The State of the Science for the Langevin-Lorentz Model

Abstract

The published experimental results suggest that e.m. exposure (from sub-ELF to RF) at fields or S.A.R. values below the current safety standards, can affect biological processes. Two elementary processes are good candidates to be the first interaction steps: the binding of messenger ions to their receptor proteins and the transport of messenger ions inside protein channels. In both cases the ion dynamics can be often described in terms of the classical Langevin-Lorentz (L-L) model1–4. The closed form integration of the L-L equations under ad hoc simplifying conditions was performed in1–3, for the first time. This rather comprehensive approach includes, as particular cases, all the classical models so far published. In order to analyse or predict the experimental results, the values of the various parameters which enter the L-L equation must be physically plausible, keeping the number of fitting parameters as low as possible. Moreover, their value must be consistent with the effectiveness of the low value of the exposure density. Toward such goals, the following features must be considered. The binding or channel crevice must be hydrophobic, so that it repels the solvent water molecules and strips away the ion hydration shells. If the gradient of the ion endogenous potential energy inside the crevice is an highly non-linear function of the spatial coordinates, the water dipoles can be drifted away from the protein crevice by the resulting endogenous dielectrophoretic force. Therefore, the ion moves in the ballistic Knudsen regime and its Langevin collision frequency can be several order of magnitude lower than in bulk water5. The resulting energy losses are small, so that the ion dynamics become more sensitive to low-intensity e.m. exposure. However, the exogenous signal is typically unable to overcome the Langevin random force (thermal noise) if the ion-protein system, in absence of the e.m exposure, is at thermal equilibrium. On the other hand, the basal state of any ion-protein systems in a living cell is maintained out of thermal equilibrium by the cell metabolism