Stochastic models for systems of interacting ion channels

We consider a variety of Markov based models for systems of ion channels ex hibiting dependence between channels. It is shown how many useful propertie s which may be calculated for an aggregated single-channel model, or a syst em of independent channels, can be extended to various types of interacting channel systems. Key structure and results from the theory of aggregated M arkov processes are summarized in a convenient matrix form. These are then applied to the superposition of independent and dependent channels, includi ng a patch of channels in a random environment, and a system of channels wi th spatial interactions. Calculations based on the resultant matrix express ions and intensity arguments can be implemented straightforwardly in a matr ix-oriented package such as Matlab. The role of reversibility is also studi ed. A number of examples illustrate the strengths of the methods and enable numerical comparisons between the different types of systems.