Generalized Mass Action Systems: Complex Balancing Equilibria and Sign Vectors of the Stoichiometric and Kinetic-Order Subspaces

Müller, Stefan; Regensburger, Georg

doi:10.1137/110847056

Cited by 86 publications

(197 citation statements)

References 32 publications

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“…Müller and G. Regensburger developed their theory of Generalized Mass Action Kinetics (GMAK) systems in a 2012 paper [14] and a subsequent one in 2014 [15]. The GMAK concepts in those papers are different, hence we denote them GMAK-12 and GMAK, respectively.…”

Section: The Bijection Between Pl-rdk and Gmak Systemsmentioning

confidence: 99%

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Positive equilibria of a class of power-law kinetics

2017

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This paper studies a class of power-law kinetics, PL-ILK, for whose subset, PL-TIK, analogues of the Deficiency Zero Theorem and the Deficiency One Theorem (DOT) for mass action systems are valid. The DOT also includes the necessary and sufficient condition of Boros for uniqueness in the non-weakly reversible case. To our knowledge, this is the first set of kinetics beyond mass action kinetics (MAK) for which the DOT has been shown to be valid. A further interesting property of PL-TIK is a certain "robustness" relative to dependence of linkage classes: existence of a positive equilibrium for each linkage class implies the existence of a positive equilibrium for the whole network. For MAK systems, the PL-ILK property is equivalent to the reactant deficiency of the linkage class containing the zero complex being one, and zero for all other linkage classes. As shown in the Supplementary Materials, an initial survey of MAK and BST systems already reveals numerous examples with PL-ILK kinetics.

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Section: The Bijection Between Pl-rdk and Gmak Systemsmentioning

confidence: 99%

“…The third useful result, Proposition 3.1 from [14], provides a condition on sign vector sets for the intersection of two interesting sets derived from two arbitrary subspaces of a finite dimensional real linear space.…”

Section: Proposition 14 For a Weakly Reversible Network Zero Kineticmentioning

confidence: 99%

Positive equilibria of a class of power-law kinetics

2017

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“…In terms of chemical reaction network theory, we assume generalized mass-action kinetics [10,11], that is,…”

Section: The Lotka Reactions With Generalized Mass-action Kineticsmentioning

confidence: 99%

The Center Problem for the Lotka Reactions with Generalized Mass-Action Kinetics

Boros

Hofbauer

Müller

et al. 2017

Qual. Theory Dyn. Syst.

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“…Some authors have defined k-deficiency as a deficiency of a network (e.g. Gunawardena [10], Otero-Murras et al [12,14]) because they mainly considered weakly reversible networks where the two values coincide (see below). Following our "structural view", we associate it with a positive vector k.…”

Section: Definition 8 the Deficiency Of Linkage Classmentioning

confidence: 99%

Reactant subspaces and kinetics of chemical reaction networks

et al. 2017

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This paper studies a chemical reaction network's (CRN) reactant subspace, i.e. the linear subspace generated by its reactant complexes, to elucidate its role in the system's kinetic behaviour. We introduce concepts such as reactant rank and reactant deficiency and compare them with their analogues currently used in chemical reaction network theory. We construct a classification of CRNs based on the type of intersection between the reactant subspace R and the stoichiometric subspace S and identify the subnetwork of S-complexes, i.e. complexes which, when viewed as vectors, are contained in S, as a tool to study the network classes, which play a key role in the kinetic behaviour. Our main results on new connections between reactant subspaces and kinetic properties are (1) determination of kinetic characteristics of CRNs with zero reactant deficiency by considering the difference between (network) deficiency and reactant deficiency, (2) resolution of the coincidence problem between the reactant and kinetic subspaces for complex factorizable kinetics via an analogue of the generalized Feinberg-Horn theorem, and (3) construction of an appropriate subspace for the parametrization and uniqueness of positive equilibria for complex factorizable power law kinetics, extending the work of Müller and Regensburger.

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Generalized Mass Action Systems: Complex Balancing Equilibria and Sign Vectors of the Stoichiometric and Kinetic-Order Subspaces

Cited by 86 publications

References 32 publications

Positive equilibria of a class of power-law kinetics

Positive equilibria of a class of power-law kinetics

The Center Problem for the Lotka Reactions with Generalized Mass-Action Kinetics

Reactant subspaces and kinetics of chemical reaction networks

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