title: Geometric analysis of pathways dynamics: Application to versatility of TGF-β receptors.
abstract: We propose a new geometric approach to describe the qualitative dynamics of chemical reactions networks. By this method we identify metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is much slower compared to the rest of the phase space. These metastable regimes depend on the network topology and on the orders of magnitude of the kinetic parameters. Benchmarking of the method on a computational biology model repository suggests that the number of metastable regimes is sub-exponential in the number of variables and equations. The dynamics of the network can be described as a sequence of jumps from one metastable regime to another. We show that a geometrically computed connectivity graph restricts the set of possible jumps. We also provide finite state machine (Markov chain) models for such dynamic changes. Applied to signal transduction models, our approach unravels dynamical and functional capacities of signalling pathways, as well as parameters responsible for specificity of the pathway response. In particular, for a model of TGFβ signalling, we find that the ratio of TGFBR2 to TGFBR1 receptors concentrations can be used to discriminate between metastable regimes. Using expression data from the NCI60 panel of human tumor cell lines, we show that aggressive and non-aggressive tumour cell lines function in different metastable regimes and can be distinguished by measuring the relative concentrations of receptors of the two types.
authors.affiliation: Algorithmic Bioinformatics, Bonn-Aachen International Center for IT, Dahlmannstraße 2, D-53113 Bonn, Germany. Electronic address: samal@cs.uni-bonn.de.
authors.forename: Satya Swarup
authors.initials: SS
authors.lastname: Samal
authors.affiliation: DIMNP UMR CNRS 5235, University of Montpellier, Montpellier, France. Electronic address: aurelien.naldi@gmail.com.
authors.forename: Aurélien
authors.initials: A
authors.lastname: Naldi
authors.affiliation: CNRS, Mathématiques, Université de Lille, Villeneuve d'Ascq 59655, France. Electronic address: dmitry.grigoryev@math.univ-lille1.fr.
authors.forename: Dima
authors.initials: D
authors.lastname: Grigoriev
authors.affiliation: Institut für Informatik II, University of Bonn, Friedrich-Ebert-Allee 144, 53113 Bonn, Germany. Electronic address: weber@cs.uni-bonn.de.
authors.forename: Andreas
authors.initials: A
authors.lastname: Weber
authors.affiliation: Inserm UMR1085 IRSET, Université de Rennes 1, Rennes, France; CNRS-Université de Rennes1-INRIA, UMR6074 IRISA, Rennes, France. Electronic address: nathalie.theret@univ-rennes1.fr.
authors.forename: Nathalie
authors.initials: N
authors.lastname: Théret
authors.affiliation: DIMNP UMR CNRS 5235, University of Montpellier, Montpellier, France. Electronic address: ovidiu.radulescu@univ-montp2.fr.
authors.forename: Ovidiu
authors.initials: O
authors.lastname: Radulescu
mesh_terms: D045744:Cell Line, Tumor; D019295:Computational Biology / Q000379:methods*; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D018125:Receptors, Transforming Growth Factor beta / Q000502:physiology*; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D018125:Receptors, Transforming Growth Factor beta
keywords: Cancer systems biology; Finite state automaton; Metastability; Tropical geometry