Cole-Moore superposition and kinetic models for the potassium conductance of nerve fiber membranes

Restrictions imposed by “Cole-Moore superposition” on a class of models for the potassium conductance of nerve fiber membranes are studied. The models studied assume that: (1) different potassium transfer sites on the membrane are not coupled; (2) each site is characterized by a set of states |α>, α = 0, …, N, each of energy E_α, and degeneracy, r_α. (3) The time dependence is described by kinetic equations.It is rigorously shown that: (a) there is superposition if, and only if, in going from one equilibrium state to another, the system passes only through equilibrium states. (b) Condition (a) is satisfied only if: (i) the energy levels are equally spaced, (ii) the state |n> is [N!/n!(N-n)!]-fold degenerate, and (iii) only transitions between nearest neighbor levels are allowed.