O. Radulescu (Coordinator), V. Noel, F. Fages, S. Gay, D. Eveillard, A. Siegel, J. Bourdon.

Model reduction methods have also to be studied. Indeed, the previous Markov models need an estimation of many parameters. It is therefore crucial to identify the fundamental elements of a model with respect to a given phenotype. Here, we propose an exploration of biological systems as hierarchical systems by defining an adapted hierarchy on the parameters (for instance, it is quite clear that some reactions are not of the same order) or the topological structure of the model. In such a way, phenotypic observation can be derived from reduction processes.

Computational model reduction, state of the art and beyond Starting from a model with a large number of variables and parameters model reduction allows to obtain a simpler model (less variables and parameters) that can be more easily (faster, precisely) simulated and analyzed. Model reduction in systems biology has some specificity. It is connected with properties of structural incompleteness, parametric incompleteness, multi-scaleness, robustness, combinatorial complexity, stochasticity of models of biochemical networks (signal transduction pathways, metabolic networks). The model reduction techniques in systems biology are usually coarse-graining of networks of biochemical reactions. There exist several classical approaches for model reduction in chemical kinetics (quasi-steady state, quasi-equilibrium approximations, lumping, averaging, finding a limiting rate reaction step). For dealing with large logical and discrete models, existing reduction methods propose suppressing nodes and defining sub-approximating dynamics (Naldi'09). This method belongs to the class of conservative reductions, which preserve essential dynamical properties in terms of attractors and, more importantly, in terms of reachability properties.

- Topological model reduction
- Kinetic model reduction
- Standard representation of uncertainty in the network description and integrated tools

- MAPK
- Cell cycle
- TGFbeta

- algorithmes de réduction pour modèles cinétiques décrits par équations différentielles avecparamètres imprécis (connus par leurs ordres de magnitude); le cas linéaire et le cas non-linéaire sans calcul automatique de fonctions de taux.
- méthodes d'analyse tropicale pour l'identification d'équilibrations d'espèces et de réactions
- études de cas: modèles de cycle cellulaire

- V. Noel, S. Vakulenko & O. Radulescu (2011): Algorithm for identification of piecewise smooth hybrid systems: application to eukaryotic cell cycle regulation. Lecture Notes in Computer Science 6833, pp. 225–236, doi:10.1007/978-3-642-23038-7_20.
- V.Noel, D.Grigoriev, S.Vakulenko, O.Radulescu (2012): Hybrid models of the cell cycle molecular machinery. Electronic Proceedings in Theoretical Computer Science 92: 88-105
- V. Noel, D. Grigoriev, S. Vakulenko & O. Radulescu (2012): Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models. Electronic Notes in Theoretical Computer Science 284, pp. 75–91, doi:10.1016/j.entcs.2012.05.016
- O.Radulescu, A.N.Gorban, A.Zinovyev, V.Noel (2012): Reduction of dynamical biochemical reaction networks in computational biology. Frontiers in Bioinformatics and Computational Biology 3, 00131, DOI=10.3389/fgene.2012.00131.

- Rocquencourt (20/07/2012). Inria Contraintes, DIMPP
- Paris (9/11/2012). DIMPP, LINA, Inria Contraintes, IRISA.