A Lorentz model for weak magnetic field bioeffects: Part I—Thermal noise is an essential component of AC/DC effects on bound ion trajectory

We have previously employed the Lorentz–Langevin model to describe the effects of weak exogenous magnetic fields via the classical Lorentz force on a charged ion bound in a harmonic oscillator potential, in the presence of thermal noise forces. Previous analyses predicted that µT‐range fields give rise to a rotation of the oscillator orientation at the Larmor frequency and bioeffects were based upon the assumption that the classical trajectory of the bound charge itself could modulate a biochemical process. Here, it is shown that the thermal component of the motion follows the Larmor trajectory. The results show that the Larmor frequency is independent of the thermal noise strength, and the motion retains the form of a coherent oscillator throughout the binding lifetime, rather than devolving into a random walk. Thermal equilibration results in a continual increase in the vibrational amplitude of the rotating oscillator towards the steady‐state amplitude, but does not affect the Larmor orbit. Thus, thermal noise contributes to, rather than inhibits, the effect of the magnetic field upon reactivity. Expressions are derived for the ensemble average of position and the velocity of the thermal component of the oscillator motion. The projection of position and velocity onto a Cartesian axis measures the nonuniformity of the Larmor trajectory and is illustrated for AC and combined AC/DC magnetic fields, suggesting a means of interpreting resonance phenomena. It is noted that the specific location and height of resonances are dependent upon binding lifetime and initial AC phase. Bioelectromagnetics 30:462–475, 2009. © 2009 Wiley‐Liss, Inc.     

Lorentz approach to static magnetic field effects on bound-ion dynamics and binding kinetics: Thermal noise considerations

The present study characterizes an ion-binding site, a molecular cleft in a signalling molecule such as calmodulin or troponin C, as a damped linear isotropic oscillator potential for small displacements about the origin. Quantitative assessments of the effects of thermal noise and exogenous static magnetic fields are made through a statistical mechanical treatment of the Lorentz-Langevin equation for an ion bound in a molecular cleft. Thermal noise causes a bound ion to be ejected from the site after a bound lifetime dependent upon the thermal noise spectral density. It is shown that the Lorentz-Langevin model requires values of the viscous damping parameter many orders of magnitude below those for bulk water in order to characterize the binding site and to obtain realistic lifetimes for a bound ion. The model predicts that milliTesla-range magnetic fields are required for static field effects on dissociation kinetics. The Lorentz equation also yields a classic coherent solution describing precession of the boundion oscillator orientation at the Larmor frequency. The bound-ion dynamics described by this coherent solution are sensitive to micro Tesla-range static magnetic fields in the presence of thermal noise. Numerical integration of the contribution of thermal noise forces to these dynamics is in good agreement with the results of statistical mechanical analysis, also producing realistic bound lifetimes for only very low viscous damping values. The mechanisms by which modulation of precessional motion might enable a signalling molecule such as calmodulin to detect an exogenous magnetic field are presently unclear. © 1996 Wiley-Liss, Inc.     

Dynamic properties of Lednev's parametric resonance mechanism

This paper presents a further development of the mechanism for the detection of weak magnetic fields proposed by [Lednev (1991): Bioelectromagnetics 12:71–75]. The fraction of excited oscillator states of an unhydrated ion is studied in a dynamic model driven by the predicted (time-varying) transition probability in the presence of thermal noise and an unspecified excitation mechanism. The main results of Lednev are confirmed. In addition, I conclude that ultraharmonic and ultrasubharmonic resonances may also be observed, provided that the response time of the dynamic system is similar to the period of the oscillating magnetic field. I discuss the time scales involved in the mechanism and present theoretical constraints on these parameters. The crucial requirement for the theory's applicability is that the lifetime of the excited states of the affected ion oscillator exceeds the period of the applied magnetic field. Numerical solutions of the dynamic system are given and are shown to correspond well to theoretical expectations. The main discrepancy between the theories of Lednev and of Blanchard and Blackman [Blanchard and Blackman (1994): Bioelectromagnetics 15:217–238] appears to be due to an inconsistency in the latter paper. The general problem of robust analysis of experimental data is discussed, and I suggest a test of compliance with the Lednev model that is independent of all parameters except for the ratio of oscillating and static field strength (B₁/B₀) for many resonance conditions and experimental models. © 1996 Wiley-Liss, Inc.     

