Identifying transition rates of ionic channels via observations at a single state

We consider how to determine all transition rates of an ion channel when it can be described by a birth–death chain or a Markov chain on a star-graph with continuous time. It is found that all transition rates are uniquely determined by the distribution of its lifetime and death-time histograms at a single state. An algorithm to calculate the transition rates exactly, based on the statistics of the lifetime and death-time of the Markov chain at the state, is provided. Examples to illustrate how an ion channel activity is fully determined by the observation of a single state of the ion channel are included.

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