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 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.
Medienart: |
E-Artikel |
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Erscheinungsjahr: |
2017 |
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Erschienen: |
2017 |
Enthalten in: |
Zur Gesamtaufnahme - volume:74 |
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Enthalten in: |
Journal of mathematical biology - 74(2017), 3 vom: 30. Feb., Seite 709-726 |
Sprache: |
Englisch |
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Beteiligte Personen: |
Rao, Shodhan [VerfasserIn] |
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Links: |
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Themen: |
Futile cycles |
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Anmerkungen: |
Date Completed 07.12.2017 Date Revised 02.12.2018 published: Print-Electronic Citation Status MEDLINE |
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doi: |
10.1007/s00285-016-1039-8 |
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funding: |
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Förderinstitution / Projekttitel: |
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PPN (Katalog-ID): |
NLM261881132 |
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520 | |a 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 | ||
650 | 4 | |a Journal Article | |
650 | 4 | |a Futile cycles | |
650 | 4 | |a Intermediate value property | |
650 | 4 | |a LaSalle’s invariance principle | |
650 | 4 | |a Mass action kinetics | |
650 | 4 | |a Piecewise linear in rates Lyapunov functions | |
650 | 4 | |a Processive multisite phosphorylation | |
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