A Lorentz model for weak magnetic field bioeffects: Part II—Secondary transduction mechanisms and measures of reactivity

In Part I it was shown that the thermal component of the motion of a charged particle in an oscillator potential, that is, within a molecular binding site, rotates at the Larmor frequency in an applied magnetic field. It was also shown that the Larmor angular frequency is independent of the thermal noise strength and thus offers a mechanism for the biological detection of weak (µT‐range) magnetic fields. Part II addresses the question of how the Larmor trajectory could affect biological reactivity. The projection of the motion onto a Cartesian axis measures the nonuniformity of the Larmor trajectory in AC and combined AC/DC magnetic fields, suggesting a means of assessing resonances. A physically meaningful measure of reactivity based upon the classical oscillator trajectory is suggested, and the problem of initial conditions is addressed through averaging over AC phases. AC resonance frequencies occur at the Larmor frequency and at other frequencies, and are dependent upon the ratio of AC/DC amplitudes and target kinetics via binding lifetime. The model is compared with experimental data reported for a test of the ion parametric resonance (IPR) model on data from Ca²⁺ flux in membrane vesicles, neurite outgrowth from PC‐12 cells and a cell‐free calmodulin‐dependent myosin phosphorylation system, and suggests Mg²⁺ is the target for these systems. The results do not require multiple‐ion targets, selection of isotopes, or additional curve fitting. The sole fitting parameter is the binding lifetime of the target system and the results shown are consistent with the literature on binding kinetics. Bioelectromagnetics 30:476–488, 2009. © 2009 Wiley‐Liss, Inc.     

Frequency and amplitude windows in the combined action of DC and low frequency AC magnetic fields on ion thermal motion in a macromolecule: theoretical analysis

We solved the differential equation describing combined action of DC and AC magnetic fields on thermal motion of ions in a biological macromolecule. The solution showed the occurrence of a new set of resonant peaks for ion oscillations under the influence of magnetic fields. After establishment of steady ion oscillations in the macromolecule interior that is well shielded from the action of small particles of the medium surrounding this molecule, the change in energy of ion thermal motion could be sufficient to alter the conformation state of the macromolecule. On this basis, a diversity of biological phenomena can be explained, including the appearance of the known "frequency" and "amplitude" windows, without any resort to the ideas of participation of cyclotron or parametric resonances in these effects.     

Cytoplasmic Ca2+ oscillations in human leukemia T-cells are reduced by 50 Hz magnetic fields.

The effect of 50 Hz magnetic fields on the cytosolic calcium oscillator in Jurkat E6.1 cells was investigated for field strengths within the range from 0 to 0.40 mT root mean square. The intracellular Ca2+ concentration data were collected for single Jurkat cells that exhibited a sustained spiking for at least 1 h while repeatedly exposing them to an alternating magnetic field in 10-min intervals interposed with nonexposure intervals of the same length. The obtained data were analysed by computing spectral densities of the Ca2+ oscillating patterns for each of these 10-min intervals. For every single-cell experiment the spectra of all exposure as well as nonexposure periods were then averaged separately. A comparison between the resulting averages showed that the total spectral power of the cytosolic Ca2+ oscillator was reduced by exposure of the cells to an alternating magnetic field and that the effect increased in an explicit dose-response manner. The same relationship was observed within the 0-10 mHz (10 x 10(-3) Hz) subinterval of the Ca2+ oscillation spectrum. For subintervals at higher frequencies, the change caused by the exposure to the magnetic field was not significant.     

