Markovian gating as a linear system I

The paper by R W Aldrich, D P Corey, and C F Stevens (ACS) illustrated just how important it is to understand the stochastic basis of single-channel information. A type of stochastic process, called a Markov process, was supported by experimental measures of open durations in several types of channels. Additionally, simple reasoning based on Markov mechanisms was essential to interpreting single-channel data. In this chapter, we introduce the theory of Markov processes in a more complete, systematic manner. We show that it has clear links to linear system theory, which provides us with clear insights into the workings of Markov processes. The first half of the chapter is devoted to understanding ‘discrete-step’ Markov chains. Here the ‘clock’ is not time, but an integer transition number. In particular, we ask which state a channel will occupy after k transitions, regardless of when the transitions occur. This is a ‘full-blown’ theory involving ‘ever’ probabilities. The second half of the unit is devoted to continuous-time Markov processes. Here, we calculate the probabilities of occupying various states as a function of continuous time.