Journal of Mathematical Chemistry

, Volume 50, Issue 5, pp 1111–1125 | Cite as

Oscillations in non-mass action kinetics models of biochemical reaction networks arising from pairs of subnetworks

Original Paper

Abstract

It is well known that oscillations in models of biochemical reaction networks can arise as a result of a single negative cycle. On the other hand, methods for finding general network conditions for potential oscillations in large biochemical reaction networks containing many cycles are not well developed. A biochemical reaction network with any number of species is represented by a simple digraph and is modeled by an ordinary differential equation (ODE) system with non-mass action kinetics. The obtained graph-theoretic condition generalizes the negative cycle condition for oscillations in ODE models to the existence of a pair of subnetworks, where each subnetwork contains an even number of positive cycles. The technique is illustrated with a model of genetic regulation.

Keywords

Biochemical reaction networks Non-mass action kinetics Oscillations Negative feedback cycle 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

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