ON THE MATHEMATICAL STRUCTURE OF BALANCED CHEMICAL REACTION NETWORKS GOVERNED BY MASS ACTION KINETICS

Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic equilibrium we derive a compact formulation exhibiting at the sa...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2013-01, Vol.73 (2), p.953-973
Main Authors: VAN DER SCHAFT, ARJAN, RAO, SHODHAN, JAYAWARDHANA, BAYU
Format: Article
Language:English
Subjects:
Applied mathematics
Chemical reactions
Chemicals
Dynamic tests
Dynamical systems
Dynamics
Equilibrium
Graph representations
Kinetics
Laplacians
Mathematical models
Mathematical vectors
Matrices
Networks
Reaction kinetics
Species
System theory
Thermodynamic equilibrium
Vertices
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Summary:Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic equilibrium we derive a compact formulation exhibiting at the same time the structure of the complex graph and the stoichiometry of the network, and which admits a direct thermodynamical interpretation. This formulation allows us to easily characterize the set of positive equilibria and their stability properties. Furthermore, we develop a framework for interconnection of chemical reaction networks, and we discuss how the formulation leads to a new approach for model reduction.
ISSN:0036-1399
1095-712X
DOI:10.1137/11085431x