Mf. Schumaker et Cj. Kentler, FAR-FIELD ANALYSIS OF COUPLED BULK AND BOUNDARY-LAYER DIFFUSION TOWARD AN ION-CHANNEL ENTRANCE, Biophysical journal, 74(5), 1998, pp. 2235-2248
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).