Transit time conception for ion diffusion through membrane channels

Abstract

The diffusion path of an ion is considered as a one-dimensional random walk between binding sites along the channel, where the potential energy profile may consist of an arbitrary sequence of different barriers and binding sites. It is shown that the conception of discrete transit times leads to a very simple calculation of transport quantities such as diffusion constant and stationary transmembrane current. The diffusion constant obtained here is the discrete counterpart of the diffusion constant obtained from the exact solution of the Smoluchowski equation. The resulting current–voltage characteristics indicate that the assumption of a discrete random walk represents a fairly good approximation. Furthermore, the first passage time problem for the present model is discussed and solved for the homogeneous case with the aid of a difference equation for successive first passage times.