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

Authors:
Vincent Noel;Dima Grigoriev;Sergei Vakulenko;Ovidiu Radulescu
Affiliations:
IRMAR UMR 6625, University of Rennes 1, Rennes, France;CNRS, Mathématiques, Université de Lille, 59655, Villeneuve dAscq, France;Saint Petersburg State University of Technology and Design, St. Petersburg, Russia;DIMNP UMR CNRS 5235, University of Montpellier 2, Montpellier, France
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2012

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Abstract

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.