Solutions of the Field Equations in the Fixed-Charge Model of Cell Membranes

Abstract

A general method is given for the numerical solution of the equations governing the diffusion of charged ions through layers containing specified concentrations of fixed charge. Using this method, the properties of a membrane model 50 A thick in which the first half is positively and the second half negatively charged are investigated. Results presented are: the required ionic mobility to give resistance values similar to those observed, the voltage-current relation in such a model, the profiles of ionic concentration. The ionic concentrations found were compared with those given by the Boltzmann distribution. It is found that there is good agreement with the Boltzmann values for zero current, but that for finite membrane currents there is a significant disagreement.