Computations on sodium channel gating were conducted using a closed- open-inactivated coupled kinetic scheme. The time constant of inactivation (τ(h)) derives a voltage dependency from coupling to voltage-dependent activation even when rate constants between inactivated and other states are strictly voltage independent. The derived voltage dependency does not require any physical, molecular link between the structures responsible for inactivation and the charges producing voltage-dependent activation. The only requirement is that the closed to inactivated rate constant (k(Cl)) differs from the open to inactivated (k(Ol)), consistent with experimental results. A number of mutations and other treatments uncouple sodium channel activation and inactivation in that the voltage dependency of τ(h) is substantially reduced while voltage-dependent activation persists. However, a clear basis for uncoupling has not been described. A variety of experimental results are accounted for just by changes in the difference between k(Ol) and k(Cl). In wild type channels, k(Ol) > k(Cl) and inactivation develops with a delay whose time constant is just that for channel opening. Mutations that reduce the k(Ol) - k(Cl) difference reduce the amplitude of the delay process and the derived voltage dependency of τ(h). If k(Ol) = k(Cl), inactivation develops as a single exponential (no matter what the number of closed states), activation and inactivation become independent, parallel processes, and any voltage dependency of τ(h) is then entirely intrinsic to inactivation. If k(Ol) < k(Cl), inactivation develops as the sum of exponentials, τ(h) at negative potentials speeds and then slows with more positive potentials. These predicted k(Ol) < k(Cl) effects have all been seen experimentally (O'Leary, M.E., L.-Q. Chen, R.G. Kallen, and R. Horn. 1995. J. Gen. Physiol. 106: 641-658). An open to closed rate constant of zero also removes the derived voltage dependency of τ(h), but activation and inactivation are still coupled and the inactivation delay remains.
Goldman, L. (1999). On mutations that uncouple sodium channel activation from inactivation. Biophysical Journal, 76(5), 2553–2559. https://doi.org/10.1016/S0006-3495(99)77408-4