Algorithms to study large metabolic network dynamics
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.
Keywords: attractors, Metabolic networks
Bibtex
@ARTICLE{GregorievEtAl2015a, author = {Grigoriev, Dima and Samal, Satya and Vakulenko, Sergey and Weber, Andreas}, pages = {100--118}, title = {Algorithms to study large metabolic network dynamics}, journal = {Mathematical Modelling of Natural Phenomena}, volume = {10}, number = {5}, year = {2015}, keywords = {attractors, Metabolic networks}, 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.}, doi = {10.1051/mmnp/201510507} }