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

Abstract

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.