Electrostatic potential between surfaces bearing ionizable groups in ionic equilibrium with physiologic saline solution

Abstract

In the past calculations of electrostatic properties of interacting cellular surfaces have been restricted by assumptions of fixed surface charge or surface potential. For the most part these calculations have been confined to a linear approximation and neglect the small but important complement of divalent cations in the cellular environment. In the present paper these limitations are removed. Solutions are obtained to the full non-linear Poisson-Boltzmann equation, treating the fraction of dissociated ionizable surface groups as a self-consistent functional of the electrostatic potential. The potential is expressed in terms of relations between Jacobian elliptic functions. A general and efficient method of computation is developed through the theory of Jacobian theta functions. The treatment given here offers wide flexibility in dealing with cell surfaces in the languages of the cell physiologist, biochemist and physical chemist.