Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 48138, 14 pages
Research Article

Marked Continuous-Time Markov Chain Modelling of Burst Behaviour for Single Ion Channels

Frank G. Ball,1 Robin K. Milne,2 and Geoffrey F. Yeo2

1School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK
2School of Mathematics and Statistics, The University of Western Australia, Crawley 6009, WA, Australia

Received 2 May 2007; Accepted 8 August 2007

Academic Editor: Graeme Charles Wake

Copyright © 2007 Frank G. Ball et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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. A number of authors have obtained results for important properties of theoretical and empirical bursts when channel gating is modelled by a continuous-time Markov chain with a finite-state space. We show how the use of marked continuous-time Markov chains can simplify the derivation of (i) the distributions of several burst properties, including the total open time, the total charge transfer, and the number of openings in a burst, and (ii) the form of these distributions when the underlying gating process is time reversible and in equilibrium.