Positive equilibria of a class of power-law kinetics

Talabis, Dylan Antonio S. J.; Arceo, Carlene Perpetua P.; Mendoza, Eduardo

doi:10.1007/s10910-017-0804-2

Cited by 21 publications

(44 citation statements)

References 14 publications

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“…We recall some fundamental notions about chemical reaction networks (CRNs) and chemical kinetic systems (CKS) assembled in [5,17]. Some concepts introduced by Feinberg in [9,10] are also reviewed.…”

Section: Fundamentals Of Chemical Reaction Network and Kinetic Systemsmentioning

confidence: 99%

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A Deficiency-One Algorithm for power-law kinetic systems with reactant-determined interactions

et al. 2018

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Robustness against the presence of environmental disruptions can be observed in many systems of chemical reaction network. However, identifying the underlying components of a system that give rise to robustness is often elusive. The influential work of Shinar and Feinberg established simple yet subtle network-based conditions for absolute concentration robustness (ACR), a phenomena in which a species in a mass-action system has the same concentration for any steady state the network may admit. In this contribution, we extend this result to embrace kinetic systems more general than mass-action systems, namely, powerlaw kinetic systems with reactant-determined interactions (denoted by "PL-RDK"). In PL-RDK, the kinetic order vectors (which we call "interactions") of reactions with the same reactant complex are identical. As illustration, we considered a scenario in the pre-industrial state of global carbon cycle. A power-law approximation of the dynamical system of this scenario is found to be dynamically equivalent to an ACR-possessing PL-RDK system.

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Section: Fundamentals Of Chemical Reaction Network and Kinetic Systemsmentioning

confidence: 99%

“…Savageau [15] and Voit [18,19] highlighted the advantages of using power-law formalism for modelling biochemical systems. In this light, many CRN-based results on PLK systems are established ( [6,11,13,17] among others), some of which are extensions or modifications of existing results on MAK systems.…”

Section: Introductionmentioning

confidence: 99%

A Deficiency-One Algorithm for power-law kinetic systems with reactant-determined interactions

et al. 2018

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“…In [16], D. Talabis introduced for any PL-RDK system the map F T := T •proj R • I a where R = R ρ(R) , which we now call the "truncated kinetic map".…”

Section: The Kinetic Flux Subspace Of a Pl-rdk Systemmentioning

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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“…In further papers [11,14] they refined their approach to construct linearly conjugate systems which are not only weakly reversible but also have desirable deficiency properties: minimal deficiency and satisfying the Deficiency One Theorem conditions. Since Deficiency Theory for PL-RDK systems is little developed (s. [21] for a detailed discussion), we focus only on extending the first algorithm for constructing weakly reversible linear conjugate systems.…”

Section: Adaptation Of the Johnston Et Al Milp Algorithm To Pl-rdk Smentioning

confidence: 99%

“…. In [1], it is shown that PL-RDK systems are precisely the power law systems for [16] (which we call GMAK-14) are discussed in detail in [21]. We specify the kinetics of PL-RDK systems with their rate vector and T matrix.…”

Section: Introductionmentioning

confidence: 99%

A computational approach to linear conjugacy in a class of power law kinetic systems

2017

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This paper studies linear conjugacy of PL-RDK systems, which are kinetic systems with power law rate functions whose kinetic orders are identical for branching reactions, i.e. reactions with the same reactant complex. Mass action kinetics (MAK) systems are the best known examples of such systems with reactant-determined kinetic orders (RDK). We specify their kinetics with their rate vector and T matrix. The T matrix is formed from the kinetic order matrix by replacing the reactions with their reactant complexes as row indices (thus compressing identical rows of branching reactions of a reactant complex to one) and taking the transpose of the resulting matrix. The T matrix is hence the kinetic analogue of the network's matrix of complexes Y with the latter's columns of non-reactant complexes truncated away. For MAK systems, the T matrix and the truncated Y matrix are identical. We show that, on non-branching networks, a necessary condition for linear conjugacy of MAK systems and, more generally, of PL-FSK (power law factor span surjective kinetics) systems, i.e. those whose T matrix columns are pairwise different, is T = T , i.e. equality of their T matrices. This motivated our inclusion of the condition T = T in exploring extension

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Positive equilibria of a class of power-law kinetics

Cited by 21 publications

References 14 publications

A Deficiency-One Algorithm for power-law kinetic systems with reactant-determined interactions

A Deficiency-One Algorithm for power-law kinetic systems with reactant-determined interactions

Reactant subspaces and kinetics of chemical reaction networks

A computational approach to linear conjugacy in a class of power law kinetic systems

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