , 0 , 1, and in a magnetic field it forms a triplet. In a strong external MF the energy ofits interaction with proton magnetic moments, µH, is larger than the energy ofmagnetic dipole–dipole interaction

µ 2 /r 3. That occurs in the field

µ

H >

10 G .

r 3

Proton spins will then behave as good as independently ofone another. In a weak MF, a combination ofproton spins make up a molecular spin that interacts with the MF as a whole.

The adsorption ofwater molecules f

rom a gaseous phase is sensitive to the

rotational state ofwater molecules, and theref

ore it reveals the molecular spin

state. In a specially weak 1H NMR MF

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B(150) B p(5) f ( 6384)

that provides quantum transitions between the states Iz = 0 and Iz = ± 1, it was possible to record a growth in the adsorption rate ofwater ortho-molecules (Konyukhov and Tikhonov, 1995) and then to obtain, on that basis, liquid water with a non-equilibrium content ofortho- and para-molecules. The authors dubbed it spin-modified water. It was found, using submillimeter spectroscopy, that the lifetime of spin-modified water is 45 min at room temperature and 4.5 months at liquid nitrogen temperature.

Mechanisms responsible for such long lifetimes of nuclear spin degrees of freedom in liquid water are yet unclear. It may well be that it is connected with the details ofproton exchange in liquid water in an MF (Binhi, 1996, 1998b). However, the very fact ofthe existence ofsuch states at room temperature points to their possible significance in biology.

An MBE observed by Blackman et al. (1988) under the conditions B(38) b(?) e(?) f (405) was associated with the NMR ofcarbon 13C, whose frequency in a given MF is 406.9 Hz.

Direct changes ofparameters ofa biosystem in a weak MF at the 1H NMR

frequency were observed by Lednev et al. (1996b). They found that the MBE variation in neoblast cells of regenerating planaria with frequency had a resonance form, Fig. 4.33. However, the MBE spectrum was measured with magnetic fields aligned in parallel

B(42 . 74 ± 0 . 01) b(78 . 6 ± 0 . 8) f (1808 1830 /∼ 3) .

With such an alignment there is no NMR. It is indicative ofanother physical mechanism for MBEs that is concerned with the spin. One such mechanism is discussed in Binhi (1997a,b) and in this book in some detail.

Ossenkopp et al. (1985) observed the variation ofthe morphine anesthetic effect in mice exposed to an MF following the protocol of the standard NMR tomograph.

It is unclear yet whether that effect was concerned with excitation ofthe spin subsystem, or rather the driving force was the strong DC MF of the tomograph as such. In any case, these factors point to possible unpredictable consequences of the common procedure ofNMR scanning ofhumans.

2.6EFFECTS OF LOW-FREQUENCY ELECTRIC FIELDS

Biological action ofan electric field reduces primarily to the action ofion currents it induces in intra- and intercellular plasma. A redistribution ofions results in local changes ofelectropotentials on the surf

ace ofmacromolecules and cellular

membranes. This in turn is accompanied by a change in biochemical reaction rates.

It is well known that relatively intensive and short pulses ofelectric current encourage penetration oflarge molecules ofDNA or protein type into biological cells. For instance, anticarcinogenic effectiveness ofbleomycin is hampered by the fact that a bleomycin molecule is unable to get through a cell membrane. Current

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97

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Figure 2.39. Frequency–amplitude dependences of the rubidium tracer uptake in erythrocyte suspension on exposure to an AC electric field.

pulses improve the membrane permeability and bring about corresponding biological effects. The fact that relatively strong DC and AC electric fields can affect things raises no doubt, although in that case as well mechanisms for such an action are not always clear (Mir et al. , 1995).

Fibroblast cells on human skin were exposed (Whitson et al. , 1986) to the action ofa 100-kV/m, 60-Hz electric field to find no changes in cell growth and DNA reparation rate. Also, no changes were observed in the behavior ofcancer cells upon exposure to electric fields, in contrast to the case ofradiation combined with an MF (Phillips et al. , 1986b). A summary ofworks on biological effects of5–105 kV/m electric fields is given in Stern and Laties (1998).

Serpersu and Tsong (1983) have established that an AC electric field affects the work of(Na,K)AOFase on membranes ofhuman erythrocytes. They placed some erythrocyte suspension enriched in 86Rb rubidium isotope between electrodes and measured the uptake ofa radioactive tracer by erythrocytes on a 1-h exposure. It appeared that the passage rate ofrubidium ions, which because oftheir similar size sort ofsubstitute for potassium in the workings ofa membrane pump, varies in an extremal manner both with the frequency and with the field amplitude. The same exposure did not influence the passage ofNa ions, as measured from the 22Na tracer.

The findings given in Fig. 2.39 show a relatively wide “resonance” in frequency with a center at around 1 kHz. The authors note that this corresponds to the frequency ofnatural conformational changes in proteins. A decline in the effect with the field amplitude was explained by a field-induced change in protein geometry, which leads to a violation in its normal functioning.

2.6.1 Weak electric fields

It has been found that in a number of cases biological effects are caused by weak electric fields induced by low-frequency MFs. Correlation between the level of

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an induced electric field and a biological effect was observed, for instance, by Schimmelpfeng and Dertinger (1997). Proliferation of HL-60 cells was studied in a sinusoidal 2.8-mT, 50-Hz MF. A homogeneous MF affected the cells only where the induced electric field exceeded the threshold level of4–8 mV/m.

An overview ofexperiments that had demonstrated the effectiveness ofelectros-timulation ofcell metabolism was compiled by Berg (1993). Changes were observed in biopolymer synthesis, enzyme activity, membrane transport, proliferation, and morphological structures. These changes occurred, in particular, under the action oflow-frequency variable MFs ofabout 0.1–10 mT, which engender in a biological medium electric fields ofthe above level. In certain cases in a given range some frequency and amplitude windows of stimulation effectiveness (Lei and Berg, 1998) were found. It is hard to analyze experiments on the stimulation of an MF in the millitesla range in the absence ofdetailed amplitude–frequency spectra, because mechanisms ofvarious nature, e.g., spin and electrochemical ones, can contribute to the formation of an ultimate response. Therefore, to study the biological effects ofan electric field it is preferable to employ electric, rather than magnetic fields.

Although here too it is unclear, in the absence ofdetailed studies, what is responsible for the final biological response: an electric field as such or an electric current (electrochemical processes).

In some cases the intensity ofthe current induced by an electric field is small.

At the same time the electric field itselfcan have a value comparable, in terms ofthe atomic effects it produces, with a weak magnetic field, see Sections 1.4 and 4.6. The biological action ofan electric field can then be viewed in the same context as an MBE. The similarity ofbiological effects oflow-f

requency MFs and

electric fields and the correlation oftheir effective parameters were discussed by Blank and Goodman (1997). The problem here is that it is unclear beforehand with what situation they handle in an experiment where they use relatively small non-thermal electric fields: with the action ofan electrochemical current or with the action of the field itself. Therefore, the choice of experiments considered below is to a certain degree subjective.

Bawin and Adey (1976) found on exposure to a low-frequency electric field some frequency and amplitude windows in the efflux rate from chicken brain tissue of 45Ca ions, Fig. 2.40. A maximum effect was observed in the region of16 Hz and 10–60 V/m. Shown are field strengths between plates ofthe capacitor, where tissue samples were placed. The electric field within the tissue decreases owing to the fact that ambient molecules are polarized dielectrically, and that charge carriers, in this case ions, are redistributed.

Interestingly, the opposite effect ofcalcium efflux rate growth was observed by Bawin et al. (1975) upon exposure to a modulated EMF ofhigh frequency, 147 MHz.

An effectiveness window near a frequency of 16 Hz was registered at frequency modulation scanning in the low-frequency range.

McLeod et al. (1987b) studied 3H-proline incorporation into a newly synthesized collagen in the collagen matrix ofthe bull fibroblast cell carrier. They found

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99


+]

+]


+]

+]


&DHIIOX[UHOXQLWV


(OHFWULFGLVSODFHPHQW9P

Figure 2.40. Frequency and amplitude windows when an electric field affects the efflux of calciumions pre-introduced into brain tissue, according to Bawin and Adey (1976).

Figure 2.41. The threshold density amplitude of the current that reduces the protein synthesis rate in fibroblasts in an electric field, according to McLeod et al. (1987b).

that a weak, 0.1–100 µ A/cm2, low-frequency electric current, switched on for 12 h, retarded proline incorporation beginning with some threshold level, the value of that threshold being dependent on the field frequency, Fig. 2.41. A maximum 30 %

response was attained at a frequency of 10 Hz and a current density amplitude of 0.7 µ A/cm2. Since the specific resistance ofthe tissue was about 65 ohm cm, the authors concluded that AC electric fields ofabout 4.5 mV/m are able to cause a biological reaction. They also observed a reduction in the reaction threshold for long cells aligned along the field. Note that a field induced by a 50-Hz, 100- µ T AC

MF in a sample 1 cm in size on the solenoid axis is an order ofmagnitude smaller ( 0 . 2 mV/m).

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OVERVIEW OF EXPERIMENTAL FINDINGS

Blackman et al. (1988) studied the efflux ofcalcium ions from chicken brain tissue in vitro in a wide frequency range for a combined action of weak magnetic and electric fields. The experiment formula is

b(0 . 085 0 . 1) e p(20 V/m) f (1 510 / 15) B p( < 38) B(?) .

They used double controls: sham-controls and controls outside ofthe exposure device. What is noteworthy here is the fact that the amplitude of an AC MF (tens ofnanoteslas) is relatively small, which corresponds to the level ofsome geomagnetic variations. For 16 out of38 tested frequencies a statistically significant MBE was found, P < 0 . 05. Also found were MBE frequency windows. A large frequency step, 15 Hz, is insufficient to warrant any conclusions about the potential target for an MF. It is not to be excluded that in various ranges work various primary biophysical mechanisms. One important observation, however, consisted in that virtually over all the frequency spectrum the MBE had the same sign; that is, the calcium efflux increased when an EMF was switched on.

Fitzsimmons et al. (1989) addressed the proliferation of chicken bone tissue cells in a weak low-frequency electric field as 3H-thymidine was incorporated into the cells. They also measured the mitogenic activity ofexposed culture on another, unexposed one. A plate with a cell culture was placed between a capacitor’s plates, in the absence ofconductive coupling. The AC field between the plates, in the absence ofa dish, was 10 V/2.3 cm. The experiment formula

e(430 V / m) B(?) f (8 24 / 4) n(6) made it possible to establish the presence ofan effectiveness frequency window, Fig. 2.42. In terms ofan ion interference mechanism, in a variable electric field, Section 4.6, the effective frequencies are the same as in the case of a uniaxial MF: the cyclotron frequency and its (sub)harmonics. If we take a local MF, of which there was no mention in the paper, to be 20 µ T, then the frequency maximum 16 Hz will correspond to a Larmor frequency of calcium ions.

The activity ofion-activated membrane enzyme Na,K-ATPase was investigated by Blank and Soo (1990). The suspension contained substrate and enzyme. To platinum electrodes separated by 5 cm they applied a sinusoidal voltage with an amplitude from 1 to 1000 mV for 15 min. Correspondingly, an electric displacement for the smallest voltage was about 20 mV/m, the current amplitude in the circuit being about 70 µ A/cm2. Frequency windows were found for effectiveness with a maximum effect at 100 Hz, Fig. 2.43. These dependences can hardly be referred to as spectral ones owing to the log scale of frequency variation. However, the frequency selectivity ofthe effect is obvious. The value ofthe MF was not controlled. The authors assumed that the processes ofNa and K ion binding by an enzyme were involved in electroreception.

Amplitude dependences were observed by Blank et al. (1992) when they addressed biological transcription in low-frequency electric fields. They studied the

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Figure 2.42. Response of embryonic chick calvaria cells to a variable electric field. Proliferation and mitogenic activity depending on the field frequency, according to Fitzsimmons et al.

(1989).

$FWLYLW\UHOXQLWV


9

P9


P9


9ROWDJH


P9

ORJI+]


Figure 2.43. Frequency windows of relative activity of Na,K-ATPase enzyme for various amplitudes of the voltage across the electrodes, according to Blank and Soo (1990).

behavior ofHL-60 cell culture on passing a current offrequency 60 Hz and amplitude density 0.1–100 µ A/cm2. A maximum statistically significant 40 % response was observed on a 20-min exposure to a current of1 µ A/cm2. At 0.1 and 100 µ A/cm2

the effects were 9 and 5 %, respectively; at 10 µ A/cm2, the effect did not differ from controls. The authors note that their findings do not support the hypothesis that the effect is proportional to the electric field. The data suggest that there is an effectiveness window in the amplitude ofan internal electric field near 10 mV/m, which approximately corresponds to a current density of1 µ A/cm2 in a biological

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OVERVIEW OF EXPERIMENTAL FINDINGS

tissue.

Liburdy (1992) designed a special dish with concentric sections, which was placed in a solenoid. The sections enabled a passage through a cell culture (rat thymocytes) ofa 60-Hz AC electric current equal to the one that was induced by a 60-Hz, 22-mT

MF in a solenoid. In both cases, the electric field in the cell had the same geometry and was 62–170 mV/m. Correspondingly, the current density for the observed electrical conductivity σ = 1 . 685 S/m was 10–30 µ A/cm2.

The field value correlated with the value ofthe effect, i.e., with the intracellular calcium density, measured spectrophotometrically in real time. In these assays the AC electric field with any exposure form increased, in 10–15 min, the calcium density by 20–30 % as compared with controls. Thereby, the AC MF per se seemed to be immaterial. Using various biochemical techniques, the author also established the probable target for the action of a field, namely the calcium membrane channel.

It was maintained in the paper that the GMF component parallel to the solenoid axis was 20.5 µ T, which generally speaking does not exclude ion interference mechanisms for the action of an electric field.

Nazar et al. (1996) found a frequency selectivity in the action of a sine electric field on the specific activity ofthe enolase enzyme in a E. coli cell culture. The cells were exposed to an electric field ofamplitude 65.4 V/m. The frequency interval was 10–72 Hz. The effect, i.e., the difference ofexposed and control activities divided by the control value, is shown in Fig. 2.44. It is seen that as the electric field frequency was varied, the effect changed not only its value but also its sign. Local MF parameters, it seems, were not controlled. The picture obtained is characteristic for MBE

frequency spectra in low-frequency EMFs, although the authors only determined the statistical confidence ofthe effect at a frequency of60 Hz. The mean frequency step and data dispersion were relatively large; therefore no reliable conclusions could be made. However, it is interesting to note a similarity ofthe data in Fig. 2.44 and the MBE frequency spectrum, also for E. coli, from Alipov and Belyaev (1996), see also Fig. 4.32. Such a similarity also points to a similar physical nature ofthe above biological effects ofelectric and magnetic fields.

Cho et al. (1996) studied, using a fluorescent video-microscope, the reorganization ofcytoskeleton threads as an electric current was passed through a cell culture of Hep3B human hepatoma. The electric field parameters varied within a frequency range of0–60 Hz, the zero frequency corresponding to the passage ofa DC current, and field amplitudes of0–1 kV/m. The amplitudes were worked out from the measured current and conductivity ofthe cell medium. Only some cells responded when a field was switched on. Figures 2.45 and 2.46 give the results — the relative number ofsensitive cells that responded when a field was on for 15 min. The non-resonance form of the spectrum suggests that underlying the effect is a reaction to a DC field with a characteristic time of0.1 s, oppositely directed fields producing opposite effects. In such a case, the actions ofpositive and negative half-waves ofa sine signal with a frequency of > 10 Hz largely compensate for each other.

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EFFECTS OF LOW-FREQUENCY ELECTRIC FIELDS

103


(SHDN 9P


QRODVHDFWLYLW\UHOXQLWV(


I+]

Figure 2.44. The relative activity of enolase in E. coli at various electric field frequencies, according to Nazar et al. (1996).


IUDFWLRQRIFHOOV

FRQWURO


I+]

Figure 2.45. The relative number of human hepatoma cells that respond by restructuring their cytoskeleton to a 500 V/m EF depending on the frequency. According to Cho et al. (1996).

It is seen that an effect occurs already in a weak electric field (about 1 V/m), and it does not possess an amplitude selectivity. Underlying such effects, which are characterized by the absence offrequency–amplitude windows, could be activation-type mechanisms as described in Section 3.4.

The glycolysis rate in mouse brain exposed to an electric field of50–1500V/m was measured by Huang et al. (1997). A cell culture in a flat dish was located between capacitor planes separated by 1 cm. When the negative electrode was at the top, the glycolysis rate was about 20 % larger at 1000 V/m. A polarity change reversed the effect sign, but its magnitude was much smaller, about 4 %. It is of interest that the effect magnitude varied with the field voltage in a non-trivial

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OVERVIEW OF EXPERIMENTAL FINDINGS


IUDFWLRQRIFHOOV


FRQWUROOHYHO


(9P

Figure 2.46. The relative number of human hepatoma cells that respond by restructuring their cytoskeleton to a 1-Hz EF depending on the amplitude. According to Cho et al. (1996).


DWHRIJO\FRO\VLV5


9ROWDJH9

Figure 2.47. The glycolysis rate in mouse brain upon a 30-min exposure to an electric field of a given value, in percent to controls at U = 0 V, according to Huang et al. (1997).

manner, Fig. 2.47.

Considering that the cell culture with a permittivity of > 50 and the dish bottom with a permittivity of 5 took up 1 mm each (the cell size was about 0.01 mm), the authors worked out that the cells were subjected to a field of 30 mV/m, when a voltage of15 V was applied. Even such a relatively small electric field is able to cause a biological effect with a complicated voltage dependence. The authors believe that a static electric field can affect the orientation ofan electrically charged protein ofNa+,K+-ATPase in a cellular membrane, and hence it can affect the extracellular K+ density. The asymmetry ofthe response upon field polarity changes can be caused by cells being primarily oriented either in a gravitational or in an uncontrolled local magnetic field.

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105


FRQWURO


H[SRVXUH

@FKDQJHUHOXQLWV L


>&D


(9P

Figure 2.48. Intracellular calciumdensity in an osteoblast culture in mice upon exposure to a 10-Hz EF of various amplitudes. According to Tang et al. (1998).

Sontag (1998) used plane electrodes inside or outside to apply to a medium with HL-60 cells a low-frequency electric field with an amplitude range of 1–4000 V/m and a frequency range of 0.1–100 Hz. After a 15-min exposure to such fields, measurements ofthe intracellular content offree calcium ions using a fluorescent spectrometer yielded no results. The GMF component normal to an electric field was 12 µ T; no reference was made to the other component. Effective exposure to a current of250 µ A/cm2 at a frequency of 4 kHz in an amplitude window that was about 200 µ A/cm2 wide was found later (Sontag, 2000) in measurements of interleukin release from cells. Here they used 0–125 Hz low-frequency modulation of the current.

Tang et al. (1998) studied the proliferation of osteoblast cells in mice. Cells subjected to a 10-Hz, 20-V/m electric field for 20 min would grow 60 % faster than controls. Also measured using the fluorescent method was the intracellular calcium density, while exposing the cells to rectangular electric field pulses by the scheme e(20 1000 V / m) f (1 1000) .

Frequency and amplitude windows were also found. A maximum effect was found in the range 5–15 Hz. The amplitude spectrum is shown in Fig. 2.48; it has a maximum effect at 500 V/m.

2.6.2 Frequency–amplitude windows

We can identify in the above experiments two groups by the manner in which an electric field is applied. In the first case, a system under study is placed between a capacitor’s plates, without any direct electric contact. In the second case, a current is passed using electrodes introduced into the biological medium. In both cases effectiveness windows for parameters of an electric field are observed.

Data for the first group are summarized in Table 2.2. In all experiments there are only several experimental points, which are hard to associate with any smooth

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OVERVIEW OF EXPERIMENTAL FINDINGS

Table 2.2. Experiments with an externally applied EF

Medium

f , Hz

E, V/m

Effect

Brain tissue enriched in 3–24

10–60

15 % Ca discharge

45Ca

(Bawin and Adey, 1976)

Bone cell culture

12–20

430

+50 % cell proliferation

(Fitzsimmons et al. , 1989)

E. coli cell culture

10–70

65

20 % special activity ofenolase

(Nazar et al. , 1996)

Osteoblastic

cells

in 5–15

500

> 50 % proliferation and con-

mice

centration [Ca2+] i (Tang et al. ,

1998)

curve. However, a general conclusion is possible that effective electric fields approximately feature the following intervals: 10–100 Hz in frequency, and 10–100 V/m in amplitude.

In the second group ofexperiments, the observable was the current passed through a physiological medium containing cells to be studied. In that case, the internal electric field can be worked out knowing the medium conductivity. The findings are summarized in Table 2.3. It follows from the table that the expected effectiveness ranges in such experiments are 10–100 Hz and 1–10 µ A/cm2.

Expected frequency effectiveness windows of 10–100 Hz are the same for both groups of experiments. Larmor and cyclotron frequencies are fundamental for any EMF biological reception mechanism involving ions. These frequencies fall precisely into the interval for most of the biologically important ions exposed to an MF similar to the geomagnetic field.

A note on amplitude windows is in order. In the first group ofexperiments the mean electric field within a medium falls off approximately by two orders of magnitude as compared with the external field owing to the polarization ofwater with ε ∼ 80. The effective dielectric permittivity ofthe medium can grow further several fold because ofthe special properties ofa double electric layer surrounding the charged surface of the cellular membrane (Chew, 1984). This means that effective internal electric fields in a medium are at least about 100–1000 mV/m and are perhaps yet smaller.

In the second group of experiments, the internal EF can be found from the relationship E = j/σ, where j is the current density in a medium and σ is the medium conductivity. For biological tissues σ ≈ 1 S/m. It follows that the effective field range corresponds to the interval 5–500 mV/m. There is thus an approximate coincidence also ofamplitude windows in both groups. A question emerges as to whether the above windows are physically equivalent when an EF is applied to

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107

Table 2.3. Experiments involving the passage of a current

Medium

f , Hz

J , µ A/cm2 Effect

Fibroblasts in collagen 1–10

> 1

30 % DNA synthesis

medium

(McLeod et al. , 1987b)

Substrate-enzyme sus- 20–1000

> 70

15 % Na,K-ATPase activity

pension

(Blank and Soo, 1990)

HL-60 cell culture

60

0.3–3

+30 % transcription level

(Blank et al. , 1992)

Rat thymocytes

60

20

+25 % [Ca2+] i density

(Liburdy, 1992)

Fibroblasts in collagen 10–100

5–7

+60 % DNA synthesis

medium

(Goldman and Pollack, 1996)

HL-60 cell culture

0-100

200–400

+100 % interleukin release

(mod)

(Sontag, 2000)

a medium in various ways. In any case, there are no grounds to maintain that the physical mechanisms underpinning the biological effects in the two groups are different. It is shown in Sections 4.6 and 4.9.6 that quantum interference of ions is capable ofaccounting for the biological effectiveness ofweak EFs, irrespective of the way it was transported to a microlevel.

Some other experiments on DNA–RNA synthesis, enzyme activity, cell proliferation, and calcium transport, which reveal window spectra ofeffective electromagnetic exposure, are provided in a concise overview by Berg (1995). They also point to the existence of an optimal frequency–amplitude regime in a frequency range of 10–100 Hz and field amplitudes of10–100 mV/m.

2.7 BIOLOGICAL EFFECTS OF HYPERWEAK FIELDS

A body ofexperimental evidence is gradually taking shape that testifies to biological activity ofhyperweak MFs, 1 µ T. There are no data so far on the dependence ofthese effects on the level ofa DC MF at experiment site. The mean intensity of an AC MF in those observations being much lower than the possible level ofa DC

field, it makes sense to class such experiments in a separate group. Mechanisms for biological effectiveness of hyperweak fields seem to be different from those for the action offields at the geomagnetic level.

Earlier experimental evidence for the biological detection of hyperweak variable signals, both magnetic, up to 1 nT, and electric, up to 0.1 mV/m, are given by Presman (1970). Sensitivity ofsea sharks and rays to fields ofup to 0.5 µ V/m was discussed by Bastian (1994).

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OVERVIEW OF EXPERIMENTAL FINDINGS

Changes in peroxidase activity in leukocytes ofperipheral blood in rabbits upon a 3-h exposure to hyperweak MFs of8 Hz were observed by Vladimirskii et al.

(1971). In those experiments MF strengths were 0.02, 0.2, 1, and 2 nT. At all of those field values they observed changes in cytochemical activity ofneutrophiles as compared with controls. The changes varied from about 9 ± 2 % at 0.02 nT to 72 ± 23 % at 2 nT. The authors believe that this could bear witness to living systems being directly affected by geomagnetic storms.

Keeton et al. (1974) reported that natural GMF fluctuations ( 100 nT) influence orientation in pigeons.

Delgado et al. (1982) studied changes in morphological parameters ofchicken embryo growth upon a 48-h exposure to pulsed MFs. The body ofevidence is insufficient to construct amplitude or frequency spectra, however a statistically significant effectiveness ofregimes 0.12 µ T 100 Hz and 1000 Hz is shown.

Rea et al. (1991) reported that 16 humans they had studied showed a sufficient sensitivity to an EMF to sense the switching on ofan MF. Volunteers were exposed to an inhomogeneous MF, which varied from 2.9 µ T in the region oftheir feet to 0.35 µ T near their knees, and to 70 nT near their heads.

The influence ofa 0.05–5 Hz, 100-nT sine-wave field on the pulsed activity of neurons in a mouse cerebellum section was observed by Agadzhanyan and Vlasova (1992). The assays were conducted in a chamber shielded from external magnetic interferences.

Jacobson (1994) used variable MFs as small as 5 to 25 pT to treat epilepsy and Parkinson disease cases. A sinusoidal field of2–7 Hz was applied to the brain so that to affect the epiphysis. MF stimulation was correlated with melatonin production.

Kato et al. (1994) determined the action ofa circularly polarized 50-Hz, 1- µ T

MF on the level ofnocturnal melatonin density in mouse blood. Controls were animals placed in a similar exposure chamber with a residual field of < 0 . 02 µ T. By the end ofa 6-week exposure in both chambers melatonin density was in controls 81 . 3 ± 4 . 0 pg/ml, and in exposed groups 64 . 7 ± 4 . 2 pg/ml. That difference vanished when measurements were made a week after the exposure. Obviously, division into control and exposed groups here is fairly conditional, since exposure in fields of such a low intensity is in itselfnot indifferent to animals. In any case, however, the studies have demonstrated the effectiveness offields at a level of1 µ T.

Works by Novikov (1996) and Fesenko et al. (1997) are devoted to investigations into the molecular polycondensation reaction ofsome amino acids in solutions exposed to a variable MF ofabout 20 nT parallel to a local DC MF ofabout the geomagnetic field. The MF had a frequency of several hertz, which corresponded to cyclotron frequencies of amino acid molecules. Unfortunately, the authors did not report how they determined cyclotron frequencies of amino acid molecules. That is important since the electric charge ofthose molecules in solution is dependent on its acidity. At the same time, the very fact of MF being effective at such a low level was shown quite convincingly. There is no evidence so far on the confirmation of those assays in independent laboratories.

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109


I +]

&RQWURO


0%(UHOXQLWV


+ µ7

$&

Figure 2.49. The activity of membrane ion pump in a hyperweak variable MF, according to Blank and Soo (1996).

Blank and Soo (1996) determined the sensitivity limit for the activity of Na,K,-

ATPase enzyme in a medium with microsomes in relation to power–frequency MFs.

The sensitivity level was 200–300 nT, Fig. 2.49.

West et al. (1996) found that when a JB6 cell culture of mouse epidermis was exposed for several days to a 60-Hz, 1- µ T MF against the background ofa static laboratory MF, the number ofcells grew by a factor of1.2–2.4 as compared with controls.

Akerstedt et al. (1997) studied the effect ofnocturnal exposure to a 50-Hz, 1-µ T MF on various physiological characteristics ofhuman sleep (with 18 volunteers).

They found that such an MF drastically curtailed the so-called slow sleep phase.

Harland and Liburdy (1997) found that a 60-Hz, 1.7- µ T (and even 0.28 µ T) MF

b(1 . 7) b stray( < 0 . 06) B( < 0 . 3) B p( < 0 . 3) f (60) suppresses the inhibitory action ofmelatonin and tamoxifen. Melatonin at a physiological concentration 10 9 M and tamoxifen at a pharmacological concentration 10 7 M were used to inhibit the growth ofMCF-7 cancer cells in humans. The evidence was ofimportance since it pointed to a potential hazard ofeven very weak fields, and so the research was reproduced in another laboratory by other workers, see Blackman et al. (2001). In both cases, the results appeared to be the same, with inhibitory effects declining in a statistically significant manner by tens ofpercent.

Some experimental works were performed by various groups using the Tecno AO

device, Tecnosphere, France, reg. PCT/FR93/00546 (Hyland et al. , 1999). When the device is located close to an object under study (chicken embryos, human volunteers), the harmful influence of videomonitors and mobile phones is more or less compensated for (Youbicier-Simo et al. , 1998). The device is essentially a metal vessel filled with an aqueous solution. The nature ofthe active agent is still unknown.

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OVERVIEW OF EXPERIMENTAL FINDINGS

The most obvious approach is to link it to the hyperweak magnetic field reemitted by the aqueous solution.

In some works, biological effects of microwaves ofvery small intensity

were

observed:

10 2 µ W/cm2

(Aarholt et al. ,

1988),

5 · 10 6 µ W/cm2

(Grundler and Kaiser, 1992), and 10 12 µ W/cm2 (Belyaev et al. , 1996).

Kuznetsov et al. (1997) exposed a S. cerevisiae yeast culture to the action of 7.1-mm microwaves within a wide range ofpowers. There was a response that consisted in the emergence in a synchronous cell culture ofa proliferation process, such that the temporal dependence ofthe density looked like a step function. Such a response occurred some time t after the beginning of the exposure, and that time depended on the microwave power. The measured dependence was close to a linear one (from power logarithm) within t = 5 min at 1 mW/cm2 and t = 240

min at 10 12 µ W/cm2. It is interesting to note that the value 10 10–10 11 µ W/cm2

corresponds to a sensitivity threshold ofsight and hearing receptors.

The physical nature ofbiological effects ofweak variable MFs (about the geomagnetic one) remains unclear. Therefore, experimental data on biological reception ofMFs that are 3–10 orders ofmagnitude weaker look, ofcourse, quite challenging.

The body ofthat evidence is not large so far, but knowledge is being gleaned.

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THEORETICAL MODELS OF MBE

With such quantitative scantiness we must

resign ourselves to the fact that our Pegasus is

piebald, that not everything about a bad writer

is bad, and not all about a good one good.

