Reaction networks and kinetics of biochemical systems

Arceo, Carlene Perpetua P.; Jose, Editha C.; Lao, Angelyn R.; Mendoza, Eduardo

doi:10.1016/j.mbs.2016.10.004

Cited by 28 publications

(63 citation statements)

References 17 publications

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“…For example, as shown in [1], the Feinberg-Horn Theorem on the coincidence of kinetic and stoichiometric subspaces extends precisely to this set of power law kinetics.…”

Section: Definitionmentioning

confidence: 88%

“…We use the following characterization which was derived in [1] as our working definition: Definition 6 A PL-RDK kinetics is factor span surjective if and only if all rows with different reactant complexes in the kinetic order matrix F are pairwise different (i.e. ρ(r ) = ρ(r ) implies F r,.…”

Section: Definitionmentioning

confidence: 99%

“…. As shown in [1], this property is equivalent to the linear independence of the non-zero coordinate functions of the factor map K . Again, MAK systems form a subset of PL-FSK, and various properties of MAK systems can be extended to PL-FSK, e.g.…”

Section: Introductionmentioning

confidence: 96%

“…. 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%

“…Again, MAK systems form a subset of PL-FSK, and various properties of MAK systems can be extended to PL-FSK, e.g. the Feinberg-Horn Theorem on the coincidences of the kinetic and stoichiometric subspaces [1]. The GMAK-14 systems whose map of kinetic complexesỹ : ρ(R) → R S is injective correspond to PL-FSK.…”

Section: Introductionmentioning

confidence: 99%

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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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“…For example, as shown in [1], the Feinberg-Horn Theorem on the coincidence of kinetic and stoichiometric subspaces extends precisely to this set of power law kinetics.…”

Section: Definitionmentioning

confidence: 88%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

2017

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Robustness in Power-Law Kinetic Systems with Reactant-Determined Interactions

Fortun

Lao

Razón

et al. 2021

Discrete and Computational Geometry, Graphs, and Games

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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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Reaction networks and kinetics of biochemical systems

Cited by 28 publications

References 17 publications

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

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

Robustness in Power-Law Kinetic Systems with Reactant-Determined Interactions

Positive equilibria of a class of power-law kinetics

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