Tropical Geometries and Dynamics of Biochemical Networks Application to Hybrid Cell Cycle Models

Vincent Noël (1) , Dima Grigoriev (2) , Sergey A. Vakulenko (3) , Ovidiu Radulescu (4)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 SPbU - St Petersburg State University
4 Département de Mathématiques [Montpellier]

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.

Mots clés: systems biology; model reduction; hybrid models; tropical geometry

Vincent Noël, Dima Grigoriev, Sergey A. Vakulenko, Ovidiu Radulescu. Tropical Geometries and Dynamics of Biochemical Networks Application to Hybrid Cell Cycle Models. Electronic Notes in Theoretical Computer Science, 2012, 284, pp.75-91. ⟨10.1016/j.entcs.2012.05.016⟩. ⟨hal-00714358⟩