Nonlinear electrical effects in lipid bilayer membranes. 3. The dissociation field effect

In the course of an analysis of nonlinear electrical effects in lipid bilayer membranes, the influence of the dissociation field (or Wien) effect on the membrane conductivity is investigated. It is shown that the theory of Onsager for the Wien effect in a macroscopic phase can be applied to a thin membrane when the proper boundary conditions at the membrane-solution interface are introduced. It is assumed that an activation energy is associated with the passage of the ion across the interface. The mathematical treatment of the model is restricted to the case for which cations and anions have identical properties except for the charge sign. The resulting differential equations for the ion concentration within the membrane are integrated numerically. The analysis shows that the influence of the Wien effect on the membrane conductivity is appreciable only if the energy barrier at the interface is sufficiently high, i.e. if the rate limiting step for the ion transport is the passage of the ion across the interface.