Isomorphism on a physical system of the Hodgkin-Huxley equations for sodium conductance: toxin allosteric effects and gating currents.

An isomorphism on a physical system of the Hodgkin-Huxley equations for sodium ion conductance in the nerve membrane is derived. The physical system consists of 8 states. It shows that the voltage dependence of the sodium conductance arises from a change in ionization of the molecule that provides the ion-selective conductance channels. It associates reversibly with singly charged (H+?) and doubly charged (Ca++?) ions. The inactivation process is the result of the associating of an ionized particle by half of the states. The effect of toxins and narcotics in blocking or inactivating sodium conductance can be understood as an enzyme or allosteric change of the standard free energy difference of the molecule that provides the sodium channels. The effect of changing pH and Ca++ substrate concentration on the sodium conductance is predicted. The gating charge current is predicted. The time constant predicted is in agreement with experiment.