Diffusion layer caused by local ionic transmembrane fluxes.

Ionic concentrations in the close proximity of a carrier may be different from those in the bulk solution. An immediate layer in the solution in which this situation occurs is known as a diffusion layer. Such diffusion layers were calculated using general diffusion equations and postulating a membrane to be homogeneous in the plane with respect to its permeability. In contrast, the present mathematical model considers single-carrier mediated transport of ions across the membrane and their diffusion away from the carrier site into the electrolyte solution. In particular, the transport of Ca2+ ions is considered. The diffusion of electrolyte ions (Na+ and Cl-) and of Ca2+ ions is described by the Nernst-Planck electrodiffusion equation. The relation between the local electric potential and the ion concentrations is taken into account by the Poisson equation. The equations are solved numerically for radial symmetry by the relaxation method. The model predicts concentration and potential profiles in dependence of the flux rate of Ca2+ ions. It is shown that for fluxes mediated by a single carrier, a diffusion layer becomes significant if the flux is larger than 10(5) Ca2+ ions per second.