Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models

Details Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models

2011-09-19

arxiv.org/abs/1109.4085v2

Biology

Quantitative Biology

Molecular Networks

conference SASB 2011, to be published in Electronic Notes in Theoretical Computer Science

Scientific paper

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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