Chemical reaction network approaches to Biochemical Systems Theory

Issue Date

9-2015

Abstract

This paper provides a framework to represent a Biochemical Systems Theory (BST) model (in either GMA or S-system form) as a chemical reaction network with power law kinetics. Using this representation, some basic properties and the application of recent results of Chemical Reaction Network Theory regarding steady states of such systems are shown. In particular, Injectivity Theory, including network concordance [36] and the Jacobian Determinant Criterion [43], a "Lifting Theorem" for steady states [26] and the comprehensive results of Müller and Regensburger [31] on complex balanced equilibria are discussed. A partial extension of a recent Emulation Theorem of Cardelli for mass action systems [3] is derived for a subclass of power law kinetic systems. However, it is also shown that the GMA and S-system models of human purine metabolism [10] do not display the reactant-determined kinetics assumed by Müller and Regensburger and hence only a subset of BST models can be handled with their approach. Moreover, since the reaction networks underlying many BST models are not weakly reversible, results for non-complex balanced equilibria are also needed.

Source or Periodical Title

Mathematical Biosciences

ISSN

0025-5564

Volume

269

Page

135-152

Document Type

Article

Physical Description

figures, tables, diagram

Language

English

Subject

Chemical reaction network, Complex balanced steady states, Complex factorizable kinetics, Generalized mass action, Reactant-determined kinetics

Identifier

doi:10.1016/j.mbs.2015.08.022.

Digital Copy

yes

Link to Full Text

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