Exploration of the Parameter Space of an Ion Channel Kinetic Model by a Markov-Chain-Based Methodology

In this work, we propose a methodology based on Monte Carlo Markov chains to explore the parameter space of kinetic models for ion channels. The methodology allows the detection of potential parameter sets of a model that are compatible with experimentally obtained whole-cell currents, which could remain hidden when methods focus on obtaining the parameters that provide the best fit. To show its implementation and utility, we considered a four-state kinetic model proposed in the literature to describe the activation of the voltage-gated proton channel (Hv1), Biophysical Journal, 2014, 107, 1564. In that work, a set of values for the rate transitions that describe the channel kinetics at different intracellular H⁺ concentration (pH_i) were obtained by the Simplex method. With our approach, we find that, in fact, there is more than one parameter set for each pH_i, which renders the same open probability temporal course within the experimental error margin for all of the considered voltages. The large differences that we obtained for the values of some rate constants among the different solutions show that there is more than one possible interpretation of this channel behavior as a function of pH_i. We also simulated a proposed new experimental condition where it is possible to observe that different sets of parameters yield different results. Our study highlights the importance of a comprehensive analysis of parameter space in kinetic models and the utility of the proposed methodology for finding potential solutions.