Isomorphism on a physical system of the Hodgkin-Huxley equations for potassium conductance

Abstract

A physical system is derived which has properties which are the same as those computed for the potassium conductance system in the squid axon with the Hodgkin-Huxley equations. The system describes a molecule with five ionization states which, on hyperpolarization, are stripped of singly charged ions (H+?), and doubly charged ions (Ca++?). The dependence of potassium conductance on pH and on the calcium substrate concentration is predicted by the physical system. The effect of enzyme or allosteric interactions in producing inactivation or blocking of conductance is discussed. To consider these effects, the isomorphism is augmented to an 8-state system. This 8-state system encompasses the properties of both the potassium and, with different parameters, the sodium conductance. It is thus general enough to describe all the HH equations in the potential region used for the determination of the HH parameters, namely, -30 to 110 mV transmembrane potential.