EFFECTS OF MAGNETIC FIELDS ON SOLITON MEDIATED CHARGE TRANSPORT IN BIOLOGICAL SYSTEMS

Abstract

In this paper, we analyze biological effects produced by magnetic fields in order to elucidate the physical mechanisms, which can produce them. We show that there is a chierarchy of such mechanisms and that the mutual interplay between them can result in the synergetic outcome. In particular, we analyze the biological effects of magnetic fields on soliton mediated charge transport in the redox processes in living organisms. Such solitons are described by nonlinear systems of equations and represent electrons that are self-trapped in alpha-helical polypeptides due to the moderately strong electron-lattice interaction. They represent a particular type of disssipativeless large polarons in low-dimensional systems. We show that the effective mass of solitons in the is different from the mass of free electrons, and that there is a resonant effect of the magnetic fields on the dynamics of solitons, and, hence, on charge transport that accompanies photosynthesis and respiration. These effects can result in non-thermal resonant effects of magnetic fields on redox processes in particular, and on the metabolism of the organism in general. This can explain physical mechanisms of therapies based on applying magnetic fields.

Full text

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EFFECTS OF MAGNETIC FIELDS ON SOLITON MEDIATED CHARGE
TRANSPORT IN BIOLOGICAL SYSTEMS
L. Brizhik1,2
1Bogolyubov Institute for Theoretical Physics
Metrolohichna Str., 14b, Kyiv 03680, Ukraine
2Wessex Institute of Technology, Ashurst, Southampton SO40 7AA, UK
E-mail: brizhik@bitp.kiev.ua
ABSTRACT
In this paper, we analyze biological effects produced by magnetic fields in order to elucidate the physical mechanisms,
which can produce them. We show that there is a hierarchy of such mechanisms and that the mutual interplay between
them can result in the synergetic outcome. In particular, we analyze the biological effects of magnetic fields on soliton
mediated charge transport in the redox processes in living organisms. Such solitons are described by nonlinear systems of
equations and represent electrons that are self-trapped in alpha-helical polypeptides due to the moderately strong
electron-lattice interaction. They represent a particular type of disssipativeless large polarons in low-dimensional systems.
We show that the effective mass of solitons is different from the mass of free electrons, and that there is a resonant effect
of the magnetic fields on the dynamics of solitons, and, hence, on charge transport that accompanies photosynthesis and
respiration. These effects can result in non-thermal resonant effects of magnetic fields on redox processes in particular,
and on the metabolism of the organism in general. This can explain physical mechanisms of therapies based on applying
magnetic fields.
Indexing terms/Keywords
Solitons; charge transport; cyclotron resonance; biological effects of magnetic fields; magnetic field therapy
Academic Discipline And Sub-Disciplines
Physics, Biological and Medical Physics, Interdisciplinary Physics, Non-linear dynamical systems
SUBJECT CLASSIFICATION by PACS 2010
73.20.Mf (Collective excitations) ; 87.50.-a (Effects of electromagnetic and acoustic fields on biological systems); 87.50.ct
(Therapeutic applications); 87.18.-h (Biological complexity)
TYPE (METHOD/APPROACH)
Theoretical study, experimental data review
Council for Innovative Research
Peer Review Research Publishing System
Journal: JOURNAL OF ADVANCES IN PHYSICS
Vol. 6, No. 2
www.cirjap.com, japeditor@gmail.com

