Send to

Choose Destination
See comment in PubMed Commons below
J R Soc Interface. 2006 Feb 22;3(6):185-96.

Topology and static response of interaction networks in molecular biology.

Author information

  • 1IRMAR-CNRS Campus de Beaulieu, 35042 Rennes Cedex, France.


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.

[PubMed - indexed for MEDLINE]
Free PMC Article
PubMed Commons home

PubMed Commons

How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for HighWire Icon for PubMed Central
    Loading ...
    Support Center