FAR-FIELD ANALYSIS OF COUPLED BULK AND BOUNDARY-LAYER DIFFUSION TOWARD AN ION-CHANNEL ENTRANCE

We present a far-field analysis of ion diffusion toward a channel embe dded in a membrane with a fixed charge density. The Smoluchowski equat ion, which represents the 3D problem, is approximated by a system of c oupled three-and two-dimensional diffusions. The 2D diffusion models t he quasi-two-dimensional diffusion of ions in a boundary layer in whic h the electrical potential interaction with the membrane surface charg e is important. The 3D diffusion models ion transport in the bulk regi on outside the boundary layer. Analytical expressions for concentratio n and flux are developed that are accurate far from the channel entran ce. These provide boundary conditions for a numerical solution of the problem. Our results are used to calculate far-field ion flows corresp onding to experiments of Bell and Miller (Biophys. J. 45:279, 1984).