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INTRODUCTION
It is well known that a biological system exposed to a physical stimulus is able to detect its presence and to modify its own
biological activity depending on the characteristics of the applied stimulus such as mechanic, electric or magnetic. In
particular, it has been known since last few decades that electromagnetic fields of weak intensity in the broad interval of
frequencies and intensities can cause various biological effects. Such effects can be positive or detrimental. Especially
important from the point of view of technical appliances in the modern life and promising from the point of view of medical
applications are low and extremely low frequency (ELF) fields which are widely used in various therapies to treat broad
class of diseases. In particular, one of such medical applications is based on the therapy, administered with the devices
produced by THERESON company. The corresponding method, called Therapeutic Magnetic Resonance TMR™, turned
out to show positive results in treatment of diabetic foot disease and vascular ulcers [1]. The method TMR™ consists of
exposing patients to low intensity Pulsating Electro-Magnetic Fields (PEMF), at specific patented protected shapes and
frequencies of pulses.
In spite of the fact of relatively long history of using pulsating magnetic fields in medicine, little is known about the
mechanisms of such therapies. To understand the physical mechanism(s) of the action of magnetic fields on biological
systems and to develop a reliable working principle of the pulsating electromagnetic field (PEMF) therapies it is worth to
summarize the experimentally observed biological effects caused by electromagnetic fields. In the next section the review
is given of the corresponding experimental data. In Section 3 we suggest some mechanisms, which could lead to such
biological effects, and summarize them as a possible working principle of PEMFT. Detailed study of some of the
mechanisms will be provided elsewhere in the result of our future studies.
REVIEW OF EXPERIMENTAL DATA
From the very beginning it is worth to stress that the analysis of the literature with experimental data of the biological
effects of electromagnetic fields of low frequencies shows these data sometimes can be contradictory. For instance, in
1990s many experiments have been performed with Escherichia coli exposed to oscillating magnetic fields. Out of 18
papers, cited in review [2], in which the corresponding results have been reported, 6 papers describe ‘some effect’, using
terminology of the author, 6 other papers report the effect of the ‘opposite sign’, and in the rest experiments no effects
have been observed. Qualitatively similar situation was reported about the experiments with some enzymes, bacteria and
fungi [2].
To a great extent this is an often situation, when we are dealing with biological systems, whose complex structure and
organization are determined by many parameters, due to which living matter is very sensitive to some ‘minor’ details of the
experiments which can be indeed minor details for the conventional physical systems, but can be significant for biological
systems. This is especially so in the experiments with magnetic fields in view of the high degree of electromagnetic
‘pollution’ coming from the surrounding technical appliances, power lines, telecommunication nets, computers, inclusions
of magnetic materials in the building compounds, etc. Also an important role belongs to local terrestrial magnetic field and
solar electromagnetic activity. All these factors can cause a synergetic effect as well. Above this the results can depend on
the phase of the development of biological cells and their synchronization if any, ‘history’ of the system under study, etc.
It is well established, that non-thermal biological effects of magnetic fields depend not only on the concrete biological
system, but depend significantly also on the parameters of the field, including the field intensity, frequency, modulation,
duration of the exposition, etc. For instance, in the alternating field of 50 Hz at 3 Gs the rate of lac transcription in E. coli is
suppressed, while at 5.5 Gs it increases. Weak magnetic fields of the intensity 0.8-8.0 Gs at 60 Hz increase transcription
of gene c-myc in mice and humans [3]. More experimental data on the relation stimuli--effect for various systems are cited
in [4, 5].
As one could expect, the biological effects of weak static and oscillating magnetic fields are different and,
respectively, the mechanisms of such effects can be different. Static magnetic fields affect mainly the nervous system. In
particular, such functions as navigation and hunting [6, 7], biological clock [8] and some other biological processes are
based on the recognition of magnetostatic changes, mainly through certain cells in the visual system. These effects we will
not consider in the present paper. Very differently, low-frequency weak magnetic fields cause physiological effects and are
system-wide: at certain low frequencies magnetic fields can affect all types of cells.
More experimental data will be described in the next sections.
POSSIBLE MECHANISMS OF BIOLOGICAL EFFECTS
From the theory of electromagnetism we know, that the electric and magnetic components of the electromagnetic field are
connected through the Maxwell equations. In many cases, considered above, the magnetic component of the oscillating
electromagnetic field is weaker than the electric component. Nevertheless, namely magnetic component can be the main
one, which affects the biological system. This is possible because biological tissues contain a significant amount of water,
which is known to absorb significantly electrical radiation, while the magnetic component can penetrate deeply in the
biological tissues, and can affect them locally deeply inside, not only on the skin at the biologically active points, like it is
the case of the electrical component of the oscillating electromagnetic fields. Therefore, in this paper we will consider the
influence of the magnetic component of the oscillating electromagnetic fields on biological organisms.
At least three physical mechanisms of biological effects of magnetic fields can be identified, namely molecular,
supramolecular and system, depending on the level of organisation, at which such effects takes place. Molecular
mechanism involves effects of magnetic fields on ions, radicals, paramagnetic particles with unpaired electrons and spin,
molecules, macromolecules. Magnetic fields can induce spin singlet-triplet transitions in such molecules, change their

