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Math Biosci. 2017 Jan;283:13-29. doi: 10.1016/j.mbs.2016.10.004. Epub 2016 Nov 4.

Reaction networks and kinetics of biochemical systems.

Author information

1
Institute of Mathematics, University of the Philippines Diliman, Quezon City, 1101, Philippines. Electronic address: cayen@math.upd.edu.ph.
2
Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Laguna, 4031, Philippines. Electronic address: ecjose1@up.edu.ph.
3
Mathematics Department, De la Salle University, Manila, Philippines. Electronic address: angelyn.lao@dlsu.edu.ph.
4
Institute of Mathematics, University of the Philippines Diliman, Quezon City, 1101, Philippines; Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Laguna, 4031, Philippines; Max Planck Institute of Biochemistry, Martinsried near Munich, Germany; Faculty of Physics and Center for Nanoscience, Ludwig Maximilian University, Geschwister -Scholl- Platz 1, 80539 Munich, Germany. Electronic address: mendoza@lmu.de.

Abstract

This paper further develops the connection between Chemical Reaction Network Theory (CRNT) and Biochemical Systems Theory (BST) that we recently introduced [1]. We first use algebraic properties of kinetic sets to study the set of complex factorizable kinetics CFK(N) on a CRN, which shares many characteristics with its subset of mass action kinetics. In particular, we extend the Theorem of Feinberg-Horn [9] on the coincidence of the kinetic and stoichiometric subsets of a mass action system to CF kinetics, using the concept of span surjectivity. We also introduce the branching type of a network, which determines the availability of kinetics on it and allows us to characterize the networks for which all kinetics are complex factorizable: A "Kinetics Landscape" provides an overview of kinetics sets, their algebraic properties and containment relationships. We then apply our results and those (of other CRNT researchers) reviewed in [1] to fifteen BST models of complex biological systems and discover novel network and kinetic properties that so far have not been widely studied in CRNT. In our view, these findings show an important benefit of connecting CRNT and BST modeling efforts.

KEYWORDS:

Chemical reaction network; Complex factorizable kinetics; Embedded kinetic system; Embedded representation; Kinetic subspace; Kinetics set; Power law kinetics; Span surjective kinetics; Total kinetic system; Total representation

PMID:
27818257
DOI:
10.1016/j.mbs.2016.10.004
[Indexed for MEDLINE]

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