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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.
Thomas, R.: On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. Springer Ser. Synergetics 9, 180–193 (1981)Google Scholar
Levchenko, A., Bruck, J., Sternberg, P.W.: Scaffold proteins biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. PNAS 97, 5818–5823 (2000)CrossRefGoogle Scholar
Ventura, A.C., Sepulchre, J.A., Merajver, S.D.: A hidden feedback in signaling cascades is revealed. PLoS Computational Biology (to appear, 2008)Google Scholar
Markevich, N.I., Hoek, J.B., Kholodenko, B.N.: Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. Journal of Cell Biology 164, 353–359 (2005)CrossRefGoogle Scholar
Calzone, L., Fages, F., Soliman, S.: BIOCHAM: An environment for modeling biological systems and formalizing experimental knowledge. BioInformatics 22, 1805–1807 (2006)CrossRefGoogle Scholar
Fages, F., Soliman, S., Chabrier-Rivier, N.: Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM. Journal of Biological Physics and Chemistry 4, 64–73 (2004)CrossRefGoogle Scholar
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81, 2340–2361 (1977)CrossRefGoogle Scholar
Qiao, L., Nachbar, R.B., Kevrekidis, I.G., Shvartsman, S.Y.: Bistability and oscillations in the huang-ferrell model of mapk signaling. PLoS Computational Biology 3, 1819–1826 (2007)CrossRefMathSciNetGoogle Scholar
Ciliberto, A., Novák, B., Tyson, J.J.: Steady states and oscillations in the p53/mdm2 network. Cell Cycle 4, 488–493 (2005)Google Scholar