Na channel kinetics: developing models from non-stationary current fluctuations by analytic methods

In a previous study, we analyzed Na current fluctuations in myelinated axons from Xenopus laevis under voltage clamp conditions. The statistical properties were analyzed in terms of covariance functions for consecutive time intervals of varying duration during the pulse step. The underlying channel kinetics was analyzed by performing stochastic simulations of published Na channel models and calculating corresponding covariance functions. None of the models explained the fluctuation results. We therefore developed a novel minimal Na channel model that satisfactorily described the results. In the present paper, we extend the analysis and specify the possible models explaining the experimental data by using analytical methods. We derive general relations between the experimental data, including the covariance functions, and the rate constants of specific one-open-state models. A general feature of these models is that they comprise an inactivation step from the first closed state and a relatively low backward rate from the open state. This is in accordance the minimal model inferred from numerical stochastic calculations in the previous study.