The Electric Double Layers of Semipermeable Membranes: Analytical and Numerical Solutions of the Poisson-Nernst-Planck Equations.

Abstract

Cable theory is often used to describe the electrical properties of axons, but new findings have deemed it possibly fruitful to do further research that accounts for ion diffusion in the submyelin region in terms of the Poisson-Nernst-Planck equation. This approach is not often used for axons, so preliminary work was done to directly treat the electric double layers on the inside and the outside of a semipermeable membrane. Steady-state analytical solutions were found for a membrane with one permeant ionic species, and extended to two permeant ionic species. It was shown that more ionic species surrounding the membrane and more permeant ionic species can be added straightforwardly. This is thus a generally valid and broadly applicable result. The results were also found numerically using the program "COMSOL Multiphysics". Lastly a time-dependent study conducted by COMSOL found the passive membrane response to a depolarization, as predicted by cable theory.