title: A constraint solving approach to model reduction by tropical equilibration.
abstract: Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While singular perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these methods is in the computation of tropical equilibrations. In this paper we show that constraint-based methods, using reified constraints for expressing the equilibration conditions, make it possible to numerically solve non-linear tropical equilibration problems, out of reach of standard computation methods. We illustrate this approach first with the detailed reduction of a simple biochemical mechanism, the Michaelis-Menten enzymatic reaction model, and second, with large-scale performance figures obtained on the http://biomodels.net repository.
authors.affiliation: Inria, Domaine de Voluceau, Rocquencourt, 78150 France.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Soliman
authors.affiliation: Inria, Domaine de Voluceau, Rocquencourt, 78150 France.
authors.forename: François
authors.initials: F
authors.lastname: Fages
authors.affiliation: University of Montpellier 2, Place Eugene Bataillon, Montpellier, 34095 France.
authors.forename: Ovidiu
authors.initials: O
authors.lastname: Radulescu
keywords: Constraint programming; Model reduction; Systems biology; Tropical algebra; Tropical equilibration