From Reaction Models to Influence Graphs and Back: A Theorem

  • François Fages
  • Sylvain Soliman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5054)


Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also more and more employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this paper, we study the formal relationship between these graphs. We consider systems of biochemical reactions with kinetic expressions, as written in the Systems Biology Markup Language SBML, and interpreted by a system of Ordinary Differential Equations over molecular concentrations. We show that under a general condition of increasing monotonicity of the kinetic expressions, and in absence of both activation and inhibition effects between a pair of molecules, the influence graph inferred from the stoichiometric coefficients of the reactions is equal to the one defined by the signs of the coefficients of the Jacobian matrix. Under these conditions, satisfied by mass action law, Michaelis-Menten and Hill kinetics, the influence graph is thus independent of the precise kinetic expressions, and is computable in linear time in the number of reactions. We apply these results to Kohn’s map of the mammalian cell cycle and to the MAPK signalling cascade. Then we propose a syntax for denoting antagonists in reaction rules and generalize our results to this setting.


Reaction Model Kinetic Expression System Biology Markup Language Reaction Rule MAPK Signalling Cascade 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • François Fages
    • 1
  • Sylvain Soliman
    • 1
  1. 1.Projet ContraintesINRIA RocquencourtLe Chesnay CedexFrance

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