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Fokker–Planck analysis of the Langevin–Lorentz equation: Application to ligand-receptor binding under electromagnetic exposure

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3 Author(s)
Moggia, Elsa ; Department of Biophysical and Electronic Engineering, University of Genoa, via Opera Pia 11a, 16145, Genoa, Italy ; Chiabrera, A. ; Bianco, B.

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The statistical properties of the solution of the Langevin–Lorentz equation are analyzed by means of the Fokker–Planck approach. The equation describes the dynamics of an ion that is attracted by a central field and is interacting with a time-varying magnetic field and with the thermal bath. If the endogenous force is assumed to be elastic, then a closed-form expression for the probability density of the process can be obtained, in the case of constant magnetic exposure and, for the time-varying case, at least asymptotically. In the general case, a numerical integration of the resulting set of differential equations with periodically time-varying coefficients has been implemented. A framework for studying the possible effects of low-frequency, low-intensity electromagnetic fields on biological systems has been developed on the basis of the equation. The model assumes that an exogenous electromagnetic field may affect the binding of a messenger attracted by the endogenous force field of its receptor protein. The results are applicable to the analysis of experiments, e.g., exposing a Petri dish, containing a biological sample, to a periodically time-varying magnetic field generated by a pair of Helmholtz coils, most widely used in the scientific literature. The proposed model provides a theoretical mean for evaluating the biological effectiveness of low-frequency, low-intensity electromagnetic exposure. © 1997 American Institute of Physics.

Published in:

Journal of Applied Physics  (Volume:82 ,  Issue: 9 )

Date of Publication:

Nov 1997

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