Ion current and potential across membranes

Abstract

Theoretical treatments of the membrane process in the steady state were presented by using the rate equation in the preceding paper (Kimizuka & Koketsu,1964). It was shown that the equation for the ion conductance and transport number were expressed as functions of the membrane permeability, the composition and the membrane potential. The transport numbers of ions to the membrane of frog's sartorius muscle in normal Ringer's solution were calculated according to the derived equation. The membrane potential calculated according to the Nernst equation by using the transport numbers and the equilibrium potentials of potassium, sodium and chloride ions was in agreement with the observed value. The membrane conductance was shown to be a function of the applied potential, by which the difference between the calculated membrane resistance at rest and the observed one, could be explained. The equation for the passive ion flux at rest was given as a function of the composition and the membrane permeability, and it was shown that the calculated passive movements of ions were consistent with the directions of the active transports. The equation for the resting potential, as well as the membrane conductance, were obtained for the case in which the external solution contains the bivalent ions. The prolonged action porential of the crustacean muscle fibers (Fatt & Ginsborg, 1958) in the presence of strontium ions could be expressed in terms of the derived equation, and the membrane permeabilities to the ions were evaluated according to the proposed relationships. It was shown that the current-voltage relation measured with the giant axon of loligo (Hodgkin, Huxley & Katz, 1952) could be expressed by the derived equations. The discussion for the states of the membrane was given in terms of the proposed theory. The current-voltage relation for the cable has also been derived.