Current voltage curves of biomolecular lipid membranes

The first part of this paper describes the current voltage curves of bimolecular membranes of oxidized cholesterol formed between two aqueous solutions of tetrabutylammonium chloride. These membranes are selectively permeable for cations and the membrane interfaces are electrically uncharged. The dependence of the membrane conductivity on the membrane potential can be described as the product of the conductivity at zero current ("zero conductivity") and a function called "overlinearity". The zero conductivity increases linearly with the concentration of tetrabutylammonium chloride. The overlinearity is independent of the concentration of tetrabutylammonium chloride. In the second part the Nernst-Planck and Poisson equations are integrated numerically for a three-phase system consisting of an aqueous electrolyte solution, a membrane and an aqueous electrolyte solution. Each phase is characterized by material constants. Appropriate boundary conditions cause the electric current to build up electrical double layers on both sides of the membrane. The opposing double layers with opposite electrical signs inject the soluble ions into the membrane. This ion injection accounts for the overlinearity of the current voltage curves, thus explaining the measured characteristics.