Solute translocation probability, lifetime, and “rectification” in membrane channels with localized constriction

Abstract

We study the translocation probability and lifetime of a solute molecule in a cylindrical membrane channel that contains a localized constriction at an arbitrary location. Using a one-dimensional continuous diffusion description of solute dynamics in the channel, we explore two models. The first one describes a molecule's interaction with the constriction in terms of a narrow rectangular barrier in the potential of mean force. The second novel model proposed here represents this interaction by introducing an infinitely thin permeable partition. It is shown that when the parameters of the two models are chosen to warrant the same translocation probability, both models predict the same mean lifetime of the molecule in the channel. While the translocation probability is independent of the constriction location, the mean lifetime is a function of the location. The benefit of the thin partition model is that it allows one to lump together the height and length of the potential barrier into a single parameter, which is the partition's permeability. It is shown that in the case of an asymmetric location of the localized constriction and strong repulsion between the solutes, the solute flux through the channel is a function of the direction in which it goes, analogous to the phenomenon known in ion channel electrophysiology as rectification.