Electrodiffusion of ions inside living cells

Abstract

Electrodiffusion of ions, both inside and outside biological cells, are of utmost importance to proper cellular functions. Experiments indicate that both ion concentrations and electropotential can jump discontinuously across the cell membranes. We study a system of nonlinear partial differential equations modelling such phenomena. Jump conditions for species concentrations and electropotential across cell membranes are imposed. Under zero-flux boundary conditions for one-dimensional domains, the solutions are proved to exist for all times. With further assumptions, these transient solutions will converge to the unique steady-state solution. Numerical experiments in one- and two-dimensional domains are also performed in order to study some unresolved theoretical issues.