Statistical mechanical equilibrium theory of selective ion channels

A rigorous statistical mechanical formulation of the equilibrium properties of selective ion channels is developed, incorporating the influence of the membrane potential, multiple occupancy, and saturation effects. The theory provides a framework for discussing familiar quantities and concepts in th e context of detailed microscopic models. Statistical mechanical expression s for the free energy profile along the channel axis, the cross-sectional a rea of the pore, and probability of occupancy are given and discussed. In p articular, the influence of the membrane voltage, the significance of the e lectric distance, and traditional assumptions concerning the linearity of t he membrane electric field along the channel axis are examined. Important f indings are: 1) the equilibrium probabilities of occupancy of multiply occu pied channels have the familiar algebraic form of saturation properties whi ch is obtained from kinetic models with discrete states of denumerable ion occupancy (although this does not prove the existence of specific binding s ites; 2) the total free energy profile of an ion along the channel axis can be separated into an intrinsic ion-pore free energy potential of mean forc e, independent of the transmembrane potential, and other contributions that arise from the interfacial polarization; 3) the transmembrane potential ca lculated numerically for a detailed atomic configuration of the gramicidin A channel embedded in a bilayer membrane with explicit lipid molecules is s hown to be closely linear over a distance of 25 Angstrom along the channel axis. Therefore, the present analysis provides some support for the constan t membrane potential field approximation, a concept that has played a centr al role in the interpretation of flux data based on traditional models of i on permeation. It is hoped that this formulation will provide a sound physi cal basis for developing nonequilibrium theories of ion transport in select ive biological channels.