Stochastic models for systems of interacting ion channels.
We consider a variety of Markov based models for systems of ion channels exhibiting dependence between channels. It is shown how many useful properties which may be calculated for an aggregated single-channel model, or a system of independent channels, can be extended to various types of interacting channel systems. Key structure and results from the theory of aggregated Markov processes are summarized in a convenient matrix form. These are then applied to the superposition of independent and dependent channels, including a patch of channels in a random environment, and a system of channels with spatial interactions. Calculations based on the resultant matrix expressions and intensity arguments can be implemented straightforwardly in a matrix-oriented package such as Matlab. The role of reversibility is also studied. A number of examples illustrate the strengths of the methods and enable numerical comparisons between the different types of systems.
Ball
F G
FG
School of Mathematical Sciences, University of Nottingham, UK. fgb@maths.nott.ac.uk
Milne
R K
RK
Yeo
G F
GF
D003198:Computer Simulation; D015640:Ion Channel Gating; D007473:Ion Channels / Q000378:metabolism*; D007700:Kinetics; D008390:Markov Chains; D008433:Mathematics; D008954:Models, Biological; D013269:Stochastic Processes
D007473:Ion Channels