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Modeling ion channel dynamics through reflected stochastic differential equations

Dangerfield, Ciara E., Kay, David, & Burrage, Kevin (2012) Modeling ion channel dynamics through reflected stochastic differential equations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 85(5), 051907-1.

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Abstract

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

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6 citations in Scopus
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5 citations in Web of Science®

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ID Code: 50919
Item Type: Journal Article
Keywords: Ion channels , membrane proteins
DOI: 10.1103/PhysRevE.85.051907
ISSN: 1539-3755
Subjects: Australian and New Zealand Standard Research Classification > ENGINEERING (090000)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 American Physical Society
Deposited On: 18 Jun 2012 08:32
Last Modified: 28 Jun 2012 10:09

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