Stochastic models and simulation of ion channel dynamics

Dangerfield, C.E., Kay, D., & Burrage, K. (2010) Stochastic models and simulation of ion channel dynamics. Procedia Computer Science, 1(1), pp. 1581-1590.

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The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

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6 citations in Scopus
7 citations in Web of Science®
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ID Code: 45855
Item Type: Journal Article
Refereed: Yes
Keywords: Hodgkin-Huxley, Langevin equation, Wright-Fisher model, Boundary preserving, Hybrid
DOI: 10.1016/j.procs.2010.04.178
ISSN: 1877-0428
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > OTHER INFORMATION AND COMPUTING SCIENCES (089900)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Deposited On: 12 Sep 2011 01:16
Last Modified: 27 Oct 2014 01:51

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