V. Nabokov, The Gift

How can a weak, under 1 G, low-frequency magnetic field cause a biological response? The question has no straightforward answer. The magnetobiological effect is conditioned by processes occurring at different levels ofthe organization ofa living system, from physical ones to complicated adaptational biological ones (Kholodov and Lebedeva, 1992). Workers in various fields come up with their own answers. Human health workers single out, in humans, organs and general physiological processes that are sensitive to magnetic fields. Biologists attempt to reveal cellular and subcellular structures that form biological responses to the action of a field. Biochemists search for targets — links of biochemical reactions — whose rates are dependent on the parameters ofan MF. (Bio)physicists try to isolate magnetosensitive processes in the interaction ofa magnetic field with relatively simple molecular structures. It is at that level that occur involved spectral or “window”

conditions ofthe correlation ofbiophysical processes with biotropic parameters of an MF.

This chapter takes a critical look at the hypotheses and models (including some author’s work) ofthe biological reception of weak magnetic fields. A review of possible mechanisms ofthe magnetoreception ofstrong MFs, from fractions ofTesla and beyond, has been made by Piruzyan and Kuznetsov (1983).

3.1 THEORETICAL STUDIES IN MAGNETORECEPTION

It would perhaps be a good idea to begin an overview ofmagnetoreception theory with the identification ofgroups ofsimilar accounts ofmagnetobiological effects.

Such groups do exist, and they lead to some conditional classifications ofmodels in magnetobiology. So, Polk (1991), Adey (1993), and Berg and Zhang (1993) came up with their MBE classification. The fact that such classifications are in existence and that they are ambiguous and date quickly attests to the difficulties in the accounting for magnetobiological effects, to their paradoxical nature, and to the 111

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dearth ofknowledge ofthe nature ofthe biological activity ofweak electromagnetic fields.

The above reviews could be complemented with those ofgroups ofphysical processes and ideas (Binhi, 1999a, 2001) that are assumed to underlie magnetoreception. In so doing, we will have to class them as phenomenological, macroscopic, and microscopic. Phenomenological descriptions are not concerned with the nature ofan event; they only offer mathematical toolkits to handle external manifestations ofan object. In contrast, macro- and microscopic accounts are attempts at gaining insights into the physical nature ofan object; they establish limitations on the validity ofspecific phenomenological models. They differ in the scale ofobjects under consideration.

There is also a group oftheoretical treatments that could be described using the following general terms. The thesis that A does exist as a physical event lends itselfto a relatively easy proof. Suffice it to provide an experimental support ofits existence under any feasible conditions. In contrast, the opposite thesis that A as a physical event does not exist is more difficult to prove. To this end, the validity ofthe thesis will have to be proven under all feasible conditions. More often than not, all the feasible conditions are impossible to identify. It is exactly the case with the biological reception ofweak MFs. Substantiating the thesis is a matter ofpractical scientific work. Within the framework ofpositivistic conceptions, the whole body ofexperimental evidence has falsified the thesis that there is no MBE.

There is no denying the existence ofthe phenomenon either experimentally or logically. In the latter case, ifwe set out to identify the conditions, i.e., the possible mechanisms ofthe action ofan MF, we will never exhaust the possibilities. There will always remain a possibility that we have overlooked some special cases. Nevertheless, despite the intrinsic logical inconsistency ofany attempts to theoretically refute the very existence of MBE, such attempts do occur. Some works (e.g., Adair, 1991, 1992), and also Bioelectromagnetics, 19, 136, 19,181, 1998, contain physical models ofthe hypothetical processes underlying the MBE that are proposed in the literature. However, since they are refuting in nature, the models contain no productive element and are devoid ofany predictive power. The substance ofthose works cannot be tested; therefore we will overlook those models in our reasoning.

3.1.1 Classification of MBE models

In a way, the classification bellow is conventional, and the selection ofspecific works included into a group is fairly arbitrary — it is not always possible to unambiguously refer a work to this or that group. This author does not claim to provide a complete treatment, and does not maintain that the models considered are better or worse than other members ofa group. At the same time, such a division appears to be handy, enabling one to consider not some specific ideas, mechanisms, and models, but rather their types. The classification does not cover the mechanisms ofthe biological action ofstrong MFs. A review ofconcepts, such as diamagnetic orientation, liquid-crystal effects, the redistribution ofmolecules in an inhomogeneous MF, and

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magnetohydrodynamic effects, is available, for instance, in Kuznetsov and Vanag (1987); a review ofrelevant experiments is available in the book by Simon (1992).

In what follows we will only focus on a priori probable origins ofthe MBE — the biological effects ofweak MFs.

3.1.1.1 Phenomenological models

— Complicated behavior ofthe solutions to chemical-kinetics-type equations (Grundler et al. , 1992; Kaiser, 1996; Galvanovskis and Sandblom, 1998).

Stochastic resonance as an amplifying

mechanism in

magnetobiology

and other random processes (Makeev, 1993; Kruglikov and Dertinger, 1994; Bezrukov and Vodyanoy, 1997a).

— Magnetosensitive phase transitions in biophysical systems viewed as liquid crystals (Simonov et al. , 1986) or ordered membrane proteins (Thompson et al. , 2000).

— “Radiotechnical” models, in which biological microstructures and tissues are presented as equivalent electric circuits (Jungerman and Rosenblum, 1980; Pilla et al. , 1994; Astumian et al. , 1995; Barnes, 1998).

3.1.1.2 Macroscopic models

Biomagnetite

in

a

magnetic

field

and

ferromagnetic

contamination

(Kirschvink et al. , 1985; Kobayashi et al. , 1995).

— Joule heat and eddy currents induced by variable MFs (Chiabrera et al. , 1984, 1985; Polk, 1986).

— Superconductivity at the level ofcellular structures (Cope, 1973, 1981; Achimowicz et al. , 1979; Achimowicz, 1982; Costato et al. , 1996) and alpha-spiral protein molecules (Davydov, 1994).

— Magnetohydrodynamics, see the overview Kuznetsov and Vanag (1987).

— Ion macroclusters, charged vortices in cytoplasm (Novikov and Karnaukhov, 1997).

3.1.1.3 Microscopic models

— The motion ofcharged and spin particles in a magnetic field, including resonance effects (Chiabrera et al. , 1985; Liboff et al. , 1987a; Lednev, 1991; Binhi, 1995b); oscillatory effects (Chiabrera et al. , 1991; Belyaev et al. , 1994; Lednev, 1996; Zhadin, 1996); interference effects (Binhi, 1997b, 1998a, 1999b, 2000); free-radical reactions (Buchachenko et al. , 1978; Steiner and Ulrich, 1989; Brocklehurst and McLauchlan, 1996); and collective excitations ofmanyparticle systems (Fröhlich, 1968b; Davydov, 1984b; Wu, 1996).

— Biologically active metastable states ofliquid water that are sensitive to variations ofan MF (Kislovsky, 1971; Binhi, 1992; Fesenko et al. , 1995; Binhi, 1998b).

— Biological effects offields that are assumed to be connected with an MF and with a modified geometry ofspace (Akimov et al. , 1997; Shipov, 1998).

These papers vary strongly in the depth oftreatment. Only some ofthem have been brought up to the level ofmathematical models f

eaturing some predictive

potential. A theoretical account seems to be ofany value only when it admits a numerical correlation with experimental data. It is important here to be able to compare, not numbers, but functions. That is, the theory must be able to compute

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the amount ofthe effect depending on MF parameters. That is why mechanisms that do not meet this requirement — and there are many ofthem — are not considered in some detail, but are just mentioned. It makes no sense to criticize such mechanisms, because it is impossible in principle to compare theory with experiment, a major yardstick ofthe validity ofany scientific judgment.

The MBE macromodels form a more or less independent group. By contrast, phenomenological models need a microscopic substantiation. So, the models that are built around some special solutions to chemical-kinetics equations need a clarification as to what chemical reaction has its rate dependent on the MF and in what manner. When considering a stochastic resonance one should be specific as to what physical object is involved. Models with magnetosensitive phase transitions require that objects interacting with an MF be specified. In the general case, such objects are microparticles that have a charge or a spin. Anyway, all the non-macroscopic mechanisms rely on some special dynamics ofparticles in an MF. Dynamics, both classical and quantum, is sort ofunderlying any theoretical treatment ofthe MBE, especially where the MBE is paradoxical in nature.

The body ofevidence on the dynamics ofparticles in a magnetic field to account for the MBE is fairly large. Virtually all of the mechanisms proposed have been realized as models. It would therefore be advisable to classify models within that group by their dynamics type, whether classical or quantum, and by the type of the quantity that varies as the particles interact with an MF. Such a classification is quite objective, and thus convenient to compare the model types.

Before we embark on this classification, we will note the nontrivial similarities and differences in the behavior ofsingle- and multiparticle systems. Virtually all the objects one encounters in physics are multiparticle systems. However, it is often possible to isolate more or less independent particles whose motion is determined by the combined action ofall the other particles. These latter sort ofproduce an effective potential for the motion of an isolated particle. In that case, single-particle models are capable offeaturing the main properties ofthe isolated system. Such is, for instance, the atomic model in which each of the electrons can be satisfacto-rily described by the joint potential ofthe nucleus and the cloud ofthe remaining electrons. Another example is the rotation ofa molecule in gaseous phase. Single-particle models properly describe many physical systems. They are singularly convenient and graphic, although not always correct.

However the motion ofseveral particles is, as a rule, analytically intractable. The motion is too involved. In certain cases, where the interparticle coupling causes structures that are more or less symmetrical at equilibrium to be formed, it is possible to determine the generalized coordinates ofa multiparticle system, their number being proportional to the number ofthe particles. The system’s motion can then be represented as a superposition ofindependent motions along those coordinates. The vibrational spectra ofsymmetrical molecules, for instance, can be studied analytically using group theory, ifthe number ofatoms is about ten or less.

As the particles grow in number and ifthey interact fairly strongly, there occur collective cooperative motions ofparticles, the so-called collective excitations or

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Table 3.1. MBE models with particle-magnetic field interaction Dynamics

Classical

Quantum

Variable

coordinate

Lorentz force

Interference of quantum states

particle deviation

(Binhi,

1997b,c,

1998a,

1999b;

(Antonchenko et al. , 1991),

Binhi and Goldman,

2000;

Binhi,

oscillation polarization

2000; Binhi et al. , 2001)

(Edmonds, 1993)

momentum,

Energy pumping

Quantum transitions

angular

cyclotron resonance (Liboff,

at Zeeman and Stark sublevels

momentum,

1985; Zhadin and Fesenko,

(Chiabrera et al. , 1991),

energy

1990),

parametric resonance (Lednev, 1991;

parametric resonance

Blanchard and Blackman, 1994)

(Chiabrera et al. , 1985; Zhadin,

1996)

spin

Spin dynamics

spin resonance (Binhi, 1996), rad-

ical

(Vanag and Kuznetsov,

1988)

and exchange reactions (Binhi, 1992,

1995b, 1998b), spin-dependent quan-

tum interference (Binhi, 1997b)

dynamic oscillation modes. Normally, that situation is described in the so-called continuum approximation, where instead ofthe particle coordinates their continuously varying density is introduced. Mathematically, the dynamics ofsuch modes is equivalent with single-particle systems and is, therefore, more convenient and graphic. In the classic case, the dynamic variable is the amplitude ofthe collective excitation; in the quantum case, it is the number ofexcitation quanta. Interaction with an MF may result in the pumping ofexcitation energy, which could be a mechanism responsible for the MBE. Original works considered collective excitations, the vibrations ofbiological membranes, and the waves ofrectilinear and torsional shifts in biopolymer molecules (Bohr et al. , 1997). The natural frequencies of such collective excitations, however, fall into the microwave range. There is no evidence for the collective excitations ofbiophysical structures in the range of1–100 Hz that is ofinterest to us, so we will confine ourselves to a summary ofsingle-particle models for the MBE mechanisms, for which natural frequencies on the order of ∼ qH/M c have been found. For particles such as biologically significant ions with mass M and charge q in a field H that is similar to the geomagnetic one, these frequencies fall within the specified range. A summary ofmodels by dynamics groups and variables affected by an MF is given in Table 3.1.

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3.1.2 Overview of MBE mechanisms

We will consider in some detail the magnetoreception mechanisms that are especially popular in the literature. It is assumed that they can form the foundation for the MBE.

Historically, one ofthe early ideas in magnetobiology is concerned with the so-called biogenic magnetite (ofbiomineralization) in a magnetic field. The systems ofsome animals and microorganisms develop in a natural way some microscopic crystals, usually ofmagnetite, which can be magnetized. When exposed to an external magnetic field, the crystals are subjected to a torque and exert a pressure on the surrounding tissues, which causes a biological reaction. This mechanism, which is studied consistently by Kirschvink et al. (1992), seems to take place. Magnetite crystals have been found in the brain of some birds, which are known to possess a striking capability to take their bearings in the geomagnetic field, and also in some insects and bacteria.

The explanation ofthe biological action ofa low-frequency MF on cells in vitro in terms offerromagnetic contaminants (Kobayashi et al. , 1995) is a development ofthe idea ofbiogenic magnetite. The magnetic contaminants are present not only in the ambient dust, but also in plastics and glasses, and in laboratory chemical preparations and water. The average size ofsuch particles is about 10 5 cm; they are ferro- and ferrimagnetic in nature, i.e., they feature spontaneous magnetization.

The authors have shown that routine laboratory procedures ofpouring and rinsing enrich cellular cultures with magnetic particles so that they can outnumber the cells manifold. The energy ofa magnetic particle is around three orders ofmagnitude higher than κT . The authors believe that such a particle, when adsorbed on the cellular surface, may transfer its energy to the neighboring cellular structures, e.g., to mechanically activated ion channels.

These magnetoreception mechanisms are in a class by themselves, and they do not account for the major issue of magnetobiology. After all, unicellular organisms that do not contain magnetite are also able to react to an MF, and depending on the field parameters in many cases the reaction may be complicated non-linear and multipeak in nature. The main task ofmagnetobiology is exactly to account for that phenomenon, which is a paradox in terms ofclassical physics.

Sometimes the biological activity ofweak MFs is explained using the representation ofbiological matter or biophysical structures as equivalent distributed electric circuits. In any case, this approach, being a phenomenological one, gives no answers to the issues ofmagnetobiology. Even the descriptive potential ofsuch an approach is dubious. So, in Biophysics, 38(2), 372, 1993, one finds an explanation of the influence ofa DC MF on the propagation ofthe action potential along a nerve fiber. Ion channels ofbiological membranes were represented as oscillatory circuits with electric solenoids. These microsolenoids produce MFs, when their channels are open, and thus interact with one another and with an external MF. Underlying that representation were, for one thing, the experimental measurements of the natural inductance and capacitance ofbiomembrane areas and, for the other, the

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assumption that an ion in an ion channel moves along a spiral. It was shown in Binhi (1995c), however, that (1) the equivalent inductance only reflects the inertia ofthe ion channels on changing the voltage; (2) the propagation ofan ion along the channel is hardly classical in nature; and (3) the ions in the channel move one after another, and the MF caused by that motion does not correspond by far to the MF caused by the charges moving simultaneously in all the solenoid sections. It is clear that any explanation drawing on the model ofion channels–solenoids is just an illusion ofexplanation.

The hypothesis has been tested many times that a driving force behind the irradiation ofbiological system by a low-frequency MF is the eddy currents induced by an AC MF in biological tissues. The current can bring about the heating of the tissue, see Section 1.4.1. Polk has shown that eddy currents can also cause electrochemical EMF effects owing to a redistribution ofcharges. The current varies with the strength ofthe induced electric field, which is proportional to the product ofthe amplitude and frequency ofthe MF. Ifthe hypothesis holds true, then in experiment the MBE should correlate with the variations ofthat quantity. There are indeed experimental data pointing out that such a correlation occurs as the strength ofthe AC MF grows (Lerchl et al. , 1990; Schimmelpfeng and Dertinger, 1997), but with relatively weak MFs (like the geomagnetic one), no correlation has been revealed (Juutilainen, 1986; Liboff et al. , 1987b; Ross, 1990; Blackman et al. , 1993; Jenrow et al. , 1995; Prato et al. , 1995). Specifically, it was shown in Ross (1990) that within a certain frequency range the MBE remained unchanged as the value ofthe induced currents was changed nearly 40 times. This attests to the existence ofprimary MBE mechanisms that are not connected with the eddy currents.

It is often maintained that the action of weak physico-chemical factors on biological systems is an information action. This suggests that a biosystem is in a state close to the conditions ofan unstable dynamic equilibrium. The system is believed to need some pushing for it to transfer to another state due to some external resources. Put another way, the so-called biological amplification ofa weak MF

signal will occur. To arrive at a phenomenological description ofthe process they use the equation ofchemical kinetics. Under certain conditions, their solutions feature a bifurcation, i.e., when exposed to a weak excitation they may pass into a qualitatively different dynamic condition. Kaiser (1996) discussed that concept in the electromagnetobiological context.

There is one important question. Thermal fluctuations have energy scales that are ten orders ofmagnitude larger than the energy ofthe quantum ofan MF, but they do not destroy the MBE. Why? The answer is generally linked to the idea ofthe coherent action ofan external factor against an incoherent thermal noise background. It is then possible to drive some high-Q oscillator (time coherence) to a state, where its energy will be sufficient to make an initiating push, or to drive synchronously a system ofoscillators (spatial coherence) for it to yield a quantum ofcollective excitation (Fröhlich, 1968a; Popp, 1979). Another answer is that it is not energy but some other oscillator variables, such as oscillation polarization, that

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acquire in an MF some properties that are ofconsequence for the biophysical systems involved. For example, Zhadin and Fesenko (1990) and also Edmonds (1993) discussed the application ofthe Larmor theorem to an ion bound in the calmodulin microcavity. The discussions relied heavily on the fact that the ion oscillation direction was of critical importance for the protein form, which in turn causes the enzyme activity to change. In terms ofclassical dynamics, the variation ofthe oscillation direction in AC MFs ofdifferent configurations was studied. In the context of effects to be expected, the Larmor frequency was found to be effective with perpendicular MFs. No answer was found to the question as to why the parallel configuration ofthe AC and DC fields can change the enzyme activity, but precisely that configuration was found earlier to be the most effective in many experiments.

The oscillators here were various microscopic-level objects, molecular groups, biological membranes, and whole organelles. It is noteworthy that neither the oscillator idea nor the collective excitation idea has led so far to some predictive mechanisms. Wu (1996) has shown that for a biological response to emerge there must be a threshold exposure time and a threshold amplitude ofmicrowave radiation.

A further idea of overcoming a thermal factor appeals to the so-called stochastic resonance. This resonance is basically an amplification ofa small signal against a background caused by energy redistribution in the signal-plus-noise spectrum.

What is essential is that noise here is no hindrance but a useful asset of a system. Under stochastic resonance, relatively weak biological signals can bring about noticeable changes in the behavior ofa dynamic system against the background ofa wide variety ofrelatively strong perturbations. It is shown in Wiesenfeld and Moss (1995) that the response ofmechanoreceptor cells in crayfish to an acoustic stimulus in the form of a subthreshold signal superimposed upon a Gaussian noise could be described in terms ofa stochastic resonance. The phenomenon was used in Makeev (1993) and Kruglikov and Dertinger (1994) to handle the “kT problem”, but real gains, around one hundred, when the signal declines in quality and coherence (McNamara and Wiesenfeld, 1989), are not enough by far to account for the biological activity ofweak low-frequency MFs.

The rate off

ree-radical reactions varies with the strength ofthe DC MF

(Buchachenko et al. , 1978). The probability for a product to be produced from two radicals that have a spin angular momentum is dependent on their total momentum, i.e., on the relative spin aligning. A DC MF affects the probability ofa favorable orientation and is, thereby, able to shift the biochemical balance. At the same time, the mechanism shows no frequency selectivity. The lifetime of a radical couple before the reaction or dissociation, i.e., the time when the radical couple is sensitive to an MF, is about 10 9 s. The couple sees a low-frequency MF as a DC field, and no resonances emerge. Therefore, to give an explanation of the multipeak dependences ofthe MBE on the MF variables Grundler et al. (1992) and Kaiser (1996) made an assumption that the magnetosensitive free-radical reaction is a part of the system described by a set ofnon-linear equations ofchemical kinetics with bifurcations.

The problems ofthis model group are concerned with the primary process ofthe action ofa DC MF on the radical reaction rate. There are some physico-chemical

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factors that limit the MF sensitivity of the rate to within 1 %/mT, which is not enough to account for the bioeffects ofweak AC MFs with an amplitude ofabout 50 µ T and below.

Sometimes weak MFs feature resonance-type effects, with their natural frequencies being close to cyclotron frequencies of the ions Ca2+, Na+, and others. Liboff (1985) assumed that it is the cyclotron resonance that underlies the phenomena observed. Various authors propounded the concept ofsuch a resonance in magnetobiology, but it seems to have received no recognition due to the difficulties ofcorrect physical justification. At the same time, these experiments have demonstrated the significant role played in magnetobiology by ions, especially by Ca2+. It is to be noted that the coincidence of natural frequencies with cyclotron frequencies is no conclusive indication in favor of the cyclotron resonance concept in biology. For instance, any MBE theoretical model based on the electric-charge dynamics will be in terms ofcharacteristic frequencies Ωc = qH/M c. There is no other combination ofthe charge and MF variables that would have frequency dimensions.

To circumvent the hurdles ofthe cyclotron resonance concept assumptions were made ofcharged macrostructures in biological plasma, or vortices formed by ion clusters (Karnaukhov, 1994). Such targets for weak MFs are chosen because they have fairly large energies, which are comparable with κT . Then even a weak MF

can change markedly the energy ofan object that carries, f

or instance, a large

macrocharge. To be sure, that requires a strictly defined condition: the center of mass ofthe object must have an angular momentum (Binhi, 1995b). It is fairly unlikely that such a motion is possible. Moreover, for a comparison of the energy of a vortex with κT to have a meaning, it requires a mechanism to deliver the energy ofa macroscopic vortex to an individual degree offreedom, i.e., to a microscopic object, but to imagine such a mechanism would be fairly difficult. Also unclear is the nature ofthe molecular forces needed to support the existence and stability of such an ion cluster.

Some magnetobiological effects ofa modulated MF display effectiveness bands in the frequency and amplitude ofthe MF. The spectra ofthe variations ofthe MBE with the MF parameters yield much information on the primary magnetoreception mechanisms. The spectra have been described using the mechanisms ofthe transformation of the MF signal in the context of microdynamics, classical and quantum models ofthe coupling ofsome ions by proteins (Chiabrera and Bianco, 1987; Chiabrera et al. , 1991; Lednev, 1991; Zhadin, 1996). The biological activity ofa protein is conditioned by the presence ofa respective ion in a bound state. It was also assumed that some magnetobiological effects are determined by the intensity ofthe transitions in the ion quantum levels, which in turn is affected by an MF. However, the parallel static and low-frequency MFs only act upon the phases ofwave functions, so that they cause no transitions in Zeeman sublevels and do not change the intensities oftransitions due to other factors. The population of each state remains the same irrespective ofthe MF variables. Nevertheless, ifwas found (Lednev, 1991) that some MBE have amplitude spectra similar to those in the parametric resonance effect in atomic spectroscopy (Alexandrov et al. , 1991),

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a science that studies quantum transitions. That all has generated a number of publications (Blanchard and Blackman, 1994; Lednev, 1996; Zhadin, 1996), which, however, have failed to provide any additional support for that similarity. The authors refer to the mechanisms under discussion as ion parametric resonance.

The author has brought in the well-known phenomenon ofthe quantum state interference to gain an insight into the physical nature of the magnetoreception found in Binhi (1997b,c). As an MF is varied in magnitude with the orientation being unchanged, it only changes the phases ofthe wave functions ofa charged particle. It is the interference that relates the variations in the wave function phases with the physical observables. The interference of quantum states is observed in physical measurements either for free particles, including heavy ones such as atoms, or for bound particles. In the latter case, the interference of particle states is only observed from the characteristics of the re-emitted electromagnetic field. This reduces the particles whose interference could be observed to atomic electrons. We made an original assumption that the interference ofstates ofheavy bound particles, ions, can also be observed, using circumstantial nonphysical measurements on natural active biophysical structures. The assumption is in good agreement with experiment (Binhi, 1997b, 1998a, 1999b). The interference of bound ions can be regarded as a previously unknown physical effect, which is in principle only to be registered by biochemical or biological means. The phenomenon ofinterference ofquantum states, which is well known in atomic spectroscopy, is concerned with coherent quantum transitions in the atom and is independent ofthe inner structure ofthe electron wave function. At the same time, it is this inner structure of the ion wave function that defines the effect of the ion interference in the protein cavity subject to a variable MF in the absence ofquantum transitions. Currently, the ion interference mechanism predicts, see Chapter 4, the following multipeak biological effects:

strength/orientation-modulated MF

magnetic vacuum

DC MF with natural rotations ofion–protein complexes taken into account

pulsed MFs against the background ofa parallel DC MF

MF in the range ofNMR frequencies with spin degrees offreedom ofion isotopes taken into account

AC–DC MFs with the interference ofthe states ofa molecular group with a fixed rotation axis (interfering molecular gyroscope) taken into account

weak variable electric fields

shifts ofspectral peaks ofthe MBE under the rotation ofbiological specimens.

The biological effects accountable in terms ofthe interference mechanism have been observed in various experiments. The formulas yield the variation of the probability ofthe dissociation ofthe ion–protein complex with the MF characteristics, the frequency of the variable components, the values and mutual orientation of the DC, and variable components. The spectra characteristics and the positions ofthe peaks are dependent on the masses, charges, and magnetic moments ofthe ions

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involved. Most studies have revealed that the relevant ions are those ofcalcium, magnesium, zinc, and hydrogen, and sometimes ofpotassium.

Many authors connect the biological action ofan MF with changes in water states (Kislovsky, 1971; Binhi, 1992; Fesenko et al. , 1995; Konyukhov et al. , 1995).

The states change owing to an action ofexternal fields on the water and the change is passed on further to the biological level as the water gets involved in various metabolic reactions. It is not clear so far what in the liquid water can be a target for the action of an MF. It was assumed (Kislovsky, 1971) that some calcium ions in the water form hexaaquacomplexes [Ca(H2O)6]2+ with octahedral coordination ofwater molecules, in relation to oxygen atoms. The complexes in turn form closed o

pentagon dodecahedrons with cavities, whose size (4.9–5.2 A) is about the size of the complexes. That sort ofprovides a relative stability ofthe structures. An MF shifts an equilibrium so that more free calcium gets bound into complexes to influence the biological signalization. Fesenko et al. (1995) used the results ofthe studies oflow-frequency spectra of water electric conductivity to look into stable water-molecular associates that possess a memory ofelectromagnetic exposure.

Stable structural changes in the water were observed in Lobyshev et al. (1995) based on the luminescence spectra. The changes were associated with the presence in the water ofall sorts ofdefects with specific centers ofirradiation.

Changes in the biological activity ofthe water under the action ofa DC MF

were found in Rai et al. (1994) and Pandey et al. (1996). The radiation ofa household TV set also changed the biological activity ofthe water (Akimov et al. , 1998).

When a physiological solution was preliminarily exposed for several minutes to a DC MF ofseveral microteslas and nerve cells were then kept in it, the cells’ physiological parameters changed (Ayrapetyan et al. , 1994). In Binhi (1992) nuclear spins ofprotons in the water were considered as primary targets ofan MF, and the metastability was associated with orbital current states ofprotons in the hexagonal water-molecule rings and deviations from normal stoichiometric composition of the water. The existence ofsuch states is testable in relatively simple experiments (Binhi, 1998b). Memory effects ofthe water exposed to an MF were observed in Sinitsyn et al. (1998) from radio-frequency spectra. They were associated with oscillations ofhexagonal water-molecular ring associates. There is no consensus yet as to the nature ofthe memory carriers in the liquid water and their interaction with an MF.

There is an evidence, both experimental and theoretical, that warrants the hypothesis that there exist long-range fields ofthe changed space geometry. The scientific endeavor to geometrize physical fields is with us since the last century.

The common element ofnovel theories, specifically ofthe theory by Shipov (1998), is fields, which are related with the well-known geometric property ofspace–time by the property oftorsion. Mathematically, they are tensor fields that describe the curvature ofspace and the Ricci torsion, rather than the Cartan torsion, as in standard gravitational field theories. The well-known fundamental fields and their equations emerge here as some limiting cases. We will note that the theory has difficulties (e.g., Rubakov, 2000).

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The presumptive fields do not change the energy ofquantum systems with which they interact; they can only act on the phases ofwave functions. In the process, a charged particle, such as a bound ion in the protein cavity, might react to such a field in a resonance-type manner. Therefore, one possible explanation of biological sensitivity to very weak EM fields might be concerned with the specific changes in space geometry they engender (Akimov et al. , 1997). It should be emphasized that this idea is for today just a hypothesis.

3.2 FUNDAMENTAL LIMIT OF SUSCEPTIBILITY TO EMF

The ever growing body ofmagnetobiological evidence indicates that an MF ofless than 10 µ T can also affect biological processes. These data, shown schematically in Fig. 3.1, are ofgreat interest. They agree with neither ofthe assumed primary mechanisms ofthe biological action ofan MF. This leads to the question ofphysical constraints that stem from the possible fundamental nature of the bioeffects of very weak fields.

The areas denoted by numerals in the figure are the ranges ofthe variables of the following fields: 1, low-frequency EMFs used in most magnetobiological experiments; 2, the EMF ofmagnetic storms, which are known to correlate in time with exacerbations ofcardiovascular disorders; 3, background EMFs that are engendered by a wide variety ofhousehold electric appliances, TV, and computer screens; 4, an MF that causes changes in solutions ofsome amino acids (Novikov and Zhadin, 1994; Fesenko et al. , 1997); 5, MFs supposedly reemitted by the protective device Tecno AO, Tecnosphere, France, patent reg. PCT/FR93/00546, which sort ofmake up at the biological level for the radiation of video monitors and cellular phones (Youbicier-Simo et al. , 1998); 6, an EMF below the QED limit, which causes the biological reaction in a cell culture E. coli (Belyaev et al. , 1996); 7, the sensitivity limit ofthe human eye to an EMF within the optical range; and 8, MFs used in the treatment ofsome diseases (Jacobson, 1991).

The picture also shows theoretical limits concerned with various mechanisms and descriptions ofthe EMF bioeffects. The upper inclined line divides, approximately, the areas ofthermal and nonthermal effects, the lower inclined line, the quantum-electrodynamic (QED) limit. It is natural to describe the EMF in quantum terms below that line. The stepped line — one ofthe well-known thresholds of safe values of the EMF — is given following the version of the American Conference ofIndustrial Hygiene (ACGIH) (Nakagawa, 1997). The kT- and thermal limits are well known. On the left of the dashed vertical line that separates the “paradoxical area” a quantum ofEMF energy is many orders ofmagnitude smaller than the characteristic energy ofthe chemical transformations ∼ κT . Many physicists who do not specialize in magnetobiology believe that such fields are unable to cause any biological reactions. Now such a view appears to be quite superficial, since there is a large body ofexperimental data that ref

ute it. It is seen that virtually all

electromagnetobiology falls into “paradoxical area”.

