Theoretical Limits on the Threshold for the Response of Long Cells to Weak Extremely Low Frequency Electric Fields Due to Ionic and Molecular Flux Rectification

Abstract

Understanding exposure thresholds for the response of biological systems to extremely low frequency (ELF) electric and magnetic fields is a fundamental problem of long-standing interest. We consider a two-state model for voltage-gated channels in the membrane of an isolated elongated cell ( L cell = 1 mm; r cell = 25 μm) and use a previously described process of ionic and molecular flux rectification to set lower bounds for a threshold exposure. A key assumption is that it is the ability of weak physical fields to alter biochemistry that is limiting, not the ability of a small number of molecules to alter biological systems. Moreover, molecular shot noise, not thermal voltage noise, is the basis of threshold estimates. Models with and without stochastic resonance are used, with a long exposure time, t exp = 10 4 s. We also determined the dependence of the threshold on the basal transport rate. By considering both spherical and elongated cells, we find that the lowest bound for the threshold is E min ≈ 9 × 10 −3 V m −1 (9 × 10 −5 V cm −1). Using a conservative value for the loop radius r loop = 0.3 m for induced current, the corresponding lower bound in the human body for a magnetic field exposure is B min ≈ 6 × 10 −4 T (6 G). Unless large, organized, and electrically amplifying multicellular systems such as the ampullae of Lorenzini of elasmobranch fish are involved, these results strongly suggest that the biophysical mechanism of voltage-gated macromolecules in the membranes of cells can be ruled out as a basis of possible effects of weak ELF electric and magnetic fields in humans.