Possible mechanism for the influence of weak magnetic fields on biological systems

A physical mechanism is suggested for a resonant interaction of weak magnetic fields with biological systems. An ion inside a Ca(2+)-binding protein is approximated by a charged oscillator. A shift in the probability of ion transition between different vibrational energy levels occurs when a combination of static and alternating magnetic fields is applied. This in turn affects the interaction of the ion with the surrounding ligands. The effect reaches its maximum when the frequency of the alternating field is equal to the cyclotron frequency of this ion or to some of its harmonics or sub-harmonics. A resonant response of the biosystem to the magnetic field results. The proposed theory permits a quantitative explanation for the main characteristics of experimentally observed effects.     

细胞离子在振荡电磁场作用下的受力模型分析

本文通过生物细胞模型,研究振荡电场、振荡磁场以及振荡磁场产生的感应电场对细胞离子的作用机理。模型分析结果表明,电场力和罗仑兹力对细胞膜两侧的自由离子将产生加速度,振荡离子将产生周期性电位移。该模型同时也解释了脉冲电磁场比同参教的连续场产生更多的生物效应,以及连续场在开始施加和切除时的效应最大。     

Effects of very weak magnetic fields on radical pair reformation

We can expect that biological responses to very weak ELF electromagnetic fields will be masked by thermal noise. However, the spin of electrons bound to biologically important molecules is not strongly coupled to the thermal bath, and the effects of the precession of those spins by external magnetic fields is not bounded by thermal noise. Hence, the known role of spin orientation in the recombination of radical pairs (RP) may constitute a mechanism for the biological effects of very weak fields. That recombination will generally take place only if the valence electrons in the two radicals are in a singlet state and the effect of the magnetic field is manifest through differential spin precessions that affect the occupation of that state. Because the spin relaxation times are of the order of microseconds, any effects must be largely independent of frequency up to values of a few megahertz. Using exact calculations on an appropriately general model system, we show that one can expect small, but significant, modifications of the recombination rate by a 50 microT field only under a narrow range of circumstances: the cage time during which the two elements are together must be exceptionally long--of the order of 50 ns or longer; the hyperfine field of either radical must not be so great as to generate a precession period greater than the cage containment time; and the characteristic recombination time of the radical pair in the singlet state must be about equal to the containment time. Thus, even under such singularly favorable conditions, fields as small as 5 microT (50 milligauss) cannot change the recombination rate by as much as 1%. Hence, we conclude that environmental magnetic fields much weaker than the earth's field cannot be expected to affect biology significantly by modifying radical pair recombination probabilities.     

Effects of sinusoidal magnetic field observed on cell proliferation, ion concentration, and osmolarity in two human cancer cell lines

Low frequency magnetic fields have previously been shown to affect cell functions. In this article, the effects of 20 mT, 50 Hz sinusoidal magnetic field on cell proliferation, ion concentration, and osmolarity in two human cancer cell lines (HL-60 and SK-Hep-1) were investigated. Inhibition of cell growth was observed. On the other hand, the exposure also increased the Na+, K+ ion concentration and osmolarity in cell supernatant compared to the control group. To our knowledge, this is the first study on cancer cells where magnetic fields affect osmolarity in cell supernatant. In addition, a model of cells exposed to the oscillating magnetic field is described as well as the characteristics of ions in and out of cells. The experimental data appears to be consistent with the theoretical analysis. The results are also discussed in terms of the relationships among cell growth, ion concentration, and osmolarity. Magnetic field inhibitions of cell growth in vitro may relate to changes in cell ion concentration and osmolarity.     

Electromagnetic gating in ion channels.