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N7OLPLW

$&*,+

7KHUPDOHIIHFWV


(+OLPLW


ORJ%*


&ODVVLFDO(0)V

4XDQWXP

HOHFWURG\QDPLFV


ORJI+]

Figure 3.1. Shown are various limits and fields of biological effects of an EMF as a function of two variables, the EMF frequency f and the classical amplitude of its magnetic induction B. Explanation is given in the text.

The thermal limit has been repeatedly derived in fundamental and standard-ization works concerned with safe levels of EMF radiation, see also Section 1.4.1.

The dashed horizontal line in the range ofrelatively high frequencies is defined in relation to the idealization ofplane waves. Below that line one can ignore the influence ofthe electric component ofa plane wave on the dynamics ofa bound particle, see Section 1.4.3.

A couple ofcomments are in order about the quantum-electrodynamical limit.

Interactions ofEMF and matter can be classed by description types, either classical or quantum, both ofthe field and ofthe matter. Most ofproposed primary mechanisms use the classical description ofmatter particles that interact with a classical EMF, a wave field. The mechanisms that describe EMF bioeffects on the basis ofthe quantum description ofion particles in a classical EMF rely on a semiclassical approximation. The validity ofthe classical description ofthe EMF is conditioned by quantum electrodynamics: the population ofthe quantum states of the EMF oscillators must be large enough as compared with unity. This suggests the relationship that relates the frequency and the classical amplitude of the mag-

netic EMF component: H >

c(2 π/c)2 f 2. The lower line in the figure depicts this limit. As is seen for the low-frequency effects, unlike the superweak microwave radiation, it is possible to apply the classical description ofthe EMF using the Maxwell equations. In certain cases, however, we can also speak about low-frequency EMF

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quanta. A semiclassical approximation could be sufficient to describe bioeffects of low-frequency MFs, but the presence of EMF bioeffects in area 6 does not rule out involvement ofQED mechanisms ofmagnetoreception.

The quanta ofthe EMF seem to be related with the natural fundamental limit of the sensitivity to a low-frequency field. As with any receptor of physical nature, the natural limitation on the electromagnetic sensitivity ofbiosystems has to be predetermined by the general laws ofquantum mechanics. All the physical limitations, as proposed to date, are based on a priori assumed primary mechanisms ofreception, rather than on elementary physical principles. It is, therefore, of interest to obtain some estimations ofthe limiting sensitivity, however approximate, proceeding from the general laws ofphysics.

It is worth noting, first ofall, that the formulation ofthe issue ofthe minimum amplitude ofa variable MF registered by a receptor is not correct. The most general description ofthe interaction ofa field and an idealized atom is in terms ofthe quantized EMF and the quantized oscillator. A low-frequency EMF quantum, which has been initially delocalized in an indefinitely large volume, is absorbed by an atom-like microscopic system as the field wave function is being reduced. This increases the number ofexcitation quanta ofthe atom by one. The QED limit shown in Fig. 3.1 determines approximately the boundary ofthe MF value, where the notion ofthe amplitude ofa classical field is no longer valid. In the quantum description, this boundary corresponds to several excitation quanta offield oscillators.

In the general case, the receptor sensitivity can be characterized by an energy flux p, i.e., the number N ofquanta Ω, absorbed by a system during the time t of its coherent interaction with the field:

p = N /T .

However, in the range where the classical description holds well that quantity displays no unique relation to the field amplitude H, thus indicating that that notion is not applicable as a limiting sensitivity. The constraints on the value of p follows from the fundamental relation of quantum mechanics between the variations of a quantum system energy e and the time τ required for that variation to be registered eτ > .

Given N registered quanta, the relation can be written as τ > 1 /N Ω, since e ∼

N Ω. However, in any case the variation registration time cannot exceed the time ofthe coherent interaction ofa field with an atomic system.

For a low-frequency EMF, the time of coherent interaction is basically the lifetime ofthe quantum state T defined by the details ofthe interaction with the thermostat. This gives the inequality T > τ > 1 /N Ω, i.e., T > 1 /N Ω, which, when substituted into the expression for p, gives a simple estimate for the limiting sensitivity

p > /T 2 .

(3.2.1)

The limiting sensitivity to a low-frequency EMF is thus determined by the lifetime ofa quantum state ofthe receptor target. For instance, the spin states ofprotons

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ofliquid water “live” for several seconds. The appropriate limiting sensitivity of p ∼ 10 19 W is close to the sensitivity limit ofphysical measuring instruments at ambient temperature. It is to be recalled that the limit (3.2.1) follows from the fundamental principles alone. The sensitivity of devices, including biophysical targets, is also dependent on the probability oftheir absorbing EMF quanta, and it seems to be markedly less and the limiting sensitivity accordingly markedly greater than (3.2.1).

It is ofprinciple, however, that the probability for EMF quanta to be absorbed is now determined by the specific target structure. The primary principles ofphysics impose virtually no limitations on the limiting sensitivity. The microscopic structure ofa bioreceptor and the time ofits coherent interaction with an EMF control the level ofsensitivity in any special case. It is important that the time ofcoherent interaction may be sufficiently large if the state of the living system is far from a thermal equilibrium.

3.2.1 Noise limits of susceptibility of biostructures to EMF

One ofthe phenomenological approaches to the definition ofthe limiting sensitivity ofbiosystems to an EMF postulates that an EMF biological detector ofwhatever nature can be regarded as an equivalent, in a way, electric circuit or a radiotechnical structure that consists ofresistors and capacitors. That is convenient since the proper electric noise can then be estimated using the Nyquist formula. It is further maintained that the assumed biodetector, which does not possess any prior information on the signal being detected, is only able to record a signal that is no less than its intrinsic noise. It follows that the estimation ofthe sensitivity ofa biological system boils down to the estimation ofthe level ofthe intrinsic noise of a detector.

In the simplest case, a biodetector has assigned to it a complex impedance Z( ω) with an active resistance R = ( Z). The spectral density ofthe random electromotive force (e.m.f.) will then be

( 4 2) ω = 2 κT R .

In this case, the validity conditions for the Nyquist formula are assumed to be met: ω κT , λ c/ω, where λ is the size ofthe detector. It is believed that biological tissues and biophysical structures possess no internal inductive impedances.

Sometimes measurements yield an inductive component due to current retardation caused by electro-chemical processes (Binhi, 1995c). The reactive impedance component is, therefore, determined by the capacitive reactance, which is inversely proportional to the frequency ( Z) = 1 /ωC. The effective frequency range of the detector will then be ω ∼ 2 π/RC. The Nyquist formula gives to that range the average squared noise e.m.f. of the detector 4 2 = 4 πκT /C.

A hypothesis has been repeatedly voiced that the molecular target for an EMF

is ion channels ofbiological membranes. Membranes formed by phospholipids have

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a thickness ofabout d ≈ 5 · 10 7 cm and a permittivity ofabout ε ≈ 10. Since the capacitance ofthe membrane section with a radius ofabout that ofthe ion channel r ≈ 10 7 cm is C ∼ εr 2 / 4 d, the noise e.m.f. divided by the membrane thickness, i.e., the noise electric field in the ion channel, will be


E noise 1

πκT /d ∼ 3 · 10 3 CGS units 100 V/m .

r

It is to be recalled that a field induced by a 50-Hz, 100- µ T AC MF in a specimen ofsize 1 cm near the solenoid axis has an order ofmagnitude of0 . 1 mV/m. It has also been found that biosystems exhibit some response to currents in tissues induced by fields 3–5 mV/m, and so, constraints imposed by noises do not enable a single channel to act as a receptor ofweak electric fields within the framework of

“radiotechnical” representation.

Formally, the inverse proportionality of E noise to the size r ofthe membrane area warrants an assumption that a detector with a relatively larger size could be much more sensitive. There are some indications that such treatments could be linked with the estimation ofthe sensitivity ofa hypothetical detector ofa weak electric field as a large ensemble ofsingle channels or as an isolated cell, see Astumian et al.

(1995).

This topic is approached from another angle by Jungerman and Rosenblum (1980), who supposed that the fact that Lamelibranchia find their bearings in the geomagnetic field is conditioned by an e.m.f. induced in large (the order of the transverse dimension ofa fish) circuits by changes in the magnetic flux through the circuit. Electroreceptors in fishes are highly sensitive (Brawn and Iliinsky, 1984) and could be responsible for the magnetoreception in connection with electroconductive circuits.

According to sources (Jungerman and Rosenblum, 1980), electroreceptors in rays have a resistance of105 ohm. Suppose that the characteristic frequency associated with the ray motion, just as the effective frequency range of the electroreceptor, is about ω = 10 Hz, and the area ofthe conductive circuit is S = 10 cm2. Then, by equating the mean noise and the e.m.f. SωV /c induced by circuit tilts we can easily derive the relationship for the threshold sensitivity to an MF


c

2 κT R

B =

10 µ T .

S

ω

The figure is not at variance with the hypothesis that relates the magnetoreception in those fishes with the magnetic induction and electroreceptors. It also agrees with the experimental data ofKalmijn (1982).

Despite the apparently general nature ofthe estimations they are only applicable to mechanisms concerned with the currents flowing through a detector caused by the additional deterministic e.m.f. of a signal. If the signal modulated, for instance, only the internal resistance ofa detector, there would be no detection. Also conflicting with this scheme are mechanisms in which the signal causes the chemical reaction rate to be changed: that process has no electric analogue. Also, the mechanisms

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that provide amplitude windows in the MF effectiveness cannot be considered in terms ofthis treatment: linear electric circuits, even the most complicated ones, because oftheir linearity, possess selective properties only in relation to frequencies ofsignals, and not to their amplitudes. On the other hand, if ad hoc additional non-linear elements were introduced into equivalent electric structures, it would be impossible to apply the Nyquist formula. The fluctuation–dissipation theorem that underlies the Nyquist formula is limited to systems with a linear response.

We note that the very possibility ofrepresenting a biosystem as an electric circuit needs a justification. Pilla et al. (1994) assumed that a biological tissue can be described by a linear one-dimensional circuit ofelectrically connected single cells, each ofwhich has an equivalent electric circuit ofresistors. Such a circuit will, under certain conditions, overcome the noise limit beginning with fields ofaround 1 mV/m, but, for one thing, the reduction of a biological tissue to a one-dimensional circuit does not carry much weight. On the other hand, effects ofweak electric fields are also observed at the level ofcellular systems where cells are not in direct contact. There is no evidence so far that the calculated limiting sensitivity in this representation would agree not with the number but with experimental curves. Barnes (1998) suggested that neurons, the pyramidal cells from the cortex of the brain, be viewed as some sort ofradiotechnical phased array antennas with amplifiers and filters.

Such arrays would be responsible for the detection of coherent signals induced by low-frequency external fields in neuron dendrites against the background of thermal noise. However, no way oftesting the hypothesis has been proposed yet. There is thus much room for the search for alternative non-linear mechanisms of bioreception ofweak MFs that are not concerned with electric currents.

Ifwe restrict ourselves to the bioeffects ofan MF at the level ofthe geomagnetic field, then the most important in terms off

undamental physics would be

two problems ofequally paradoxical nature: (1) the mechanism or process ofthe transformation of an MF signal into a biochemical response with an energy scale κT that is ten orders ofmagnitude larger than the MF energy quantum and (2) the question as to why thermal fluctuations ofthe same scale κT do not destroy the above transformation process. At first glance, the paradox of the second issue is more apparent, as the “obvious” answer to the first one is to accumulate the energy ofthe MF signal or to amplify it. Appropriately, most effort was devoted to the second issue, the transformation mechanism being chosen almost arbitrarily. However, it is the transformation mechanism that conditions the presence of

“windowed” multipeak spectra observed in experiment, and it is the transformation mechanism that is responsible for the predictive power of a model. That is why so far we have had no predictive model that would solve both problems. At the same time, some predictive models (Binhi, 1997b, 1998a; Binhi and Goldman, 2000; Binhi, 2000; Binhi et al. , 2001) that take care ofthe first problem have made their appearance. That is a significant phase that is characteristic ofthe state ofthe art in magnetobiological theoretical studies. With the models becoming more predictive, we can now work out such an important ecological factor as the bioeffects ofweak MFs.

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Let us now take a closer look at some ofthe commonest MBE mechanisms.

Critique ofsuch works, however unrewarding, seems to be a necessary exercise.

First ofall, we note that there is some terminological confusion. Speaking of

“cyclotron resonance in magnetobiology” authors often imply several models by Liboff, which are different in nature. These models are remembered nearly always, when they find an MBE at a cyclotron frequency Ωc ofan MF. In so doing, they normally overlook the fact that such a combination of ion constants has to do not only with cyclotron resonance but also with a number ofother effects. On the other hand, in the literature “parametric resonance in magnetobiology” is concerned not with a concrete name, but rather with the specific features of mathematical equations, so that it is concerned with a multitude ofmodels, both classical and quantum, with and without potential forces, etc. However, we still will retain that terminology, ifonly because ofthe literature tradition, and we do believe that the reader is going to have no difficulty identifying each of the following models in terms ofthe objective classification proposed above. To begin with, we will consider the phenomenological models, and then we will pass on to macroscopic ones. We will then go on to look at the most promising MBE mechanisms, i.e., microscopic ones.

3.3 CHEMICAL-KINETICS MODELS

The equations ofchemical kinetics are written for concentrations Ci(x , t) ofsubstances that enter into a reaction


Ci = di∇ 2 Ci +

aiCi +

bikCiCk + . . . ,

(3.3.1)

∂t

i

ik

where 2 is the Laplacian, di are the diffusion coefficients for molecules or other objects ofa given kind, and a, b, . . . are the coefficients determined by reaction rates, and hence by external parameters. In the general case, the coefficients may also depend on coordinates, thus representing sources and drains ofreagents.

Even when we ignore the spatial distribution ofreagents, the above relations, especially for biochemical systems, are complicated non-linear sets of differential equations. Such sets often offer a wide variety of solutions, oscillatory ones included, depending on the variable values and the initial conditions. The phase snapshot of such sets can include several areas of“attraction” ofa dynamic point. When it gets into one such area, a system undergoes in it oscillatory movements, i.e., it resides in a dynamic equilibrium, or it seeks a stable static equilibrium. Ifnot exposed to some external controlling actions on their parameters or variables, such systems, dubbed polystable ones, are unable to transfer into other stability regions. If a system is in a stable area close to an unstable one, i.e., it lies between the stability areas, then even minute controlling or noise perturbations are capable of“switching” a system over from one dynamic condition to another. The situation is known as bifurcation.

Provided that ∂Ci/∂t = 0, i.e., under stationary conditions, some solutions (3.3.1) are so-called dissipative structures. Those are inhomogeneous distributions

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\


Figure 3.2. The bifurcation in the change of the stability of the Van der Pole oscillator with the frequency of the exciting force.

ofreagent densities that occur when there are energy or mass flows through systems, which in this case are open systems. The existence ofdissipative structures, some sort ofpatterns or spatial structures, is also controlled by a combination of parameters and can undergo some bifurcations as parameters are varied.

By way ofexample, Fig. 3.2 depicts the variation ofthe coordinates ofthe Van der Pole oscillator excited by an external harmonic force

y − (1 − y 2) y + y = 10 sin(Ω t) with the excitation frequency, which was varying smoothly in time. It is seen that there emerge qualitatively different dynamic conditions with a two-frequency spectrum at a certain value ofthe frequency.

At present a wide variety ofapplications are known for the above and similar equations describing different processes, not necessarily chemical ones. Their overview is available, for example, in the book by Prigogine (1980).

When dealing with magnetobiology, most authors rely on the assumption that an EMF is able to cause a change in the rate ofone or several biochemical reactions that constitute a system under study. It is also shown that the system can exist in a region close to an unstable condition and that normally studied are various dynamic conditions ofchemical processes, which emerge as some parameters or other are changed slightly. Ifthe nature ofthe dynamic conditions turns out to be close to those observed in experiment, then that strongly suggests that the experimental system is indeed in a nonstable equilibrium, and that an EMF acts exactly on the link in the chain ofbiochemical transformations that has been subjected to a variation.

It is clear that the physical or biophysical processes ofthe primary reception ofan MF fall out ofthe scheme. The relationship between the reaction rate, for instance, and the MF value is normally postulated as a linear dependence. It is

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then possible to correlate with experiment both frequency and amplitude spectra ofthe response ofa dynamic system to an excitation ofa constant that is potentially sensitive to an EMF, but the importance ofsuch a correlation would be questionable. The primary reception process is not prohibited to feature some frequency or amplitude selectivity. Because of that, it is unlikely to obtain a good agreement ofthe responses to an EMF in experiment and in models using the chemical-kinetics equations. Even when such a correspondence is available, it is fairly difficult to interpret. There are works that put forward “through” models where the primary reception process with its characteristics is built into a kinetic scheme. Grundler et al. (1992) and Kaiser (1996) have considered a group ofsuch mechanisms based on the assumptions as to the properties ofthe primary process.

Also considered is the interaction ofan MF with spatial structures in motion, such as autowaves in excitable media, e.g., spiral waves (Winfree, 1994), which are also solutions to some special cases ofEq. (3.3.1).

Plyusnina et al. (1994) used the equations ofchemical kinetics with special solutions to describe premembrane processes in an EMF. The model by Eichwald and Kaiser (1995) relies on experiments concerned with the influence oflow-f

requency fields on the cells ofthe immune system, specifically on T-

lymphocytes. That work considers the possibility for an external field to affect the process ofsignal transduction between activated receptors on the cellular membrane and G-proteins. It was shown that depending on the specific combination of intracellular biochemical and external physical factors there may occur absolutely different response forms.

The number and diversity ofmodels ofthat class are great. The scheme ofthe search for an MF target drawing on responses of non-linear systems has been realized quite consistently by Kaiser (1996) and Galvanovskis and Sandblom (1998).

The latter is a study ofthe spectrum ofintracellular oscillations ofthe concentration ofCa2+ ions caused by an external stimulus under periodic modulation ofthe rate ofone ofthe intracellular reactions involving calcium. The Ca2+ oscillations were modeled using the set ofconventional non-linear differential equations proposed in Goldbeter et al. (1990). It was shown that a system’s response expressed as a total spectral power ofthe oscillations is complicated in nature and is dependent on the frequency and amplitude of the modulating signal. The frequency windows of the effect emerged in the characteristic natural frequency of oscillations ( 0 . 01 Hz) and smaller windows at its harmonics. An amplitude window was also noted. The authors varied all the system parameters in order to determine the most sensitive area in the system ofreactions. The reaction appeared to be the reaction ofthe liberation ofcalcium within the cell from a state bound in intracellular proteins.

We will stress the value ofthe chemical-kinetics models. In the process ofthe development and comparison ofthe models with experiment the most sensitive points ofbiochemical systems may be sought. That simplifies the search for primary mechanisms, since the potential circle ofreactions sensitive to an EMF becomes more definite.

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3.4 MODELS OF BIOLOGICAL EFFECTS OF WEAK ELECTRIC FIELDS

One ofthe possible scenarios ofthe action ofa low-frequency MF on a biological system is for the MF to induce in a tissue a variable electric field. That field, in turn, causes eddy currents and electrochemical phenomena. The frequency- and amplitude-selective action ofexternal weak variable EFs is a problem in its own right. The appropriate mechanisms are described using the chemical-kinetics equations, where some reactions are characterized by a relatively large change in the electric dipole moment, and the constants ofthese reactions are assumed to be dependent on the EF strength.

Normally, when assessing the action ofa weak EF on a cell one proceeds from the additional potential on the surface of the cell in the EF. The models consider spherical or cylindrical dielectrics placed in an external field. It is known that the EF potential E in a spherical system that coincides with the center ofa dielectric sphere has the form (Landau and Lifshitz, 1960)

ϕ = Er(1 − A/r 3) ,

where the constant A is found from the conditions on the boundary of the sphere.

On a spherical or cylindrical surface of radius R, see Appendix 6.4, 3 ε

2 ε

ϕ sphere = ER

,

ϕ cyl = ER

,

(3.4.1)

2 ε + ε i

ε + ε i

where ε and ε i are the permittivity ofthe medium and ofthe object being modeled.

Since usually ε ∼ 80 and ε i 3, the additional potential on the sphere is given by ϕ ≈ − 1 . 5 ER cos θ ,

(3.4.2)

which is often used in the literature, see, for instance, Weaver and Astumian (1990); the accurate data on dielectric parameters ofbiological cells and tissues are available in the review (Markx and Davey, 1999). In addition, the two-layer cell membrane carries a large charge, negative on the inner membrane, which creates the trans-membrane potential difference U m 70 mV. It is caused by the action of membrane pump-enzymes, which push ions against their density gradient. The additional potential difference on the cell surface at points that are opposite in relation to the field direction follows from (3.4.2) and is 3 ER. The conductivity ofthe intracellular plasma is large as compared with the membrane conductivity; it is therefore assumed that the potential difference is composed only of the contributions from the opposite membrane areas. Thus the additional EF inside the membrane induced by an external field is larger than the external one by a factor of R/ 2 d.18 On the one side ofthe cell the transmembrane potential grows; on the 18This statement occurs quite often in papers on the action of an EF on biological cells, e.g., Bioelectromagnetics, 21(4), 325, 2000. It is based on erroneously ignoring the thermal effects and dielectric properties of the intracellular medium. The conductivity of the cytoplasm is conditioned

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ε σ σ σ

ε

Figure 3.3. The fields and polarizations on the external membrane surface. The surface density of charges is formed by external and polarization charges.

other, it decreases. It can easily be worked out that the relative change for a cell of the size R ∼ 10 µ m in the field 1 V/m will be

3 ER ∼ 10 4 .

(3.4.3)

2 U m

The smallness ofthat quantity is also a problem in electromagnetobiology. What is not clear is how such small changes can affect membrane processes.

In actual fact, the situation is even more dramatic, since there are biological reception data for fields of about 1 mV/m. Besides, the very formula (3.4.2) is hardly valid for the evaluation of the potential changes in a void structure, since it was derived for a solid dielectric. We do not want to complicate matters by spherical symmetry, which in this case yields only the insignificant coefficient ofaround unity.

The cell can be better modeled by a rectangular box filled with cytoplasm whose dielectric properties are similar to those ofintercellular solution. On the surface ofthe membrane box there are external charges due to pump-proteins and also charges due to the polarization by an external electric field E. The surface density ofcharges induced by the field is equal to the difference ofpolarizations ofthe medium on the internal and external sides ofthe membrane (Landau and Lifshitz, 1960), see Fig. 3.3,

σ( E) = P i − P .

Since we consider the polarization effects in a linear approximation, the polarization density ofcharges can be found by supposing that there are no external charges.

by free ions, i.e., by well-localized charge carriers. The energy of thermal scale is greater than the energy of displacement of the charge q by the cell length in an external EF not stronger than 1 kV/m: κT qϕ. The thermal diffusion of free ions, therefore, prevents ion redistribution and effective field screening within the cell. It follows that the potential drops mainly due to the dielectric polarization of cytoplasm, whose conductivity can be ignored.

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δ

Figure 3.4. The dependence of the free energy of the protein channel on the generalized coordinate. Both open and closed states are stable.

In that case, on the boundary ofthe dielectric holds the relationship εE = ε i E i.

Using also the equality 4 πP = ( ε − 1) E on either side ofthe membrane gives 4 πσ( E) = ε i E i − E i − εE + E = (1 − ε/ε i) E .

The surface charge density is related to the transmembrane potential by the relationship ofthe flat capacitor

U m( E) = 4 π[ σ s + σ( E)] d/ε i , where d ∼ 5 nm is the biomembrane thickness. We then find the change δU m( E) ofthe transmembrane potential in relation to its value in the absence ofthe field U m(0) = U m,


δU m( E)

dE

= 1 − ε

10 6 ;

U m

ε i

ε i U m

i.e., it is another two orders ofmagnitude smaller than (3.4.3).

The relationship (3.4.2) was used, for example, by Astumian et al. (1995). They proposed a hypothetical mechanism to illustrate the action ofa variable electric field on a biological cell. That mechanism possesses neither frequency nor amplitude selectivity. Anyway, we will consider the idea itself, which will help us to clarify the prospects of its use.

The membrane channels ofthe cell can be either in an open state or in a closed state, Fig. 3.4. Such a point ofview is supported by the experimental observations ofthe discrete variation ofthe conductivity ofsingular protein channels. In a thermodynamic equilibrium, at Boltzmann distribution, the ratio ofthe channel probabilities in open and closed states is

p ≡ p open /p close = exp( U/κT ) .

(3.4.4)

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THEORETICAL MODELS OF MBE

Ifthe external electric field causes the potential difference to vary according to U = U 0 + δU ,

then the probability ratio can be represented as a series in the powers ofthe small parameter x = δU/U 0. In terms ofthe notation β = U 0 /κT , we have p( x) = eβeβx = p(0) + p(0) x + px 2 / 2 + ... .

The variation of p with time on average seems to be associated only with a term that is quadratic in x:

1

δp =

β 2 eβx 2 .

2

The supposition consisted in that the deviation of p from an equilibrium value can result in a growth ofthe rate ofthe transfer by protein ofoxidant molecules inside a cell and in an accumulation due to that ofdamages ofDNA for a sufficiently long time.

The quantity U 0 in Fig. 3.4 corresponds to the transmembrane potential ofa cell with a transferable charge of several units. Then δU will be the change ofthe potential in an external electric field. As was shown above, the amplitude ofthe relative change ofthe transmembrane potential in a field 1 V/m has the order of magnitude 10 6. Therefore, the time average of the square x 2 is x 2 1 10 12 ,

2

where x ∼ cos Ω t. On the other hand, the quantity β for physiological temperatures is about eight. This gives an estimate ofthe permanent component in the variation of p in a variable field

δp ∼ 10 6–10 8 .

The smallness ofthat quantity questions the application ofthis idea. According to the authors ofthe idea, the specified level ofthe variable field could lead to a biological effect, but several idealizations in the course ofthe calculations markedly reduce the value ofsuch a conclusion. The mechanism predicts a quadratic dependence of the effect with the amplitude ofan electric field.

The mechanism ofthe action ofan EF on biological systems and cells that feature a frequency selectivity was put forward in a number of works, whose overview is given in Tsong (1992). The concept of the mechanism is as follows: if conformational states A and B ofa molecule have a dipole electric moment, then the chemical equilibrium ofthese forms

k 1

A B

k− 1

can be shifted in an external electric field E by a van’t Hoff-type equation

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[ ln K/∂E] P,V,T = M/RT ,

(3.4.5)

where K = k 1 /k− 1 is an equilibrium constant, M is the difference ofmole electric dipole momenta ofstates A and B, and R is the gas constant. This has been applied to conformational states, both active and inactive, of the enzyme of ATP-ase type, which catalyzes the reaction ofthe membrane transport ofthe substrate within the cell. The frequency selectivity is a postulate and a corollary of the correspondence ofthe frequency ofthe external field and rates ofreagent relaxation. The model features no amplitude selectivity, although the review ofATP-ase reaction experiments in a strong EF of 0 . 5–5 kV/m contained in that work attests to the presence ofa maximum in the region of2 kV/m. A qualitative result obtained by computer simulation for certain combinations of some parameters that describe enzyme transport indicates that an EF can cause the pumping ofthe substrate through the membrane that is on average constant in time. No theoretical estimates ofthe magnitudes of effective fields are given. Such an estimate follows from Eq. (3.4.5), normalized to one molecule,


δD E

K/K 0 = exp

,

κT

where δD is the difference ofmolecular dipole momenta at states A and B. This quantity is sometimes associated with the traveling ofseveral elementary charges through a distance ofabout the membrane thickness d, i.e., δD ∼ 10 ed. For physiological temperatures and a field E ∼ 1 kV/m, we obtain δK/K 0 10 3. This suggests that we should recognize, perhaps, the promise ofthat model to account for biological effects of strong electric fields. One weakness here is the inadequate predictive power ofthe model and the complexity ofits experimental verification.

Specifically, the authors did not predict the dependences ofthe effect on some other variations ofthe electromagnetic environment.

In Tsong (1992) a further mechanism is proposed to account for the biological reception ofweak (about µ V/m) variable EFs. The mechanism assumed that the height ofthe barrier W that separates active and inactive states ofthe membrane protein-enzyme in the Michaelis–Menten-type reaction, see Fig. 3.4, changes in sympathy with the electric field. The frequency selectivity is here postulated, and its nature is associated with the high-Q oscillations ofa charged group ofatoms within the protein induced by an external field. Those oscillations cause the barrier height to be modulated. It is clear that the name ofthe game here is not the change in the state probabilities, but rather the change ofthe rate ofthe transition between those states. According to the theory ofabsolute reaction rates, the rate constant for the direct and return reactions can be written as


1 = k 0 exp − W ± U/ 2

.

κT

Since the transition rate constants have a non-linear exponential dependence on the barrier height, we get a non-zero time-averaged input due to the external variable

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THEORETICAL MODELS OF MBE

EF. This expression is quite analogous with (3.4.4), thus suggesting that the relative change ofthe reaction rate has the same order ofmagnitude as the relative change ofthe equilibrium constant, i.e., also very small. The mechanism possesses no amplitude selectivity. Additionally, the quantitative estimates were based on some model assumptions. Physically, the main assumption was dubious — an external EF can be amplified by a plasma membrane so that the change ofthe field induced within the membrane is larger than the initial external EF by a factor of R cell /d membr. The use ofthat mechanism in the process ofbiological reception ofweak electric fields is still questionable, since no special-purpose experiments to test the mechanism have been conducted.

Markin et al. (1992) proposed the model of“electroconformational coupling”, which predicts not only the frequency window, but also the amplitude one. The model proceeds from the supposition that both the state of an ion in a membrane protein-transporter and the state ofthe transporter itself— open whether inside or outside — are dictated by an electric field and are thermally activated processes. The interaction ofthese processes causes an amplitude window to emerge.

A frequency window is caused by relaxation processes, just as in Tsong (1992). An amplitude window was found in the region of 2 kV/m for (Na, K)-ATP-ase of the human erythrocytes. That is too much for the model to be applied to account for frequency- and amplitude-selective biological reception of weak electric fields, e.g., those induced in biological tissue by low-frequency MFs.

