CALCIUM-ION CURRENT FROM AN EXTRACELLULAR ELECTROLYTE TOWARD A CHANNEL OPENING IN AN INSULATING MEMBRANE - QUANTITATIVE MODEL WITH ROTATIONAL SYMMETRY

A mathematical model of three-dimensional (3-D) ion transport is formu lated in an approximation assuming rotational symmetry, The model cons ists of three particle-conservation equations for sodium, calcium, and chlorine ions complemented with the Poisson equation, The numerical m ethod of solution is based on the Gummel-Scharfetter semianalytical ap proach, the program is written in FORTRAN and the system of discrete e quations is solved explicitly in the axial direction and by iterations in the radial direction, The present report deals with calcium flux t oward a channel opening in an insulating impermeable membrane, assumin g depolarization to zero potential, The initial homogeneous concentrat ions of sodium, calcium, and chlorine ions are 8.729 x 10(19), 6.02 x 10(17), and 8.849 x 10(19) (cm(-3)), respectively, corresponding to mo lar concentrations of 145-mM NaCl and 1-mM of CaCl2; the calcium conce ntration in the circle representing the channel entry is set at 0.1 mu M, corresponding approximately to the concentration of free calcium i ons in the cytoplasm, The calculations were carried out up to 3 mu s. The calcium Aux caused a perturbation of quasi-neutrality and the form ation of a space charge, which reached the maximum value (i.e., maximu m in absolute value) of -0.2 Ccm(-3) at the channel entry; the corresp onding maximum of the axial component of the electric held was about 1 kV/cm. The maximum value of the calcium current was 0.362 pA, decreas ing to 0.283 pA at 3 irs, A review of several experimental studies of calcium currents yielded the average current values for higher and low er conductance channels (mainly L- and T-type) 0.76 and 0.42 pA, respe ctively, This implies that, at Ca++ concentrations of 1 mM or lower th e calcium ion current may be limited by the ion influx from an extrace llular medium.