Membrane potential Hodgkin-Katz equation

Equation (3) suggests that the membrane potential in the presence of sufficient electrolytes in Wl, W2, and LM is primarily determined by the potential differences at two interfaces which depend on charge transfer reactions at the interfaces, though the potential differences at interfaces are not apparently taken into account in theoretical equations such as Nernst-Planck, Henderson, and Goldman-Hodgkin-Katz equations which have often been adopted in the discussion of the membrane potential. 

An equation (also referred to as the constant field equation, the Goldman-Hodgkin-Katz equation, and the GHK equation) which relates the membrane potential (Ai/r) to the individual permeabilities of the ions (and their concentrations) on both sides of the membrane. Thus,... 

If the permeability is significant for both potassium and sodium, the Nernst equation is not a good predictor of membrane potential, but the Goldman-Hodgkin-Katz equation may be used. 

Thus, one can artificially change the concentrations of Na+, K+, and Cl on either side of the membrane. Then, one can go back to the Hodgkin-Katz equation (14.5) and ask what change in potential these artificial changes of ionic concentrations should bring about. There is found (Jahn, 1962) to be a poor match between theory and experiment. Ionic concentration differences alone, then, do not completely determine membrane potentials in living systems. 

S. Ohki, Membrane Potential of Squid Axons Comparison between the Goldman-Hodgkin-Katz Equation and the Diffusion/Surface Potential Equation, in Charge and Field Effects in Biosystems (M. J. Allen and P. N. R. Usherwood, eds.), pp. 147-156, Abacus Press, Tunbridge Wells (1984). 

This Goldman-Hodgkin-Katz voltage equation is often used to determine the relative permeabilities of ions from experiments where the bathing ion concentrations are varied and changes in the membrane potential are recorded [5],... 

The diffusion potential within the membrane may be expressed by the Goldman and Hodgkin and Katz equation [Eq. (126)] as follows ... 

There are no longer any experimental or logical reasons to doubt that under ordinary conditions the action potential of the squid axon membrane does indeed arise, as suggested by Hodgkin, Huxley and Katz in 1949, from the membrane conductance changes to sodium and potassium ions and the inward flow of sodium ions occurs with a time course as calculated from the equation of Hodgkin and Huxley in 1952. 

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