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| HAL : hal-00714358, version 1 |
| DOI : 10.1016/j.entcs.2012.05.016 |
| Fiche détaillée |  Récupérer au format |
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| Electronic Notes in Theoretical Computer Science 284 (2012) 75-91 |
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| Tropical Geometries and Dynamics of Biochemical Networks Application to Hybrid Cell Cycle Models |
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| Vincent Noël 1, 2Dima Grigoriev 3 |
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| (2012) |
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| We use the Litvinov-Maslov correspondence principle to reduce and hybridize networks of biochemical reactions. We apply this method to a cell cycle oscillator model. The reduced and hybridized model can be used as a hybrid model for the cell cycle. We also propose a practical recipe for detecting quasi-equilibrium QE reactions and quasi-steady state QSS species in biochemical models with rational rate functions and use this recipe for model reduction. Interestingly, the QE/QSS invariant manifold of the smooth model and the reduced dynamics along this manifold can be put into correspondence to the tropical variety of the hybridization and to sliding modes along this variety, respectively. |
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| 1 : | Laboratoire de Météorologie Dynamique (LMD) |
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CNRS : UMR8539 – INSU – Université Pierre et Marie Curie [UPMC] - Paris VI – Polytechnique - X – Ecole normale supérieure de Paris - ENS Paris |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3 : | Laboratoire de Mathématiques Paul Painlevé |
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CNRS : UMR8524 – Université Lille I - Sciences et technologies |
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| 4 : | Saint-Petersburg state university |
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Saint-Petersburg State University |
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| 5 : | Département de Mathématiques [Montpellier] |
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Université Montpellier II - Sciences et techniques |
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| Théorie ergodique |
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| systems biology – model reduction – hybrid models – tropical geometry |
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| hal-00714358, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00714358 | |
| oai:hal.archives-ouvertes.fr:hal-00714358 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Mercredi 4 Juillet 2012, 11:17:11 | |
| Dernière modification le : Mercredi 4 Juillet 2012, 11:17:11 | |
