Equivalent Circuits as Related to Ionic Systems

Abstract

The purpose of this paper is to clarify the relationship between certain "equivalent circuits" and the fundamental flux equations of Nernst and Planck. It is shown that as a direct algebraic consequence of these equations one may construct two types of equivalent circuits for a homogeneous (charged or uncharged) membrane. The one, which we term the "pure electrical equivalent circuit," correctly predicts all of the electrical properties of the membrane for both steady and transient states. The other, which we call the "mixed equivalent circuit," predicts the steady state I, Psi characteristics of the membrane and the steady state ionic fluxes; it is not applicable to non-steady state properties or measurements. We emphasize that with regard to the portrayal of the physical basis of the properties of a homogeneous membrane, the mixed equivalent circuit can be misleading. This is particularly significant because this same circuit can also be used to depict a mosaic membrane, in which case the circuit gives a realistic pictorialization of the physical origin of the membrane properties. It is hoped that our analysis will be of aid to workers in electrophysiology who make use of equivalent circuit terminology in discussing the behavior of the plasma membrane.