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states and reactivity. Supramolecular mechanisms involve effects on membranes, mitochondria, microcrystalls, cell nuclei
etc. System mechanism is more complex and is based on the synergetic effect of molecular and supramolecular effects
and is manifested on the level of the biological system (endocryne, nerve, etc.). The biological effects via this mechanism
are more delayed in time, since they are result of the primary effects of the first two mechansims, which are processed
with time by the corresponding system or by the whole organism.
The dependence of the biological effects of oscillating magnetic fields on the frequency indicates the resonant
character of such effects. Among such resonant mechanisms the first to be mentioned, is the ion cyclotron resonance. In
biological systems there are various ions and groups of ions, which are sensitive to the alternating magnetic fields. Due to
the Lorentz force, a free ion of the mass m and electric charge Ze in a static magnetic field of the intensity B moves along
the circular trajectory with the angular frequency
B
m
Ze
=ωc
. (1)
The electromagnetic oscillating signal of the frequency f will therefore resonate with ions which have a mass-to-charge
ratio m/Z given by the relation
B
2ππ
e
=
Z
m
(2)
Such phenomenon is called ion cyclotron resonance. In a more general case the circular motion of ions is superimposed
with a uniform axial motion, resulting in a helix, or in a more complex trajectories depending on the given ‘geometry’ of the
experiment.
Another ‘sensors’ of magnetic fields in biological organisms are electrons. It is well established that all metabolic
processes in living organisms are accompanied by the transport of electrons [9], e.g., in the redox processes or in
photosynthesis. Similarly to (1), electron cyclotron resonance frequency is
B
m
e
=ω
e
ec,
(3)
Here me is mass of a free electron.
It might be useful to recall that in SI units the elementary charge e is measured in Coulombs. Thus, e= 1.602×10-
19 Coulombs, the mass is measured in kilograms, e.g., me= 9.109×10–31 kg, the magnetic field B is measured in Teslas,
and the angular frequency ω is measured in radians per second.
In the redox processes in respiration, the transport of electrons takes place along the so-called electron transport
chain [9, 10]. Such chain represents a series of macromolecules that transfer electrons from one another via redox
reactions, so that each compound plays the role of a donor for a molecule 'on the left' and acceptor for the molecule 'on
the right'. Electron transport chains take place also in photosynthesis [9, 10], where the energy is extracted from sunlight
via redox reactions, such as oxidation of sugars and cellular respiration. The location of electron transport chains varies for
different systems: it is located in inner mitochondrial membrane in eukaryotes, where oxidative phosphorylation with ATP
synthase takes place, or in thylakoid membrane of the chloroplast in photosynthetic organisms, or in the cell membrane in
bacteria [9, 10].
Some molecules in the electron transport chains, like quinone or cytochrome cyt-c, relatively small molecular
mass. They are highly soluble and can move relatively easy outside the mitochondrial membrane, carrying electron from a
heavy donor to a heavy acceptor. In theoretical studies such electron transport systems are modeled as complexes which
include a donor molecule weakly bound to a bridge molecule, which in its turn is weakly bound to an acceptor molecule.
The bridge itself can be modeled as some potential barrier through which the electron tunneling takes place (see, e.g., [11]
and references therein. In some other studies the bridge is modeled as a molecule with super-exchange electron
interaction taken into account [12]
It has been shown that properties of electrons in these systems differ little from properties of free electrons. Therefore,
their cyclotron resonance frequency is close to the frequency determined in Eq. (3).
Some other molecules in the electron transport chain, such as NADH-ubiquinone oxidoreductase, flavoproteids,
cytochrome c-oxidase cyt-aa3 and cytochrome cyt-bc1 complex are proteins with large molecular weight, and, thus, they
are practically fixed in the corresponding membrane. Qualitatively and quantitatively different situation takes place for
electrons, when they are transported through these proteins of large molecular mass. First of all, a significant part of such
proteins is in alpha-helical conformation, which is stabilized by relatively weak hydrogen bonds between every fourth
peptide group (a group of atoms H-N-C=O), so that along the helix there are three hydrogen-bounded polypeptide chains.
The softness of hydrogen bonds and quasi-one-dimensional structure of polypeptide chains suggests a possible
significant role of the electron-lattice interaction in them. Indeed, it has been shown (see [13]) that this electron-lattice
interaction is relatively strong and that it results in a self-trapping of electrons: electrons, transferred into a protein from a
donor molecule, create a local deformation of the protein. Such deformation acts as a potential well, which attracts an
electron. As a result, a bound state of an electron and lattice deformation is formed. This state is described by the
nonlinear Schroedinger equation for the electron wave-function,
),( tx
:
 
