Numerical Simulation of Piecewise-Linear Models of Gene Regulatory Networks Using Complementarity Systems - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2013

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

Résumé

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.
Fichier principal
Vignette du fichier
RR-8207.pdf (1.99 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

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

Identifiants

  • HAL Id : hal-00778412 , version 1

Citer

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⟩
340 Consultations
251 Téléchargements

Partager

Gmail Facebook X LinkedIn More