A new approach to the rest potential of biological membranes

In a series of recent papers, Bonciocat et al., have shown that the faradaic current density of an electrode redox reactions occurring with combined limitations, of charge transfer and nonstationary linear, semi-infinite diffusion, is the solution of an integral equation of Volterra type. This integral equation has been transformed to describe the transport of ions through the interface between two immiscible electrolytic solutions. According to Goldman, Hodkin, Katz theory, the rest potential of a biological membrane is determined by the maintenance of different concentrations of the ions Na+, K+ and Cl−, in the two aqueous solutions separated by the membrane. Using the integral equations (of Volterra type) for the ionic current densities iNa, iK, iCl, and applying the open circuit condition (i.e., iNa + iK + iCl = 0), the potential differences at the junctions: aqueous solution (I)/membrane, respective membrane/aqueous solution (II), have been obtained. To get the diffusion potential across the membrane, the Planck's theory has been used. The sum of these three contributions gives the expression of the rest potential (and a comparison with the Goldman-Hodkin-Katz formula is made, showing in what conditions they become identical formulae).