There have been many attempts to develop a theoretical explanation of the phenomena of electromagnetic field interactions with biological systems. None of the reported efforts have been entirely successful in accounting for the observed experimental results, in particular with respect to the reports of interactions between extremely low frequency (ELF) magnetic fields and biological systems at ion cyclotron resonance frequencies. The approach used in this paper starts with the Lorentz force equation, but use is made of cylindrical co-ordinates and cylindrical boundary conditions in an attempt to more closely model the walls of an ion channel. The equations of motion of an ion that result from this approach suggest that the inside shape of the channel plus the ELF magnetic fields at specific frequencies and amplitudes could act as a gate to control the movement of the ion across the cell membrane.     

Oscillation spectrum of an electron gas with a small density fraction of ions

The problem is solved of the stability of a nonneutral plasma that completely fills a waveguide and consists of magnetized cold electrons and a small density fraction of ions produced by ionization of the atoms of the background gas. The ions are described by an anisotropic distribution function that takes into account the characteristic features of their production in crossed electric and magnetic fields. By solving a set of Vlasov-Poisson equations analytically, a dispersion equation is obtained that is valid over the entire range of allowable electric and magnetic field strengths. The solutions to the dispersion equation for the m = +1 main azimuthal mode are found numerically. The plasma oscillation spectrum consists of the families of Trivelpiece-Gould modes at frequencies equal to the frequencies of oblique Langmuir oscillations Doppler shifted by the electron rotation and also of the families of “modified” ion cyclotron (MIC) modes at frequencies close to the harmonics of the MIC frequency (the frequencies of radial ion oscillations in crossed fields). It is shown that, over a wide range of electric and magnetic field strengths, Trivelpiece-Gould modes have low frequencies and interact with MIC modes. Trivelpiece-Gould modes at frequencies close to the harmonics of the MIC frequency with nonnegative numbers are unstable. The lowest radial Trivelpiece-Gould mode at a frequency close to the zeroth harmonic of the MIC frequency has the fastest growth rate. MIC modes are unstable over a wide range of electric and magnetic field strengths and grow at far slower rates. For a low ion density, a simplified dispersion equation is derived perturbatively that accounts for the nonlocal ion contribution, but, at the same time, has the form of a local dispersion equation for a plasma with a transverse current and anisotropic ions. The solutions to the simplified dispersion equation are obtained analytically. The growth rates of the Trivelpiece-Gould modes and the behavior of the MIC modes agree with those obtained by numerical simulation.     

DC和AC磁场混合作用下的离子运动

本文研讨了在微弱ＤＣ磁场和频率非常低的ＡＣ磁场并行作用下，位于大分子内部的离子运动情况。主要焦点是大分子中磁场对离子热运动的影响，通过一些离散频率的分析揭示了热运动的共振效应。指出当ＤＣ和ＡＣ磁场施加或切断时离子热运动能量将发生变化，如果大分子周围的媒介质的粒子能充分阻止瞬间接触，就会引起大分了子量子态的变化。     

Mechanism for action of electromagnetic fields on cells

A biophysical model for the action of oscillating electric fields on cells, presented by us before [Biochem. Biophys. Res. Commun. 272(3) (2000) 634-640], is extended now to include oscillating magnetic fields as well, extended to include the most active biological conditions, and also to explain why pulsed electromagnetic fields can be more active biologically than continuous ones. According to the present theory, the low frequency fields are the most bioactive ones. The basic mechanism is the forced-vibration of all the free ions on the surface of a cell's plasma membrane, caused by an external oscillating field. We have shown that this coherent vibration of electric charge is able to irregularly gate electrosensitive channels on the plasma membrane and thus cause disruption of the cell's electrochemical balance and function [Biochem. Biophys. Res. Commun. 272(3) (2000) 634-640]. It seems that this simple idea can be easily extended now and looks very likely to be able to give a realistic basis for the explanation of a wide range of electromagnetic field bioeffects.     

