Numerical Simulation of Piecewise-Linear Models of Gene Regulatory Networks Using Complementarity Systems

Vincent Acary 1, * Hidde De Jong 2 Bernard Brogliato 1
* Auteur correspondant
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 IBIS - Modeling, simulation, measurement, and control of bacterial regulatory networks
LAPM - Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble], Inria Grenoble - Rhône-Alpes, Institut Jean Roget
Abstract : Gene regulatory networks control the response of living cells to changes in their environment. A class of piecewise-linear (PWL) models, which capture the switch-like interactions between genes by means of step functions, has been found useful for describing the dynamics of gene regulatory networks. The step functions lead to discontinuities in the right-hand side of the differential equations. This has motivated extensions of the PWL models based on differential inclusions and Filippov solutions, whose analysis requires sophisticated numerical tools. We present a method for the numerical analysis of one proposed extension, called Aizermann-Pyatnitskii (AP)-extension, by reformulating the PWL models as a mixed complementarity system (MCS). This allows the application of powerful methods developed for this class of nonsmooth dynamical systems, in particular those implemented in the {\sc Siconos} platform. We also show that under a set of reasonable biological assumptions, putting constraints on the right-hand side of the PWL models, AP-extensions and classical Filippov (F)-extensions are equivalent. This means that the proposed numerical method is valid for a range of different solution concepts. We illustrate the practical interest of our approach through the numerical analysis of three well-known networks developed in the field of synthetic biology.
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https://hal.inria.fr/hal-00778412
Contributeur : Vincent Acary <>
Soumis le : dimanche 20 janvier 2013 - 09:32:24
Dernière modification le : mercredi 11 avril 2018 - 01:58:08
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  • HAL Id : hal-00778412, version 1

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Vincent Acary, Hidde De Jong, Bernard Brogliato. Numerical Simulation of Piecewise-Linear Models of Gene Regulatory Networks Using Complementarity Systems. [Research Report] RR-8207, INRIA. 2013, pp.42. 〈hal-00778412〉

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