Topology and static response of interaction networks in molecular biology

Ovidiu Radulescu; Sandrine Lagarrigue; Anne Siegel; Philippe Veber; Michel Le Borgne

Topology and static response of interaction networks in molecular biology

Ovidiu Radulescu ^{1, 2, *} Sandrine Lagarrigue ³ Anne Siegel ¹ Philippe Veber ¹ Michel Le Borgne ¹

* Corresponding author

1 SYMBIOSE - Biological systems and models, bioinformatics and sequences

IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique

2 IRMAR - Institut de Recherche Mathématique de Rennes

3 GARen - Génétique Animale

Abstract : We introduce a mathematical framework describing static response of networks occurring in molecular biology. This formalism has many similarities with the Laplace-Kirchhoff equations for electrical networks. We introduce the concept of graph boundary and we show how the response of the biological networks to external perturbations can be related to the Dirichlet or Neumann problems for the corresponding equations on the interaction graph. Solutions to these two problems are given in terms of path moduli (measuring path rigidity with respect to the propagation of interaction along the graph). Path moduli are related to loop products in the interaction graph via generalized Mason-Coates formulae. We apply our results to two specific biological examples: the lactose operon and the genetic regulation of lipogenesis. Our applications show consistency with experimental results and in the case of lipogenesis check some hypothesis on the behaviour of hepatic fatty acids on fasting.

Document type :

Journal articles

Domain :

Computer Science [cs] / Bioinformatics [q-bio.QM]

Life Sciences [q-bio] / Quantitative Methods [q-bio.QM]

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https://hal.inria.fr/inria-00178842
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Submitted on : Friday, October 12, 2007 - 12:04:12 PM
Last modification on : Tuesday, March 26, 2019 - 12:42:09 PM
Long-term archiving on : Monday, September 24, 2012 - 1:21:13 PM

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