Mathematical description of the dynamics of ion conductances and action potential

Abstract The basis of any nervous system that converts information is a nerve cell. The properties of the neuron comprise the basis that in many respects ensures the most diverse reactions of biological systems. The electrophysiological investigations of the physicochemical bases of excitation carried out by Eccles, Kostyuk, and many other physiologists laid the foundation for an accurate quantitative study of the action potential phenomenon. The mathematical interpretation of the biological rules of excitation, started by Lazarev and developed by Rashevsky, and lately by Hodgkin and Huxley, makes it possible to examine quantitatively, with more confidence, the process of the excitation of a cell by using mathematical methods that describe its course in time. Guided by their own experimental data, Hodgkin and Huxley found a system of equations that permitted accurate description of the dynamics of the change in conductance, and consequently the ionic currents and action potential. In so doing, as they themselves indicate, attention was paid, first of all, to the achievement of exact agreement of the calculated and experimental data and then to the physical meaning of the mathematical symbols and equations.