Weaver and Astumian (1990) worked out the limiting sensitivity ofa cellular system to an electric field, assuming that the EF reception is caused by some process similar to the mechanisms considered above. Such a process is determined by the transmembrane potential difference. Therefore, according to the authors, the limiting sensitivity could correspond to the noise fluctuations ofthe transmembrane potential difference. To evaluate those fluctuations use was made ofthe Nyquist formula (e.g., Lifshitz and Pitaevsky, 1978). As to the legitimacy of the usage of that formula a word is in order. The formula follows from the fluctuation–dissipation theorem for generalized susceptibilities of linear systems, which specifically can be the electric resistance. The current in a circuit, which is a reaction to an external electric field, is related to the field strength in a linear manner, but the main electric characteristic ofthe plasma membrane is its significant non-linearity. It is this property that is responsible for the emergence of a transmembrane potential, which is at the core ofthe processes ofnervous excitability. It is to be admitted that in this case the general physical laws oflinear responses were used beyond their applicability ranges. At any rate, such a dramatic idealization calls for some justification.

Other electrochemical mechanisms ofthe cellular reception ofelectric fields that are based on electrophoresis, electro-osmosis, and receptor and channel redistribution on the surface of cellular membranes are reviewed by Robinson (1985).

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3.5 STOCHASTIC RESONANCE IN MAGNETOBIOLOGY

It is now beyond doubt that theoretical MBE models must include thermal excitations. Nevertheless, no models are in existence so far in which a consistent consideration ofthe influence ofthe thermostat would not destroy the desired effect ofa weak MF. Thermal excitations ofa medium behave as random forces acting on a supposed MF target, and more often than not those are charged particles. Search is going on for subtle details in the behavior of dynamic systems exposed to random forces that might be responsible for conservation and transformation of a weak MF

signal to the level ofa biochemical response. Actually, those works deal with the very essence ofthe so-called “kT problem”.

It is fairly easy to identify several areas of research in this domain where thermal noise would be considered explicitly as a stationary random process ofsome spectrum or other. It seems quite obvious that applications ofthe methods ofequilibrium thermodynamics or statistical physics cannot yield appropriate results. Current studies focus mainly on dynamic systems with quasichaotic behavior.

3.5.1 Stochastic resonance

Benzi et al. (1981) suggested that a phenomenon that consists in a relatively significant redistribution ofthe power spectrum ofa dynamic variable ofa non-linear multistable system under the action ofa weak deterministic component against the background ofadditive noise under certain resonance-type conditions be referred to as a stochastic resonance (SR). Just like atomic parametric resonance, so a stochastic resonance is no resonance in the sense that it does not increase the response as the frequency of a controlling signal is fine-tuned to the system’s natural frequency.

The analogy lies in the fact that the output signal-to-noise ratio appears to be largest as the noise level in an output signal is adjusted to some definite value.

Stochastic resonance is known to occur in systems described by first-order differential equations. For a mechanical system, that corresponds to overdamped motion, i.e., one without inertia forces. In that case, the equations contain no accelerations, and the rates ofcoordinate variations vary with the forces applied. For one particle, the equation becomes

˙

x = − ∂ U ( x, t) +

( t) ,

(3.5.1)

∂x

where ξ is a random process, which is normally taken to be δ-correlated, with a zero mathematical expectation, and D is the dispersion ofthe random force on a particle. The case is well studied where the potential function U ( x, t) corresponds to the motion ofa particle in a double-well potential under a regular harmonic force:


U ( x, t) = U 0 2 x 2 + x 4 − U 1 x cos(Ω t) .

The constant part ofthe potential is depicted in Fig. 3.5. From (3.5.1) we get

˙

x = 4 U 0 x(1 − x 2) + U 1 cos(Ω t) +

( t) .

(3.5.2)

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THEORETICAL MODELS OF MBE

8[


8


FRRUGLQDWH

Figure 3.5. A simple double-well potential, which makes a dynamic system bistable.

Computer simulation ofEq. (3.5.2) for illustration purposes is not difficult. We have performed our own calculations. The equation had the following parameters: U 0 = 1 , U 1 = 1 , Ω = 0 . 1. The random process ξ( t) was modeled by a sequence ofnormally distributed virtually uncorrelated numbers with a zero mathematical expectation and unity dispersion. The coordinates ofa particle were calculated using the Runge–Kutta method at 8192 points with a time step t = 0 . 1. Appropriate spectra were obtained by fast Fourier transform. The amplitude of the spectral density S ofthe signal was obtained by averaging the height ofthe spectral peak at a frequency of Ω = 0 . 1 over six spectrum realizations. The realizations were derived by repeated computations with different input points for the random number generator.

Figure 3.6 shows the variation ofthe signal-to-noise ratio with the spectral noise density D. It has a local maximum at a certain noise density and is in agreement with well-known results. For instance, McNamara and Wiesenfeld (1989) carried out more detail computations: the local maximum appeared to be several times higher. Such a behavior ofthe curve could be easily understood, Fig. 3.7.

When a deterministic periodic force is fixed at a level that is insufficient for a particle to overcome a barrier, the particle will stay at all times within one ofthe potential wells, ifthe noise level is small, Fig. 3.7 (upper left). The amplitude of the displacement ofa particle will on average be constant. As the noise intensity D

goes down, the signal-to-noise ratio will obviously grow with D− 1, as is shown on the left part of the curve in Fig. 3.6.

As the noise intensity is increased, a particle can sometimes leap from well to well when it is shifted to the barrier by a deterministic force, and some random noise pulses appear to be sufficiently large and also oriented in the direction of the barrier, Fig. 3.7 (upper right). This gives rise to a correlation between the deterministic periodic force and random transitions of the particle from well to well. The amplitude ofsuch displacements is seen to be much larger than that of displacements within one well. This increases the signal-correlated component in the displacement spectrum.

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8

8



6,*1$/7212,6(DX


Figure 3.6. Signal-to-noise ratio in the spectrumof a displaced particle under a harmonic force at various noise levels. A computer simulation of the dynamics (3.5.2).

1

0

-1

ts

D=0.5

D=2.0

unib.

, ar 1

x

0

-1

D=4.0

D=30

0

400

800

0

400

800

time, arb. units

Figure 3.7. Displacements of a coordinate of an overdamped particle in a double-well potential under the action of a harmonic force and a random force of various levels D.

This component on average reaches a maximum at a certain (resonance) noise level, when virtually any half-cycle of the action of a regular force gives rise to a transfer of a particle from well to well, Fig. 3.7 (lower left).

Further growth ofnoise does not lead anymore to a noticeable increase in the mean displacement amplitude; therefore the signal-to-noise ratio again becomes inversely proportional with noise ∝ D− 1, Fig. 3.7 (lower right). This corresponds to the right-hand side of the dependence in Fig. 3.6.

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It appeared that a stochastic resonance is a more general phenomenon than is illustrated by a bistable system. Specifically, it is also observed in one well when the combined action ofsignal and noise, which upsets the equilibrium and exceeds some threshold, triggers some other process. One example is the firing ofa neuron by the combined action ofsignal and mediator density fluctuation.

The middle section ofthe curve in Fig. 3.6, which corresponds to a situation where noise growth at the input improves the signal-to-noise ratio at a system’s output, is a subject ofheated debate. Stochastic resonance has been observed in artificial systems with noise, such as Schmitt trigger circuits, ring bistable lasers, and superconductive quantum interferometers, as summarized in the work by Wiesenfeld and Moss (1995). Also discussed is whether it is possible to describe some natural phenomena, specifically, biological ones, using the laws ofstochastic resonance. The discussions focus on the ability of weak biological signals to bring about marked changes in the behavior ofa dynamic system against the background ofa wide variety ofrelatively intense perturbing factors — in a stochastic resonance.

It was reported (Wiesenfeld and Moss, 1995) that the reaction of mechanoreceptor cells in crayfish to an acoustic stimulus in the form of a subthreshold signal against Gaussian noise obeyed a dependence similar to that in Fig. 3.6.

3.5.2 Possible role of stochastic resonance in MBE: “Gain”

It is believed that all sensor biosystems are threshold devices to a certain degree.

Therefore, the assumption that magnetoreception of organisms is caused by, or employs, the stochastic resonance mechanism is quite justified. The effectiveness of detection ofweak MF signals can be improved through the action ofnoise factors.

Theoretical considerations ofvarious stochastic resonance models yields an approximate relation for the variation of signal-to-noise ratio R with the noise level D around a maximum


U

2

1

U 0

R ∝

exp 2

.

(3.5.3)

D

D

The relationship is derived assuming that the output signal is only generated when a particle jumps from well to well or only on reaching some threshold. It follows that the formula gives an approximate description of the fast growth and further decline of R, dashed line in Fig. 3.6. It does not describe the rise on the left of the figure, which is of no consequence for applications. That is quite enough for analysis.

We would like to know to what extent the signal-to-noise ratio can increase with noise D. At fixed U 0 , U 1, according to (3.5.3), R has a maximum U

2

1

R max =

e− 2 .

U 0

That maximum is attained for the optimal noise level

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D = U 0 .

(3.5.4)

As D decreases, the signal-to-noise ratio drops theoretically to 0: R min = lim R = 0 .

D→ 0

It would seem that we can get an arbitrarily large “gain” ofthe signal K =

R max /R min due to noise, but that is not the case for the following reasons.

For small noise D, the probability ofwell-to-well transitions W becomes exponentially small. It is exactly this that yields arbitrarily small values of R. At the same time, to observe such rare transitions requires exponentially large times. That is why small values of D are ofno practical significance. A reasonable estimate of real gain K can be obtained f rom the relation f or the mean time of the first crossing ofa barrier (Cramer, 1946)


2 U 0

τ = W− 1 = exp

,

(3.5.5)

D

where τ is dimensionless and expressed in units ofsystem relaxation time scale.

The quantities U 0, D, and U 1, as was already assumed in writing Eq. (3.5.2), are dimensionless as well.

We suppose that a biological receptor senses a subthreshold signal at a certain optimal noise level D = U 0 during the time t( D). Let, for instance, it be such that N intersections are needed for the receptor to respond after the appearance of a signal

t( D) = N τ ( D) .

At a lower noise level D, under ideal conditions, it would take the receptor more time t( D) = N τ ( D) to sense a signal. We should consider that the physiological or biochemical readiness ofthe receptor to sense the signal is only retained during some characteristic time T . If T < t( D), it will be impossible in experiment to detect a signal at a given noise level. Accordingly, there will be no estimating the signal-to-noise ratio as well. The receptor “lifetime” T will thus determine the lower noise boundary in experiment, when the signal-to-noise ratio still has some meaning.

To arrive at some estimates we will assume that the receptor lifetime T is n orders ofmagnitudes longer than the time ofits optimal reaction t( D), i.e., for D = U 0.

It follows immediately that

τ ( D) = 10 n .

(3.5.6)

τ ( D)

Using (3.5.3) and (3.5.5), we can write the relation for the maximum gain 2

R( D)

ln τ ( D)

τ ( D)

K =

=

.

R( D)

ln τ ( D)

τ ( D)

Considering (3.5.6) and τ ( D) = τ ( U 0) = e 2, we will write the last equality as

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ln τ ( D)

2

10 n

K =

10 n =

.

(3.5.7)

ln τ ( D) + n ln 10

(1 + 1 . 15 n)2

It follows that if, for example, the lifetime of a receptor is longer than the time of its reaction to n = 1 , 2 , 3, or is about 4 orders ofmagnitude, then the largest gain will be about K ≈ 2 , 9 , 50, and 320, respectively. In decibels19 these quantities are 3, 9.5, 17, and 25.

We note that during the receptor lifetime all the biochemical conditions that support the reaction are maintained. Homeostasis in the organism, i.e., a status where all ofits functions, composition, etc., remain relatively unchanged, only occurs as a dynamic equilibrium. Therefore, it is safe to say that whereas some receptors are destroyed by metabolic processes or discontinue their operations, other just emerge.

Considering that for most receptors the reaction time is a fraction of a second, the quantity n that is not higher than n = 3–4 looks quite plausible; in such a case, the receptor lifetime would be a matter of minutes.

Experiments, however, yield slightly smaller gains. Signal-to-noise vs noise dependences derived from the results of pertinent experiments and numerical models ofstochastic resonance show the f

ollowing (data are given in

McNamara and Wiesenfeld (1989) and Wiesenfeld and Moss (1995); they summarize the results ofseveral studies). In a ring laser the gain was 11 dB; in an experiment with mechanoreceptor in crayfish, 6 dB; in computer models ofthe double-well potential, 4 dB, ofthe neuron, 7 dB, ofSQUID,20 12 dB; ofthe trigger, 10 dB. In our own two-well model we obtain a gain of1.5, i.e., about 2 dB, Fig. 3.6. This implies that in most studies performed so far the noise caused the signal-to-noise ratio to increase on average only by an order ofmagnitude. To reveal larger gains under the action ofnoise requires a possibility ofputting the noise down and increasing observation times. That possibility is not always available in real experiments.

3.5.3 Constraints on the value of detectable signal

After amplification, the signal-to-noise ratio must clearly be no less than unity, approximately. Otherwise, we should look for another system with another level of organization, which would ensure that the signal be isolated from noise.

There are some constraints imposed on the value ofa deterministic signal U 1 to be “amplified”. On the one hand, the signal has to be not very large. Otherwise, the signal, irrespective ofnoise, will be large enough for a particle to get through a barrier. This occurs when the potential at the maximum signal

U ( x) = U 0( 2 x 2 + x 4) − U 1 x has only one extremum, a minimum. That is, the equation U = 0 only has one x

solution. Hence it easily follows that the upper boundary of the amplified signal is

U 1 = 8 U 0 / 3 3.

19A decibel, dB, is one tenth of the decimal logarithm of the ratio of two quantities.

20SQUID — superconductive quantum interference device.

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On the other hand, for a weak signal to be detected against a noise background requires that it be “accumulated” during some time. In numerical simulations, for instance, that implies averaging over many, say m, realizations ofoutput signal spectra, when the noise wing ofthe spectrum irons out and the δ-like peak ofthe signal in the spectrum becomes apparent. The same occurs when the time span ofan observation ofa random (ergodic) system is increased by a factor of m. As was mentioned above, in experiment or in a biosystem, that time T is limited for some considerations. That imposes some constraints on the value ofthe weakest detectable signal.

The following considerations lead to rough estimates of a barely detectable signal, which are still sufficient for our purposes. In the presence of a signal, the Cramer’s time becomes21

τ ∝ exp [2( U 0 + U 1 cos Ω t) /D] .

Changes in the Cramer’s time, i.e., the difference τ ofquantities τ ( U 0)

exp[2 U 0 /D] and τ ( U 0 + U 1) exp[2( U 0 + U 1) /D], make a signal detectable. That difference is only made apparent when a system passes from well to well. For the difference, i.e., a signal, to be apparent, it should be reproduced a sufficient number oftimes, say, in n transitions, and n τ should correspond to the characteristic scale ofthe process, i.e., n[ τ ( U 0 + U 1) − τ ( U 0)] = τ ( U 0). Hence ( U 0)

D

n

U 1 = τ ( U 0) ,

that is,

U 1 =

.

dU 0

2 n

For a weak signal to be detected requires a sufficient number n oftransitions to be accumulated, but it is limited by the receptor lifetime ( U 0) < T . This yields a boundary for detectable signals in the optimal noise range D = U 0, U 1 ∼ U 0 τ ( U 0) / 2 T . Detectable signals thus fall into the range ( D) U 1 D .

(3.5.8)

T

In terms ofthe concepts ofbioreceptor lifetime laid down above, for a signal to be just detectable, it could be (10 1–10 4) D. Recall that corresponding to the signal levels U 1 ∼ D ∼ U 0 is the maximum signal-to-noise ratio.

3.5.3.1 SR and microparticles

A further limiting factor is noteworthy. A stochastic resonance is observed in dynamic systems described by first-order differential equations. That means that a particle that is a supposed target for an MF is overdamped; i.e., the forces of

“viscous friction” must be larger by far than inertia forces. For a microparticle such friction occurs on the same degrees of freedom of the ambient environment as does 21That holds true if a signal varies rather slowly and does not disturb the transition statistics (adiabatic approximation), i.e., if the frequency Ω is smaller than the inverse relaxation time of a system.

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thermal noise. It is not consistent, however, to repeatedly take into consideration one and the same factor, i.e., the random displacement of particles that interact with a target, both as phenomenological damping and as a perturbing force. A change over to quantum dynamics will then offer no new possibilities for a microparticle.

The particle Hamiltonian includes inertia forces — terms that include operators of double differentiation with respect to coordinates. Introducing damping needed for a stochastic resonance to occur is fraught with the same difficulties as in classical dynamics. Even for spin degrees of freedom, whose Hamiltonians contain no differentiation with respect to spatial coordinates at all, the situation does not change.

The dynamic equations in that case are first-order equations, but they are written for a complex function and are in a way counterparts of second-order equations for a real function. Thus here damping for the stochastic resonance model will have to be introduced as well, but the forces that cause spin relaxation will again look like thermal perturbations.

A way out could be to assert that a random external force has the same physical nature as a signal; i.e., it is electromagnetic. However, we have already seen that input signal and noise should be similar, so that the resonance mechanism would work for a unity signal-to-noise ratio. The problem of the biological detecting of a weak electromagnetic signal would then boil down to the problem ofdetecting a weak sum ofelectromagnetic signal and noise, which would definitely give us no clues. The difficulty ofapplying the stochastic resonance mechanism to a microparticle consists in that there are no sufficient grounds for writing appropriate equations.

It follows that the idea of stochastic resonance as applied to a microparticle, a potential target for an MF, appears to be unlikely for the following reasons:

the “gain” of a signal at stochastic resonance is far from 1010, a value required to account for MBEs in the low-frequency range,

the amplitude of magnetic signals is far from the expected level of noise perturbations ofa particle; a stochastic resonance could, however, manifest itselfonly when such a correspondence is available,

it is difficult to justify the writing of corresponding dynamic equations for a microparticle.

3.5.4 SR in chemical reactions

Bezrukov and Vodyanoy (1997b) have shown that a stochastic resonance can also occur in physico-chemical and other systems controlled by thermal transitions through an activation barrier. The reaction rate for such systems, which is proportional to the Boltzmann factor, is approximately described by the empirical Arrhenius equation

k ∼ a exp( −U/κT ) ,

where a is a constant and U is the so-called activation energy. The theory ofactivation complex (e.g., Glasstone et al. , 1941) has shown that U is mainly the height of

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a potential barrier that separates the states ofreagents from those ofreaction products. In a number ofcases, the barrier height depends on an external parameter. For instance, when a transition through a barrier is accompanied by a displacement of the effective charge q, the barrier height is dependent on the strength ofthe electric field E. The reaction rate will then be written as

k = k 0 exp( dE/κT ) ,

(3.5.9)

where k 0 is the reaction rate in the absence ofthe field E and d is the dipole moment ofthe transition. The rates k have the meaning oftime-averaged quantities measured in experiment. For microtimes, a chemical reaction is a sequence of separate random events, elementary acts ofa chemical reaction. Such a sequence is described by the Poisson flux. In the case under consideration the statistical parameter ofthe flux, which is its density, is modulated by an external field. In Bezrukov and Vodyanoy (1997b) the flux spectrum was studied for the case where an external field was an additive mix ofnoise and weak low-frequency signal: E( t) = E N( t) + E S sin(2 πf S t) , E S E N .

In the absence ofa control field E, the spectral density is close to the uniform density ofwhite noise. The length ofthe unity event pulse τ predetermines the upper boundary f c ofthat spectrum. In the presence ofa control field, the spectrum displays a low-frequency discrete component that varies with δ( f − f S). The authors introduce a signal-to-nose ratio R as the ratio ofthe amplitude ofa discrete component to the intensity ofthe continuous spectrum in a certain narrow frequency interval f ofthe discriminator near f S. The signal-to-noise ratio appears to be dependent on noise dispersion in the control field D = E 2 ( t) , where the brackets N

imply averaging over the ensemble. The calculated relative quantity R will be


1

k


0 D

Dn− 1

R( D) /R(0) = exp( −D/ 2) +

.

(3.5.10)

f c 2

n! n

1

Here R(0) = E 2 k

S 0 / 4 f is the initial signal-to-noise ratio. The variation ofthe ratio k 0 /f c = 10 2 is plotted in Fig. 3.8; it shows that signal-to-noise ratio is amplified by a factor of 4 as the noise intensity is increased from 1 to 2.

The very fact ofsuch a behavior ofa non-dynamic system is ofinterest. However, any attempts to apply the formulas to real chemical systems are difficult. After an amplification the absolute value of R is thought to be close to unity. It can be easily found that under these conditions we have

E 2 f

S c /f ≈ 100 ;

i.e., by narrowing down the frequency range of the discriminator we can have R = 1

at the output for an arbitrarily small input signal E S at the input. Physically, that result is doubtful, since range narrowing is bound to increase the time to signal

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Figure 3.8. Variation of signal-to-noise ratio with noise intensity at k 0 /f c = 1 (a), 10 2 (b), 10 5 (c), and 10 8 (d).

detection, but the times oflife and workable state ofbiological receptors are limited.

It is also seen in Fig. 3.8 that the gain R can be arbitrarily large for fairly short ( f c = 1 / 2 πτ ) pulses or pulses with a low repetition rate ( k 0). That result is nonphysical as well. Difficulties associated with the model seem to be concerned with an excessive mathematical idealization in describing a physical system.

To work out the Fourier spectrum ofthe flux ofreaction unit acts calls for a wide variety ofrealizations both for a random Poisson process at E = 0 and for the noise process in the controlling voltage. Owing to those abstractions a discrete spectrum component makes its appearance at the frequency of an input signal. A representation ofthe output signal as a δ-component ofthe spectral density is quite graphical mathematically, but quite inadequate under real-life conditions. Any real-life system, living and man-made alike, has to detect an output signal using only one realization, which is limited in time at that. The Fourier integral for a process ofa finite length θ, however, contains no discrete components. A peak at the signal frequency acquires some broadening. That fact to a large degree invalidates the reasoning about gain at stochastic resonance.

The stochastic resonance per se is no detector or discriminator. After a SR has occurred in a biological detector a discrimination system is required, which can

“make a decision” as to whether a signal is present in noise. For the discriminator, the signal-to-noise ratio is not the only parameter ofsignificance. Another, no less important, parameter to define the quality ofa signal is its coherence. A coherent signal in an additive mix with noise can be found using phase detection, i.e., accumulation ofphased realizations: the signal power will then vary with the

observation time T , and the noise power only with

T . A moment comes when the

signal-to-noise ratio becomes larger than 1, and the discriminator works.

Signal-to-noise gain under SR is achieved due to the broadening ofa signal spectral line. That is easily seen in Fig. 3.9. The signal power in the range f , i.e.,

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Figure 3.9. The spectral density of signal and noise outside of SR - A; and under SR - B.

the area between the signal curve and the noise wing, grows faster with noise under SR than the power ofthe noise itself

. The broadening ofthe signal component

in the spectrum mix implies that the signal is not coherent anymore. Information about the signal phase is lost during the autocorrelation time τ a; therefore the signal accumulation time decreases. The discriminator has to make its decision drawing on less information; hence the probability of correct detection drops and the probability offalse firing without signal goes up. Thus, this strongly suggests that as noise under SR grows, despite the fact that the signal-to-noise ratio improves, the probability oftrue detection ofa signal falls off monotonously. This agrees with common sense: an added noise does not improve the reliability ofsignal detection.

Equation (3.5.9) is a graphic indication ofthe fact that a control field must be sufficiently large for any changes to become noticeable:

dE ∼ κT .

With simple chemical reactions in most cases a charge about the electron charge e travels a distance ofseveral angstroms. The dipole moment ofthe transfer will therefore be about d ∼ 10 D, and so the electric field that markedly changes the barrier height has to be about 108 V/m. In other words, the idea ofSR holds no promise as applied to simple chemical processes. According to sources, in some proteins controlling the transport ofions through ion channels, an effective charge ofabout 10 e is transported across a distance ofthe membrane thickness 5 nm, see Section 3.4. Since the required electric field is comparable with the field within the biomembrane, a SR could occur in principle, but no reliable experimental evidence is available so far. However, even if an SR does appear, it was shown above that it is not necessarily concerned with an improvement in the signal detection situation.

We have considered some general constraints on the applicability ofthe SR idea in magnetobiology. About ten publications are available that suggest and consider various biophysical systems under SR. We will only cite some ofthem without much

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detail, since the difficulties and the range ofvalidity ofSR in those works have not been resolved.

The possible role ofstochastic resonance in MBEs was discussed by Makeev (1993), Kruglikov and Dertinger (1994), and Bezrukov and Vodyanoy (1997a) as applied to the conductivity ofpotential-dependent ion channels.

The stochastic resonance as applied to oscillatory Ca2+ biochemical processes near biological membranes was studied by Kaiser (1996); the biochemical model ofcalcium oscillations was developed earlier in Goldbeter et al. (1990) and Eichwald and Kaiser (1995). In the set ofchemical-kinetics equations a link that can be dependent on an MF was found. At the same time, the primary mechanism for the action of an MF on the rate of that reaction has not been considered.

Also, no calculations ofthe dependence ofobservables on MF variables have been conducted.

Semm and Beason (1990) report that amplitude modulation ofthe geomagnetic field by a 0.5-Hz sine signal with an amplitude of2.5 µ T causes spike activity ofa ganglion nerve cell to fire simultaneously with MF maxima. The authors assumed that biomagnetite crystals contribute to the formation of a cell response. In such a case, the stochastic resonance mechanism is quite suitable for accounting for the effect. Thermal fluctuations ofa crystal bring about spikes at random moments of time, and the superposition ofa weak harmonious signal synchronizes the appearance ofspikes.

The idea ofstochastic resonance somewhat improves the situation with possible explanations for MBEs, but not to the extent sufficient for the problem to be solved.

It is possible that the idea that a variable MF signal has to be “amplified” because ofits energy quantum being small as compared with κT is no good in principle as an account for the primary MBE mechanism. Moreover, even if a stochastic resonance does occur in one system or another, that gives rise to a further question. Does nature here employ an SR for its natural purposes, or rather is the phenomenon no more than just an epiphenomenon?

3.6MACROSCOPIC MODELS

3.6.1 Orientational effects

All the substances feature magnetic properties to some degree or other. Diamagnetics and paramagnetics are magnetizeable; i.e., they acquire a magnetic moment in an external MF. Ferromagnetic materials possess spontaneous magnetism. In both cases, the magnetic moment µ ofa magnetized particle in an external MF H

produces a torque

d

m =

( −µ H)

m = µ × H ,

which tends to bring the particle into a state with the lowest energy. That is stopped by the random forces ofthermal excitations ofa medium. Under certain conditions,

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where magnetic forces on a rotational degree of freedom impart to it an energy of about the mean energy ofthermal fluctuations per degree offreedom κT / 2, the orientation ofsuch particles in the medium will no longer be chaotic. A sense ofpredominant orientation appears, which in principle could produce a biological response, ifthe particles being oriented would somehow be included into the metabolic system ofan organism.

3.6.1.1 Orientation of diamagnetic molecules

Minimal magnetic properties are inherent in diamagnetics. Their acquired magnetic moment points mainly counter the MF. Classed with diamagnetics are substances that do not possess any other, stronger forms of magnetism — either spin paramagnetism or ferro- or ferrimagnetism. Virtually all the substances that make up living tissues, specifically, molecules ofwater, fats, proteins, and hydrocarbons, are diamagnetic in their principal state.

Diamagnetism stems from the quantum properties of molecules. The electron clouds that surround the nucleus ofan atom or a molecule are some circular areas ofhigher electric conductivity. When the MF flux through such areas grows, an electric current is induced in them, which produces an oppositely directed MF that reduces the external flux.

The very existence ofdiamagnetism, that common phenomenon, often suggests the question ofwhether it can underlie at least some ofthe magnetobiological effects.

Let us consider a charge q ofmass M in a “box” ofsize a. The energy of a moment in an external field is ε = −µ H. A simplifying assumption is that the moment induced by the external field is parallel with it. Then the magnetic moment in an n th state could be found µn = −∂εn/∂H. The induced magnetic moment of the atom is not quantified and can be arbitrarily small. It is the magnetic moment ofa closed system that is quantified. In this case, the system consists ofan atom and a source ofan external MF.

We arrive at the thermal-equilibrium value ofthe magnetic moment by averaging with the Boltzmann distribution fn: µ =

f

n

nµn. However, the electrons

at room temperature are most probably at a ground state. We will take this into consideration. Moreover, the electrons often fill up the inner shells, and the valence bonds are formed by electron couples with zero total spin. To illustrate diamagnetism, it is thus sufficient to have the model ofa particle at a ground state (zero orbital momentum) with zero spin. That state is not subject to Zeeman splitting in a magnetic field.

A measure ofdiamagnetism is the proportionality factor between the induced magnetic moment I ofa unit volume ofmatter, in our case I ≈ µ/a 3, with the external field, i.e., the magnetic susceptibility

∂I

2 ε

χ =

= 1

.

(3.6.1)

∂H

a 3 ∂H 2

It is possible to estimate the value ifwe know the Hamiltonian ofa system, e.g., (4.1.1), where the Zeeman term must be omitted. The correction to the energy of

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the ground state in terms ofperturbation theory will then be

q 2 H 2

ε = ψ| q 2 (H × r)2 =

ψ|( x 2 + y 2) |ψ ,

(3.6.2)

8 M c 2

8 M c 2

where the DC MF is aligned with the z axis. In that expression q and M are, of course, the charge and mass ofan electron. For axially symmetric atoms ψ|x 2 =

ψ|y 2 = ψ|r 2 |ψ/ 3. In a real atom, in the general case, many electrons occupy their states within the same volume. The expression has to be summed up over all the electrons. It is clear, however, that the greatest contribution is made by valence electrons with the largest mean orbit size; in our model that is the box size. Ifwe denote the mean squared radius ofthe atom in the xy plane as ψ|r 2 = r 2 , we obtain by substituting the Langevin formula for the diamagnetic susceptibility χ =

q 2

( r/a)2 .

6 aM c 2

The quantity in brackets is clearly around unity. On the other hand, the atomic size a is about the Bohr radius a ∼ 2 /M q 2. It follows that the diamagnetic susceptibility will approximately be

χ ∼ α 2 / 6 10 5 ,

where α = q 2 /c = 137 1 is the fine structure constant.

The additional energy acquired by a molecule in a magnetic field thus varies with the diamagnetic susceptibility. Molecular electron shells do not show spherical symmetry. This manifests itself as some anisotropy of diamagnetic susceptibility, i.e., its dependence on the mutual alignment ofmolecule and MF. The energy correction is always positive, as follows from (3.6.1),

ε = −χa 3 H 2 / 2 ∼ r 2 .

It is minimal for molecules with electron shells aligned with the field. At a thermodynamic equilibrium there are more such aligned molecules, which amounts to the appearance ofan aligning torque when an MF appears or changes. The probability density for a diamagnetic molecule at an angle ϕ to the MF varies with the Boltzmann factor


β = exp χ( ϕ) a 3 H 2 / 2 κT ∼ exp( −ε( ϕ) /κT ) , which for low-atomic molecules is very nearly unity. This implies that the molecules are oriented in all directions with equal probability.

