Algorithms to Study Large Metabolic Network Dynamics
We consider a class of systems of dierential equations with quadratic nonlinear- ities. 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 bio- chemical 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.