Interpretation of the sodium permeability changes of myelinated nerve in terms of linear relaxation theory

Ionic conductance data of the axonal membrane were interpreted in terms of relaxation theory in order to develop a kinetic model which describes the effects of changes in the external calcium concentration on the sodium permeability changes observed under voltage clamp conditions. The calculated model is based on the hypothesis that calcium binding renders transfer sites inaccessible for sodium passage. Three elementary steps were identified for the sodium permeability mechanism. The rate constants for the elementary processes were determined by the dependence of the reciprocal time constants on the calcium ion concentration. The model parameters were given numerical values appropriate for single myelinated nerve fibers of Rana pipiens at 4 °C. Substantial agreement with experimental data was seen for the effect of changes in external calcium ion concentration on the maximum sodium permeability versus voltage curve, the steady state inactivation curve, the time course of inactivation, and the time constants of the sodium tails.