Interaction mechanism between electromagnetic fields and ion adsorption: endogenous forces and collision frequency

Abstract

The adsorption of an ion messenger at a cell receptor is a potential target of electromagnetic exposure, which may affect the binding rate coefficient. The role of the endogenous field force experienced by an ion approaching the binding site is of paramount importance. In order to evaluate the effects of the exogenous field, the endogenous force obtained from the protein data bank has been approximated as a central field by means of a linear restoring force (“spring-like”) and by means of an inverse square field (“coulombic-like”). The first approximation is used in the classical Langevin-Lorentz model and the second in the quantum Zeeman-Stark model. The ion losses due to “collisions” near the binding site are modelled in the classical approach by a viscous collision frequency and in the quantum approach by a set of suitable inverse collision frequencies (lifetimes). In the case of collisions with solvent dipolar molecules (e.g. water), it is shown that the number of colliding solvent dipoles can be very small owing to the large gradients of the endogenous electric field. On the contrary, a binding site is, by definition, a spatial domain finite in size, where colliding molecules move in the Knudsen (ballistic) regime. As a consequence, the mean free path cannot exceed the domain dimension, irrespective of the low concentration of colliding molecules. It is concluded that the ion collision frequency (i.e. in classical terms, the effective viscosity of a binding site) can be many orders of magnitude lower than in the bulk solvent (lifetimes are longer in the quantum model), so that electromagnetic bioeffects may occur at low intensities of the exogenous fields.