Multiscale modeling of chemical kinetics via the master equation

Macnamara, Shev, Burrage, Kevin and Sidje, Roger B. (2007) Multiscale modeling of chemical kinetics via the master equation. Multiscale Modeling And Simulation, 6 4: 1146-1168. doi:10.1137/060678154

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Author Macnamara, Shev
Burrage, Kevin
Sidje, Roger B.
Title Multiscale modeling of chemical kinetics via the master equation
Journal name Multiscale Modeling And Simulation   Check publisher's open access policy
ISSN 1540-3459
Publication date 2007
Year available 2008
Sub-type Article (original research)
DOI 10.1137/060678154
Open Access Status File (Publisher version)
Volume 6
Issue 4
Start page 1146
End page 1168
Total pages 23
Place of publication Philadelphia, PA, United States
Publisher Society for Industrial and Applied Mathematics
Language eng
Abstract We present numerical methods for both the direct solution and simulation of the chemical master equation (CME), and, compared to popular methods in current use, such as the Gillespie stochastic simulation algorithm (SSA) and τ-Leap approximations, this new approach has the advantage of being able to detect when the system has settled down to equilibrium. This improved performance is due to the incorporation of information from the associated CME, a valuable complementary approach to the SSA that has often been felt to be too computationally inefficient. Hybrid methods, that combine these complementary approaches and so are able to detect equilibrium while maintaining the efficiency of the leap methods, are also presented. Amongst CME-solvers the recently suggested finite state projection algorithm is especially well suited to this purpose and has been adapted here for the task, leading to a type of “exact τ-Leap.” It is also observed that a CMEsolver is often more efficient than an SSA or even a τ-Leap approach for computing moments of the solution such as the mean and variance. These techniques are demonstrated on a test suite of five biologically inspired models, namely, stochastic models of the genetic toggle, receptor oligomerization, the Schl¨ogl reactions, Goutsias’ model of regulated gene transcription, and a decaying-dimerizing reaction set. For the gene toggle it is observed that important experimentally measurable traits such as the percentage of cells that undergo so-called switching may also be more efficiently approximated via a CME-based approach.
Keyword Chemical master equation
Stochastic simulation algorithm
Systems biology
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Chemistry and Molecular Biosciences
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Created: Thu, 03 Sep 2009, 10:07:17 EST by Mr Andrew Martlew on behalf of Faculty of Science