title: Chemical reaction network approaches to Biochemical Systems Theory.
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.
authors.affiliation: Institute of Mathematics, University of the Philippines Diliman, Quezon City 1101, Philippines. Electronic address: cayen@math.up.edu.ph.
authors.forename: Carlene Perpetua P
authors.initials: CP
authors.lastname: Arceo
authors.affiliation: Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Laguna 4031, Philippines. Electronic address: ecjose1@up.edu.ph.
authors.forename: Editha C
authors.initials: EC
authors.lastname: Jose
authors.affiliation: Division of Systems Biotechnology, Technische Universität München, Munich, Germany. Electronic address: amsanguino@gmail.com.
authors.forename: Alberto
authors.initials: A
authors.lastname: Marin-Sanguino
authors.affiliation: 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.
authors.forename: Eduardo R
authors.initials: ER
authors.lastname: Mendoza
mesh_terms: D001669:Biochemical Phenomena; D006801:Humans; D007700:Kinetics; D055641:Mathematical Concepts; D008954:Models, Biological; D008956:Models, Chemical; D013598:Systems Theory
keywords: Chemical reaction network; Complex balanced steady states; Complex factorizable kinetics; Generalized mass action; Reactant-determined kinetics