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. 

Equation (3.63) is known as the the Goldman-Hodgkin-Katz equation for passive flux of an ion through a membrane [108, 123],... 

Three assumptions are usually made in calculating ion current density through a membrane (a) an ion does not interact with any other ion while traversing the membrane (independence principle) (b) the membrane is homogeneous and (c) the electric field in the membrane is constant in space. The linear transport equation then leads to the Goldman-Hodgkin-Katz equation - for the I -V relation ... 

It was then that Hodgkin and Katz made the important discovery that the magnitude of this overshoot is quantitatively related to the logarithm of the external Na concentration. This discovery led to the formulation of the ionic theory of cell potentials described by the Hodgkin-Katz equation, following a prior formulation of Goldman. 

The data reviewed above showed that, of the relationships predicted between j/ and the variables in the Hodgkin-Katz equation [Eq. (1)], only the relation between ij/ and T, between and ln[K ]ex, and between and ln[Na ]e, have been unequivocally established. These three relationships are in fact the only ones predicted by Eq. (4). In other words, each of the predictions based on the surface adsorption theory has already been verified. 

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). 

Heart Muscle, Frog, Ionic Activity, 159 Helium Glow Photometer, 78 Hemorrhage, Muscle pH, 176 Henderson-Hasselbalch Equation, 94 Heterogeneous Distribution, 15 Hodgkin-Katz Equation, 99 H Secretion, Renal Tubules, 95... 

We shall treat each of these four contributions separately in the following sections, along with discussions of their effects in the context of experimental results. The same mathematical procedures described in Chapters 6 and 8, namely, the Fokker-Planck formalism, first passage times, Poisson-Nernst-Planck formalism, and the Goldman-Hodgkin-Katz equations, are implemented (Muthukumar 2010) to obtain the steady-state flux of the polymer chains and the probability of successful barrier crossing. 

Part of the system reacts "classically and can be described by the Goldman-Hodgkin-Katz equation for transmembrane diffusion of ions. We believe that our earlier measurements were done on chloroplasts which completely fit such a system description (fig. 3A). Such chloroplasts revealed only monophasic decay kinetics (reaction 1) after the light was turned off. 

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