GoldmanHodgkinKatzekvationen

The Goldman–Hodgkin–Katz (GHK) equation is a fundamental relation in cellular physiology that describes the resting membrane potential of a cell that is permeable to several ions. It generalizes the Nernst equation by incorporating the relative permeabilities and concentrations of multiple permeant ions across the membrane. The equation is named after David Goldman, Alan Hodgkin, and Bernice Katz.

For a membrane permeable to potassium (K+), sodium (Na+), and chloride (Cl−), 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) ). At physiological temperature (about 37°C), this is often written using base-10 logarithms as E_m ≈ 61.54 mV × log10( (P_K [K+]_o + P_Na [Na+]_o + P_Cl [Cl−]_i) / (P_K [K+]_i + P_Na [Na+]_i + P_Cl [Cl−]_o) ). The treatment of Cl− reflects its negative charge and inward/outward orientation in the equation.

Applications and assumptions: The GHK equation assumes a constant electric field across the membrane and independence of ion fluxes, and it is used to estimate resting potentials when ion permeabilities are known. It helps explain how changes in conductances or ionic gradients alter the membrane potential, particularly in neurons and epithelial tissues. The equation reduces to the Nernst equation when only a single ion is permeant.

Limitations: As an approximation, the GHK equation neglects active transport, channel rectification, and nonuniform field effects that can occur in real membranes. It is most accurate under steady-state, moderate conditions and when permeabilities are relatively constant during the period of interest.