Math. Model. Nat. Phenom.
Volume 10, Number 5, 2015Dynamics of Chemical Reaction Networks
|Page(s)||100 - 118|
|Published online||27 August 2015|
Algorithms to Study Large Metabolic Network Dynamics
1 CNRS, Mathématiques, Université de Lille, Villeneuve d’Ascq,
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: firstname.lastname@example.org
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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