On the stochastic properties of single ion channels

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Abstract
It is desirable to be able to predict, from a specified mechanism, the appearance of currents that flow through single ion membrane channels to enable interpretation of experiments in which single channel currents are observed and to allow physical meaning to be attached to the results observed in kinetic (noise and relaxation) experiments in which the aggregate of many single channel currents is observed. Distributions (and their means) are derived for the length of the sojourn in any specified subset of states (e.g., all shut states). In general, these depend on the state in which the sojourn starts and on the state that immediately follows the sojourn. The methods described allow derivation of the distribution of, e.g., the number of openings and total length of the burst of openings, that may occur during a single occupancy and the apparent gap between such bursts. The methods are illustrated by their application to 2 simple theories of agonist action. The Castillo-Katz (non-cooperative) mechanism predicts, e.g., that the number of openings per occupancy and the apparent burst length are independent of drug agonist concentration a simple cooperative mechanism predicts that both will increase with agonist concentration.