However, the energy ofa polymer-type molecular structure made up ofsimilarly aligned anisotropic molecules grows with the polymer size in proportionality to the number N ofthe molecules. Thus the degree ofthe alignment ofsuch rigid structures that possess the same number ofrotational degrees offreedom is given by the factor βN ∼ 1 + N ε/κT .

Therefore, for fairly large and rigid stacks, N ∼ 105–1010, the diamagnetic alignment becomes significant.

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Kuznetsov and Vanag (1987) have considered a wide variety offorms ofordered molecular structures ofsimilarly aligned anisotropic molecules to come to the conclusion that fields stronger than 1–10 T could produce a marked alignment, and hence a biological response. To be sure, the mechanism for the orientation of diamagnetic molecules and their complexes cannot account for the biological effects of weak MFs.

In a weak MF, the paramagnetic susceptibility ofradicals, i.e., molecules with uncoupled valence electron, is small as well (Ashcroft and Mermin, 1976), χ ∼ µ 2 /a 3 κT < 10 3 ,

B

where µ is the Bohr magneton. Such molecules form no ordered complexes. ThereB

fore, their spin paramagnetism,, which is three orders of magnitude stronger than diamagnetism, supplies no physical justification for the magnetoreception of weak MFs. Dorfman (1971) addressed the pulling of diamagnetic and paramagnetic molecules into the area ofa stronger field in nonhomogeneous MFs, and f ound

that the effect could have some biological consequences in fields ofaround 0.1–1 T.

It is common knowledge that in some aromatic substances a residual magnetization can occur that is associated with the fact that π-electrons ofthe molecular rings ofaromatic substances produce circular currents that are able to catch a magnetic flux like that in the Meissner effect in superconductive rings. Such substances, upon special treatment, behave like paramagnetic substances (Pohl and Pollock, 1986), and in the crystalline form they display a constant magnetic moment of around 10 4 µ per molecule (Tolstoi and Spartakov, 1990). A minute effect, it can hardly B

be ofuse in magnetoreception mechanisms.

3.6.1.2 Biomagnetite in a magnetic field

There is one group ofmacroscopic models, or rather one idea, that is being addressed by many authors. It relies on the presence in a multicellular living organism of crystals ofa f

erromagnetic compound, known as magnetite. In a DC MF such

a crystal is exposed to a significant rotational moment, which is many orders of magnitude larger than that in diamagnetic substances. It can therefore exert some pressure on a near-by receptor (Pasechnik, 1985; Kirschvink et al. , 1992). In all probability, such a mechanism does exist. Magnetite crystals have been found in the brain ofsome birds, which are known to f

eature a striking ability to take

their bearings in the geomagnetic field (Walcott et al. , 1979; Kirschvink et al. , 1985; Beason and Brennan, 1986; Wiltschko et al. , 1986). Such crystals are also found in some insects (Gould et al. , 1978, 1980) and bacteria (Blakemore, 1975; Frankel et al. , 1979).

At the same time, such a magnetoreception mechanism is in a class by itself, and is no answer to the main problem ofmagnetobiology. Af

ter all, unicellular

organisms that contain no magnetite are also able to sense an MF. The main task ofmagnetobiology is exactly to account for that phenomenon, which is a paradox in terms ofclassical physics.

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Kobayashi et al. (1995) suggested a mechanism to account for the biological action oflow-frequency MFs on cells in vitro in the presence offerromagnetic contaminants. Magnetic contaminants are available not only in the ambient dust, but they are also adsorbed by the surfaces of laboratory equipment; they enter into the composition ofplastics and glasses, laboratory chemical preparations, and water.

Their mean particle size is about 10 5 cm, and they consist of ferro- and ferrimagnetic substances; that is, they display spontaneous magnetization. The saturation magnetic induction varies within 4 πJ s = 500–7000 G.

The authors have shown that routine laboratory procedures ofpouring and rinsing enrich cellular cultures in vitro with magnetic particles, these latter outnumbering the cells dozens oftimes. The magnetic particle energy V in a magnetic field of H = 0 . 5 G will be about ε p = 4 πJ s V H ∼ 10 11 erg; i.e., it is larger than κT by three orders ofmagnitude. The authors believe that such a particle, when adsorbed on the cellular surface, can transfer its energy to neighboring cellular structures, e.g., to mechanically activated ion channels.

The problem is concerned with the fact that the magnetic particle energy being much larger than κT provides no explanation for the effect. That energy should be somehow transferred to the molecular level. A transfer of kinetic energy is impossible because the particle and the molecule have different sizes and masses. For a molecule with thermal velocity v m the particle is a kind ofwall that travels at v p

2 ε/M p.

It can be easily found that upon a collision the molecular velocity cannot increase by more than 2 v p. The relative increase in the molecular energy will be no more than 4 v p /v m. Substituting the velocities estimated from the respective energies and the masses ofthe magnetic particle and the molecule gives


ε ∼

M m

100

1 .

ε

M p

This suggests that even ifwe can talk about some mechanism that makes use of the energy ofthe magnetic moment ofa magnetic particle, it will be rather realized through the pressure exerted by the particle on the surrounding tissue, i.e., through a transfer of potential energy. The energy will then be transferred to a large number ofmolecules, so that each will receive an energy that is small in comparison with κT . Here we will need detailed calculations.

The mechanism holds well to explain the reception ofa DC FM, but for variable fields it is dubious. The natural frequencies of the oscillations of a magnetic particle introduced into an elastic tissue lie much higher than the low-frequency range.

Therefore, it would hardly be possible to explain low-frequency efficiency windows, let alone amplitude ones, using that mechanism.

Edmonds (1996) addressed the possibility ofutilizing the magnetic properties ofsuspensions ofnematic liquid crystals and magnetite microcrystals in the magnetic compass orientation ofbirds. In an idealized model situation, a nematic suspension with filamentary magnetite microcrystals was placed between glass plates with specially treated surfaces, which resulted in a certain anisotropy of the liquid

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crystal director vector. In this case, the polarization ofthe radiation that passed through the stack varied with the applied MF. The torque on the microcrystals was transferred to the nematic molecules and changed the director sense. The relative intensity ofthe radiation passed through two crossed polarizers was measured.

Between the polarizers a system with a liquid-crystal substance was placed. The MF dependence ofthe intensity was a curve with saturation, the maximum slope being about 3 %/ µ T. Given is an estimate ofthe magnetic moment alignment for a 5- µ m drop that contains magnetite microcrystals in a liquid matrix with a volume concentration of10 3. The alignment is significant even in a field of0.15 µ T, which could form the foundation for the mechanism of the optomagnetic aligning capability in animals.

In search for uses for such a mechanism, the question of whether birds’ eyes contain structures with extended dye molecules of β-carotene type that absorb light radiation at a certain orientation to the electric field vector and magnetite microcrystals that are responsible for the orientation of dye molecules in a magnetic field was discussed.

This mechanism relies on the interaction ofmagnetic microcrystals with nematic molecules. Liquid-crystal molecules per se display general magnetic properties of diamagnetic type. The anisotropy ofthe induced magnetic moment causes the director to turn in a magnetic field. However, this effect is fairly small to account for any MBEs. Known are only optomagnetic sensors ofstrong MFs, on the order of tens oftesla, constructed using that principle.

3.6.2 Eddy currents

One ofthe MBE mechanisms establishes that the driving force in the exposure of biological systems to a low-frequency MF is electric eddy currents induced by a variable MF in biological tissues.

The current is, on the whole, proportional with the strength E ofthe electric field related to the MF B by one ofthe Maxwell equations

B

rotE = 1

.

c ∂t

For a sinusoidal MF with frequency Ω and amplitude b, the electric field amplitude varies with the product Ω b. Ifthe hypothesis is true, then observed MBEs should correlate with changes in that quantity. However, no correlations have been found for the case of relatively weak fields (around the geomagnetic field).

Juutilainen (1986) reports the absence ofa dependence ofthe MBE on B /∂t.

Liboff et al. (1987b) cited four independent works on different biological systems within various ranges ofthe variable MF, where the eddy current hypothesis had been checked and not supported. Specifically, Liboff et al. (1984) studied the action ofvariable MFs on the growth ofthe DNA synthesis rate in human fibroblasts within the range of b(1 . 6 400) f (15 4000). However, the effect, which on average was no

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more than 50 %, was independent ofthe product bf , which was varied within four orders ofmagnitude.

Statistically meaningful 6 % variation ofthe fibroblast cell proliferation rate, as measured by Ross (1990), remained virtually unchanged under various magnetic conditions that correspond to the cyclotron configuration ofcalcium ions: B(131) b(131) f (100), as well as B(98) b(98) f (75) and B(21) b(21) f (16). The product f b is seen to change nearly 40 times, with the effect remaining the same.

Blackman et al. (1993) have shown that a 50-Hz MF with an amplitude of0–

42 µ T against the background ofa DC field similar to the geomagnetic one makes up for the action of matter that induces a double neurite outgrowth in certain animal cells. Such changes, beginning with an amplitude of6 µ T and stabilized at a new level ofabout 10 µ T, emerged. Therefore, to clarify the role of an induced electric field, an amplitude of8 µ T was taken, which corresponds to the maximum sensitivity ofa system to MF changes. Petri dishes with concentric sections of various diameters containing cells were placed in a homogeneous MF coaxially with a vertical solenoid. With that configuration the electric fields in various sections differed markedly and their amplitude was varied from 3 to 65 µ V/m, whereas the MF was the same. Measurements yielded the same quenching level in various sections, which pointed to the fact that the induced electric fields were insignificant.

The recent results ofJenrow et al. (1995) have also shown that there is no correlation ofMBEs with induced currents.

Very strong evidence against the eddy current hypothesis was supplied by Prato et al. (1997), where the parameters B DC, B AC, and f grew concurrently at first twofold and then fourfold. In the process, the product f B AC increased up to 16 times, but the statistically certain MBE level remained constant, Fig. 4.41.

It is to be noted that as the amplitude or frequency of a variable MF grows, a moment is still reached, when induced fields and currents become ofbiological significance, provided that a small biological system is not placed at the geometric center ofan exposure system, see Section 1.4.1. Experimental evidence that, as the variable MF strength grows, there emerges a correlation ofbiological response with the product f B AC is available in Schimmelpfeng and Dertinger (1997). Greene et al.

(1991) specially studied the transcription rate ofthe HL-60 leukemia cells in Petri dishes with concentrically divided sections placed on the axis ofa solenoid with a variable MF of60 Hz. Figure 3.10 shows the kinetics ofinclusion ofa radioactive marker 3H introduced into a cellular culture with uridine into RNA molecules being synthesized. The cells were 0.2 and 2 cm away from the axis and were exposed, in addition to an MF, to the action ofan induced electric field. It is seen that the cells responded to the variations ofthe electric, rather than magnetic, field.

Eddy currents can produce a biological response either due to tissue heating by Joule heat, Section 1.4.1, or due to electrochemical effects by the action ofinduced electric currents on charge carriers in the tissue — ions or charged molecular groups in various biophysical structure. Polk (1986) discussed a possible mechanism for the action ofa low-f

requency MF on the distribution and dynamics ofions on

the surface ofcellular membranes. He used the classical dynamics ofcharges in a

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*P9P

*P9P


*P9P


5DWH


7LPHKUV

Figure 3.10. The kinetics of the transcription of HL-60 leukemia cells in various electric and MFs with a frequency of 60 Hz, according to Greene et al. (1991).

magnetic field in the presence ofthermal diffusion and phenomenological damping, and the equations ofthe electrodynamics ofcontinua for the current density j

j = − ∂ ρ , j = E − uκT ∇ρ .

∂t

q

The first equation is the continuity equation; it relates the current density to the density ρ offree charges q ofmobility u. The second equation shows that the current is determined by the electric field E and the diffusion thermal dissipation ofinhomogeneities ofcharge density distribution. From this we can find the perturbations in the distribution caused by the electric eddy fields.

It was shown that induced currents on the membrane surface would under certain conditions exceed the thermal level. Specifically, the movement ofions must o

be constrained to a thin, around 10 A, layer on the cellular surface, and the cells themselves must form macroscopic > 3 cm, closed chains. A threshold level was found for the product f B ∼ 1 T/s when exposed to a sine MF. This, for instance, corresponds to the amplitude B ∼ 100 µ T at frequency f = 1 kHz. Although this estimate relies on a possible electrochemical mechanism, its value is close to the thermal effect threshold, see Section 1.4.1. We note that the condition ofmacroscopic cellular chains imposes a significant constraint on the applicability ofthat model. For instance, it cannot be used to account for MBEs in cellular cultures in homogeneous solutions in vitro.

There are also other electrochemical mechanisms for biological effects of an MF.

Chiabrera et al. (1984) discussed the possibility ofan action ofinduced electric fields on the transportation ofions and molecules through biological membranes.

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3.6.3 Superconductivity at the cellular level

The idea ofa superconductive state in a biological matter is attractive in that it enables the problem ofelectromagnetobiology to be reduced to the substantiation ofsuperconductivity in a biological tissue. In actual fact, ifsuch a superconductive state does exist, its characteristics beyond doubt change even in hyperweak MFs. It is exactly the properties ofthe superconductive state and its inter-phase boundaries (Josephson junctions (Josephson, 1962), see Addendum 6.7) that are used by supersensitive detectors ofan MF — quantum interf

erence devices

(SQUIDs). The “kT problem” as well requires no explanation — after all we here deal with superconductivity at normal physiological temperatures, i.e., with high-temperature superconductivity. In the literature, there are many speculations on that topic (Achimowicz et al. , 1979; Cope, 1981; Achimowicz, 1982; Miller, 1991; Costato et al. , 1996).

Fröhlich was one ofthe first to point to the biological cell as a possible receptor ofEM waves (Fröhlich, 1968a,b). That follows from the Bose-condensation mechanism he proposed for some modes of collective excitations in systems of interacting molecular dipoles in a living cell, within the millimeter (mm) range. Ever since search is under way for other mechanisms at the cellular level that would be able to account for biological reception of weak MFs in the low-frequency range as well.

For instance, in Costato et al. (1996) the possibility ofthe presence ofsuperconductivity in living cells and the appearance ofJosephson effects at junctions of such superconductive areas are discussed. It is maintained that properties similar to the dynamics ofthe Josephson junctions are observed for single cytoskeleton cells and for two neighboring cells. It follows that an EMF can affect intercellular communication.

Electron bisolitons, which transfer a double elementary charge and travel along alpha-spiral protein molecules without damping, were given a theoretical treatment by Davydov (1994). No way to experimentally test the existence ofbisolitons in living organisms was proposed.

A manifesto ofsorts ofcellular superconductivity is a review by Miller (1991).

It contains an extensive bibliography on the subject. At the same time, there are no sufficient theoretical grounds so far for the emergence of a superconductive phase in cellular structures. Also absent are productive predictive models for such a state. It should be noted that no high-temperature (300 K) superconductivity as a physical effect has been found as yet. Therefore, the idea of the emergence of a high-temperature superconductive state in biological tissues raises some doubts.

Attempts are known to support that idea experimentally. They rely on the fact that indicators ofa superconductive state are an abnormally high conductivity of the medium, and hence abnormal diamagnetism, and the quantization ofthe magnetic flux through an area constrained by a superconductive contour. This causes the current through the contour, other parameters being fixed, to assume only a series ofdiscrete values. Under some, fairly rigid, conditions, specifically where the contour contains a section with disrupted superconductivity — a Josephson junction

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— one can observe current oscillations and an electromagnetic emission at a characteristic frequency as the e.m.f. in the contour grows. Miller (1991) pointed to some experimental works that treat magnetic measurements ofbiological and organic media as the presence ofmolecular or subcellular superconductivity domains.

We also note the experiments ofAhmed et al. (1975), which measured the diamagnetic susceptibility ofweak solutions oflysozyme enzyme in a static MF of 40–200 mT. Variation ofsusceptibility with the MF, temperature, and enzyme concentration behaved in an involved multipeak manner. A susceptibility maximum was observed in the region of60 mT, such that the susceptibility per molecule exceeded normal values by a factor of more than one thousand. The authors came up with an explanation in terms ofsuperconductive domains with superconductivity disrupted in a stronger MF.

Del Giudice et al. (1989) assumed that the properties ofJosephson junctions are inherent in the biological membrane that separates two new cells as the initial cell undergoes a mitosis process. The authors assumed that Josephson-type phenomena could occur not only at superconductor junctions, but also in a more general case — at the boundaries between the phases ofa correlated state. The role ofelectron pairs will then be played by quasi-particles — correlation carriers, e.g., bosons ofcoherent excitations ofmolecular dipoles in the Fröhlich model, see Addendum 6.6. We will put aside those esoteric ideas and consider experiments described in Del Giudice et al. (1989). According to the authors, they support the existence ofsuperconductivity or similar macroquantum states in a biological tissue.

They measured the current in a circuit including an electrochemical cell unit with cellular culture S. cerevisiae in a de-ionized solution ofsucrose immediately before, during, and after mitosis. The cells in the unit between electrode needles formed chains after the fashion of pearl threads, which was observed under microscope. Also measured was the voltage across the unit. Using a current generator with an internal resistance of12 Mohm, the current in the circuit was increased bit by bit and voltage jumps across the unit were observed. This means that the voltage–current characteristic was stepwise in nature. That effect was not observed with sterilized cells. In general, such a dependence is characteristic ofthe current in a superconductive contour with a Josephson contact, since the magnetic flux through the contour only assumes values that are multiples ofthe magnetic flux quantum. The jumps occur when the superconductive current component reaches a critical value and destroys specific quantum phenomena in the region ofthe contact.

It was ofimportance for the observation that the synchronized cell suspension displayed current and voltage jumps only in cytokines, the final stage ofmitosis, when a wall between two daughter cells was being formed. Moreover, the voltage jumps were varied in the range of0.3–3 from a mean value, which is rather due to a scatter ofcell sizes. Ifwe consider this wide scatter ofjump values and the fact that dividing cells formed threads between the electrodes, we will get another explanation ofthe observed results, which does not rely on the idea ofbiological superconductivity. When a cell splits to form two cells, the electric resistance jumps, and so does the voltage across the electrodes with the result that the current in the

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circuit drops. The small current drop is well seen in the curve (Del Giudice et al. , 1989), thus suggesting that the internal resistance ofthe current generation is similar to the unit resistance. It is noteworthy that the voltage jumps were influenced by the value ofan external MF. The mean values ofthe jumps V were 1580, 470, and 15 nV, the field H taking up values 400 mT, 50, and 1 µ T, respectively. The last value of1 µ T was not measured, but it was characteristic ofthe MF inside mumetallic magnetic screens, a place where the appropriate measurements were made. That series forms a near-logarithmic dependence V ( H), a curious fact, but such a behavior does not fit properly with the idea ofsuperconductivity.

In that work, they also observed electromagnetic emission ofcells in the cytokines phase. The emission was also observed by other authors, Hoelzel and Lamprecht (1994) and Berg (1995), under similar conditions. The emission ofyeast cells at around 7 MHz displayed a spectral maximum ofwidth 5 KHz.

The measurements were performed in a magnetically screened chamber, when the above experiments with voltage jumps yielded a value ofabout 15 nV. The authors assumed that the emission is caused by quantum transitions ofa system to a neighboring current state. One justification was the following coincidence. The calculated frequency of the emission by a Josephson junction fed by a 15-nV voltage source is eV /π 7 . 3 MHz, which agrees with the experimentally observed values, but that justification is hard to accept. Even ifwe assume for a minute that in both cases —

the voltage jumps and the radiation — there occurs a Josephson effect, then we get a significant contradiction. In the first case, that would be a stationary effect; in the second, a non-stationary Josephson effect. The voltages under these conditions have different physical meanings. Therefore, one cannot use voltages obtained for some conditions to compute effects under other conditions.

It should be emphasized that dividing cells could emit due to current impulses on the membrane surface caused by a redistribution of surface charges as a cell membrane splits in two. The impulse length can be easily estimated from the formula for the mean square of the ion diffusion displacement r 2 6 Dt, where D is the diffusion coefficient, see p. 281. Substituting the characteristic size ofthe charge redistribution area 0.1–1 µ m and considering that the ion diffusion on the cellular surface, the so-called lateral diffusion, is a couple of orders of magnitude faster than the volume diffusion (Eremenko et al. , 1981) gives a rough estimate ofthe impulse length of0.01–1 µ s. Such impulses produce an electromagnetic field in the range of1–100 MHz. This range characterizes the estimation inaccuracy, rather than the radiation spectrum width. In the final analysis, the spectrum width is determined by the scatter ofphysical parameters ofcells, primarily by the scatter oftheir sizes.

The experiment under consideration and the Josephson effects seem to display only external similarity, rather than uniformity of causes. Biological superconductivity still remains one ofmarginal hypotheses in magnetobiology. Being still of interest, it has no reliable theoretical and experimental substantiation.

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3.6.4 Magnetohydrodynamics

There are treatments ofmagnetohydrodynamic effects occurring as blood or other bioplasm flowing through vessels is exposed to an MF, see review (Kuznetsov and Vanag, 1987). Studied was, for instance, the additional pressure on vessel walls under a Lorentz force acting on free charges in the blood. Those treatments, however, generally overlooked the fact that macroscopic pressure effects are provided for by appropriate microprocesses. If in that case no explanation is forthcoming for marked changes in the state of a single microparticle in an MF, then any positive statements on macroscopic corollaries look feeble. Such statements must contain derivation mistakes — mathematical, physical, and, most often, logical and conceptual ones, i.e., those relying on concepts beyond the validity area.

Magnetic hydrodynamics looks into the interplay ofelectromagnetic fields and moving liquid or gaseous media with a relatively high conductivity, such as in metals. When a medium moves in a magnetic field, it has currents engendered in it. These latter, for one thing, are subject to an external MF; for the other, they are themselves a source ofadditional MFs. To estimate the degree ofthe influence ofan MF on the liquid flow they normally use the Hartmann number, the density ratio of magnetic and viscous forces (Landau and Lifshitz, 1960)


rH

σ

G =

,

c

η

where r is the characteristic distance, σ is the electric conductivity ofa medium, and η is the viscosity coefficient. Hartmann investigated the flow ofa viscous incompressible liquid between two planes in a perpendicular MF H to show that if G 1, then magnetic effects will be small. Conversely, if G 1, then the viscous properties ofthe liquid can be ignored. For example, the movement ofblood with a conductivity of 1 S/m = 9 · 109 CGS units and a viscosity of0.01 g/cm · s along a vessel about 10 2 cm in diameter in a magnetic field 1 G is characterized by a Hartmann number of G ∼ 10 6. Consequently, magnetohydrodynamic effects in magnetobiology do not warrant any studies.

To evaluate contributions ofother possible effects we will pass over to a reference system moving in a magnetic field H with the liquid at a velocity v. In such a system an electric field that is around E ∼ vH/c emerges. Generally speaking, the electric field could align molecules with a dipole moment, e.g., water molecules with the moment d = 1 . 855 D. However, the additional energy dE acquired by a water molecule in this EF for an MF of1 G and a velocity of1 cm/s is 14 orders of magnitude smaller than the disordered thermal scale κT . That makes useless any discussion ofbiological consequences ofdipole aligning. Another scenario looks at the pulling ofoppositely charged ions in opposite directions. The work needed to move a charge e a macroscopic distance r in a field E is erE, whereas the diffusion processes that hinder that movement have the same energy scale κT . This suggests that for changes in ion concentration on volume walls to be observed requires five or six more orders ofmagnitude, even for r ∼ 1–10 cm.

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3.6.5 Macroscopic charged objects

Macroscopic objects as targets for weak MFs are chosen because of their sufficiently large own energy comparable with κT . This takes care ofthe problem. In fact, even a weak MF is capable ofsignificantly changing the energy ofan object that carries, for instance, a large electric charge (Karnaukhov, 1994), or moves at a high velocity relative to other objects. True, this requires that the object travel under strictly defined conditions. A change in the object energy in an MF is associated with some biochemical processes. However, in all works ofthat class known to this author the existence ofsuch objects was postulated. They have not been observed in any other experiments not concerned with magnetobiology. Therefore, that postulate can hardly be justified. Models can be thought to be ofvalue, where an insignificant assumption, or even an idealization, yields some consequences ofsignificance. In our case, however, the “weight” ofa postulate is comparable with that ofthe problem itself. Postulating the existence of such objects — macroscopic charged ion vortices (Karnaukhov, 1994), etc. — amounts to postulating the absence ofthe issue of magnetobiology per se.

Novikov and Karnaukhov (1997) explained MBEs and the action ofa combined MF at a cyclotron frequency on amino acid solutions. Instead of individual ions in a solution they considered their clusters with a macroscopically large number N

ofions. The mean value ofrandom forces with which the thermostat acts on the cluster at sufficiently large N becomes smaller than the mean value ofthe force produced by an MF, i.e., the Lorentz force. The authors believe that this sort of removes the problem. Without criticizing the quality oftheir reasoning we will only bring out the following bottlenecks of the idea.

Firstly, the nature of interion forces that are responsible for the existence of a cluster is unclear. Secondly, according to this work, a cluster is a system with mass N M and charge N q, whose dynamics in an MF is controlled by the motion ofthe center ofmass; otherwise the notion ofthe cyclotron frequency for a cluster would become meaningless. The thermal energy ofthe motion ofthe center ofmass is then the same as with an individual ion, since both an ion and a cluster are, in that respect, identical with a point particle with three degrees offreedom. It is common knowledge that thermal energy is distributed uniformly between the degrees offreedom, not between individual particles ofa system.

At the same time, the contribution ofan MF to the cluster energy does not grow with its charge in proportion to N , as it might seem due to the growth of the Lorentz force. This author (Binhi, 1995b) estimated the instantaneous power of transformation ofthe energy ofa variable MF into the energy ofthe momentum of a classical particle (Eq. (20) in the article). In terms ofconventions adopted here, the formula has the form 22

G ≤ ω 1Ω L ,

22For a quantum particle in an MF, energy splitting is εm ∝ m ω 0 = m qH/ 2 Mc. In an AC

MF we have dH ∼ Hdt, hence the power dε/dt ∝ ω 1Ω m. Here m is an angular momentum of the m state.

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where ω 1 = qH AC / 2 M c is the Larmor frequency related to the amplitude of a variable MF, and L is the angular momentum. It is worth noting that the Larmor frequency ofan individual ion equals that ofan ion cluster; the same is valid concerning the cyclotron frequency. Therefore, it is of interest to evaluate the angular momenta L ofthe ion and the cluster. The question boils down to the following: whether there exist some mechanisms or constructions in a living tissue or a solution, which are able to provide a non-zero angular momentum ofa particle during a time ofabout Ω 1? It can be assumed that for an ion such a construction is the macromolecule cavity. When an ion gets into the cavity for some time it retains an initial angular momentum, and so it can exchange energy with an MF. A cluster being a macroscopic system, it would be hard to make whatever assumptions.

The only reasonable estimate in this case is L = 0, since nothing can cause the cluster center ofmass that undergoes numerous thermalizing collisions to move in a circle or an arch. There are also no reasons for a toroidal cluster to have an angular momentum, but assumptions ofsuch a cluster form are also available in the literature. It is, thus, hard to agree that ion clusters will somehow clarify the magnetobiological issue.

Generally speaking, when exposed to an MF ions in a solution acquire an angular momentum, although an extremely small one. It can readily be found from the equation

dL = K = r × qv × H , dt

c

where L is the angular momentum, K is the torque, and r is the radius vector of a particle. Clearly, the derivative dL/dt is bounded from above by rqvH/c. Since an ion undergoes thermalizing collisions with ambient media particles, the angular momentum between collisions is

L ∼ τ rqvH/c ∼ τ 2 qv 2 H/c ,

where r ∼ 10 8 cm is the length, and τ is the time of the mean free path. Since the squared velocity ofa particle in a solution is about κT /M , then f or τ ∼ 10 10 s, Ωc 100 Hz

L ∼ κT Ωc τ 2 .

That is, the angular momentum ofa free ion is much smaller than the quantum uncertainty for the momentum. To prove that, we will find the diamagnetic contribution concerned with the emergence ofthat momentum. The gyromagnetic ratio for the orbital motion is γ = q/ 2 M c, and so the magnetic moment for a volume unit equals I = γL/r 3, and the diamagnetic susceptibility χ = ∂I/∂H will be τ 2

χ ∼ q κT ∂ Ωc

∼ q 2 10 9 .

M c

∂H r 3

M c 2 r

There is no need to average over particles since that quantity is extremely small, namely several orders ofmagnitude smaller than the atomic diamagnetic susceptibility, see Section 3.6.1.1.

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3.7 CYCLOTRON RESONANCE IN MAGNETOBIOLOGY

In a number ofcases biological effects ofweak MFs have a resonance nature; it was initially established in Liboff (1985) and Liboff et al. (1987b) that the effective frequencies are close to cyclotron frequencies of Ca2+ and Na+ ions, and so on. This suggested that the phenomena observed rely on a cyclotron resonance.

The idea ofcyclotron resonance in magnetobiology is credited to A. Liboff ofOak-land University, USA. Various authors elaborated the topic ofsuch a resonance in magnetobiology, but it failed to receive any recognition because it was impossible to supply a correct physical substantiation. At the same time, these experiments demonstrated the significant role ofions, especially Ca2+, in magnetobiology. Nearly 12 % ofworks on electromagnetobiology contain discussions on the role ofions, and 9 % on the role ofcalcium.

3.7.1 Cyclotron resonance

For a classical charged particle in an electromagnetic field

A

E = grad A 0 1

,

H = rotA ,

(3.7.1)

c ∂t

equations ofmotion are (e.g., Landau and Lifshitz, 1976a)

dv

q

M

= qE +

v × H ,

(3.7.2)

dt

c

where the right part is the Lorentz force. Considering that the kinetic energy of a particle is ε = M v 2 / 2, we can easily find from (3.7.2) the energy variation rate dε/dt

d ε = qvE .

(3.7.3)

dt

Let a particle move in a plane perpendicular to a direction H z, and the field E

be aligned along the x axis. Also let the EF Ex ∼ cos Ω t be so small that the orbit ofthe motion ofa particle varies little during the time 1, so that the particle can be viewed as free. From (3.7.2) it follows that the particle moves in a circle with cyclotron frequency Ωc = qH/M c. The x component ofits velocity will then, up to a phase, vary as cos Ωc t. Correspondingly, we find from (3.7.3) d

1

1

ε ∼ cost cos Ωc t =

cos(Ω Ωc) t +

cos(Ω + Ωc) t .

dt

2

2

The energy change is mainly dictated by the first term with the small frequency β = Ω Ωc. Let that change be measured during the time span from t − T to t + T .

