Energy barriers for passage of ions through channels. Exact solution of two electrostatic problems

Exact solutions are given to two electrostatic problems relevant to ion permeation through pores in membranes. The first assesses the importance of the pore forming molecule as a dielectric shield. It is shown on the basis of structural and dielectric considerations alone (neglecting effects attributable to possible charge distribution at the interior surface of the pre-former) that the minimum electrostatic barrier for monovalent ion passage through a gramicidin-like channel is 11 kT. It is further shown that given favorable circumstances, dielectric shielding might dramatically reduce the barrier to ion passage through potassium channels. The second problem considers the error introduced by treating ions as point charges. It is shown that for structureless pores the point charge approximation introduces no meaningful error, even if the ratio of ion radius to pore radius is as great as 0.95.