ELECTRIC-POTENTIAL AND CONCENTRATION OF ION SPECIES IN THE PROXIMITY OF A CELL-MEMBRANE - AB-INITIO CALCULATIONS

The mathematical model of ion transport in the field of electric force s and diffusion gradients is based on particle conservation equations and the Poisson equation which governs the distribution of the electri c potential. Designed for evaluating the currents through passive ion channels in cellular membranes, the model is formulated in a two-dimen sional approximation assuming rotational symmetry. Three ionic species are considered in the present study: sodium, calcium and chlorine. Th e program developed for the numerical solution is based on a semi-anal ytical approximation suggested by Gummel & Scharfetter. The present co ntribution reports calculations of the steady-state distributions of i onic species induced by an electric field due to a negative potential drop across the cellular membrane, which represent initial conditions for future calculations of the time development of the ion flux throug h the calcium channel. The numerical calculations were performed from the moment of potential application up to the time 6.2 mu s, when a ne w steady state is established. At this stage, the maximum values of th e sodium and calcium concentrations at the membrane surface are about 22% and 47% above the initial values of 145 mM and 1 mM, respectively, while the chlorine concentration is approximately 18% below. The elec tric field at the membrane surface is about 6.7 x 10(4) and decreases exponentially with distance. The length of the boundary layer is about 40 Angstrom. Since the model is based on fundamental principles, it c an be used for the quantitative solution of any problem possessing rot ational symmetry where a continuum approach is applicable and some ele mentary conditions are fulfilled, such as equilibrium (or at least qua si-equilibrium) of the particle energy distributions with respect to t ime and electric field, and the assumption that the transport coeffici ents are defined as functions of the field and their numerical values are known. (C) 1997 Academic Press Limited.