Dependency plots suggest the kinetic structure of ion channels

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Abstract
Ion channels are integral membrane proteins that regulate ionic flux through cell membranes by opening and closing (gating) their pores. The gating can be monitored by observing step changes in the current flowing through single channels, and analysis of the observed open and closed interval durations has provided a window to develop kinetic models for the gating process. One difficulty in developing such models has been to determine the connections (transition pathways) among the various kinetic states involved in the gating. To help overcome this difficulty we present a transform (dependency plot) of the single-channel data that can give immediate insight into the connections. A dependency plot is derived by calculating a contingency table from a two-dimensional (joint density) dwell-time distribution of adjacent open and closed intervals by assuming that the two classified criteria are the open and closed durations of each pair of adjacent intervals. A three-dimensional surface plot of the fractional difference between the numbers of observed interval pairs and the numbers expected if the durations of adjacent intervals are independent then gives the dependency plot. An excess of interval pairs in the dependency plot suggests that the open and closed states (or compound states) that give rise to the interval pairs in excess are directly connected. A deficit of interval pairs suggests that the open and closed states (or compound states) that give rise to the interval pairs in deficit are either not directly connected or that there are additional open–closed transition pathways arising from the directly connected states.