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Reports (Research Report) Year : 2013

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

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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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Dates and versions

hal-00778412 , version 1 (20-01-2013)

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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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