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
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.
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Ovidiu Radulescu, Sandrine Lagarrigue, Anne Siegel, Philippe Veber, Michel Le Borgne. Topology and static response of interaction networks in molecular biology. Journal of the Royal Society Interface, the Royal Society, 2006, 3 (6), pp.185 - 196. ⟨10.1098/rsif.2005.0092⟩. ⟨inria-00178842⟩

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