A comparative tool for the validity of rate kinetics in ion channels by Onsager reciprocity theorem

The precise form of the rate constant functions of ion channels is very crucial for reproducing the electrophysiological behavior. Therefore, how well they account for experimental data plays an important role in the behavior of the model. In this study, we derive kinetic coefficients of activation and inactivation gates in ion channels by Onsager reciprocity theorem for an ensemble of gating particles, and propose that the obtained kinetic coefficients can be used as a comparative tool for the empirical validity of fitted rate constant functions to experimental data. We also illustrate its applicability based on the activation and inactivation kinetics of T-type calcium channel in thalamic relay neurons. We show that the shape of the steady-state curve by itself seems to be a poor indicator of the functional form of the rate functions, but the time constant curves reflect considerable variation depending on the particular form of the rate functions, and that the kinetic coefficients related to the time constants provide a powerful tool to determine the empirical validity of the fitted rate constants.