0=t)Ψ(x,t)Ψ(x,2Jg+
tt)Ψ(x,
J+
tt)Ψ(x,
i2
2
2





. (4)

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Here x is the coordinate along the polypeptide chain, J is the electron exchange interaction constant coming from the
overlap of electron wave-functions on the neighboring peptide groups, g is the dimensionless nonlinearity constant, which
is determined by the electron-lattice coupling constant, χ, and elasticity of the hydrogen bond, w, through the relation
Jw
g2
2


. (5)
Equation (4) has the so-called soliton solution:
 
 
(t)i+Vx/imexpVt/a)/2xg(xSechg
2
1
t)(x,Ψ=t)Ψ(x, se0s 
, (6)
where V is the velocity of the soliton, a is the lattice constant (distance between the neighboring peptide groups), and φs(t)
is the time-depending phase of the soliton.
The corresponding deformation of the chain in the soliton state is proportional to the probability of the electron
presence in the corresponding place:
 
2
s
2t)(x,Ψ
)sw(1
χ
=t)ρ(x, 
(7).
It follows from the Eqs. (5) and (7), that the electron probability, and chain deformation are localized functions with the
width of the localization
g
πa
=ls
. (8)
Such solitons, in fact, are a particular case of large polarons in low-dimensional systems, which represent the crossover
between small polarons and almost free electrons. They correspond to the ground electron state (the state with the lowest
energy) at intermediate values of the electron-lattice coupling and small values of the nonadiabaticity parameter. Namely
such conditions are fulfilled in polypeptides (see [13]).
From Eq. (5) and (7) it follows also, that the electron and lattice deformation propagate along the polypeptide
chain with constant velocity V from one end to the other one, from a donor to an acceptor molecule, as a coherent
localized wave. Such a wave practically does not emit phonons and is exceptionally stable, able to propagate on
macroscopic distances in view of the extremely low energy dissipation and the nonlinear nature of it formation.
In view of the binding of an electron with the lattice deformation, effective mass of a soliton is bigger than the
mass of a free electron, me:
)
ses Δ+(1m=m
. (9)
Therefore, the soliton cyclotron resonance frequency is different from the frequency of a free electron:
B
m
e
=ω
s
sc,
. (10)
In weak magnetic fields electrons can have arbitrary orientation of their spins, and in such a case bound
bisolitons in singlet states correspond to the ground electron state [14]. Such bisoliton represents two extra electrons with
antiparallel spins that are localized within the same deformational potential well. Effective mass of a bisoliton is bigger than
the sum of masses of two free solitons:
sbsebs 2m>)Δ+(12m=m
, (11)
and the corresponding bisoliton cyclotron resonance frequency is given by the relation
B
m
e
=ω
bs
bsc,
. (12)
The oscillating character of the propagation of soliton and bisoliton with frequencies (10) and (12), respectively,
according to the relation (7), is accompanied by the propagation of the local deformation of the polypeptide chain, ρ(x,t),
which also is the oscillating function of time. This deformation will excite additional vibrational modes in the polypeptide
chain and can change its conformation. Thus, we see that the magnetic field affects the electrosoliton transport, and,
therefore, it can affect the redox processes. Indeed, it has been demonstrated experimentally in [15] that electromagnetic
induction of protection against oxidative stress takes place. More detailed study is needed for the analysis of the effects of
PEMF on the dynamics of solitons and bisolitons, namely, how dynamics of (bi)solitons depends on the frequency, pulse
duration and pulse modulation. This will be done in the nearest future.

