Issue |
Math. Model. Nat. Phenom.
Volume 10, Number 5, 2015
Dynamics of Chemical Reaction Networks
|
|
---|---|---|
Page(s) | 100 - 118 | |
DOI | https://doi.org/10.1051/mmnp/201510507 | |
Published online | 27 August 2015 |
Algorithms to Study Large Metabolic Network Dynamics
1 CNRS, Mathématiques, Université de Lille, Villeneuve d’Ascq,
59655, France
2 Algorithmic Bioinformatics,
Bonn-Aachen International Center for Informationtechnology Dahlmannstraße 2, 53113,
Bonn,
Germany
3 Institute for Mechanical Engineering Problems Bolshoy pr. V.
O.61, Saint Petersburg, Russia and ITMO University, Saint Petersburg
4 Institut für Informatik II,
University of Bonn, Friedrich-Ebert-Allee 144, 53113, Bonn, Germany
⋆
Corresponding author. E-mail: dmitry.grigoryev@math.univ-lille1.fr
We consider a class of systems of differential equations with quadratic nonlinearities. This class describes important biochemical models. We show that systems of this class can realize any structurally stable dynamics. Given a low dimensional dynamics, we describe algorithms that allow to realize this dynamics by a large biochemical network. Some concrete biochemical examples are studied. Moreover, we show how a big system with random kinetic rates can simulate a number of low dimensional ones. The proposed method is applied on Calcium oscillations, extracellular signal-regulated kinase (ERK) signaling pathway and multistationary Mitogen-activated protein kinase cascade system (MAPK) models from biochemistry.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: Metabolic networks / attractors
© EDP Sciences, 2015
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