The Goldman-Hodgkin-Katz Equation

The Goldman–Hodgkin–Katz voltage equation, used in cell membrane physiology, can be written
The GHK equation is used to determine the resting membrane potential in real cells. It is a generalization of the Nernst equation. This Demonstration shows the Goldman–Hodgkin–Katz voltage function, plotted in gray, in terms of the argument :
, where
is the membrane potential in volts;
is the ideal gas constant in joules per kelvin-mol;
is the temperature (Kelvin);
is Faraday's constant in coulombs/mol;
, , are the permeabilities of the potassium, sodium, and chloride ions;
, , are the extracellular concentrations of potassium, sodium, and chloride;
, , are their intracellular concentrations.
Also shown are the derivatives of the GHK function (red) and the Nernst function (green), . The region between the GHK and Nernst functions is shown filled.



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