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EXPERIMENTAL SUPPORT OF THE DESCRIBED MECHANISMS
In [16] a table is given of the ion cyclotron resonance frequencies, corresponding to biologically active ions, such as H+,
Li+, Mg2+, H3O+, Ca2+, Zn+, K+, arg2+, asn+, glu+, tyr+ . Indeed, it has been shown that ELF EMFs are able to trigger ion and
molecular cyclotron resonance phenomena in living systems – see [16, 17] and references therein.
In numerous experimental studies it has been shown, that lymphocytes, fibroblasts, leukemic cells, epithelial, cardiac
stem cells, bone cells (osteoblasts), pinealocytes, thymocytes, liver cells (hepatocytes), and salivary gland cells of animals
and humans are electromagnetically sensitive. One of the cell structures, able to receive the applied signal, has been
identifid to be cell membrane [18]. It has been demonstrated that electric or magnetic filds can affect membrane functions
not only by a local effect on ion fluxes or ligand binding, but also by altering the distribution and aggregation of the
intramembrane proteins [19]. Among such proteins there are different specialised molecules, such as receptors, enzymes,
ion channels, integrins that are essential for many fundamental functions mainly related to signal transduction and cell
adhesion. In particular, the influence of electromagnetic exposure on ligand binding to hydrophobic receptor proteins is a
possible interaction mechanism [20]. Indeed, studies reveal a modulation in the activity of adenylyl cyclase by coupling
with specific receptor sites in the membrane surface after the exposure to magnetic and electric fields [21].
Recently, it has been demonstrated that PEMFs mediate the modulation of gene transcription [22]. Some
experimental studies show and that chronic exposure to PEMFs may alter human cardiac rhythm, it may enhance the
effects during surgery, transplantation or heart attack in humans [23]. The predominant effect of PEMF is also shown on
the different phases of bone repair, in particular, it has a positive effect on the repair process [24, 25, 26]. The stimulation
of repair processes in clinical practice using the effectiveness of PEMF stimulation for enhancement of bone healing has
been reported also in [25, 27, 28].
Such physical stimuli are able to trigger a more complex biologic response such as cell proliferation as it is evident from
some clinical results [29-31]. Exposure to PEMF induces an increase in the proliferation of human articular chondrocytes
suggesting an important role also in cartilagine repair [32]. On the other hand, PEMFs induce programmed cell death in
cultured T-cells and determine a decreased T-cell proliferative capacity [33]. It has been shown that repeating pulses of 1-
10 Hz increase expression of genes which translate proteins c-fos and zip/28 in cortex of rats [34]. Low-frequency (0.1 Hz)
high amplitude modulation (3,000-100,000 Hz) magnetic fields cause significant changes in proliferation and differentiation
of neuron stem cells in cortex of rats [35].
It has been established that in inflammation massive infiltration of T-lymphocytes, neutrophils and macrophages into
the damaged tissue takes place [36]. The presence of A2A adenosine receptors in human neutrophils suggests that
adenosine could play an important role in modulating immune and inflammatory processes. Therefore, activation of A2A
receptors by PEMFs may have a relevant therapeutic effect [37, 38]. It is known that neutrophils are the most abundant
white cells in the peripheral blood and are usually the first cells to arrive at an injured or infected site. Adenosine,
interacting with specific receptors on the surface of neutrophils, has been recognized as an endogenous anti-inflammatory
agent [39]. The activation of A2A receptors in human neutrophils affects the immune response in cancer, auto-immune and
neurodegenerative diseases and decreases inflammatory reactions [40]. Experimental evidence suggests that PEMFs are
able to suppress the extravascular oedema during early inflammation [41]. It has also been demonstrated that the
complete healing of wounds depends on the presence of A2A adenosine receptor agonists [42]. It has been reported that
PEMFs mediate positive effects on a wound healing, controlling the proliferation of inflammatory lymphocytes and
resulting in beneficial affects on inflammatory disease [43].
In biological systems there is a whole set of signaling mechanisms, based on various biochemical reactions [9]. Cells
as no other known system can convert one type of stimulus into another, using chains of biochemical reactions involving
enzymes. Such enzymes are activated by specific molecules, called messengers. In the endocrine system such
messengers are epinephrine, insulin, estrogen, etc., other messengers are cAMP (cyclic AMP), cGMP (cyclic guanosine
monophosphate), IP3 (inositol triphosphate), nitric oxide (NO), and other. Many of them can be affected by oscillating
magnetic fields. These chains of biochemical reactions are referred to as transduction pathways. Some of the biochemical
reactions include up to 15-20 different intermediate stages, some of which take place with participation of ionic radicals
[10]. The mostly studied ionic second messenger in cell magneto-sensitivity is the cellular calcium ion, Ca2+. Respectively,
many experiments have been performed on the effects of magnetic fields on the processes, involving calcium.
As far, as in 1978, Adey, Bawin and Sabbot [44] studying experimentally radiofrequency effects on chick brain, have
discovered that calcium transport is profoundly affected when the radiofrequency signal is modulated by specific extremely
low frequencies. It has been shown in [45] the exposure to the magnetic field at the low frequency equal to 7.0 Hz at the
intensity 9.2 µT, which provide Ca ion cyclotron resonance frequency, initiates differentiation of pituitary corticotrope-
derivated AtT20 D16V cells. Similarly, differentiation of human LAN-5 neuroblastoma cells can be induced by extremely
low frequency magnetic field [46].
Moreover, not only sensitivity to some frequencies has been shown, but it has been reported in [47] that through the
ion cyclotron resonances the magnetic field can be useful in the regenerative medicine. Namely, through such resonance
mechanism oscillating magnetic field effects on human epithelial cell differentiation and, thus, it can transfer the
information in cells [48, 49]. These effects as well as other, described below, are frequency, intensity, dose, and time
dependent.
One of the possible physical mechanisms of the bioeffects of weak magnetic fields at Calcium resonance can be
determined with the effect of the field on the Ca2+-binding proteins. In 1985 A. Liboff has suggested that calcium and
potassium ions can be specifically activated by the magnetic field through the ICR effect, which enhances their transport
through membrane ion channels, thereby altering signaling mechanisms and cellular function [50]. These signals are
mediated in cells by the cytoplasm, in which water is in a structurized state, known as exclusion zones [51, 53], and plays
an important role [53]. According to [54], water is able to form coherent domains, which can store the energy of the
electromagnetic field and release it at the resonant frequency.

