Potential distribution across a membrane with surface charge layers: Effects of nonuniform charge distribution

Abstract

A model for the potential distribution across a membrane with surface charge layers (H. Ohshima and S. Ohki, Biophys. J.47, 673 (1985)) is extended to include the effects of nonuniform charge distribution in the surface layer. We treat the case in which the charge layer on the membrane surface consists of two (outer and inner) layers having different thicknesses and different densities of fixed charges, and assume that electrolyte ions can penetrate into these layers. Equations are derived which give the potential profile across the surface charge layers. The potential profile is found to depend strongly on the charge density and thickness of each layer as well as on the average charge density and total thickness of the surface charge layers. In particular, for the case where the fixed charges of the outer and inner surface layers are of opposite sign, the potential at the outer surface (i.e., the potential at the boundary between the outer surface layer and the surrounding solution) and the net charge of the whole surface layer may, in some cases, be of opposite sign. Also, in some cases, the potential at the outer surface, when plotted as a function of the concentration of electrolyte ions in the surrounding solution, is found to reverse its sign at large concentrations.