Divided by the time span it is equal to


1

t+ T

εT =

cos βτ dτ ∼ sin βT cos βt .

(3.7.4)

2 T

t−T

βT

The energy change can be both positive and negative, depending on the random moment ofobservation t. Therefore, the intensity of the particle energy variation

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Ω Ω

Figure 3.11. The energy exchange intensity between an EM field and a charged particle at a cyclotron resonance measured during the time interval [ −T, T ].

can conveniently be characterized by the mathematical expectation ofthe squared quantity (3.7.4), i.e.,


sin βT

2

I = ε 2

,

T

βT

where the overbar implies the averaging ofan ergodic process over the time interval T .

That function is plotted in Fig. 3.11. It is seen that the particle energy variation rate is largest at a cyclotron resonance when frequencies Ω and Ωc coincide.

The supposition that an ion cyclotron resonance also occurs at odd harmonics of cyclotron frequency and does not occur at even harmonics (Smith et al. , 1995) is not quite justified. For instance, under certain conditions in metals the time interval between successive collisions ofelectrons with dissipating centers is on average larger than the FM period. When the MF vector is strictly parallel with the metal surface, electrons only spend a small part of the motion period near the metal surface, where they are exposed to an external variable electric field. Conditions then emerge for a resonance at all the multiple frequencies. Similar conditions are realized in cyclotrons, accelerators ofcharged particles. In a biological medium or in biophysical structures, there is no way for an external EF to act on ions through a small section oftheir orbits, ifonly because there are no orbits as such. Therefore, resonances at multiple frequencies are impossible. Generally speaking, with circular EFs induced by a variable MF, a resonance is possible at a cyclotron frequency or its subharmonics. However, that is not a cyclotron resonance, but rather a parametric one. It will be considered later in the book.

The idea ofcyclotron resonance has been employed many times to explain biological effects oflow-frequency MFs. Being quite graphic, the idea enjoys support ofmany researchers, mostly biologists. The main argument ofits advocates is that MBEs appear mostly at frequencies formally predicted by the cyclotron resonance

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formula Ωc = qH/M c for biologically significant ions of Ca, Mg, etc. A effective frequency shift that varies with H (Liboff et al. , 1987b) was observed, along with a shift in accordance with ion isotope mass (Liboff et al. , 1987a).

The main argument ofthe opponents ofthat concept (e.g., Sandweiss, 1990; Adair, 1991) boils down to the following. In a living matter ions occur in a water solution at a temperature ofabout 300 K. They feature a thermal energy ofabout κT . A particle in a magnetic field moves in a circle, whose radius can be easily worked out from the fact that the thermal energy is equal to the energy of motion: 1

κT

R =

.

Ωc

M

In an MF similar to the Earth’s field, for a calcium ion this yields more than 1 m.

It is clear then that this value does not match an ion cyclotron resonance, say, in a biological cell ofsize that is six orders or magnitude smaller.

What is more, an ion in a solution is hydrated; i.e., it carries on it a shell of water molecules. Its effective charge is then several times smaller. It then makes no sense to correlate the external field frequency with the cyclotron frequency of an ion without a shell.

There are also other considerations that lead to the same conclusion. An ion particle in a cytoplasm or intercellular medium undergoes numerous thermalizing collisions with neighboring molecules, the particle moving about in a diffusion manner. Ofcourse, that motion, which is correlated in phase with an external MF, is limited by the free path time, i.e., by the time between two consecutive collisions with media molecules. In a water solution that time T is 10 11 s. In Sandweiss (1990) that estimate for calcium follows from the formula

1

T =

,

nσv


where v =

2 ε/M is the thermal velocity ofan ion, n ≈ 4 · 1028 m 3 is the atom density in a biological medium, σ ≈ πa 2 = 8 · 10 21 m2 is the collision cross-section, 0

and a 0 is the Bohr radius.

Clearly, the “resonance bandwidth” 1 /T (see below) is many orders ofmagnitude larger than the cyclotron resonance frequency. This also suggests that the cyclotron resonance concept does not hold good for an ion in a solution.

3.7.2 Cyclotron resonance in ion channels

To circumvent the difficulties, it was suggested that an ion cyclotron resonance occurs within ion channels ofbiological membranes, where the orbit radius could not be large. Ion channels that pierce the membranes are formed by spiraling proteins.

They are responsible for the life-supporting exchange of ions and some molecules with the cytoplasm and the extracellular medium. The most complete treatment of the model is given by McLeod et al. (1992b). That work maintains that the motion

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ofan ion within a channel occurs largely without random thermalizing collisions.

Then it is phased in for a sufficiently long time with an external MF, and can thus be described by an equation ofclassical dynamics for a particle under a Lorentz force.

The work also postulated that (1) an ion begins its motion from a channel’s mouth from rest, and (2) a channel of cylindrical symmetry has two contractions: at the middle and at the end ofthe channel. As it sets out from the mouth, the ion is spiraling under the action ofa transmembrane potential difference and a variable MF. The idea underlying the model is the ability ofan ion to acquire under special conditions an extremely small energy near the contractions. Therefore, the cyclotron orbit diameter is smaller than that ofthe contractions, so that the ion finds its way through the channel’s bottlenecks. The structure ofthe protein that f orms the

channel in that model acts as a filter or a gate for a variety of spiral paths for ions.

The filter efficiency is determined by the parameters ofan external low-frequency MF. That enables theoretical ion paths in the channel to be correlated with the conditions in magnetobiological experiments.

It is common knowledge that the equation ofmotion for a charged particle in a medium with energy dissipation under an electromagnetic field and an external force has the vector form23

dU

q

q

1

=

E +

U × B 1 U +

F .

(3.7.5)

dt

m

m

τ

m

Cylindrical coordinates Pr, Pϕ, Pz ofan arbitrary vector P will be (Korn and Korn, 1961)

Pr = Px cos ϕ + Py sin ϕ ,

= −Px sin ϕ + Py cos ϕ ,

Pz = Pz .

Using these rules, we easily find the physical coordinates ofthe velocity vector U

dr

Ur =

,

= r

,

Uz = Uz

(3.7.6)

dt

dt

and the acceleration vector d U

dt


d

d 2 r

2

dUr

U

=

− r

=

− Uϕ

,

(3.7.7)

dt

dt 2

dt

dt

dt

r


d

d 2 ϕ

dr dϕ

dUϕ

1

U

= r

+ 2

=

+

UrUϕ ,

dt

dt 2

dt dt

dt

r

ϕ


d

dUz

U

=

dt

dt

z

in a cylindrical coordinate system. Substituting (3.7.6) and (3.7.7) into (3.7.5) gives the following equations of motion

23MKS unit system.

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dUr − dϕ

q

q

Fr

=

Er +

UϕBz − Ur +

,

dt

dt

m

m

τ

m

dUϕ

1

q

+

UrUϕ =

Eϕ − q UrBz − Uϕ +

,

dt

r

m

m

τ

m

dUz

q

Fz

=

Ez − Uz +

,

(3.7.8)

dt

m

τ

m

where, as in McLeod et al. (1992b), it was assumed that the MF is aligned along the z axis, which coincides with the channel axis, i.e., Bx = By = 0.

The equations used by McLeod et al. (1992b) differ from (3.7.8) and contain some inaccuracies. Further, the dissipative term U in the equation ofmotion (3.7.5) implies that there occur numerous chaotic collisions ofa macroscopic particle under consideration with a host ofmicroparticles, which are molecules ofthe liquid medium. At the same time, the walls only confine an ion in a channel, so that each collision will markedly change its momentum. That means that the physical conditions under which the use ofthe phenomenological dissipative term is valid are ignored.

The most fundamental challenge of the model is concerned with rigid initial conditions for an ion. The ion has to have a near-zero initial velocity, so that cyclotron radii ofmotion would be smaller than the transverse size ofan ion channel.

o

At a channel radius ofabout R ∼ 10 A, the velocity that can be estimated from a formula for cyclotron motion in a magnetic field similar to the Earth’s field,

50 µ T, must be at least

q

U ≤ R

B ∼ 10 7 m/s

M

for a potassium ion, and 40-fold larger for a hydrogen ion. Can ions move so slowly at the channel entrance? The mean thermal velocity ofa potassium ion at T = 300 K

will be

κT

U ∼

102 m/s .

M

o

Even ifan ion is placed within a channel oflength L ∼ 50 A, the uncertainty, according to the Heisenberg relation, will be more than


U ≥

0 . 3 m/s .

M L

Correspondingly, the ion velocity will not be smaller, a fact that is at variance with the assumption underpinning the model.

The idea underlying the model is attractive, but removing the mathematical inaccuracies does not save it. The equation ofthe Lorentz force is hardly applicable to describe the ions that are constrained by the ion channel. Such ions are rather waves than particles, although their mass is relatively large, see p. 215.

3.7.3 Ion cyclotron resonance

In the literature there is one broad treatment ofthe subject ofcyclotron resonance.

It is known as “ion cyclotron resonance” (ICR). ICR appeals, for one thing, to the

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fact that ions contribute to magnetoreception, and, for the other, to the fact that the effective frequencies coincide with the frequencies of the cyclotron series. In this broad sense, the idea ofcyclotron resonance is obviously correct and useful, since it proceeds from more or less reliable experimental evidence. In that case, ICR is also a prototype ofmore advanced models still to be constructed, which will meet all the criteria ofscientific methodology. It is important that the broad treatment ofthe cyclotron resonance leaves much room for specific realizations of that concept. One interesting suggestion is that an ion is exposed to internal or endogenous electric fields (Liboff, 1997). These are always present in an organism owing to a wide variety ofbiochemical processes involving charge transport. Liboff assumes that such fields can have complicated frequency spectra; specifically, they can excite ions at characteristic frequencies of the cyclotron series. That makes it possible to interpret the biological effects ofweak DC MFs. In a modified MF, cyclotron frequencies change, and so does the picture of their “superposition” on the frequency spectrum of endogenous electric fields. This changes the conditions under which ions undergo excitations. There is no testing the hypothesis so far, since to this end spectra ofendogenous fields will have to be measured concurrently with an MBE.

3.7.4 On the bandwidth of a resonance-like response

It is seen in Fig. 3.11 that there is some resonance width caused by the fact that the measurement time T is limited. Such a broadening also occurs in the absence ofdamping factors. The peak, or maximum, width is about Ω = 2 π/T . In the ideal case ofinfinite measurement time T = , the width becomes zero, as the case should be for the ideal oscillator without damping.

The damping, or relaxation, is often taken into consideration phenomenologically by including into a particle’s equation of motion an additional friction force, which is proportional with the velocity, e.g., the term U on the right-hand side of (3.7.5). That yields an additional factor ofthe broadening ofthe resonance curve.

It is impossible to know beforehand which of the two broadening factors will prevail. In magnetobiological experiments the measurement time T is not totally controlled by the researcher, so that it cannot be made arbitrarily long. The time-limiting capability is passed over to a biological system under study, or rather to those biochemical processes that are involved in the interaction with a particle, the primary target for an MF. The measurement time T here should be taken to be the characteristic communication time during which a biophysical or biochemical system “enables” the primary oscillator, an MF receptor, to accumulate the MF

energy or, more generally, to stay at a state that is in phase with the MF. We can talk here about the time ofthe coherent interaction ofthe particle with the MF.

The characteristic time ofthe development ofbiochemical processes, from split seconds to minutes, seems to be able to substantially affect the width ofobserved frequency responses in the low-frequency range, when the order of magnitude of the

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observed frequencies is comparable with the characteristic frequency T − 1. This circumstance is often overlooked. For instance, in Liboff et al. (1987b), Lednev (1991), Blanchard and Blackman (1994), and Lednev (1996) the resonance width is only discussed in connection with the damping factor, or the oscillator attenuation.

For sufficiently large measurement times, the shape ofa resonance curve or the variation ofthe power off

orced oscillations, i.e., the squared amplitude of

oscillations y, with the frequency Ω of an external force, has the form


1

y 2 Ω2 + a Ω + b

,

where a b are coefficients. A similar Lorentz form is displayed by the amplitude of resonance transitions in a quantum system, see. Fig.4.19. In Blackman et al. (1999) an attempt was made to show that the contour ofthe frequency dependence ofan MBE experimental peak in Fig. 2.25 (for five fixed frequency values) has the form ofa Gaussian distribution. The authors believe that this shape should emerge in the MBE spectral peak, since the latter is the collective response ofan ensemble of individual resonating systems with a random spread ofparameters. We note, however, that the five points located more or less symmetrically about the maximum, as in Fig. 2.25, could also be approximated by several other functions, including the Lorentz form and the interferential motif (sin x/ x)2.

This author doesn’t know ofworks where the width ofMBE experimental spectral peaks would be given a treatment different than the damping ofclassical oscillators or resonance quantum transitions. For a Zeeman multiplet there are no resonance transitions induced by uniaxial MFs, and then, since there is no resonance, the very idea ofresonance width becomes void. At the same time, the broadening ofspectral peaks due to the limited time ofcoherent interaction, or the communication time, has a general nature and manifests itself irrespective of the physical nature ofthe spectra.

3.8 PARAMETRIC RESONANCE IN MAGNETOBIOLOGY

3.8.1 Parametric resonance of a free particle in an MF

The binding ofions or macromolecules with their receptors in terms ofthe classical dynamics ofa particle in an MF was studied by Chiabrera et al. (1985). In a DC MF, the motion ofa free particle is finite, and there is no time-averaged displacement ofthe particle. Studied was the case ofthe parallel orientation ofa DC and an AC

MF

H = H DC + H AC cos(Ω t) .

It was shown that ifthe frequency ofan AC MF is the n th subharmonic ofthe cyclotron frequency of a particle, then the MF is responsible for a constant component in the particle’s displacement. The authors believe that this affects the probability for a ligand to be found with a receptor. The displacement has been obtained as a combination ofthe Bessel functions oforder n, n + 1, and n − 1. It is

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noteworthy that if n = 1, i.e., if the field frequency equals the cyclotron frequency, then the first zero ofthe response function emerges at a definite DC-to-AC field amplitude ratio H AC /H DC 1 . 85, with a maximum at H AC /H DC 0 . 9. Applying that model to the Ca2+ ion enabled the model to be correlated with Blackman’s data on MBEs obtained at various frequencies and at various H AC /H DC ratios.

That seems to have been the first ever, although fairly imperfect, model of magnetosensitive binding ofions.

We will provide the derivation of a relationship for the velocity, rather than for the ion displacement, in the notation ofthat book, and using a procedure that is in a way somewhat simpler than that in Chiabrera et al. (1985). That work considered the motion ofan ion in the xy plane in a magnetic field H ⊥ z, in the limiting case ofvery small damping. We will write the equations ofmotion for a particle under the Lorentz force in coordinate form, where x and y below are velocity components,

˙

x = f + gy ,

˙

y = −gx ,

f = qE( t) /M ,

g = qH( t) /M c ,

(3.8.1)

where an electric field is along the x axis. Mathematically, (3.8.1) is the Hill set of equations, and its special solutions are a parametric resonance.

An implicit assumption in Chiabrera et al. (1985) was that the area ofmotion for a particle is small in comparison with the size ofthe source ofa homogeneous MF. Only in that case can one suppose that the induced electric field on the particle is independent ofthe particle coordinates (see Section 1.4.1), a fact that is reflected in the form ofEq. (3.8.1). With no loss ofgenerality, the field E can be viewed as directed along the x axis and having the strength

R dH

E =

.

c dt

Here R is the constant that characterizes the size ofthe MF source, the scalar field potential being assumed to be zero.

The solution (3.8.1) can be easily found by the method of the variation of constants. We will write the equations in matrix form


x

0 g

f

˙

u = Au + B ,

u =

, A =

, B =

.

(3.8.2)

y

−g 0

0

There are two linearly independent solutions ofthe appropriate homogeneous ( B =

0) equation:


sin w

cos w

u1 =

, u

,

w =

g dt .

cos w

2 =

sin w

The solution (3.8.2) will be found in the form u = c 1u1 + c 2u2. Substituting the solution into that equation gives for the coefficients c

˙ c 1 sin w + ˙ c 2 cos w = f ,

˙ c 1 cos w − ˙ c 2 sin w = 0 ,

which has the obvious solution ˙ c 1 = f sin w, ˙ c 2 = f cos w or

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c 1 =

f sin w dt ,

c 2 =

f cos w dt .

(3.8.3)

It follows from the form of u that the velocity components can be written as x = c 1 sin w + c 2 cos w ,

y = c 1 cos w − c 2 sin w .

We will then find that the squared velocity modulus is v 2 = x 2 + y 2 = c 2 + c 2. That 1

2

could be written as the sum ofsquared real and imaginary parts ofthe complex coefficient


v 2 = 2 {c} + 2 {c} ,

c =

f e iwdt .

(3.8.4)

Integrating g, we get


w =

g dt = 2 ω 0 t + 2 ω 1 sin(Ω t) /, where ω 0 and ω 1 are the Larmor frequencies, associated with the fields H DC and H AC, respectively. Hence, substituting into (3.8.4), introducing the notation z 0 =

2 ω 0 / Ω, z 1 = 2 ω 1 / Ω, and using the relationship e iz sin τ =

J n( z)e inτ ,

n

we find, having calculated f = 2Ω ω 1 R sin(Ω t), after fairly simple transformations, the coefficient c in the form


c = 2 ω 1 R

J n( z 1)

sin τ e i( z 0+ n) τ dτ .

(3.8.5)

n

The integral is derived by repeated integration by parts. It will be sin τ − cos τ e iατ , α = z 0 + n .

1 − α 2

We will ignore both the the initial conditions and the fact that the system observation time is finite, since we only desire to illustrate the general nature ofthe response. The expression for the integral suggests that under resonance conditions, α = ± 1, the coefficient c and the particle velocity grow indefinitely. It is seen that the terms ofthe sum in (3.8.5) decline quickly with n due to the integral properties. In our estimates we will confine ourselves to two terms that make the most contribution; their numbers n can be worked out from z 0 + n = ± 1. Then the real and imaginary parts ofthe coefficient c will be

{c} = −ω 1 R J n( z 1) sin2 τ , {c} = ω 1 R J n( z 1)(sin τ cos τ − τ) , τ = Ω t .

Hence the squared velocity averaged over a large time interval becomes v 2 = ω 2 R 2J2 ( z

1

n

1) sin4 τ + sin2 τ cos2 τ + τ 2 2 τ sin τ cos τ .

The input ofthe first two terms is 1/2, and that ofthe last term is zero. The input ofthe term τ 2 reflects the unlimited growth ofvelocity under resonance conditions z 0 + n = ± 1 in the absence ofdamping.

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A part ofthe mean square velocity is ofinterest that varies in a non-trivial manner with the MF amplitude. We will agree to call that part magnetodependent.

It is

v 2 1 ω 2

2 1 R 2J2 n( z 1) .

With a DC MF fixed, the frequency of (parametric) resonance, given by z 0 + n =

± 1, is equal for two above-mentioned terms (3.8.5) Ω = 2 ω 0 /(1 + n) and Ω =

2 ω 0 /(1 − n). Ifthe MF frequency Ω is selected so that its modulus equals that ofthe Larmor frequency, then the appropriate values of n will be 1 and 1, and the values ofthe argument z will be 2 ω 1 0 and 2 ω 1 0. However, since for real arguments and integer n the Bessel functions satisfy the equalities J2 n( −z) = J2 n( z) and J2 −n( z) = J2 n( z), then both terms will make equal inputs to the mean square velocity. Since ω 1 0 = H AC /H DC, then


H AC

v 2 ∼ ω 21 R 2J21 2

.

(3.8.6)

H DC

This formula is a fairly good illustration of the variation of the velocity with MF

parameters. The fact that this function more or less fits experimental data in Fig. 2.11 seems to be a coincidence. The magnetodependent part ofthe squared velocity does not exceed ω 21 R 2. Consequently, the change in the energy, or rather its part that depends in a multipeak manner on the AC MF amplitude, does not exceed dε ∼ M V dV , where V is the particle velocity, and dV = ω 1 R is the change ofthe velocity in the induced electric field. Ifwe assume that the ion was at first moving with a thermal velocity, then the relative change in its energy is easily seen to be limited by dε/κT ∼ 10 %. That might be of interest, if it were not for the fact that at thermal velocity the area ofthe ion motion ofabout the cyclotron radius in the geomagnetic field is much higher than not only the size ofa biological cell, but also the reasonable size R ofan MF source. That makes the above treatment invalid due to the initial form ofthe equations irrespective ofthe size ofa biological system. Moreover, interaction with ambient molecules leads not to processes that could be described by phenomenological damping, but rather to the Brownian motion ofions. To all intents and purposes, that leaves no hope that the response to an MF signal in any dynamic parameter ofthe ion will accumulate.

In order to circumvent that difficulty, Chiabrera and Bianco (1987) proposed that the motion (flat) ofa charged particle, such as an ion, hormone, or antigen, be considered at a binding site, where, according to the authors, the intensity of thermalizing collisions with water molecules is small because these latter are forced out ofthe binding area by hydrophobic forces. However, the residence or “flight”

time for a free particle in such an area is small, and so the mechanism under consideration has no time to develop properly. After all, for the averaged velocity and displacement to have a meaning, it is necessary for the averaging time to cover at least several periods ofcyclotron motion. At ion thermal velocities such a motion scale will in any case be much larger than the binding site size. The metastable motion ofan ion with small non-thermal energy could occur within some molecular

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cavity protecting from thermal perturbations, but then no equations of free motion will be applicable.

The work (Chiabrera et al. , 1985) was not without its positive influence. It showed for the first time that some parameters ofthe motion ofa charge, specifically ofa Ca2+ ion, in a combined MF are, in a complicated manner, e.g., via Bessel functions, dependent on the ratio of the amplitude of an AC MF and the magnitude of a DC MF. Clearly, the model is no good for real motions of ions in biological structures. This notwithstanding, the presence in the model ofamplitude and frequency efficiency windows for an MF, which are a good match to the experimentally observed windows, suggested that the search for MBE mechanisms associated with ion dynamics holds promise. Later, Lednev (1991) drew attention that such involved dependences on the parameter H AC /H DC emerge when optical radiation is dispersed by an atomic system exposed to an MF. That occurs owing to transitions in quantum states ofa bound atomic electron. For ions confined within the binding cavities ofsome proteins, Lednev assumed that their dynamics could also follow some parametric resonance patterns in an atomic system. That idea is considered in Section 3.8.3.

Since the model (Chiabrera et al. , 1985) uses the equations ofclassical dynamics to describe the microscopic motion ofan ion, it is unable to describe some effects observed in experiments. The model predicts response maxima at a cyclotron frequency and its subharmonics, and does not predict peaks at harmonics and subharmonics ofthose harmonics. Such predictions are shown in Chapter 4, to yield a mechanism ofion interference.

Lednev (1991) assumed that an MF causes a parametric resonance ofa Ca2+

ion bound with some proteins (calmodulin, proteinkinase C, etc.). Therefore, an MF shifts an equilibrium of the reaction

protein( .. ) + Ca2+ ←→ protein(Ca2+)

and causes the response observed. In a model that described the influence ofan MF on a bound Ca2+, the author used the analogy with the phenomenon of paramagnetic resonance known in atomic physics. When one modulates an MF

with a frequency Ω close to the time-averaged frequency difference ω ofZeeman sublevels ofthe particle, the intensity ofspontaneous luminescence excited by a wide-band electromagnetic radiation, generally ofoptical range, also appears to be modulated with a frequency Ω. The modulation depth attains a maximum at Ω = ω/n, n = 1 , 2 , ... .

The author postulated that the magnitude ofthe biological effect in an MF is approximately described by the relation for the radiation intensity or the probability ofspontaneous radiative transitions in a particle ensemble. Underlying that postulate was the fact that in certain magnetobiological experiments the effect plotted as a function of the AC MF amplitude could be well approximated by the parametric resonance formulas of atomic spectroscopy.

Liboff guessed the connection ofexperimental frequency spectra with cyclotron frequencies of ions and attempted, therefore, to draw on cyclotron resonance the-

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ory to account for the MBE. Likewise, Lednev divined the association of observed amplitude spectra with the Bessel-type dependences in atomic parametric resonance and tried to draw on that theory to account for the experimental evidence. Later on various forms of the idea were discussed by various authors in the literature (Adair, 1992; Blanchard and Blackman, 1994; Blackman et al. , 1994; Engström, 1996; Zhadin, 1996), but no consensus has been reached so far (Lednev et al. , 1997; Blackman et al. , 1997). This seems to be due to the fact that the authors, except for Zhadin (1996), relied in their reasoning on an oversimplified illustration of the parametric resonance theory in atomic spectroscopy, sort ofoverlooking the physical content ofthe effect. To perceive the essence ofthe differences it would perhaps make sense to lay down the theory ofparametric resonance in atomic spectroscopy in more detail.

3.8.2 Parametric resonance in atomic spectroscopy

Let us consider the so-called parametric resonance in atomic spectroscopy (Alexandrov et al. , 1991), abiding, where appropriate, by the terminology and notation ofthat monograph. We will arrive at the main properties ofthat effect using the simple example ofa three-level atomic system in the field ofan exciting electromagnetic irradiation, normally ofoptical range, in a combined low-f requency

MF.

Common idealizations consist in that (1) the exciting irradiation is constant in time and has a constant spectral density within a fairly wide frequency band, the spectral components being δ-correlated; (2) the absorption and spontaneous emission ofan electromagnetic wave are independent processes; (3) the perturbation introduced by the wave is small, so that the population ofthe ground level can be taken to be constant, and that ofthe excited levels to be relatively small; (4) the excited level splits in a magnetic field H( t) into a Zeeman doublet, Fig. 3.12; and (5) the Raman scattering is small.

Let an electron state in an atom be a superposition ofeigenstates |k ofthe Hamiltonian H 0


Ψ =

ck( t) |k .

k

The intensity ofspontaneous emission from levels 1 and 2 to level 0 is determined by populations ofthe states, |ck| 2, and also by other elements ofthe density matrix σnk = c∗ c

n k .

Since the amplitude ofthe electric field ofthe emitted wave, in the transition from a ground state |n to a state | 0 , is proportional to the matrix element E 0 n ∝ 0 |de |n ,

where d is the operator ofthe electric dipole moment ofan atomic electron and e is the polarization vector ofthe emitted wave, then the amplitude ofthe superposition ofthe waves emitted from levels 1 and 2 is

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THEORETICAL MODELS OF MBE

ω

ω

ω

ω

ω

ω

Figure 3.12. The diagramof the energy levels of an idealized quantumsystem.


E ∝

c∗ 0 cn 0 |de |n ,

n

and the intensity ofthe wave I = E∗E is


I ∝ c∗ 0 c 0

σnkGnk ,

(3.8.7)

nk

where Gnk = 0 |de |n 0 |de |k∗ is the so-called observation matrix. We note that in addition to terms that vary with the population oflevels 1 and 2, i.e., σ 11 and σ 22, which determine the invariable part ofthe radiation intensity, this expression includes the cross-terms σ 12 , σ 21, concerned with the interference of waves emitted from levels 1 and 2. Those terms make a contribution to the intensity that is governed by magnetic conditions.

Let an atomic system be subjected to a field ofa wide-band electromagnetic radiation, and the perturbation operator look like


V = dE( t) , E( t) = e exp ( −iωt − iϕω) + c.c.

(3.8.8)

Here and ϕω are the amplitude and phase ofspectral components, and e is the polarization vector for the external radiation.

The dynamic equation for the density matrix, known as the Liouville quantum equation, i ˙ˆ

σ = [ H 0 ˆ

σ] written in matrix f orm in the |n representation is i ˙ σnk =

[( H 0)

σ

] .

nm

mk − σnm ( H 0) mk

m

Considering the equality H 0 |n = ωn|n, which can also be written as ( H 0)

=

nm

ωnδnm, this leads to the equation for the density matrix elements with coefficients ωnk = ωn − ωk:

˙ σnk = −iωnkσnk .

In terms ofperturbation V and phenomenological damping introduced by the additional term Γ nkσnk, the equation becomes

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˙ σnk = nk + iωnk) σnk − i

( Vnmσmk − σnmVmk) .

(3.8.9)

m

We will at first consider elements with n = 0 , k = 0. Since in the spectrum V

contains no low-frequency components, the elements Vnk are only non-zero for the transitions between ground and excited states. Then

2


i

˙ σ 0 k = (Γ0 k + 0 k) σ 0 k − i V


0 mσmk + σ 00 V 0 k .

m=1

Due to postulate (3) we can ignore the term

2

V

m=1

0 mσmk , and take σ 00 to be

a constant. We have

˙ σ 0 k = (Γ0 k + 0 k) σ 0 k − i σ 00 V 0 k .

A solution to the equation ˙ σ = f σ + g( t), where f = (Γ0 k + 0 k) ,

g( t) = − i σ 00 V 0 k ,

(3.8.10)

has the form


σ = eft

C +

e−ftg dt

.

(3.8.11)

We will simplify the situation by setting the initial conditions so that C = 0. Since in (3.8.10)


V 0 k = v 0 k

exp ( −iωt − iϕω) + c.c. ,

v 0 k ≡ (de)0 k ,

(3.8.12)

then the integral in the solution will be


−i

σ 00

exp (Γ0 kt + 0 kt) v 0 k

exp ( −iωt − iϕω) + c.c. dt.

It contains the exponential functions exp [ i( ω 0 k − ω) t] and exp [ i( ω 0 k + ω) t]. The fast-oscillating term is insignificant; therefore taking the time integral gives i

exp {[Γ0 k + i( ω 0 k − ω)] t − iϕω}

e−ftg( t) dt = σ 00 v 0 k Eω

dω ,

Γ0 k + i( ω 0 k − ω)

which on substituting into (3.8.11) yields


i

exp( −iωt − iϕω)

σ 0 k = σ 00 v 0 kE

dω .

(3.8.13)

Γ0 k + i( ω 0 k − ω)

Hence we have


−i

exp( iωt + iϕω)

σn 0 = σ∗ 0 n = σ 00 v∗ 0 nE

dω .

(3.8.14)

Γ0 n − i( ω 0 n − ω)

We assume in (3.8.13) and (3.8.14) that the spectral density = E is constant in the range ofinterest to us.

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We now consider the elements ofthe density matrix for excited states n = 0 , k =

0. In that case, what remains ofthe sum over m (3.8.9) is the only term m = 0, since the remaining terms contain multipliers Vmn = 0:

˙ σnk = nk + iωnk) σnk − i ( Vn 0 σ 0 k − σn 0 V 0 k) .

(3.8.15)

We introduce the notation


exp[ ±i( ωt + ϕω)]

b± ≡

exp [ ±i( ωt + ϕω)] dω ,

c± ≡=

dω .

