Abstract
Patch clamp recordings from ion channels often show bursting behaviour, that is periods of repetitive activity, which are noticeably separated from each other by periods of inactivity. In this paper, bursting behaviour is considered for a general finite state space continuous-time Markov chain model of channel gating, allowing for one or more non-zero conductance levels. A unified semi-Markov framework, that encompasses both theoretical and empirical bursts, is described for analysing a broad range of properties of bursts, including the total charge transfer, the number of sojourns at distinct conductance levels and the number of openings in a burst, with the results presented when the channel is in equilibrium. When the gating mechanism is time reversible, it is shown that the distribution and autocorrelation function of each of the above properties are necessarily finite linear combinations of exponentially or geometrically decaying components with non-negative coefficients. Three methods for choosing a critical time for empirical bursts are investigated. The theory is illustrated by numerical examples from ryanodine, chloride and nicotinic acetylcholine receptor channels, demonstrating the power and flexibility of the methodology, and permitting comparison between the methods for choosing the critical time.
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