The Nernst Equation

The relationship you observed in the previous simulation between the diffusion potential that develops across the membrane (the membrane potential, E_m ) and the concentration gradient of the diffusing ion can be expressed quite precisely, in a specific form of an equilibrium equation developed by the German physical chemist Nernst more than 100 years ago. Thus,

where R is the gas constant (1.987 cal K^-1 mol^-1), T is the absolute temperature, z is the valence of the diffusing ion, and F is the Faraday constant (23.062 cal volt^-1 mol^-1). [C]_o and [C]_i are the concentrations of the diffusing ion in the inside and outside compartments respectively.

At 20^o C, enumerating the constants and converting natural to base-ten logarithms, this expression becomes the more useful and familiar:

Thus, if the external cation concentration is one-tenth the internal concentration, the membrane potential should be -58 mV. Suppose the external cation concentration were ten times greater than the internal concentration? Suppose further, that the diffusing ion were an anion and its external concentration were ten times greater than its internal concentration?

How many ions must actually cross the membrane to establish the Nernst potential? How we estimate this flux depends greatly on the membrane capacitance.