title: Topology and static response of interaction networks in molecular biology.
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.
authors.affiliation: IRMAR-CNRS Campus de Beaulieu, 35042 Rennes Cedex, France. ovidiu.radulescu@univ-rennes1.fr
authors.forename: Ovidiu
authors.initials: O
authors.lastname: Radulescu
authors.forename: Sandrine
authors.initials: S
authors.lastname: Lagarrigue
authors.forename: Anne
authors.initials: A
authors.lastname: Siegel
authors.forename: Philippe
authors.initials: P
authors.lastname: Veber
authors.forename: Michel
authors.initials: M
authors.lastname: Le Borgne
mesh_terms: D000818:Animals; D002468:Cell Physiological Phenomena; D003198:Computer Simulation; D015870:Gene Expression / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D008967:Molecular Biology / Q000379:methods*; D025941:Protein Interaction Mapping / Q000379:methods*; D015398:Signal Transduction / Q000502:physiology*