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Abstraction, Modularity and Compositionality in Genetic and Proteic Networks ACI VICANNE IHP, Paris 23-24 January 2006 ARC MOCA http://contraintes.inria.fr/moca François Fages IHP Paris, Jan 2006 Transposing Computer Science Notions to Systems Biology Formally, “the” behavior of a system… François Fages IHP Paris, Jan 2006 Transposing Computer Science Notions to Systems Biology Formally, “the” behavior of a system… depends on our choice of observables. François Fages IHP Paris, Jan 2006 Transposing Computer Science Notions to Systems Biology Formally, “the” behavior of a system… depends on our choice of observables. François Fages IHP Paris, Jan 2006 Transposing Computer Science Notions to Systems Biology Formally, “the” behavior of a system… depends on our choice of observables. y François Fages ý IHP Paris, Jan 2006 Transposing Computer Science Notions to Systems Biology Formally, “the” behavior of a system… depends on our choice of observables. 0 François Fages 1 IHP Paris, Jan 2006 Transposing Computer Science Notions to Systems Biology Formally, “the” behavior of a system… depends on our choice of observables. Behavior in different/all initial conditions or in different/all contexts François Fages IHP Paris, Jan 2006 Theory of Abstract Interpretation abstraction Boolean models Discrete models Differential models Stochastic models François Fages IHP Paris, Jan 2006 Query: Set of Stationary States ? abstraction Boolean analysis abstraction Boolean models abstraction Discrete models abstraction Differential models abstraction Stochastic models François Fages Discrete analysis Differential analysis Stochastic analysis Issue of correctness / optimality of an abstraction w.r.t. a query IHP Paris, Jan 2006 Modularity and Compositionality When the behavior of a complex system is a function of the behavior of its components… François Fages IHP Paris, Jan 2006 Modularity and Compositionality When the behavior of a complex system is a function of the behavior of its components… Notion relative to « behaviors » hence to our choices of observables for the complex system and for the components. François Fages IHP Paris, Jan 2006 Modularity and Compositionality When the behavior of a complex system is a function of the behavior of its components… Notion relative to « behaviors » hence to our choices of observables for the complex system and for the components. Complex systems may be modular for some observables, and not for other choices. François Fages IHP Paris, Jan 2006 Modularity and Compositionality When the behavior of a complex system is a function of the behavior of its components… Notion relative to « behaviors » hence to our choices of observables for the complex system and for the components. Complex systems may be modular for some observables, and not for other choices. Mathematically, any system can be made modular by considering the behaviors of its components in all contexts. François Fages IHP Paris, Jan 2006 Overview of Talks Abstraction M. Kaufman. Logical and differential approaches to p53-mdm2 net V. Danos. A model’s model Modularity B. Novak. Eukariotic cell cycle: modules and mathematical models A. Siegel. Analysis of ODEs by decomposition into modules Compositionality R. Blossey. A compositional approach to regulation networks F. Tarissan. Analysis and synthesis of self-organizational systems V. Hakim. Structure of small gene networks and evolution in silico François Fages IHP Paris, Jan 2006