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June  2008, 3(2): 295-322. doi: 10.3934/nhm.2008.3.295

Graph theory and qualitative analysis of reaction networks

Mirela Domijan 1, and  Markus Kirkilionis 1,

1. 

Zeeman Building, Mathematics Institute, University of Warwick, CV4 7AL Coventry, United Kingdom, United Kingdom

Received  December 2007 Revised  February 2008 Published  March 2008

Different types of macroscopic reaction kinetics can be derived from microscopic molecular interactions, with the law of mass action being the most widely used one in standard situations. After such a modeling step, where primarily the types of reactions are identified, it becomes a problem to analyse qualitative properties of complete regulatory networks. This problem has to be tackled, because chemical reaction networks play a part in some of the most fundamental cellular processes such as cell metabolism and regulation of cell signalling processes. This paper discusses how reaction networks can be described and analysed by graph theoretic means. Graph theory is a useful analysis tool for complex reaction networks, in situations where there is parameter uncertainty or modeling information is incomplete. Graphs are very robust tools, in the sense that whole classes of network topologies will show similar behaviour, independently of precise information that is available about the reaction constants. Nevertheless, one still has to take care to incorporate sufficient dynamical information in the network structure, in order to obtain meaningful results.
Keywords: Graph Theory, Qualitative Behaviour, Reaction Networks.
Mathematics Subject Classification: Primary: 92C45, 37G15; Secondary: 14A1.
Citation: Mirela Domijan, Markus Kirkilionis. Graph theory and qualitative analysis of reaction networks. Networks & Heterogeneous Media, 2008, 3 (2) : 295-322. doi: 10.3934/nhm.2008.3.295
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