Influence of a channel-forming peptide on energy barriers to ion permeation, viewed from a continuum dielectric perspective

The continuum three-dielectric model for an aqueous ion channel pore-forming peptide-membrane system is extended to account for the finite length of the channel. We focus on the electrostatic influence that a channel-forming peptide may exert on energy barriers to ion permeation. The nonlinear dielectric behavior of channel water caused by dielectric saturation in the presence of an ion is explicitly modeled by assigning channel water a mean dielectric constant much less than that of bulk water. An exact solution of the continuum problem is formulated by approximating the dielectric behavior of bulk water, assigning it a dielectric constant of infinity. The validity of this approximation is verified by comparison with a Poisson-Boltzmann description of the electrolyte. The formal equivalence of high ionic strength and high electrolyte dielectric constant is demonstrated. We estimate limits on the reduction of the electrostatic free energy caused by ionic interaction with the channel-forming peptide. We find that even assigning this region an epsilon of 100, its influence is insufficient to lower permeation free energy barriers to values consistent with observed channel conductances. We provide estimates of the effective dielectric constant of this highly polarizable region, by comparing energy barriers computed using the continuum approach with those found from a semi-microscopic analysis of a simplified model of a gramicidin-like charge distribution. Possible ways of improving both models are discussed.