Membrane potentials at zero current. The significance of a constant ionic permeability ratio

The possibility has been examined that the Goldman-Hodgkin-Katz equation for V(0), the total membrane potential at zero current, can be derived with constant permeability ratios from a thermodynamic treatment. The flux equations have been integrated under zero current conditions subject only to the restriction that the total membrane potential should be independent of internal concentration profiles, which is the requirement for the premeability ratios to be phenomenological constants, independent of solution conditions. No assumptions have been made concerning the electric potential profile. It was found that a constant permeability ratio can only be characteristic of systems satisfying certain relationships between ionic conductances and chemical potentials. From these relationships it was possible to define the permeability ratio in terms of the thermodynamic properties of the membrane quite generally and to identify the permeability ratio as the product of mobility ratio and ratio of partition coefficients. Moreover, the ionic conductance ratio at any point in the membrane has been shown to be expressable explicitly in terms of the permeability ratio and the activities of an external solution which would be in equilibrium with the point under consideration. Lastly, a number of conclusions have been reached regarding the range of applicability of the Goldman-Hodgkin-Katz equation with constant permeability ratios.