Electrostatic coupling across a membrane with titratable surface groups

The potential drop across a membrane is calculated for the case of ionizable groups on both membrane surfaces. The presence of both acid and amine groups on the membrane surfaces is considered. The membrane surface potential is obtained from the non-linear Poisson-Boltzmann equation by treating the fraction of dissociated ionizable surface groups as a self-consistent functional of the electrostatic potential. A discussion of the error due to ignoring the electrostatic coupling of the potential across the membrane is presented. The error turns out to be quite small for most membrane problems of biological interest. Finally, the conductance data of Mozhayeva & Naumov (1970) for the frog node are reanalyzed within the context of the diffuse double layer theory. It is shown to be unnecessary to invoke a specific binding of divalent cations to the membrane.