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Linking Discrete and Stochastic Models: The Chemical Master Equation as a Bridge between Process Hitting and Proper Generalized Decomposition

Article dans une revue avec comité de lecture
Author
CHANCELLOR, Courtney
21439 Institut de Recherche en Communications et en Cybernétique de Nantes [IRCCyN]
ccAMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
ccCHINESTA SORIA, Francisco
10921 Institut de Recherche en Génie Civil et Mécanique [GeM]
MAGNIN, Morgan
21439 Institut de Recherche en Communications et en Cybernétique de Nantes [IRCCyN]
ROUX, Olivier
21439 Institut de Recherche en Communications et en Cybernétique de Nantes [IRCCyN]

URI
http://hdl.handle.net/10985/10259
DOI
10.1007/978-3-642-40708-6_5
Date
2013
Journal
Lecture Notes in Computer Science

Abstract

Modeling frameworks bring structure and analysis tools to large and non-intuitive systems but come with certain inherent assumptions and limitations, sometimes to an inhibitive extent. By building bridges in existing models, we can exploit the advantages of each, widening the range of analysis possible for larger, more detailed models of gene regulatory networks. In this paper, we create just such a link between Process Hitting [6,7,8], a recently introduced discrete framework, and the Chemical Master Equation in such a way that allows the application of powerful numerical techniques, namely Proper Generalized Decomposition [1,2,3], to overcome the curse of dimensionality. With these tools in hand, one can exploit the formal analysis of discrete models without sacrificing the ability to obtain a full space state solution, widening the scope of analysis and interpretation possible. As a demonstration of the utility of this methodology, we have applied it here to the p53-mdm2 network [4,5], a widely studied biological regulatory network.

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