Energy barrier presented to ions by the vestibule of the biological membrane channel

The role of the vestibule in influencing the permeation of ions through biological ion channels is investigated. We derive analytical expressions for the electric potential satisfying Poisson's equation with prolate spheroidal boundary conditions. To allow more realistic geometries we devise an iterative method to calculate the electric potential arising from a fixed charge and an arbitrary dielectric boundary, and confirm that the analytical expressions and iterative method give similar potential values. We then investigate the size of the potential barrier presented to an ion by model vestibules of conical and catenary shapes. The height of the potential barrier increases steeply as an ion enters the vestibule and moves toward the constricted region of the channel. We show that the barrier presented by, for example, a 15 degrees conical vestibule can be canceled by placing dipoles with a total moment of about 50 Debyes near the constricted region of the pore. The selectivity of cations and anions can result from the polarity of charge groups or the orientation of dipoles located near the constricted region of the channel.