GHKvergelijking

The Goldman-Hodgkin-Katz (GHK) equation is a fundamental relation in physiology that describes the resting membrane potential by accounting for multiple permeant ions and their concentrations and permeabilities across the cell membrane. It generalizes the Nernst equation, which applies to a single ion, to a membrane with several permeant species.

For a cell membrane with permeabilities P_K, P_Na, and P_Cl and extracellular and intracellular concentrations [K+]_o, [Na+]_o, [Cl-]_i and [K+]_i, [Na+]_i, [Cl-]_o, the membrane potential E_m is given by: E_m = (RT/F) * ln( (P_K [K+]_o + P_Na [Na+]_o + P_Cl [Cl-]_i) / (P_K [K+]_i + P_Na [Na+]_i + P_Cl [Cl-]_o) ). Here R is the gas constant, T the absolute temperature, and F the Faraday constant. At body temperature (~37°C), RT/F is about 26.7 mV.

The equation relies on the constant-field (uniform electric) assumption and assumes permeabilities are constant in time, ion activities can be approximated by concentrations, and ionic currents are at steady state with no net transmembrane current. It neglects active transport, voltage-dependent changes in permeability, and complex interactions among ions beyond simple permeation.

Applications include estimating resting potentials in neurons and other cells and interpreting how changes in ion gradients or channel permeabilities affect membrane voltage. Limitations arise when permeabilities are not constant, active transport is significant, or non-ideal ion interactions violate the model’s assumptions.

See also Nernst equation and the broader concept of membrane potential.