Global stability of a class of futile cycles

In this paper, we prove the global asymptotic stability of a class of mass action futile cycle networks which includes a model of processive multisite phosphorylation networks. The proof consists of two parts. In the first part, we prove that there is a unique equilibrium in every positive compatibi...

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Bibliographic Details
Published inJournal of mathematical biology Vol. 74; no. 3; pp. 709 - 726
Main Author Rao, Shodhan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Models, Theoretical
Phosphorylation
34D23
93D20
Intermediate value property
26C10
93D05
Mass action kinetics
Futile cycles
92C40
Processive multisite phosphorylation
Piecewise linear in rates Lyapunov functions
LaSalle’s invariance principle
34D05
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Summary:In this paper, we prove the global asymptotic stability of a class of mass action futile cycle networks which includes a model of processive multisite phosphorylation networks. The proof consists of two parts. In the first part, we prove that there is a unique equilibrium in every positive compatibility class. In the second part, we make use of a piecewise linear in rates Lyapunov function in order to prove the global asymptotic stability of the unique equilibrium corresponding to a given initial concentration vector. The main novelty of the paper is the use of a simple algebraic approach based on the intermediate value property of continuous functions in order to prove the uniqueness of equilibrium in every positive compatibility class.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-016-1039-8