# Topic 6.1 Relating the Membrane Potential to the Distribution of Several Ions across the Membrane: The Goldman Equation

Many different ions permeate the membranes of living cells simultaneously; therefore, the Nernst potential for any single ionic species seldom describes the membrane's diffusion potential. Instead, the contributions of all the ions to the diffusion potential across the membrane are described by the Goldman equation:

This equation relates the standing ion gradients across a membrane to the diffusion potential that develops. *P*_{K+}, *P*_{Na+}, and *P*_{Cl–} represent the membrane permeabilities for K^{+}, Na^{+}, and Cl^{–}, respectively. Although the equation should include terms for all ions passing through the membrane, K^{+}, Na^{+}, and Cl^{–} have the largest membrane permeabilities and highest concentrations in plant cells and therefore dominate the equation.

The relationship between the Goldman equation and the Nernst equation (see textbook p. 147) can be visualized if one imagines a membrane that is permeable to only one ion, say K^{+}, so that both *P*_{Cl–} and *P*_{Na+} equal zero. Under these conditions, the Goldman equation reduces to the Nernst equation for K^{+}. Although biological membranes are never permeable to only a single ionic species, artificial membranes can approximate this situation and are used in the manufacture of pH electrodes and other ion-selective electrodes.