Current-voltage characteristics of K+ channels estimated by MD simulations and Markov State Models

Molecular dynamics (MD) simulations have yielded important insights into ion conduction in potassium channels, but quantitative comparison with electrophysiological experiments remains challenging. Due to their high computational cost, MD simulations are typically performed at membrane potentials well above physiological values, and at only a limited number of voltages. Since current-voltage relationships are not necessarily linear, this limits direct comparison between simulations and experiments. Here, we introduce a method to estimate the current-voltage characteristics of ion channels from Markov state models (MSMs) constructed from MD simulations performed at only a few membrane potentials. Time-discrete MSMs of ion conduction are converted into continuous-time rate matrices, whose voltage dependence is modelled using a rate theory formulation with free energy barriers depending on membrane potential. This approach enables the prediction of channel currents over a wide voltage range without additional simulations. We validated the method using MD simulations of the potassium channels KcsA and MthK. In both cases, the currents predicted at low membrane potentials are in good agreement with those obtained directly from MD simulations, demonstrating the robustness and efficiency of the approach.