Goldman Equation Calculator

The Goldman-Hodgkin-Katz (GHK) equation calculates the membrane potential when multiple ions contribute to it. Unlike the Nernst equation which considers only one ion, the GHK equation accounts for the permeabilities and concentrations of multiple ions simultaneously.

The Nernst equation calculates the equilibrium potential for a single ion, while the GHK equation considers multiple ions and their relative permeabilities. The GHK equation is more realistic for biological membranes where several ions contribute to the membrane potential.

Permeability values (PK, PNa, PCl) represent how easily each ion can cross the membrane. Higher permeability means the ion has more influence on the membrane potential. These values are typically expressed relative to each other.

Temperature affects the kinetic energy of ions and influences their movement across membranes. The GHK equation includes temperature in the RT/F term, where higher temperatures generally lead to more positive potentials due to increased ion mobility.

Typical concentrations are: K+ (5mM outside, 140mM inside), Na+ (145mM outside, 15mM inside), and Cl- (110mM outside, 10mM inside). These gradients are maintained by active transport mechanisms like the Na+/K+ pump.

The ion with the highest permeability has the greatest influence on membrane potential. In resting neurons, K+ typically has the highest permeability, making the membrane potential closer to the K+ equilibrium potential (-90mV).

When multiple ion channels are open, each ion tries to drive the membrane toward its own equilibrium potential. The actual membrane potential is a weighted average based on each ion's permeability and concentration gradient.