Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade

MacNamara, Shev and Burrage, Kevin (2009) Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade. Numerical Algorithms, 51 3: 281-307. doi:10.1007/s11075-008-9239-y


Author MacNamara, Shev
Burrage, Kevin
Title Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade
Journal name Numerical Algorithms   Check publisher's open access policy
ISSN 1017-1398
1572-9265
Publication date 2009-07-01
Year available 2008
Sub-type Article (original research)
DOI 10.1007/s11075-008-9239-y
Volume 51
Issue 3
Start page 281
End page 307
Total pages 27
Place of publication Basel, Switzerland
Publisher J.C. Baltzer
Language eng
Abstract Models of chemical kinetics in which some reactions are much faster than others are often treated by a type of quasi-steady-state approximation (QSSA). The total QSSA (tQSSA) was introduced for models of Michaelis-Menten enzyme kinetics and shown to be valid over a wider parameter regime than the usual QSSA. Here, we extend the tQSSA to the Mitogen-Activated Protein Kinase Cascade, an important signaling system in cell biochemistry. These approximations were first developed in a deterministic setting, but here we also describe how to incorporate this approximation into the discrete and stochastic framework of the Chemical Master Equation (CME). The CME gives rise to a large-scale matrix exponential that can be solved by Krylov methods in combination with operator splitting and the tQSSA. © Springer Science + Business Media, LLC 2008
Keyword Total quasi-steady-state approximation
Michaelis-Menten kinetics
Chemical master equation
Stochastic simulation algorithm
Krylov subspace approximations
Systems biology
Q-Index Code C1
Q-Index Status Provisional Code

Document type: Journal Article
Sub-type: Article (original research)
Collection: Institute for Molecular Bioscience - Publications
 
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Created: Thu, 03 Sep 2009, 18:08:51 EST by Mr Andrew Martlew on behalf of Institute for Molecular Bioscience