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In the last decades, biophysical studies have shown that not only ICR, but also Molecular Cyclotron Ion Resonance
can activate some fundamental biological elements (proteins, vitamins, mineral salts) and make them more mobile,
allowing to enter more easily through the cellular membrane thus guiding all the biochemical reactions essential for the
normal cellular activity.
A combination of static and alternating magnetic fields can be useful for some positive effects [55-59]. Such
combination can change the probability of calcium ion transition between different vibrational energy levels, which, in its
turn, affects the interaction of the ion with the surrounding ligands. One can expect that such an effect is maximal when
the frequency of the alternating field coincides with the cyclotron frequency of calcium ion or with some of its harmonics,
and indeed, it has been observed in [45]. Within such a model some quantitative explanation of the main characteristics of
experimentally observed effects has been suggested in [60].
An important effect for understanding the mechanisms of the magnetic fields biological effects is magnetic isotope
effect: dependence of the biological response of the system to the substitution non-magnetic isotopes to magnetic ones. In
particular, the synthesis of adenosinethriphosphate (ATP) by creatinkinase shows significant isotope effect: enzyme with
magnetic isotopes 25Mg2+ produces 2-3 times more ATP molecules, than enzyme with non-magnetic isotope 24Mg2+ [5].
Similar effect of low frequency electromagnetic fields on A2A adenosine receptors in human neutrophils has been reported
in [61]: magnetic fields of 550 and 800 Gs cause significant effects on the synthesis of adenosinethriphosphate (ATP) by
creatinkinase.
Another important biological process, sensitive to magnetic field, is DNA transcription by polymerase. Like ATP
synthesis, catalysis of DNA transcription involves metal ions (Mg, Zn, ...) and also shows significant magnetic isotope
effect for magnetic ions 199Hg, 25Mg, 67Zn, 43Ca [62, 63]. In particular, the speed of the DNA synthesis by beta-polymerase
depends on the presence of magnetic or non-magnetic Mg isotope in a catalytic site of the enzyme: enzymes with 25Mg2+
magnetic ions surpress DNA synthesis by 3-5 times as comapring with enymes with nonmagnetic 24Mg2+ or 26Mg2+ ions
[64]. Similar results are for for beta-polymerase with zink ions: synthesis with enzymes with magnetic isotopes 67Zn2+ is 2-
3 times slower than with non-magnetic 64Zn2+ [65].
The mechanism of magnetic isotope effect is connected with the interaction of the unpaired electron of cation-radical
Mg+ with the nuclei, which results in the change of the electron spin of the pair: spin convertion of the pair from a singlet to
a triplet state takes place. Such change of the spin opens a new reaction channel in a radical pair. In other words, the
magnetic nuclei controls electron spin of the pair and its reactivity. Indeed, enzymes with magnetic ions 25Mg2+ can be
activated by magnetic field, while enzymes with a nonmagnetic 24Mg2+ are inhibited [64]. In a similar way external
magnetic field can control such reactivity.
The soliton mechanism of the redox processes in respiration and photosynthesis, described briefly in the end of
Section 3, is supported by some experimental data as well. In particular, it has been shown that weak magnetic RF and
SMFs increase rate of hemoglobin deoxygenation in a cell [66]. The treatment with specific frequencies of electromagnetic
waves corresponding to some optimal regime to optimize the redox balance (rH2) and the acidity (pH) of body fluids to
