Effect of pore structure on energy barriers and applied voltage profiles. I. Symmetrical channels

This paper presents calculations of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. The pore diameter may be variable. As long as the length-to-radius ratio in the narrow portion of a channel is large enough, the image potential for an ion in or near the mouth of a channel is determined by the geometry of the mouth. Within the constriction, the image potential of the ion-pore system may be reasonably approximated by constructing an "equivalent pore" of uniform diameter spanning a somewhat thinner membrane. When a transmembrane potential is applied the electric field within a constricted, constant radius, section of the model pore is constant. If the length-to-radius ratio of the narrow part of the channel is not too large or the channel ensemble has wide mouths, the field extends a significant distance into the aqueous region. The method is used to model features of the gramicidin A channel. The energy barrier for hydration (for exiting the channel) is identified with the activation energy for gramicidin conductance (Bamberg and Läuger, 1974, Biochim. Biophys. Acta. 367:127).