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. 1985 Feb;47(2 Pt 1):129–137. doi: 10.1016/s0006-3495(85)83886-8

Stochastic behavior of a many-channel membrane system.

M B Jackson
PMCID: PMC1435149  PMID: 2579685

Abstract

A stochastic theory of channel-gating transitions is developed for a stationary system with many channels, with applications to patch-clamp single-channel experiments. Exact probability density and distribution functions for closed times, open times, and first transit times in an N-channel system are obtained in terms of N and the solutions for a one-channel system. Once N is determined, the expressions derived here can be used to analyze data records that are crowded by many channel openings and where multilevel events are common. The three-state model is treated as a specific example. Computer simulations of three-state models indicate that the equations derived here can be used to recover useful information from crowded single-channel current records. The simulations also revealed some of the limitations to the usefulness of these equations. The probability that a channel that has not opened is in a particular closed state was examined as a function of time. This analysis led to a useful limit where the distribution of unopened channels between various closed states is constant in time. This limit simplifies the mathematical treatment of closed-time probabilities, and provides a general method for the analysis of many-channel systems when channels open infrequently.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

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