Ion concentration profile normal to cell membrane

Abstract

Mathematical expressions are developed and completely solved for ion concentration profiles normal to an electrically neutral cell membrane model. A diffuse layer of charge exists near each surface of the membrane due to the difference in the total anion and total cation concentrations. Expressions for the spatial distribution and quantity of charge and the electric field intensity and voltage associated with the diffuse layer are also developed and completely solved. Similar relationships are described for a membrane model which contains special diffusion sites such as pores. In typical models the parameters of the diffuse layer are chiefly determined by the ratio of the thickness to relative dielectric constant of the membrane at the location where ion diffusion through the membrane is occurring. This should not be associated with the average membrane capacitance. If this ratio is greater than 10 Å, the charge, voltage and concentration at the surface of the membrane differ by less than 2% from the values indicated by bulk solution measurements. If the ratio is less than 10 Å, the charge, voltage and concentration differ considerably from bulk solution measurements. This is particularly so in the model with specialized diffusion sites. Because the model systems are of molecular dimensions, considerable discussion is devoted to the validity of the mathematical expressions and their application to biological membranes.