The relationship you observed in the previous simulation between the diffusion potential that develops across the membrane (the membrane potential, Em ) 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 20o 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>.