Goldman equation

Goldman equation or Goldman -Hodgkin -Katz equation (abbreviated GHK equation) by David Elliot Goldman, Lloyd, Alan Bernard Katz Hodgkin and is a way for the calculation of the membrane potential, taking into account a plurality of permeating ions.

Explanation

It allows the calculation of a membrane potential of a membrane which is permeable to various ions such as sodium, potassium and chloride ions, and may be interpreted as a generalization of the Nernst equation, which is often the first approach for the description equilibrium potential difference ( resting membrane potential) is used on a cell membrane.

In contrast to the Nernst equation, Goldman equation is not an equilibrium state basis, but the principle of a steady state. This means here that the sum of all ion currents must be zero (may be a potassium current on the extracellular side exist while for example). Other assumptions of the Goldman equation are the independence of the ions from each other, and a linear drop of the potential across the membrane thickness - because of the resulting constant field one often speaks also of a "constant field equation". In particular, is not taken it into consideration that at resting membrane potentials, the currents do not go over the whole membrane, but on individual channels ( the equation was also established - 1943 by Goldman and 1949 by Hodgkin and Katz - before ion channels were known ).

The ion current amplitudes depend in a complicated way by the membrane voltage and ion concentration and must be calculated only approximately. In Goldman 's equation, the ion current is approximated as a function of the ion concentration and a coefficient, the so-called permeability P. The permeability is derived from Fick's law of diffusion. Is the quotient of the diffusion coefficients and the membrane thickness.

Formula

R = universal gas constant

T = absolute temperature in Kelvin

F = Faraday constant

P = permeability (see text)

K = potassium, Na = sodium, Cl = chloride

Note to unity: RT / F has the unit J / C. Since 1 Joule = 1 watt second = 1 VAs and 1 As = 1 Coulomb, are calculated as unit for this term Volt

Example

Example of the resting membrane potential of the squid Riesenaxons at:

ΔΨ = -56 ​​mV