Geodesic
Algorithms to Study Large Metabolic Network Dynamics
D. Grigoriev1 ; S. S. Samal2 ; S. Vakulenko3 ; A. Weber4
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
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 5, pp. 100-118.

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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.
DOI : 10.1051/mmnp/201510507

D. Grigoriev 1 ; S. S. Samal 2 ; S. Vakulenko 3 ; A. Weber 4

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 
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D. Grigoriev; S. S. Samal; S. Vakulenko; A. Weber. Algorithms to Study Large Metabolic Network Dynamics. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 5, pp. 100-118. doi : 10.1051/mmnp/201510507. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201510507/

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