Heating of cardiovascular stents in intense radiofrequency magnetic fields

We consider the heating of a metal stent in an alternating magnetic field from an induction heating furnace. An approximate theoretical analysis is conducted to estimate the magnetic field strength needed to produce substantial temperature increases. Experiments of stent heating in industrial furnaces are reported, which confirm the model. The results show that magnetic fields inside inductance furnaces are capable of significantly heating stents. However, the fields fall off very quickly with distance and in most locations outside the heating coil, field levels are far too small to produce significant heating. The ANSI/IEEE C95.1-1992 limits for human exposure to alternating magnetic fields provide adequate protection against potential excessive heating of the stents.     

Magneto-Electric Double Fano Resonances in Hybrid Split Ring/Disk Hetero-Cavity

In this work, we conceive and demonstrate the magneto-electric double Fano resonances of a hetero-cavity composed of Si disk and Au split ring, where Si disk can provide additional magnetic responses besides electric responses. The interference between electric and magnetic responses in proposed hetero-cavity gives rise to magneto-electric double Fano resonances with magnetic and electric near-field enhancements. Dipole radiative enhancement is used to analyze magnetic and electric responses of hetero-cavity and the spectral features of hetero-cavity can be used to quantitatively characterize by coupled oscillator model. And the spectral tunability of magneto-electric double Fano resonances is investigated, highlighting a potential for applications in low-loss sensing and nanophotonic devices.     

Increase in radiation-induced HPRT gene mutation frequency after nonthermal exposure to nonionizing 60 Hz electromagnetic fields

It is widely accepted that moderate levels of nonionizing electric or magnetic fields, for example 50/60 Hz magnetic fields of about 1 mT, are not mutagenic. However, it is not known whether such fields can enhance the action of known mutagens. To explore this question, a stringent experimental protocol, which included blinding and systematic negative controls, was implemented, minimizing the possibility of observer bias or experimental artifacts. As a model system, we chose to measure mutation frequencies induced by 2 Gy gamma rays in the redox-sensitive hypoxanthine-guanine phosphoribosyl transferase (HPRT) gene in Chinese hamster ovary cells. We tested whether a 12-h exposure to a 60 Hz sinusoidally oscillating magnetic-flux density (Brms = 0.7 mT) could affect the mutagenic effects of ionizing radiation on the HPRT gene locus. We determined that the magnetic-field exposure induced an approximate 1.8-fold increase in HPRT mutation frequency. Additional experiments at Brms = 0.23 and 0.47 mT revealed that the effect was reduced at lower flux densities. The field exposure did not enhance radiation-induced cytotoxicity or mutation frequencies in cells not exposed to ionizing radiation. These results suggest that moderate-strength, oscillating magnetic fields may act as an enhancer of mutagenesis in mammalian cells.     

Tunable Fano Resonances in Mid-Infrared Waveguide-Coupled Otto Configuration

A planar silicon carbide/dielectric multilayer structure is investigated in Otto geometry, where surface phonon polaritons and planar waveguide mode can be coupled to realize Fano resonances under transverse magnetic polarization. The resonance coupling is analytically demonstrated using the coupled harmonic oscillator model and numerically presented through rigorous coupled-wave analysis calculations, which shows that the coupling strength between different resonances and the resonant wavelength matching condition plays an important role in the bandwidth and position of the Fano resonance (FR); the magnetic field distribution was also shown to explain the origin of FRs qualitatively.

     

Biological effects of oscillating electric fields: Role of voltage-sensitive ion channels

An alternating component of potential across the membrane of an excitable cell may change the membrane conductance by interacting with the voltagesensing charged groups of the protein macromolecules that form voltage-sensitive ion channels. Because the probability that a voltage sensor is in a given state is a highly nonlinear function of the applied electric field, the average occupancy of a particular state will change in an oscillating electric field of sufficient magnitude. This “rectification” at the level of the voltage sensors could result in conformational changes (gating) that would modify channel conductance. A simplified two-state model is examined where the relaxation time of the voltage sensor is assumed to be considerably faster than the fastest changes of ionic conductance. Significant changes in the occupancy of voltage sensor states in response to an applied oscillating electric field are predicted by the model.