Research summary: A Lorentz Force Model in Biological Systems


David J. Muehsam and Arthur A. Pilla


Departments of Biomedical Engineering, Columbia University and Orthopaedics, Mount Sinai School of Medicine, New York, NY

 

Summary of research published in Biolelectromagnetics, Vol. 30, No. 6, pp. 462-488:

  • Part I - Thermal noise is an essential component of AC/DC effects on bound ion trajectory (p 462-475)
  • Part II - Secondary transduction mechanisms and measures of reactivity (p 476-488)


These papers add to our previous studies (Bioelectromagnetics, 1996;17:89-99, Bioelectrochem Bioenerg., 1994;35:71-9), which showed how the Lorenz force could affect the dynamics of an ion bound in a molecular cleft in the presence of thermal noise as a possible explanation of weak static magnetic field bioeffects. Those publications were inspired by Edmonds (Bioelectrochem Bioenerg., 1993;30:3-12) who proposed Larmor precession as a mechanism for the detection of static and alternating magnetic fields, but did not include the effects of thermal noise. However, it really all started with a paper published in 1984 in Science by Liboff et al. which quite conclusively demonstrated that magnetic fields, per se, could affect the rate of division of living cells in culture.

To rationalize these findings, Abe Liboff proposed the Ion Cyclotron Resonance (ICR) model, which was closely followed by the Ion Parametric Resonance (IPR) model developed by Lednev. Both models predicted certain combinations of very weak AC/DC magnetic fields would have peak effects at resonances based upon the charge to mass ratio of the suspected target ion.  Although both the ICR and IPR models have been criticized on theoretical grounds, resonances predicted at or near the cyclotron frequency have been observed. In fact, an effective bone growth stimulator, designed to help heal recalcitrant bone fractures, was developed using ICR predictions. It is in use today.

The Lorentz force model presented in these papers attempts to provide an alternate, and perhaps more physically realistic, explanation of weak AC/DC magnetic field bioeffects. Here, the solution of the equation of motion for a charged particle bound in a binding potential showed that the thermal component of the motion itself undergoes angular rotation around the magnetic field axis at the Larmor frequency. Thus, thermal noise does not destroy the coherence of the oscillator motion and render the dynamics random. Rather, thermal noise appears to play an essential role in the biological detection of weak magnetic fields. Charged ions in binding sites undergo thermally induced oscillations in the infrared frequency range, with the resultant velocities sufficient for a Lorentz force effect from weak AC/DC magnetic fields. The resulting trajectory of the bound ion is thus determined by the magnetic field environment in the presence of thermal noise, offering a means to modulate biochemical reactions. We have suggested a geometric method for a measure of reactivity based upon the classical oscillator trajectory, and applied the results to parallel and perpendicular AC/DC field combinations, with differing resonance regimes found for each. Resonances were shown to be dependent upon the ensemble of initial conditions and binding lifetime and were obtained through averaging over incident AC phases. AC resonance frequencies were shown to be dependent upon the ratio of AC/DC amplitudes and biochemical kinetics via binding lifetime, and were predicted to occur both at the Larmor frequency, and also at other frequencies,

Several approaches to testing the model were presented. Among these, scanning AC amplitude at fixed frequency and DC amplitude provided an acceptable description of experimental data reported for a test of the IPR model on Ca2+ membrane flux. A measure of reactivity based upon the angular position of the bound oscillator results in an AC/DC amplitude response closely fitting experimental observations and predictions of the IPR model. Other physically meaningful measures are discussed, none of which require the assumptions most often employed in the ICR and IPR models, such as multiple ionic targets, hydrogen triggering or arbitrary combinations of Bessel functions. The only required parameter is the desorption rate constant of the assumed ion target, which can normally be obtained from the literature.

There are clearly many measures of reactivity which may be employed in the Lorentz model, and we are continuing to pursue the more promising approaches. For example, a purely geometric measure of reactivity predicts previous experiments, and yields a close fit to IPR results. The Bessel function expansion of this geometric measure consists of coefficients determined uniquely by the classical orbit, rather than chosen arbitrarily, as in the IPR model, suggesting a more parsimonious explanation of weak AC and DC magnetic field bioeffects. In the final analysis, the underlying mathematics is a straightforward analysis of the classical dynamics of a bound particle in a magnetic field.

We note that the biological effects of weak electromagnetic fields result from signaling. This means there is unlikely to be a linear relationship between a field effect on ion binding and the end biological effect (e.g., ion transport, differentiation, proliferation, tissue repair, pain relief) which is usually many, many steps downstream of the site of action of the magnetic field. For this reason, verification of any model purporting to predict weak AC/DC magnetic field effects must be performed with great care to isolate the primary target of interaction. This could be accomplished by performing studies as a function of the concentration of the ion target, which has only been reported in very few studies.