restore the cellular metabolism, has been reported in [67]. A number of basic studies confirmed such effects as correction
of membrane potential, activation of enzymatic processes, promotion of intra/extracellular ionic balance, enhancement of
the biological availability of the fundamental elements in the cellular metabolism, etc., [68]. The preliminary clinical data
suggested the significant impact of such fields on cardiovascular parameters (flow mediated dilation) in healthy volunteers,
a stronger and quicker antioxidant effect than antioxidant drugs, improvement in muscular coordination and performance
through better recruitment of neuromotor units in neuromuscular diseases, increase in body (muscular) mass in unhealthy
patients. The enzymatic activation of the basal metabolism and of the fatty acid metabolism in aged rats [67, 68, 69], a
significant improvement in the wound closure and bone fractures healing process, improvement of osteogenesis in
osteoporosis have also been shown [67, 70, 71].
Catalysis of oxidation of nicotinamide adenine dinucleotide (NADH), which participates in the redox processes, by
molecular oxygen, is performed by peroxidase enzyme. This oxidation is an oscillating reaction with the period of
oscillations approximately 100 s, during which concentrations of NADH and O2 oscillate. It has been shown that in these
reactions both period of oscillations and their amplitude depend in a non-monotonic way on magnetic field in the interval
1000-4000 Gs. Frequency maximum and amplitude minimum are attained in magnetic fields at 1500 Gs [72].
ELF pulsed-gradient magnetic field may be able to inhibit the growth and division of cancer cell and enhance the
host cellular immune response. How the low frequency pulsed-gradient magnetic field induces apoptosis of cancer cell
and blocks new blood vessel development remains unknown, but it nevertheless has been found that this could be a new
method for the treatment of cancer. It has been reported in [73] that ELF pulsed-gradient magnetic field with the maximum
intensity of 0.6–2.0 T, gradient of 10–100 T/m, pulse width of 20–200 ms and frequency of 0.16–1.34 Hz treatment of mice
can inhibit murine malignant tumor growth. Such magnetic fields induce apoptosis of cancer cells, and arrest
neoangiogenesis, preventing a supply developing to the tumour. It has been reported (see [73] and references therein)
that pulsed magnetic field (0.8 T, 22 ms, 1 Hz) inhibits the growth of S-180 sarcoma in mice. Fields of these parameters
are used to treat patients with middle and late-stage sarcoma disease. The data have shown that nine of 18 cases
showed good improvement, and nine were less well inhibited (see [75] and references therein). Another results of
effective treatment of 50 cancer cases with a Nd-Fe-B permanent magnet (0.4 T) were reported, according to [73]. In [73]
electron microscopic evidences have been demonstrated that ELF pulsed-gradient magnetic field can not only inhibit the
growth of S-180 sarcoma in mice, but can also promote their oncolytic ability of host immune cells. The results of these
studies have shown that sarcomas from treated mice were smaller and harder than those from controls: sarcomas in the
control group were much larger and softer.
Pulsating magnetic fields affect also DNA. Extensive DNA degradation is characteristic in the early stages of
apoptosis. Cleavage of the DNA may yield double-stranded fragments with COOH termini as well as single strands. The
free C-ends, in DNA can be labeled with DIG-dUTP by terminal deoxynucleotidyl transferase (TdT), with the incorporated
nucleotides being detected in a second incubation step with an anti-DIG antibody conjugated with fluorescein. The

