INTERACTIONS OF DIVALENT-CATIONS WITH NEGATIVELY CHARGED MEMBRANE SURFACES .1. DISCRETE CHARGE POTENTIAL

The present paper is concerned with the mathematical description of the local potential produced by an arbitrary arrangement of polar groups in contact with an electrolyte solution containing divalent cations. The membrane-electrolyte interface is modeled, for that purpose, as a three regions-three dielectric constants system namely: a non-polar region of dielectric constant ε{lunate}m, an adsorption or polar region of dielectric constant ε{lunate} ≥ ε{lunate}m in which the polar head groups are presumed to be located, and an aqueous phase of dielectric constant ε{lunate}0 ≥ ε{lunate}. Using a mathematical procedure involving Fourier-Bessel integrals, a general expression for the local value of the surface potential is derived. For membrane systems of low surface charge densities, the proposed general solution is found to be mathematically equivalent to the expressions obtained from a linearized treatment of the discrete charge potential problem. It is shown moreover, that the space average value of the local surface potential at a given distance from the interface, corresponds formally to the surface potential produced by a uniform surface charge distribution. In addition, the present discrete charge theory is found to reproduce satisfactory Schaufs experimental observations on the effect of divalent cations on the Na+ conductance of Myxicola giant axon (Schauf, 1975). A numerical analysis of several surface charge arrangements leads us finally to conclude, that for highly charged membranes, the local value of the surface potential at one point depends more upon the point macro than micro-environment. In fact, the effect on the local surface charge potential of a change in micro-environment is found to be extremely sensitive to the average value of the membrane surface charge density. © 1979.