On the estimation of cooperativity in ion channel kinetics: activation free energy and kinetic mechanism of Shaker K+ channel.

In this paper, we have explored generic criteria of cooperative behavior in ion channel kinetics treating it on the same footing with multistate receptor-ligand binding in a compact theoretical framework. We have shown that the characterization of cooperativity of ion channels in terms of the Hill coefficient violates the standard Hill criteria defined for allosteric cooperativity of ligand binding. To resolve the issue, an alternative measure of cooperativity is proposed here in terms of the cooperativity index that sets a unified criteria for both the systems. More importantly, for ion channel this index can be very useful to describe the cooperative kinetics as it can be readily determined from the experimentally measured ionic current combined with theoretical modelling. We have analyzed the correlation between the voltage value and slope of the voltage-activation curve at the half-activation point and consequently determined the standard free energy of activation of the ion channel using two well-established mechanisms of cooperativity, namely, Koshland-Nemethy-Filmer (KNF) and Monod-Wyman-Changeux (MWC) models. Comparison of the theoretical results for both the models with appropriate experimental data of mutational perturbation of Shaker K(+) channel supports the experimental fact that the KNF model is more suitable to describe the cooperative behavior of this class of ion channels, whereas the performance of the MWC model is unsatisfactory. We have also estimated the mechanistic performance through standard free energy of channel activation for both the models and proposed a possible functional disadvantage in the MWC scheme.