Stochastic behavior of a many-channel membrane system

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.