0 k

Γ0 k ∓ i( ω 0 k − ω)

In terms ofthat notation, we will rewrite (3.8.12), (3.8.13), and (3.8.14) in the form V 0 k = Ev 0 kb− + Ev∗ b+ , V

= Ev∗ b+ + Ev

0 k

n 0 = V ∗

0 n

0 n

0 nb−

i

σ 0 k = σ 00 Ev 0 kc− , σ

c+ .

0 k

n 0 = − i

σ 00 Ev∗ 0 n 0 n

We can now write the perturbation in Eq. (3.8.15)


− i

E 2 σ 00

( Vn 0 σ 0 k − σn 0 V 0 k) =

2 v

+ v∗

b+ c− + b−c+

.

2

0 nv 0 k b−c−

0 k

0 nv 0 k

0 k

0 n

The term ( .. ) contains a fast-oscillating factor, which we will omit. The expression in the brackets in the second term is

exp[ i( ωt + ϕω)]exp[ −i( ωt + ϕω)]

Γ0 k + i( ω 0 k − ω)


exp [ −i( ωt + ϕω)] exp [ i( ωt + ϕω)]

+

dω dω .

Γ0 n − i( ω 0 n − ω)

Since ϕω is a δ-correlated random function of frequency, i.e., ϕωϕω ∼ δ( ω − ω), the last integral reduces to


1

1

+

dω .

Γ0 k + i( ω 0 k − ω)

Γ0 n − i( ω 0 n − ω)

Integration24 ofeach ofthe terms using −∞(1 + x 2) 1 dx = π gives π. Theref ore, the perturbation in (3.8.15), caused by the pumping matrix, is equal to 2 πE 2 σ 00


v∗

2

0 nv 0 k ≡ Fnk ,

(3.8.16)

and is here independent oftime. Thus the equation for the cross terms ofthe density matrix looks like

24Since the integration is within the limits ( −∞, ∞), then, for instance, the first integral is independent of ω 0 k. It can be reduced to a sum of terms Γ (Γ2 + ω 2) 1 and i (Γ2 + ω 2) 1 ωdω, where the second term contains under the integral a product of odd and even functions, and hence is zero.

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˙ σnk = nk + iωnk) σnk + Fnk .

(3.8.17)

Suppose now that the modulation ofa DC MF is on, so that the frequency ofthe Zeeman transition ωnk, a parameter in (3.8.17), becomes a periodic function of time with an external modulating field frequency H AC cos(Ω t): H AC

ωnk = 2 bH( t) = ω 0 (1 + h cos(Ω t)) , ω 0 = 2 bH

.

nk

nk

DC ,

h = H DC

In this case as well, the derivation ofEq. (3.8.17) remains valid due to the inequality Ω ω 0 n. All the quantities in (3.8.17) have identical indices; therefore it is convenient to discard them. Now the equation becomes


˙ σ = Γ + 0 [1 + h cos(Ω t)] σ + F .

(3.8.18)

Its solution has the form


σ = e gdt

C + F

e− gdtdt

,

g = Γ − iω 0 [1 + h cos(Ω t)] .

(3.8.19)

We introduce the notation

x = Γ + 0 ,

z = h ω 0

(3.8.20)

and take the integral in the exponent:


g dt = −xt − iz sin(Ω t) .

Substitution into (3.8.19) at C

= 0 and accounting for exp [ iz sin(Ω t)] =

J

n

n( z) exp( int) leads, after some straightforward transformations, to exp [ i( n − m)Ω t]

σ = F

J n( z)J m( z)

.

(3.8.21)

x + in

nm

The radiation intensity (3.8.7), related to the cross terms ofthe density matrix, varies with

˜

I ∝ σ 12 G 12 + σ 21 G 21 = 2 ( σ 12 G 12) .

(3.8.22)

Assuming G 12 ≡ G exp( ), using the formula


z 1

( z 1)

=

cos(arg z 1 arg z 2)

z 2

( z 2)

and substituting (3.8.21) into (3.8.22), we can easily obtain the relation cos ( n − m)Ω t − arctan ω 0+ n Ω + γ

˜

Γ

I ∝ GF

J n( z)J m( z)


1

.

2

nm

Γ2 + ( ω 0 + n Ω)2

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This quantity seems to have maxima25 at subharmonics ofthe unperturbed transition frequency

Ωmax = −ω 0 /n ,

(3.8.23)

proportional to the electron cyclotron frequency in a magnetic field H DC.

On average, over a fairly large time interval T 1, all the time-dependent series terms, i.e. the terms with n = m, vanish. The remaining terms produce, at the frequency of the main maximum Ω = −ω 0, an input


cos γ − arctan ω 0(1 −n)

˜

Γ

I ∝ GF

J2 ( h)

.

(3.8.24)

n


12

n

Γ2 + ω 02(1 − n)2

This series converges quickly; therefore the dependence of the relative MF amplitude h is mainly determined, as is seen from the denominator in (3.8.24), by the term n = 1:

˜

I ∝ J21( h) .

(3.8.25)

This expression attains the first maximum at h ≈ 1 . 8.

We note that at the first subharmonic frequency Ω = −ω 0 / 2 the denominator in (3.8.24) is


1

2

2

Γ2 + ω 02 1 − n

.

2

Hence the amplitude dependence, subject to (3.8.20), will look like

˜

I ∝ J22(2 h)

(3.8.26)

with a maximum in the region of h ≈ 1 . 5.

The relations (3.8.23) and (3.8.25) have attracted some attention as possible explanations ofthe primary mechanism ofsome MBEs. Similar dependences have been observed in experiments with biological systems subjected to weak combined parallel MFs. The works (Lednev, 1991; Blanchard and Blackman, 1994) are attempts to illustrate these relations using some oversimplified reasoning, which is erroneous.

The form of the dependence of ˜

I on the frequency at around maxima, i.e., the

shape ofthe spectral peaks, is determined mainly by the Lorentz factor


1

2

2

Γ2 + ω 0 + n

.

(3.8.27)

It can be easily found that the peak width is about Γ. On the other hand, the spectral peak at frequency −ω 0 will be resolved, ifits width is at least smaller 25In what follows if the index max is attached to some symbol that is a frequency or an MF, this means the presence of a maximal effect at that frequency or at the indicated value of the MF.

For other physical quantities the max index will imply, as usual, their maximal values.

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than 0 |, i.e., ifΓ < ω 0. As is seen from (3.8.9), the quantity Γ 1 has a physical meaning that is close to the lifetime of excited states τ ofthe Zeeman doublet. This imposes some constraints on the lifetime of excited states, which makes it possible to observe the effect, i.e., the variations in the intensity ofscattered light τ > 1 0 .

(3.8.28)

The concept ofparametric resonance in atomic spectroscopy, however, is associated precisely with the modulation ofthe scattered light intensity, rather than with the modulation magnitude, which has a maximum at the Zeeman frequency splitting.

The methods ofthe registration ofharmonic signal amplitude in physical measurements are well developed; therefore the constraint (3.8.28) does not hinder the observation ofthe modulation fact, although the modulation depth in itselfcan be fairly small, for instance 10 3. This notwithstanding, some measures are taken to properly prepare an atomic ensemble in the form of rarefied gas in a strong MF.

The gas being rarefied increases the lifetime of states, and a strong MF increases the splitting frequency of the Zeeman doublet, so that relation (3.8.28) is close to being met. Ifan experiment is only capable ofobserving the mean intensity, when modulation oscillations are ironed out, then constraint (3.8.28) prevails.

The amplitude offorced oscillations ofthe density matrix elements grows at certain frequencies Ω. Mathematically, that is, by definition, a parametric resonance.

Physically, the usage ofthe term “parametric resonance” in this case is rather a convention, and the correct meaning ofthe effect, as noted in Alexandrov et al.

(1991), is concerned with the parametric modulation ofscattered radiation. In relation to processes in quantum systems the term “resonance” is only applied where the frequencies ofan external radiation and ofa quantum transition coincide. In the process, transition probabilities jump sharply, which manifests itself as an increase in the intensity ofenergy exchange ofan atomic system with an electromagnetic field, i.e., ofthe intensity ofabsorption and emission ofelectromagnetic waves.

In the case under discussion ofthe wideband electromagnetic radiation that affects an atomic system, all the optical transitions appear to be saturated. It is this circumstance that is reflected by fact that the pumping matrix elements are constant. On the other hand, the integral intensity ofspontaneous emission in all direction is constant as well. The modulation ofthe intensity ofre-emitted waves shows up when an atomic system is observed at an angle that is defined by the observation matrix. The reason the intensity changes is the interference of waves emitted from Zeeman sublevels of the system. As the emission intensity is reduced in one direction, it is increased in another direction, so that the total power of scattered radiation is constant.

Thus, with parametrically modulated intensity ofscattered radiation, the intensity ofthe energy exchange ofan atomic system with an electromagnetic field is permanent, so that a resonance can only be referred to in some conventional meaning. The picture remains the same, ifwe look at another, non-electromagnetic factor ofperturbation in a system. For instance, thermal collisions ofan atom with the environment reduce to a series of δ-like perturbations within a high accuracy. Since

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these perturbations feature a continuous wideband spectrum within the frequency range under consideration, then all the relationships are derived in a similarly manner. In this case we should talk about the constancy ofthe energy exchange with the environment rather than with the electromagnetic field.

3.8.3 Ion parametric resonance

Ifwe know what atomic parametric resonance is about, we can easily see to what extent its use in magnetobiological models is justified.

Consider at first the attempt ofBlanchard and Blackman (1994) to refine the formula proposed in Lednev (1991) for the amplitude spectrum, relying on the same analogy with a spectroscopic parametric resonance. Re-emitting atomic electrons exposed to a variable MF and to optical radiation were identified with ions contained in protein capsules and excited by thermal oscillations ofcapsule walls.

The authors believe that a uniaxial MF brings about a change in the populations ofionic quantum states. As has been pointed out above, the mean radiation intensity in an atomic parametric resonance only changes in definite directions. The integral radiation intensity is constant, and so are the populations ofthe emitting Zeeman levels. The populations are in a dynamic equilibrium. Let us consider the population σnn ofsome excited levels, see (3.8.17). Since the frequency difference is ωnn = 0, the equation reduces to

˙ σnn = Γ nnσnn + Fnn ;

(3.8.29)

i.e., it contains no time-dependent parameters at all. The equilibrium constant value ofpopulations σnn( ) = Fnn/ Γ nn is determined by the balance ofpumping and relaxation factors and is independent of the MF.

The above argument “covers” those models built by analogy with atomic parametric resonance that relate the bioeffect intensity to the variation ofthe populations ofquantum ion states in a variable MF. The authors attempt to retain the apparent positive assets ofthe analogy, which consist in the similarity ofthe amplitude spectra, and assume the connection ofthe bioeffect with another physical factor, the mean intensity of ion spontaneous electromagnetic emission. So, an account ofthe biological action ofa low-frequency EMF boils down to the assertion that radio-frequency EMFs possess such an action.26 However, its mechanisms are also unclear as yet.

Further, the authors (Blanchard and Blackman, 1994) go on to expand the list of potentially meaningful ions to include atoms that form covalent bonds with protein structures: V, Mn, Cu, Ni, Co, and others. The exercise itselfmakes sense, but when determining cyclotron frequencies the authors assume the charges of those atoms to be equal to their valences, which is not exactly the case. For atoms that form ion bonds, the charge is a well-defined quantity. We can only determine in terms ofelectron charges the effective charge ofcovalently bound atoms, which, due to strong redistribution ofthe electron density, is markedly different from valence.

26The frequency of ion dipole transitions in a capsule is about 1010 Hz.

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The important positive meaning ofthe works (Blanchard and Blackman, 1994; Blackman et al. , 1994) consists in that they pay attention to the presence ofa body ofexperimental evidence, where the dependence ofthe bioeffect on the ratio h = H AC /H DC at a maximum in the frequency Ω variation corresponds to the function J n(2 nh), rather than to J n( nh), as is the case in Lednev (1991).

The assumption that the intensity ofa bioeffect when exposed to an MF can be approximated by a formula for the radiation intensity or probability of spontaneous radiative transitions ofa particle ensemble was criticized in Adair (1992) and Engström (1996). The authors ofthese works made an attempt to prove, without drawing on parametric resonance theory, that thermal perturbations make the proposed mechanism unworkable at room temperature 300 K. In so doing, they seem to have relied on the fact that the mechanism was workable in the absence of thermal perturbations, i.e., at zero temperature, but, as we have seen, the mechanism does not work irrespective ofthe temperature factor. The “con” arguments laid down in those works are based on the same illustrative concepts ofatomic parametric resonance, as are the “pro” arguments ofthe inventors ofthe model itself, and so they are unsuitable as well.

Adair (1992) has long been exploiting the idea that any magnetobiological effects, see Adair (1991), are impossible because those effects do not have any strict scientific explanation. To prove the invalidity ofexplanations available in the literature, use is made ofthe well-known and naive, as applied to living systems, concepts ofequilibrium thermodynamics: for an effect to be observed, the energy ofthe perturbation caused by an MF per degree offreedom must be around κT , but since that is impossible, any accounts ofMBEs are doomed. Such a reasoning, however naive, seems to many to be quite convincing.

Obviously, those criticisms ofthe model ofion parametric resonance in magnetobiology led Lednev (1996) to come up with another account for MBE amplitude spectra. The novel explanation appeals to the peculiarities ofthe motion ofa classical, rather than quantum, particle in a magnetic field, although the author retained the name “parametric resonance”. Mathematically, that holds well, but that work has nothing to do with parametric resonance as put forward earlier on in Lednev (1991), and so it will be considered in another section.

3.9 OSCILLATORY MODELS

Coming under this heading are both classical and quantum models in which particles move around within some space under some forces that are, as a rule, functions ofoscillatory potential.

3.9.1 Quantum oscillator

The two related works by Chiabrera et al. (1991) seem to have been the first attempt at a consistent description ofion binding under the action ofcollinear MFs in terms ofquantum mechanics. They formally calculated the probability of

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a transition between states Ψ0 and Ψ, the wave functions of an ion without and within an MF, respectively. The probability ofsuch a transition and the amount ofmagnetic bioeffect, according to the first work, are interrelated. However, that idea is at variance with the fact that an MF, when it only acts on the phase of state Ψ0, produces no quantum transitions. The probability ofthe state remains constant irrespective ofthe MF parameters.

In fact, the angular part of the eigenfunctions of the central potential is described in terms ofspherical functions exp( imϕ). On the other hand, the operator ofthe interaction ofa uniaxial MF with the orbital magnetic moment ofan ion varies with ∂/∂ϕ. Therefore, the matrix elements of the operator in states with a different magnetic quantum number contain the factor

eimϕ| ∂ |eimϕ ∼ δmm ,

∂ϕ

such an operator just shifts levels depending on the magnetic number m (Zeeman splitting). Ifwe consider states with different orbital numbers l, then the parity selection rules only allow transitions with l changing by unity. However, such states possess unlike parities; the matrix elements ofthe scalar interaction operators in unlike parity states are zero (Landau and Lifshitz, 1977).

The idea underlying that model is a quantum oscillator in a magnetic field. A uniaxial MF does not “mix” oscillator states; therefore the oscillation amplitude does not change.

The second article assumes that the biological effects ofan MF are related to the probability for an ion to reside within an imaginary sphere that bounds the central area ofthe binding cavity in proteins. At the same time, no closed relations for that probability have been obtained. It is to be noted that this idea is close to that ofthe interference ofion quantum states in a protein cavity, which forms the core ofthe book. One difference is that the interference mechanism accounts here for the redistribution of the ion probability density over the angular, rather than radial, variable. It is important since the angular redistribution as compared with the radial one practically does not require energy.

3.9.2 Phase shifts of oscillations in an MF

Belyaev et al. (1994) and Matronchik et al. (1996a) proposed a mechanism to account for the actions of a DC and low-frequency combined MF on living cells. The mechanism relies on two main postulates: (A) a target for an MF in prokaryote cells is a nucleoide that acts as a nucleus that can be represented as a three-dimensional harmonic oscillator within the EHF range; and (B) the specific electric charge of the nucleoide varies as

q( t) = q 0(1 + cos ωqt) .

To begin with, the authors look at the equation for the Lorentz force in a uniaxial MF — it coincides, up to notation, with (3.7.5) — to arrive at its approximate solution. They go on to consider the behavior ofthe phase ofhigh-frequency oscillations

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as the MF varies. The authors believe that ifa change B in the DC MF causes a change π, 3 π, ... in the phase, i.e., the phase changes up to antiphase, then such a change produces maximal bioeffects. This suggests the expression for a series of quantities

B ∝ ωq ,

q 0

which yield extreme and zero effects. It is thus possible to reach a qualitative agreement with experiment for the same group of researchers, where cells were placed for 15 min in a space with a changed field.

Let us take a closer look at the model’s postulates. A nucleoide ofbacterial cells is formed by the so-called bacterial chromosome, a single ring-shaped DNA molecule o

that forms a compact “nucleus” about 103 A in size. The DNA folded thread has a multitude ofdegrees offreedom and resides in the cell cytoplasm while changing its shape. Would it be permissible to regard the flexible thread as a point mass with 2–3 degrees offreedom?

Also unclear is the nature of the forces that are responsible for the oscillatory potential f

or the center ofmass ofa nucleoide that behaves like a high-quality

EHF resonator. We can readily work out the rigidity c ofthe oscillator “spring” by substituting the solution x = exp( it) into the pendulum equation M ¨

x + cx = 0.

The molecular mass ofthe nucleoide of E. coli being M ∼ 109 amu, the rigidity of the “spring” ofan oscillator with a frequency ofΩ 2 π · 50 GHz would be Ω2 M ≈ 105 kg/s2 .

(3.9.1)

That is a very rigid spring, and is two orders ofmagnitude more rigid than the covalent hydrogen–oxygen bond. Ifwe nevertheless admit, as a working hypothesis, that a nucleoide is a mass with three degrees offreedom on a spring with rigidity (3.9.1), then the thermal amplitude X ofoscillations ofthe center ofmass would, according to the relationship Ω2 M X 2 ∼ κT , be

o

X ∼ 10 14 A .

This is too small a quantity even for microscales; hence postulate (A) is hardly acceptable. Apropos ofpostulate (B) we note that it is obligatory for the model, since the final expression for the fields B, which produced an extreme MBE, contains some parameters ωq and q 0 ofthe postulate. At the same time, it is not properly substantiated. It is unclear why the charge ofa large macromolecule as a whole can change in such a regular and dramatic manner.

Lastly, the very connection ofthe bioeffect with the variation ofthe phase of high-frequency oscillations is not indisputable. In essence, the authors implicitly assume that an oscillating nucleoide remembers the phase state ofhigh-frequency oscillations and retains that information during the exposure time T e in a changed MF, which in experiment is several minutes. Such a time coherence can only be realized for an unrealistically large oscillator quality:

Q ∼ T e 1013 .

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THEORETICAL MODELS OF MBE

This is indicative ofthe dubious nature ofthe supposition.

The model has an advantage in that it displays a sophisticated correlation of oscillator phase oscillations with an MF. The idea is ofvalue because it provides some insights into possible magnetoreception mechanisms. It does not attract any resonance energy transformations, which in any case, when activated by MFs, will be beyond comparison with the thermal scale κT .

3.9.3 Parametric resonance of a classical oscillator

The recent work by Lednev (1996) is an attempt to elaborate on the parametric resonance concept in a direction that is not concerned with parametric resonance in atomic spectroscopy.

The author views an ion as a classical particle and considers the polarization ofion oscillations in proteins. According to that view, which relies heavily on the main assumption ofwork (Edmonds, 1993), the variation ofthe activity ofcalcium-binding proteins in an AC MF is due to the variation ofthe degree ofpolarization of ion oscillations at a binding site within a protein. That idea, although quite attractive, was not without drawbacks, however, when realized as a specific mathematical model.

First, it was shown in Binhi (1995c) that the motion ofions in microscopic volumes, e.g., in an ion channel or a protein binding site, can hardly be described in classical, as in Lednev (1996) and Edmonds (1993), rather than in quantum terms. Second, there exists the following mathematical inaccuracy. The content of formula (17) in the original paper (Lednev, 1996)


p = A 2 − A 2

/ A 2 + A 2

,

(3.9.2)

X

Y

X

Y

subject to formulas (12) and (13) from that article for squared oscillation amplitudes A 2 X = 2 A 2

cos2 α(sin Ω t − sin Ω t 0) cos2 ΩL( t − t 0)


+ sin2 α(sin Ω t − sin Ω t 0) sin2 ΩL( t − t 0) and the notation in that paper

α = ΩL /,

ΩL = qB AC / 2 m ,

reduced to the functional dependence for the sought degree of polarization p = p(Ω , B AC) ,

where Ω is the frequency of the variable component of an MF with amplitude B AC.

We note that here p is independent ofthe magnitude ofthe DC MF B DC. Further,

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185

according to the author, transforming formula (3.9.2) and averaging over time, he arrived at the following expression for the polarization of ion oscillations: 1

p = J20(2 α)

(3.9.3)

1 + Ω2c τ 2


1

1

+

J2 (2 α)

+

.

n

1 + ( n Ωc)2 τ 2

1 + ( n Ω + Ωc)2 τ 2

n=1

The author maintains that this formula is identical with the formula, known from the literature, for the polarization of radiation reemitted by an atomic ensemble.

However, formula (3.9.3), in terms of the author’s notation Ωc = qB DC /m, reduces then to a function of another type

p = p(Ω , B AC , B DC) .

There is no accounting for the appearance in the function p ofa new argument, the DC field B DC, as a result ofaveraging — that would be a mathematical revelation.

Formula (3.9.3) does not follow from (3.9.2).

Further, the author interprets relationship (3.9.3) and compares it with experiment. As follows from the above, however, such an explanation of magnetobiological effects is in no way concerned with the initial premises ofthe oscillatory model under discussion. In actual fact, the author returns to the invalid analogy with the ensemble ofcoherently emitting atoms in a magnetic field, since he notes that the well-known formula (3.9.3) describes the degree ofpolarization ofatomic emission.

Zhadin (1996) addressed the classical oscillatory dynamics ofthe molecular system ofligands ofa binding protein cavity and a bound ion under thermal perturbations. The problem has been repeatedly posed previously. Chiabrera et al. (1985) and Chiabrera and Bianco (1987) obtained for the mean ion velocity some analytical expressions that show extremes at some selected frequencies and amplitudes, although no good agreement with experiment was attained. Muehsam and Pilla (1994) numerically integrated the dynamics ofthe ion oscillator in a binding cavity, but they did not consider the frequency and amplitude spectra.

The results obtained (Zhadin, 1996) are basically two verbal statements. One of them is that it is unlikely to get a parametric ion resonance, viewed in its orthodox sense, as a growth ofthe particle energy when the MF, a parameter in an appropriate equation, is modulated. One productive and in a sense opposite statement was that at MF frequencies of Larmor or cyclotron type a redistribution of the thermal oscillation energy for the ion-environment medium might emerge and that the ion thermal energy might increase by several degrees.

To prove that, the author ofthat work at first writes the equations f or the

Lorentz force in Cartesian coordinates. The following is one of the equations for the x coordinate:

d 2 x

dx

dy


+ γ

+ ω 2

+ βy ΩLΩ sin Ω t =

Ckx cos( ωkt + δkx) .

dt 2

dt

0 x − 2ΩL(1 + β cos Ω t) dt

k

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The first and third terms here correspond to a conventional harmonic oscillator with a natural frequency ω 0, the second to damping, the fourth and fifth to the forces engendered by an AC MF, and the right-hand side to the Fourier expansion of random forces engendered by the neighboring particles. The writing of the equation is questionable.

(1) One and the same dynamic factor, namely the interaction of an ion with thermal oscillations ofligands, is included in the equation twice: as a phenomenological damping, which varies with the coordinate variation rate, and as external forces on the right-hand side ofthe equation. Note that the phenomenological damping is basically the averaged action of the external forces; therefore the coefficient γ

depends on the correlation function of external forces, as in the Langevin equation.

This dependence is absent here.

(2) Phenomenological damping, as an averaging ofmicroscopic forces, is normally introduced for macroscopic bodies, such that their infinitesimal interval of motion includes a sufficiently large number ofcollisions with the environment. That is scarcely applied to an ion in a binding cavity.

(3) A random external force is represented here by a Fourier series, rather than by a Fourier integral. At the same time, there are no grounds to regard the random force as a (quasi)periodic function.

(4) The fifth term of the equation, according to the author, is the force of an eddy electric field that is a result ofthe time variation ofan MF. One well-defined quantity in a variable MF is the rotor ofthe electric field:

H

rotE = 1

.

c ∂t

It is impossible to derive from that equality an expression for E without taking into account some additional conditions. To work out the force that acts on a charge in a variable homogeneous MF, i.e., the electric force engendered by such a field, it would be necessary to integrate the forces due to all the elementary sources ofgiven MFs that are somehow arranged around the charge. In this case the author implicitly used the condition that the origin ofthe coordinate system ofan ion coincides with the origin ofthe axially symmetric coordinate system of MF sources. It is easily seen now that this condition will be met at best only for a single ion of some ensemble, rather than for all the ions of the ensemble. Therefore, the above form of the expression for the eddy electric force is not general enough for further analysis. We note that that is quite a common mistake. It is done by advocates and opponents ofthe biological magnetoreception alike. So, a recognized

“authority” among the critics ofthe MBE, Adair, in his Note in Bioelectromagnetics 19, 136, 1998, undertook to substantiate the impossibility ofthe action ofa weak low-frequency MF on a DNA in a cell. He used the formula E = ( r/ 2 c) ∂B/∂t to estimate the maximal electric field in a cell ofsize r, induced by an MF B. It is easily seen, however, see Section 1.4.1, that it is an estimate ofthe field difference on the cell edges, rather than the magnitude ofthe electric field.

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Further, after a transition to a non-inertial, non-uniformly rotating reference frame the Coriolis force is lost. Another point is that the statement that in a rotating reference frame an ion is not subject to MFs is wrong. It relies on the Larmor theorem. According to the theorem, the behavior ofa system oflike charges q with mass M , which undergo a finite motion in a centrally symmetrical electric field and a weak homogeneous MF H, amounts to the behavior ofthat system of charges in the same electric field in a reference frame that rotates uniformly at angular velocity Ω = qH / 2 M c. The theorem holds well where the potential energy ofthe system ofcharges in the special case ofone ion is invariant to rotations of the reference frame (Landau and Lifshitz, 1976a). Clearly, this necessary condition was not met when allowing for the additional forces present in the equation as phenomenological damping or external forces. Moreover, the Larmor theorem is valid for a DC MF. There is no evidence as to whether it could be extended to include variable MFs.

The transformed equation was then reduced to the inhomogeneous Mathieu equation with a variable right-hand side, but the inference as to the nature of its solutions was made based on the well-known solutions to the homogeneous Mathieu equation, and that, at least, is questionable.

A multitude ofsuch omissions and unjustified approximations significantly reduces the value ofthe result obtained. Also, there is no way to use or test it, since no functional dependences on the MF variables have been derived.

Some comments on the conceptual aspects ofthe above treatment are in order.

There is a pendulum that is parametrically excited by a very weak signal in the presence of a more powerful additive random force. An assumption is proposed that at a resonance frequency the pendulum energy may grow markedly. However, even in the absence ofnoise and damping, under optimal conditions, the ion energy could vary noticeably only after several months of coherent swinging of such a pendulum, see Section 3.10. Consequently, this all could only refer to the case where an MF

controls the process ofenergy exchange between an ion and the source ofa random force. However, no mechanism that would act against the natural trend for thermal energy to be equally distributed over all the degrees offreedom was proposed.

Also unconvincing are computer simulation results provided in one ofthe later works on the subject. In the time interval ofinterest, which is several seconds, the noise factor is close to a δ-correlated random process with a spectrum near characteristic EHF frequencies of ion bonding. That factor was modeled by a signal that differs from the real one in three positions, which are the most significant ones at that. First, the assumption that the signal is deterministic excludes averaging over random variables ofthe noise signal; such an averaging would be quite unfavorable for modeling results; second, the signal is harmonic, which also excludes the unfavorable time averaging; third, the frequency of that signal was reduced nine orders ofmagnitude against the real one and chosen to be comparable with the Larmor frequency. As a result, within the time interval of computer calculations the relative phases were retained for both signals — “noise” and the MF. It is only natural that under such conditions some occurrences ofparametric resonance were observed.

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However, the main drawback ofprinciple ofthat and similar models is that they

“do not work” even in the absence of noise factors; therefore, they are incapable of making any productive testable assumptions.

3.9.4 Models of the enzyme reaction

Several proposals concerning mechanisms ofthe influence ofan EMF on enzyme reactions are known. All ofthem, however, provide relatively high frequencies of supposedly effective EMFs.

Zubkus and Stamenkovich (1989) considered the action ofan EMF on biochemical reactions catalyzed by transferases, i.e., reactions in which an atom or a group of particles are transferred from a substrate to a product. It was assumed that the reaction rate could vary in an AC electric field owing to the variation ofthe diffusion rate and the probability oftunneling through a barrier along the reaction coordinate. The effective EMF frequencies in such mechanisms are close to natural frequencies ofoscillations ofa particle being transported on a bond being disrupted.

For instance, that would be Ω 1013–1014 s 1 for a proton on a hydrogen bond.

There are no estimates ofeffective amplitudes ofan external field.

Belousov et al. (1993) addressed a possible scenario ofthe variation ofthe rate ofan enzyme reaction in an EMF at physiological temperatures. They used the electron-oscillatory model ofan enzyme reaction, in which adiabatic potentials have the form ofoscillatory wells along the generalized coordinate ofthe reaction. An external EMF influences the probability ofnonradiative dissociation ofa product–

enzyme complex. The influence ofmicrowave fields on the reduction ofthe activation energy ofthe complex was considered. That model predicts the appearance ofa trigger effect in the dependence ofthe reaction on the intensity ofan external field.

At the same time, no estimates ofeffective fields are available. It is still unclear whether such models include windows ofeffective variables. The model thus seems to be invalid for low-frequency MFs, since the mechanism of the “hooking” of a field to a quantum system is represented by the energy ofthe dipole moment ofa complex in the electric field component ofan EMF.

3.10 MAGNETIC RESPONSE OF SPIN PARTICLES

Underlying any mechanism ofEMF biological action is the interaction offield with matter, i.e., with atomic nuclei and electrons. A fundamental description of the interaction ofan EMF with matter particles with spin 1 is concerned with repre-2

sentation ofthe latter as a spinor Dirac field. On atomic scale, it gives a quantum-mechanical description ofelectrons and a phenomenologically correct description of protons.

The Lagrangian ofthe interaction ofan EMF with a spinor field stems from the requirement that a theory be invariant to the local phase transformation of a spinor field and have the form L( x) = eAµ( x) ( x), where e is the electron charge,

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189

= ( A 0 , A) is the 4-potential ofan EMF, and is the current ofthe particle field.

