Biomedical Engineering Reference
In-Depth Information
Chapter 5
Stochastic Modelling of Single
Ion Channels
Alan G. Hawkes
European Business Management School, University of Wales, Swansea, SA2 8PP,
U.K.
CONTENTS
5.1 Introduction
5.2 Some basic probability
5.3 Single channel models
5.3.1 A three-state mechanism
5.3.2 A simple channel-block mechanism
5.3.3 A five-state model
5.4 Transition probabilities, macroscopic currents and noise
5.4.1 Transition probabilities
5.4.2 Macroscopic currents and noise
5.5 Behaviour of single channels under equilibrium conditions
5.5.1 The duration of stay in an individual state
5.5.2 The distribution of open times and shut times
5.5.3 Joint distributions
5.5.4 Correlations between intervals
5.5.5 Bursting behaviour
5.6 Time interval omission
5.7 Some miscellaneous topics
5.7.1 Multiple levels
5.7.2 Hidden Markov Methods of analysis
References
5.1
Introduction
Biological cells are enclosed by a phospholipid bilayer, a few nanometres thick, that
is almost impermeable to water and water soluble molecules. Ion channels are pro-
teins embedded in the membrane that control the movement of ions across the mem-
brane. The channel protein, also a few nanometres wide, is arranged in a roughly
circular array that spans the membrane with a central aqueous pore that can open
 
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