An analysis of the change in K-permeability on depolarization in terms of affinity and numbers of total channels.

A theoretical relation between permeability and ionic concentrations in a bathing solution has been derived by assuming that only channels unoccupied by a competing non-permeable ion can transport ions specific for that channel. The affinities of the channel to the ion and the competitor are expressed by dissociation constants of the ion-site and competitor-site complexes in the channel.Analyses of the relation of K permeability to [K]_o obtained from myelinated nerve fibres and Nitella cells revealed that the affinity of sites in K channels was independent of membrane potential, whereas K conductivity increased with depolarization. The value of the dissociation constant of the K⁺-site complex, K₁, was estimated as 1244 mm for myelinated nerve, and $\text{K}{}_1\text{exp(ψ}{}_0\text{F}\text{RT}$) for Nitella was 17.5 mm (ψ₀ is the surface potential at the outer surface of membrane). The dependence on voltage of the total number of K channels was estimated from the dependence of K conductance on membrane potential at [K]_o = [K]₁ (obtained from the theoretical magnitude of K current computed by using the dissociation constants described above). It should be noted that when the channels are partially saturated with K⁺, neither the chord conductance nor the “permeability coefficient”, as defined in the Goldman and Hodgkin-Katz formulation, correctly represents the dependence on membrane potential of the total number of channels.