The Information Entropy Metrics to Address the Complexity of Cooperative Gating of Ion Channels

Ion channels in biological membranes often form spatially localized clusters that exhibit cooperative gating behavior, where the activity of one channel can modulate the opening probability of its neighbors. Understanding such inter-channel interactions is crucial for elucidating the molecular mechanisms underlying complex electrochemical signaling and for advancing channel-targeted pharmacology. In this study, we introduce a simplified stochastic model of multi-channel gating that enables systematic analysis of cooperative phenomena under controlled conditions. Two complementary information-theoretic measures, i.e., Shannon entropy and Sample entropy, are applied to simulated multi-channel datasets to quantify the degree and modality of inter-channel cooperativity. The analyzed signals include idealized total current traces and the corresponding dwell-time sequences of channel cluster states. We demonstrate that the dependence of Shannon entropy calculated for the idealized cluster currents on cluster size distinguishes non-cooperative from cooperative dynamics. Similarly, the Sample entropy of dwell-time series is also a potent indicator of inter-channel cooperation. Additionally, this metric provides enhanced sensitivity to temporal regularities in dwell-time data. The observed entropic signatures allow for classification of clusters according to the strength and mode of inter-channel coupling (non-, positively-, and negatively-cooperative). Thus, they extend a general analytical framework for interpreting multi-channel recordings. These findings, based on our simple model of channel cluster, establish entropy-based analysis as a promising approach for probing real collective gating in ion channel systems or simple biomimetic multi-nanopore devices, where some deviations from the idealized approach are expected.