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Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.
Stoll G., Viara E., Barillot E., Calzone L.
BMC Systems Biology 6, 1 (2012) 116 - http://www.hal.inserm.fr/inserm-00762304
Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.
Gautier Stoll () 1, Eric Viara2, Emmanuel Barillot1, Laurence Calzone1
1 :  Cancer et génôme: Bioinformatique, biostatistiques et épidémiologie d'un système complexe
INSERM : U900 – Institut Curie – MINES ParisTech - École nationale supérieure des mines de Paris
26 rue d'Ulm - 75248 Paris cedex 05
2 :  Programmation informatique 6201Z
30 Avenue du General-leclerc 91330 Yerres
ABSTRACT: Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. BACKGROUND: There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. RESULTS: Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. CONCLUSIONS: Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.
Sciences du Vivant/Biochimie, Biologie Moléculaire/Génomique, Transcriptomique et Protéomique
Sciences du Vivant/Bio-Informatique, Biostatistique

Articles dans des revues avec comité de lecture
BMC Systems Biology
Publisher BioMed Central
ISSN 1752-0509 

Boolean modeling – Continuous time – Markov process – Gillespie algorithm
This project was supported by the Institut National du Cancer (SybEwing project), the Agence National de la Recherche (Calamar project). The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013).
Acronyme HEALTH-F4-2007-200767 for APO-SYS ; FP7-HEALTH-2010-259348 for ASSET
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1752-0509-6-116-S1.PDF(315.5 KB)