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immuno-complex has an emission wavelength of 523 nm (green light) when excited at 494 nm. Labeled apoptotic cells,
counted under fluorescence microscopy, in treated sarcomas were greater on number than in the controls. The
phenomenon of immune cells, including lymphocytes and phagocytes, accumulating around cancer cells to destroy and
digest them was seen more prominently in sarcomas exposed to the magnetic field [74]. A decrease of DNA content has
been observed by Feulgen staining technique which indicated that magnetic field can block DNA replication and mitosis of
sarcoma cells. It is found that a decrease of the mitotic phases of carcoma cells is due to exposure.
It has been reported in [75] that a wide variety of challenging musculoskeletal disorders has been treated
successfully over the past two decades. The field parameters of therapeutic, pulsed electromagnetic field were designed
to induce voltages similar to those produced, normally, during dynamic mechanical deformation of connective tissues.
Clinical applications in orthopaedics: treatment of fractures (non-unions and fresh fractures) and spine fusion have been
reported in [76]. More than a quarter million patients with chronically un-united fractures have benefitted from this
surgically non-invasive method, without risk, discomfort, or the high costs of operative repair. Many of the non-thermal
biological responses, at the cellular and sub-cellular levels, have been identified and found appropriate to correct or modify
the pathologic processes for which PEMFs have been used. Not only is efficacy supported by these basic studies but by a
number of double-blind trials. Specific requirements for field intensity are being defined. The range of treatable illnesses
include nerve regeneration, wound healing, graft behavior, diabetes, and myocardial and cerebral ischemia (heart attack
and stroke), among other conditions. Preliminary data even suggest possible benefits in controlling malignancy.
CONCLUSIONS
In conclusion we stress that there are numerous experimental data which show the biological effects of constant and
pulsating magnetic fields in the broad interval of frequencies. Moreover, the magnetic fields are widely used in therapies to
treat various diseases. Such therapies are mainly phenomenological with respect to the choice of the field frequencies,
shapes of pulses, doses, etc., in view of the lack of knowledge of physical mechanisms of the biological effects of
magnetic fields. We have demonstrated that there can be several such mechanisms, acting on different levels of the
hierarchy of the organization of living organisms, and indicated possibility of the synergism of the biological effects caused
by various physical mechanisms.
Based on the experimental data indicating the dependence of the effectiveness of the redox processes on the external
magnetic field, we have suggested that one of such mechanisms can be related with the soliton mechanism of charge
transport in the redox processes during respiration or photosynthesis. We have shown that within the soliton mechanism
of charge transport the magnetic field can cause a hierarchy of changes from the primary effect on the dynamics of
electrosolitons, to the changes of the state of macromolecules, to the effects on the rate of respiration, and, finally, to the
effect on the whole metabolism of the system.
ACKNOWLEDGMENTS
The author acknowledges stimulating discussions with E. Fermi, C. Simmi and D. Zanotti from THERESON Company
(Italy) and thanks them for sharing the experimental data on TMR™ therapy. This research was carried under the partial
support from the Fundamental Research grant of the National Academy of Sciences of Ukraine.
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Author’s biography with Photo
Larissa Brizhik is a leading research fellow at Bogolyubov Institute for Theoretical Physics in Kiev( Ukraine) and
adjunct professor at the Wessex Institute of Technologies, Southampton (UK). She is the author of more than 100
publications in leading scientific journals. She was awarded Illya Prigogine gold medal in 2011 and State Award of Ukraine
for outstanding achievements in science and technologies in 2013. Her current research interests include conducting
properties and electron-phonon interactions in low-dimensional systems, nanotubes, cuprates, anharmonic lattices;
interaction of solitons and bisolitons between themselves and with external fields; solitons in two- and higher-dimensional
systems; nonlinear mechanisms of high-temperature superconductivity; soliton mechanism for energy storage and
transfer in macromolecules; bisoliton mechanism of electron transport in biological macromolecules and polymers;
influence of electromagnetic radiations on biological systems; mechanisms of the origin of endogenous electromagnetic
fields in living systems; role of the electromagnetic interactions and coherence in self-organization of living matter and
ecosystems.