In terms ofthe Hamiltonian semiclassical formalism, such a Lagrangian leads to the momentum operator P being replaced by P − eA /c. The velocity ofparticles constituting a biological system is much lower than the velocity oflight, and so relativistic effects can only yield minor corrections to relatively slow dynamics.

Therefore, in the Dirac equation for the wave function of a particle in an EMF the nonrelativistic approximation is used. Up to the terms ∼ c− 2, it yields the equation i Ψ /∂t = H Ψ(r , s) with the Hamiltonian H = H( P , U) + H( P , A) + H( S , A) + H( S , P , A 0) , where r , s are variables in the space ofcoordinates and spins. P , S are the momentum and spin operators, respectively. H( P , U ) describes the dynamics ofthe orbital r degrees of freedom for some fixed potential U (r). H( P , A) accounts for the variation ofthat dynamics under an EMF. H( S , A) defines the dynamics ofthe particle spin in am EMF; lastly, H( S , P , A 0) describes the interaction ofspin and orbital degrees offreedom.

Even at this stage there are some mechanisms ofthe action ofan EMF on orbital degrees offreedom. It is these degrees that determine the progress ofbiochemical processes and control indirectly the behavior ofbiological systems. Clearly, a biological reaction to the action ofa variable MF is, in the final analysis, conditioned by the absorption ofthe MF energy, however small it might be, and by its transformation, possibly via spin degrees, into the energy oforbital degrees offreedom.

The interaction ofan MF with possible collective excitations in biophysical systems relies on the interaction ofan MF with individual particles. Therefore, the processes of energy or signal transformation in one-particle dynamics form the foundation for MBE mechanisms. Signal transformation is only reduced to two possibilities. The first one is concerned with the terms H( P , U ), H( P , A) and has a classical analogy in the motion ofa point particle in some potential under the Lorentz force F = eE + e[vH] /c, where E , H are the electric and MFs. In the process, the MF

energy transforms either directly into the energy of the particle orbital motion or into a redistribution ofthe probability density for a particle. In the latter case, the redistribution energy ofan interference pattern is connected with a change in the number ofEMF quanta, which requires, generally speaking, that we transcend the limits ofthe Hamiltonian semiclassical description.

The second, purely quantum, possibility is associated with the terms H( S , A) and H( S , P , A 0). It is believed that the MF energy is at first transformed into the energy ofspin degrees offreedom, and then into the energy oforbital motion either following the “spin exclusion” or due to the spin–orbit interaction. The spin dynamics manifests itself in interaction with orbital degrees of freedom. Therefore, the relatively small interaction H( S , P , A 0) could be significant.

Any studies ofquantum effects in a magnetic field are normally begun with the writing ofthe magnetic Hamiltonian

H = −MH( t) ,

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where the operator ofthe magnetic moment M depends on the type ofa system under study. For instance, in some approximation, for a one-electron atomic system it looks like

M = µ ( L + 2 S ) + γ I ,

(3.10.1)

B

where L , S are the operators ofthe orbital and spin electron momentum, I is the atomic nuclear spin operator, γ = µ/I is the gyromagnetic ratio ofthe nuclear spin, and µ is the magnetic moment ofthe nucleus.

In most problems, where electron–nucleus interaction is not important, the nuclear spin is ignored, since the nuclear magneton is more than three orders of magnitude smaller than the Bohr magneton. We will be interested in the motion of an ion as a whole particle in some effective potential. The simplest idealization here will be the adiabatic approximation that is valid when a system has fast and slow variables. The slow motion can then be described“adiabatically”, i.e., in the time-averaged or effective potential, which the fast variables produce. In this case, slow and fast dynamics refer to the motion of nuclei and electrons. The internal paired electrons ofan ion make up an “elastic” atomic shell, which defines the ion effective radius, and the external valence electrons that bind the ion with ligands create the effective potential, such that an ion moves in it as a whole. Experiments on atomic interference in atomic beams support the validity of the adiabatic approximation in such cases.

To study the quantum dynamics ofan ion in a magnetic field as an individual particle in an effective potential, we will have to write the magnetic moment operator proceeding from the “primary principles”. It appears that in that case the energy ofthe orbital motion ofan ion as a whole is comparable with the energy of the ion spin. The ion spin, because ofvalence electrons being paired, is equivalent with the ion nuclear spin.

The issue thus emerges ofthe study ofthe dynamics ofcharged particles with spin in MFs. That issue has been repeatedly studied in much detail in applications to various domains ofphysics (e.g., Landau and Lif

shitz, 1976a). As applied to

biomagnetic reception models, the problem has features that make their estimation worthwhile.

The Hamiltonian ofa particle with spin 1 in an external MF, allowing for spin–

2

orbit coupling, has the form (e.g., Fermi, 1960; Akhiezer and Berestetskii, 1965; White, 1970)

( P − q A)2

H

2 µ 2

=

c

+ qA 0 2 µS H +

S ( ∇A 0 × P ) ,

(3.10.2)

2 M

q

where µ, M are the magnetic moment and mass ofthe particle, respectively; A and A 0 are the vector and scalar potentials ofthe electromagnetic field; H = rotA is the MF; S is the spin operator; and P = −i is the momentum operator in an electromagnetic field. In a homogeneous MF, A = H × r / 2, and in a centrally symmetric potential ofelectrostatic nature the Hamiltonian (3.10.2) can also be written as

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P 2

H

2 µ 2

=

+ U ( r) ( b L + γ S ) H +

S ( ∇A 0 × P ) ,

(3.10.3)

2 M

q

where b = q/ 2 M c is the ion “charge-to-mass” ratio, and the expression in parentheses is the operator ofthe effective magnetic moment ofan ion, which includes the energies ofthe orbital and spin magnetic momenta. Their inputs are comparable: the magnitude ofthe ratio γ/b = 2 γM c/q is always more than one. Therefore, generally speaking, spin effects in ion dynamics should play quite a significant role.

The dimensionless coefficient γM c/q, equal to the ratio ofthe NMR and cyclotron frequencies of an ion, appears in relationships quite often. In the book, a special name “ion–isotope constant” is introduced for it:

ΩN

γM c

Γ =

=

.

Ωc

q

Its numerical values for different ions and different isotopes of their nuclei are given in Table 6.1.

It is seen from Eq. (3.10.3) that the energy of a particle’s magnetic moments in an MF varies with b H for the angular momentum and γ H for spin. In a variable MF H sin(Ω t) we can readily find the instantaneous rate oftransformation ofthe MF energy into the energy of, say, a spin: dε/dt ∼ γ H Ω. That is a relatively small quantity. It would take a decade for an ion to accumulate an energy of about κT in a 100- µ T, 100-Hz MF for such a transformation rate.

In reality, the situation is even more hopeless. A homogeneous MF causes no quantum transitions; therefore the time-averaged energy of a particle does not change. Quantum transitions in an AC MF occur: (1) when spin–orbit interaction is taken into consideration (Binhi, 1995b), (2) when the orbit is not flat (Binhi, 1990b), and (3) when the MF is not homogeneous. However, contributions ofthese effects to the energy transformation rate is yet several orders of magnitude smaller.

Such low-energy changes ofa particle, concerned with both spin and orbital magnetic momenta, indicate that utilization ofthe energy ofan MF in MBEs, as it accumulates at some degrees of freedom, is unlikely. Therefore, it is advisable to search for alternative mechanisms, which would use not energetic, but some other, signal, properties ofan MF.

3.10.1 Weak and strong MF approximations

Although quite small in some ofits manifestations, spin–orbit interaction plays an important role in the dynamics ofparticles in weak MFs. In the absence ofan MF, spin–orbit interaction, however small, implies that, in a central potential, there exists the conservable total momentum J ofa system composed ofan orbital and spin momenta: J = L + S. That follows from the fact that in a central potential the particle Hamiltonian, in addition to the spin–orbit interaction under consideration, which in this case varies with the product L S , contains a term that only depends on the radius r and a term that varies with the squared angular momentum, ∼ L 2.

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The product L S clearly commutes with all the parts ofthe Hamiltonian. By virtue ofthe operator identity

J 2 = L 2 + S 2 + 2 L S ,

commuting with the Hamiltonian is also the operator ofthe squared total momentum J 2, which precisely implies that the appropriate physical quantity is conserved.

Also conserved is the component ofthe total momentum along any axis that is described by the operator Jz. The wave functions of the system can be taken to be eigenfunctions for all the above operators and, correspondingly, indexed by quantum numbers, such as the radial n, the total momentum j, and its component m, and also the orbital momentum l, i.e., the functions |njlm.

A homogeneous MF reduces the spherical symmetry ofa system to an axial one.

In the Hamiltonian appear additional terms ofthe Zeeman interaction oforbital and spin magnetic moments with an MF. Now the operator ofspin–orbit interaction does not commute with the Hamiltonian; therefore, a system’s total momentum is not conserved, and so j is not a good quantum number.

Ifan MF is sufficiently large, we can ignore spin–orbit interaction. The spin and orbital magnetic momenta will then interact with the MF separately, the orbital momentum magnitude is conserved, and so do the components ofthe two momenta, the appropriate eigenfunctions being the functions |nlmlms, specified by the azimuthal l and magnetic quantum numbers ml and ms. The splitting of energy levels in a relatively strong MF, which is indexed by the same numbers, is called the Paschen–Back effect. The position ofthe levels is slightly modified by spin–orbit interaction, which is regarded as a perturbation.

In a relatively weak MF, in contrast, we can take a perturbation to be the Zeeman energy, and we can work out the splitting as the diagonal elements ofa perturbation in the shells ofunperturbed functions ofthe total momentum and its component. Such a splitting, which is indexed by the quantum number j, is called the abnormal Zeeman effect. The normal Zeeman effect is defined as splitting in an arbitrary MF oflevels ofa spinless particle.

It is clear that for particles with spin a criterion ofthe applicability ofwave functions of some symmetry or other boils down to the possibility of ignoring spin–

orbit interaction as compared with the Zeeman one. For the comparison, ofthe two Zeeman energies we must take the smaller one. The ratio ofthe splittings due to spin and orbital magnetic moments is Ω / ω

N

0 = 2Γ. Since the magnitude ofthe

ion–isotope constant Γ is always larger than 1, see Table 6.1, the smaller one is the energy ofthe orbital momentum, whose magnitude is ω 0. Spin–orbit interaction has the form, see (3.10.2),

H

2 µ 2

so =

S ( ∇A 0 × P ) .

q

In a central field ∇A 0 = (r /r) ∂A 0 /∂r. We can, therefore, write H

2 µ 2 ∂A 0

so =

S L ,

qr

∂r

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where L = −ir × ∇ is the dimensionless operator ofthe orbital angular momentum. The energy scale, i.e., the constant of spin–orbit interaction, follows after the quantum-mechanical averaging ofthe operator H so regarded as a perturbation.

Using the above operator identity, we will estimate the order ofmagnitude of 2 µ 2 1 ∂A 0 .

q

r ∂r

The potential A 0 ofan ion in the cavity is not quite defined yet. Apparently, one reasonable estimate ofthe mean quantity in the last expression will be q/a 3, where a is the radius ofthe cavity potential. We thus arrive at the energy scale for spin–

orbit interaction in the form 2 µ 2 /a 3. To determine a critical MF, such that it divides areas ofvarious approximations, we will equate the energy scales for spin–orbit and orbit momenta: 2 µ 2 /a 3 = ω 0 = qH th / 2 M c. Now, using the definition ofthe ion–isotope constant Γ = µM c/ Sq, we find the critical field: H th 4 µS Γ /a 3 .

(3.10.4)

We can readily work out, using Table 6.1, that for ions in the table, which have a nuclear spin, the critical field varies in the range of5–500 mT for cavities with an o

o

effective potential ofradius 0.7 A. For an electron in a well ofradius 1 A, f rom the relationship 2 µ 2 /a 3 eH

B

th / 2 m e c, we could find the critical field in the region of 2 T, which is in full conformity with the well-known data of atomic spectroscopy.

That is, ofcourse, just a rough estimate because we do not know the exact form ofthe ion potential in a cavity. It is clear, nevertheless, that the geomagnetic field, which is somehow present in most magnetobiological experiments falls rather in the interval ofweak (in the above sense) fields. It thus makes sense to investigate approximations ofboth strong and weak fields, when an external MF interacts with the total magnetic moment ofan ion.

3.11 FREE RADICAL REACTIONS

The conditions under which reactions involving radical pairs (RP) occur are well studied; there are a multitude ofworks devoted to radical reactions in a magnetic field. Good introductions to the topic are popular reviews by Buchachenko et al.

(1978), Salikhov et al. (1984), and Steiner and Ulrich (1989). The processes ofmagnetosensitive recombination of radical pairs may form a foundation for biological effectiveness ofweak MFs. That is a common and attractive idea, primarily because these processes are virtually independent ofthe ambient temperature. Therefore, there is no “kT problem” here. Frequency and amplitude windows ofMF variables with such a primary mechanism ofmagnetoreception are associated with the non-linear equations ofchemical kinetics. The radical reaction is a sensitive link in a complicated biochemical system described by non-linear equations (Grundler et al. , 1992). At the same time such a mechanism imposes some theoretical constraints on the magnitude ofMBEs. It is possible that biological effects ofan MF, both DC

and AC, ofa relatively large intensity > 1 mT follow precisely that mechanism.

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7

7


8U

7

7

6

U

Figure 3.13. The energy of Coulomb interaction of an RP, allowing for the energy of exchange interaction with singlet S and triplet T+ , T 0 , T− states of the electrons of the pair.

3.11.1 Geminate recombination

Some organic molecules seem to consist oftwo relatively strong and large parts, A and B, connected by a single covalent bond. The latter can be broken by thermal perturbations: AB A + B. The parts are large and the medium is viscous, and so the parts are incapable ofquickly separating to a large distance and appear to be as ifconfined to a “cage”. Here we thus have a special state ofthe reagents, such that it can be identified neither with the product AB nor with reagents A and B.

The products ofthe decomposition ofthe AB molecule behave as radicals ˙

A and ˙

B,

molecules with an unpaired valence electron. The reaction is, therefore, represented as

AB ˙A ˙B ˙A + ˙B ,

where the interim state ˙

A ˙

B is a radical pair with unpaired electrons in a cage.

The spin state ofan RP with spins 1 is described by singlet–triplet states with 2

the following notation borrowed from RP chemistry: S is a singlet state with zero total spin, and T is the triplet state with unity total spin. In the latter case, spin one can have components along a selected axis equal to 1, 0, or 1. These states are designated as T+ , T 0 , and T−, respectively. Ofsignificance here is the exchange interaction ofthe electrons ofa pair, which depends not only on the spin state ofan RP, but also on the separation between the radicals, Fig. 3.13. The figure depicts the RP terms in a relatively strong MF, when the spin and orbital magnetic momenta interact with the MF individually.

It is obvious that a stable state (recombination product) ofan RP only occurs in a singlet state. There is no detailed description ofthe process ofthe formation ofAB

from ˙

A ˙

B as yet. Therefore, they use a phenomenological description: they assume that the product AB formation rate is mainly proportional to the probability (or population, or intensiveness) ofan RP singlet state. As the product f orms, the

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relative share ofRP in the singlet state (chemical polarization ofelectrons — CPE) is reduced. Since an MF in principle affects the evolution ofthe RP spin state, i.e., it causes singlet–triplet transitions, the field is capable ofchanging the equilibrium relationship offree radicals ˙

A, ˙

B and AB molecules. It is supposed that this could

be one of the MBE mechanisms.

To describe RP dynamics we will need an RP magnetic Hamiltonian, which specifically contains Hamiltonians ofthe magnetic momenta ofeach radical. The magnetic moment operator M = ( µ/S) S for the electron and the respective Hamiltonian have the form

M = 2 µ S , H = H M = 2 µ H S .

B

B

However, in a weak MF the magnetic moment operator, see Section 3.10.1, should be written as M = G J , where J is the total momentum operator. In a homogeneous MF Hz the magnetic Hamiltonian has the form H = GJzHz, and it defines level splitting, see Addendum 6.2, which is a multiple of

ε = −b gHz ,

(3.11.1)

where b = e/ 2 m e c, and g is the g-factor (6.2.2). The active electron of a radical is subject to the action ofan effective molecular field (in the solid-state theory they use the term “crystal field”). That gives rise to chaotic precession ofthe electron orbital momentum, so that its mean value is zero. The orbital angular momentum is then said to be “frozen”: L = 0. That means that the magnetic Hamiltonian only contains the spin operator: H = αSzHz. That Hamiltonian will obviously split the electron level according to

ε = αHz .

Comparing this expression with (3.11.1) gives α = −b g = −µ g. Therefore, forB

mally, the electron magnetic Hamilton becomes

H = −µ gH

B

z Sz .

(3.11.2)

In the ideal situation ofthe complete freezing ofthe orbital momentum, substituting into (6.2.2) values ofthe electron quantum numbers i = 1 , l = 0 (formally, as 2

L = 0), j = 1, Γ = 1, we find g = 2. In reality, the motion ofan electron in 2

a molecular field is not completely chaotic. There remains some measure oforder stemming from the special nature ofthe molecular field ofa given kind ofmolecule.

In that case, electron orbital motion produces some additional MF. It should be taken into consideration in spin dynamics (Slichter, 1980). In a fixed external MF

the effect manifests itself as a minor deviation of the g-factor from the ideal value 2.

That paves the way to identifying molecular radicals by their electron spin resonance (ESR) spectra.

Let us consider a simple model ofa molecule that in a singlet spin state splits under thermal excitation into a pair ofneutral radicals. The simplest idealization is that ofthe so-called exponential model. It postulates the Poisson flux ofradicals

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leaving a cage. Correspondingly, the lifetime of radicals in the cage is a random quantity distributed by the exponential law

1

f ( t) =

e−t/τ c ,

(3.11.3)

τ c

where τ c is the mean lifetime ofan RP in a cage, an important variable ofthe model. The lifetime τ c is about τ c ∼ R 2 /D, where the cage size for neutral radicals o

is R ∼ 10 A, and the diffusion coefficient for non-viscous solvents, such as water, D ∼ 10 5 cm2/s. That is, τ s 10 9 s.

Initially, an RP is in a singlet state. In that state, radicals recombine at some rate K. External and internal MFs give rise to singlet–triplet transitions. Since the spin selection rule only allows for recombination from an S-state, generally speaking, this reduces the recombination rate. It is clear that ifthe rate of ST

transitions is small, the spin state of an RP fails to change during its lifetime. In that case, the recombination rate will be K and, clearly, independent ofthe MF.

In the opposite case ofintensive ST transitions any correlation between RP spins is quickly destroyed. The recombination rate will then be independent ofthe MF

as well and will only be defined by the mean weight ofthe S-state for a random selection ofradical spin states, i.e., K/ 4. Thus, there is an MF interval normally from units to hundreds of millitesla, when the statistical weight of the S-state changes markedly during a time ofabout τ c, thus causing the recombination rate to depend on the MF. The position ofthat MF interval is, clearly, proportional with 1 s and also dependent on the nature ofmagnetic interactions inside the cage. These interactions define the mechanism type for ST transitions. There are several such types.

3.11.1.1 Relaxation mechanism

The spin state of an RP after its formation varies due to relaxation of each spin down to its equilibrium state. In general, a superposition of S- and T -states changes their relative weights, which suggests the presence of ST transitions. The relaxation time ofneutral radical spins in liquids with viscosity similar to that ofwater 1 sP

is equal to 10 7–10 6 s; i.e., it is much larger than τ c. Therefore, that mechanism becomes ofvalue, for instance, in the cellular recombination ofoppositely charged ion radicals, for which τ c, due to mutual attraction, can be much larger than 10 9 s.

3.11.1.2 g mechanism

After radicals have been formed, their spins precess, see Addendum 6.3, in a magnetic field, the latter being a superposition of(1) an external MF and (2) a field of magnetic moments ofthe radicals’ nuclei. Suppose now that the latter MF is zero, i.e., all the nuclei ofradicals are even and do not possess a magnetic moment. The precession will then go on in an external MF with a Larmor frequency. It will be proportional to the Zeeman splitting and, in the general case, will be different for each radical due to different g-factors:

1

1

ω 1 = µ g

g

B 1 Hz ,

ω 2 = µ B 2 Hz .

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The relative rate ofde-phasing, i.e., the difference ofthese frequencies, will be 1


µ

g H

B

z .

An MF exerts its influence via the g mechanism where it is large enough for RP

de-phasing during an RP lifetime to become noticeable, say, one radian. The order ofeffective MFs at g ∼ 10 3 will then be


H ∼

105 Oe .

µ g τ

B

c

These fields are too large to provide a reliable account for the MBEs that occur at fields under 1 Oe.

3.11.1.3 Resonance excitation

If RP spins have different precession frequencies, then, by choosing the frequency ofan external AC field, one can tune to a magnetic resonance ofone ofthe spins.

Its state will then begin to oscillate with a Rabi frequency, γH AC = 2 µ H

B

AC /,

executing thereby ST transitions ofan RP spin state. De-phasing ofabout one occurs in fields H AC / 2 µ τ

B s 100 Oe. Clearly, this mechanism ofthe mixing of

singlet–triplet states as well has nothing to do with the magnetobiological effects discussed in this book.

3.11.1.4 HFI mechanism

Hyperfine interaction (HFI), i.e., interaction ofelectrons with nuclear spins, yields more optimistic estimates. For example, when one ofthe radicals has nuclei with a magnetic moment, radical spins precess in markedly different MFs. Even ifthe difference ofg-factors is insignificant, RP terms do mix or ST transitions do occur.

Let an external MF be zero. Approximately, de-phasing is determined by the precession ofthe magnetic moment ofonly one electron ofa pair in the field ofa nuclear magnetic moment, 100 Oe. During the RP lifetime the phase progression will then be µ gHτ

B

s / 1, i.e., a quantity large enough to be observable. The question is whether an additional external MF ofabout the geomagnetic field is capable ofchanging noticeably the rate of ST transitions.

The relatively simple model — the influence ofan external MF on the recombination ofan RP with one magnetic nucleus with spin 1 by the HFI mechanism —

2

has been addressed many times (Buchachenko et al. , 1978). In addition to the Zeeman energy ofspins (3.11.2), the Hamiltonian ofthe model includes the exchange interaction


H exch = J( r) 1 / 2 + 2 S 1 S 2

with a constant J ( r), and hyperfine interaction, in which, due to fast chaotic rotations ofradicals in a cage, normally only its isotropic part is retained H hf = AS I .

The spin Hamiltonian ofan RP in an external MF H z looks like

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THEORETICAL MODELS OF MBE


H = H 0 + AS 1 I , H 0 = −µ gH S 1

J( r)(1 / 2 + 2 S 1 S 2) , (3.11.4) B

z + S 2

z

where g-factors are, for simplicity, assumed to be equal for all the radicals, and the Zeeman energy ofthe nuclear magnetic moment is ignored. It is common knowledge that the eigenfunctions of the Hamiltonian H 0 are singlet–triplet states, which, in terms ofone-particle spin states ψα, which are eigenfunctions of the operator Sz, are given by

ψ 1 ψ 2

m = 1

2

2


1

ψ 11 ψ 22 + ψ 12 ψ 21

m = 0

ν

2

m = 

(3.11.5)

ψ 11 ψ 21

m = 1


1

ψ 1 ψ 2 − ψ 1 ψ 2

m = 2 .

2

1

2

2

1

Here the first three basis vectors form a symmetric (in particle permutations) triplet T−, T 0 , T+; the last vector is an antisymmetric state or singlet S. The variation range ofthe index m = 1 , 0 , 1 , 2 was chosen so that for triplet states it would coincide with the magnetic quantum number — the z component ofthe total spin S 1 + S 2.

We will denote the nuclear spin state as χα, so that a basis for the investigation of the dynamic equation with the Hamiltonian (3.11.4) will be the functions ξmα = νmχα .

Then the arbitrary RP state can be represented as a superposition


Ψ =

cmαξmα .

The Latin indices assume the values -1, 0, 1, 2 (2 for the singlet state), and the Greek indices, 1 and 2 (the up and down spin states). The density matrix, whose diagonal elements are populations ofelectron singlet–triplet terms, is defined as σnm =

c∗ c

nα mβ .

(3.11.6)

αβ

It is found by solving the equation of motion for the density matrix i ˙ σnm =

[ Hnkσkm − σnkHkm] .

k

In certain cases it is assumed that the radicals ofa pair have a fixed separation.

Further, the population ofthe singlet state σ 22( t) is found. The recombination rate p is assumed to be proportional to the time-averaged population ofthe singlet state.

Since RP lifetimes in a cage are distributed by (3.11.3), the averaging is carried out using the exponential distribution

p ∼ 1

e−t/τ c σ 22( t) dt .

τ c 0

In more realistic cases, considered along with spin dynamics is the spatial motion of radicals in a cage, their repeated contacts due to diffusion. The density matrix then

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depends not only on spin variables, but also on the separation between radicals r.

Accordingly, the dynamic equation changes as well. The spin effects ofRP recombination, subject to the molecular motion ofradicals, were considered in much detail in the monograph by Buchachenko et al. (1978).

Analytical studies ofRP dynamics, even ignoring the molecular motion, are hindered by the fact that calculations use three-part spin functions. We will not provide here solutions for specific models. We will rather make use of approximate estimates and known results ofthe numerical analysis ofequations.

It follows from (3.11.4) that any significant change in spin dynamics can only be expected where the Zeeman and HFI energies have similar scales, i.e., µ gH ∼ A.

B

The HFI constant has an order ofmagnitude A ∼ 108–109 Hz, whence we find the appropriate MF scale:

A

H ∼

0 . 5–5 mT .

µ g

B

The numerical calculations (see reviews Steiner and Ulrich, 1989; Buchachenko et al. , 1978) indicate that in most cases maximal changes ofthe recombination rate in specified fields are no more than 1 %, the characteristic RP lifetime being 10 9 s.

Making quite an approximate assumption ofthe field-effect variation being linear in the range under consideration, we find that in the geomagnetic field 0 . 05 mT

the effect will not exceed 0.1 %. Experimental curves for radical reaction rates in a magnetic field (Grissom, 1995) substantiate that estimation. In a model with one magnetic nucleus, Brocklehurst and McLauchlan (1996) obtained, using numerical methods 10 %, the change as recalculated to the geomagnetic field, but they used τ c 2 · 10 7 s. For common values 10 9 s here too we have 0.1 %. Obviously, this quantity should be regarded as fairly justified for estimations of possible biological effects in a magnetic field similar to the geomagnetic one. Such insignificant changes in the reaction rate suggest that a further “biochemical” amplification is needed.

Grundler et al. (1992) and Kaiser (1996) considered the free radical reaction as an element ofa system described by a set ofnon-linear equations ofchemical kinetics with bifurcations. Even minor variations of the reaction rate could then cause significant, even qualitative, changes in the behavior ofa biological system.

3.11.2 Representative experiments

There are indirect experiments supporting the idea ofradical pairs in magnetobiology. In Lai and Singh (1997b) they measured the mobility ofbrain cell DNA in rats and found a statistically meaningful 30 % change of that variable after a 2-h exposure ofthe animals to 2.45-GHz, 2-mW/cm2 microwaves, in pulsed 2- µ s, 500-Hz mode. It is significant that an injection ofmelatonin and other scavengers offree radicals blocked the emergence ofa biological effect ofthe microwaves.

In contrast, other evidence points against the idea. In Taoka et al. (1997) they measured the rate ofsome enzyme reactions in vitro associated with a co-enzyme B12. The cobalt–carbon coupling ofthe co-enzyme can generate a spin-correlated radical pair. However, no meaningful MF dependence in the range of 50–250 mT for

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$EQRUPWRFRQWURO


0%(UHOXQLWV


0DJQHWLFLQGXFWLRQP7

Figure 3.14. The relative number of deviations from the normal development of fly larvae exposed for 30 min to a DC MF, according to Ho et al. (1992).

the two enzyme reactions studied has been found. The authors conclude that the action ofan MF on physiological processes is hardly associated with given enzymes.

Ho et al. (1992) addressed the deviations from normal development of Drosophila larvae caused by their 30-min exposure to a DC MF. Studied were more than 10 various parameters characterizing the morphological process occurring during the first 24 h ofthe development ofembryos. Figure 3.14 shows the deviation index vs MF curve. The range ofDC MFs, beginning with 1 mT, where significant changes were observed, points to possible mechanisms ofthe influence ofan MF on free radical reactions.

Galvanovskis et al. (1999) measured, using a fluorescent microscope, the spectral density ofthe power ofthe oscillations ofthe calcium ion concentration in T-cells ofhuman leukemia in the spectral interval 0–10 mHz. The magnetic layout ofthe experiment

B(36) b(0 566) B p(14) f (50) b background 50 Hz( < 0 . 2) enabled one to evaluate the variation ofthe parameter being measured with the AC MF amplitude. Figure 3.15 displays the field amplitude dependence ofthe MBE

computed as the difference ofcontrol and experimental values in relation to the control one. The scale ofMFs that cause changes, about 1 mT, and the gently sloping curve are characteristic ofmagnetosensitive radical reactions. Unfortunately, data on frequency selectivity of the effect observed were not provided.

Lai and Carino (1999) studied cholinergic activity ofrat brain tissues, those ofthe f

rontal cortex and hippocampus. To this end, they used a 60-Hz MF of

various intensities and exposure durations. The authors assumed that a statistically trustworthy effect is only caused by combinations ofvariables, such that the product ofthe field intensity by the exposure time is sufficiently high, Fig. 3.16. The body ofevidence is too small to warrant any reliable conclusions. For instance, we can

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0.5

itsn

l. u

, re 0.0

EBM

0.0

0.2

0.4

0.6

h, mT

Figure 3.15. The relative magnitude of the spectral density of intracellular Ca oscillations in an AC MF, according to Galvanovskis et al. (1999).

Figure 3.16. The MF intensity and the exposure time, which cause an MBE p < 0 . 05 in brain tissue (O), and do not cause any effect ( ), according to Lai and Carino (1999).

also assume that here too there were different physical mechanisms: an interference mechanism in the region ofrelatively weak MFs, and a spin-prohibition one, for relatively large MFs.

Li et al. (1999) undertook to find out whether a 50-Hz MF can be a promoter of carcinogenic action of12-O-tetradecanoilforbol-13-acetate (TPA). The characteristic ofintercellular communication processes was measured using the method ofdie injection with a count oftinted cells. Figure 3.17 shows that in these experiments an MF produced changes in a biological system, qualitatively similar to that ofa carcinogenic preparation. The action ofthe preparation itselfwas amplified when exposed to an MF. The interval ofeffective MFs was, just as above, in the region of1 mT.

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