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  Positive equilibria of weakly reversible power law kinetic systems with linear independent interactions

Mendoza, E. R., Talabis, D. A. S. J., & Jose, E. C. (2018). Positive equilibria of weakly reversible power law kinetic systems with linear independent interactions. Journal of Mathematical Chemistry, 56(9), 2643-2673. doi:10.1007/s10910-018-0909-2.

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Mendoza2018_Article_PositiveEquilibriaOfWeaklyReve.pdf (Publisher version), 635KB
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 Creators:
Mendoza, Eduardo R.1, Author              
Talabis, Dylan Antonio S. J.2, Author
Jose, Editha C.2, Author
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1Oesterhelt, Dieter / Membrane Biochemistry, Max Planck Institute of Biochemistry, Max Planck Society, ou_1565164              
2external, ou_persistent22              

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Free keywords: CHEMICAL-REACTION NETWORKS; BIOCHEMICAL SYSTEMS; SUBSPACESChemistry; Mathematics; Chemical reaction networks; Power law kinetics; Linear independent interactions; Complex balanced equilibria; Zero kinetic deficiency; Weak Reversibility Theorem;
 Abstract: In this paper, we extend our study of power law kinetic systems whose kinetic order vectors (which we call interactions) are reactant-determined (i.e. reactions with the same reactant complex have identical vectors) and are linear independent per linkage class. In particular, we consider PL-TLK systems, i.e. such whose T-matrix (the matrix with the interactions as columns indexed by the reactant complexes), when augmented with the rows of characteristic vectors of the linkage classes, has maximal column rank. Our main result states that any weakly reversible PL-TLK system has a complex balanced equilibrium. On the one hand, we consider this result as a Higher Deficiency Theorem for such systems since in our previous work, we derived analogues of the Deficiency Zero and the Deficiency One Theorems for mass action kinetics (MAK) systems for them, thus covering the Low Deficiency case. On the other hand, our result can also be viewed as a Weak Reversibility Theorem (WRT) in the sense that the statement any weakly reversible system with a kinetics from the given set has a positive equilibrium holds. According to the work of Deng et al. and more recently of Boros, such a WRT holds for MAK systems. However, we show that a WRT does not hold for two proper MAK supersets: the set PL-NIK of non-inhibitory power law kinetics (i.e. all kinetic orders are non-negative) and the set PL-FSK of factor span surjective power law kinetics (i.e. different reactants imply different interactions).

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Language(s): eng - English
 Dates: 2018
 Publication Status: Published in print
 Pages: 31
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: ISI: 000443702300005
DOI: 10.1007/s10910-018-0909-2
 Degree: -

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Title: Journal of Mathematical Chemistry
  Other : J. Math. Chem.
Source Genre: Journal
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Publ. Info: Basel, Switzerland : Springer
Pages: - Volume / Issue: 56 (9) Sequence Number: - Start / End Page: 2643 - 2673 Identifier: ISSN: 0259-9791
CoNE: https://pure.mpg.de/cone/journals/resource/954925497050