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

Erscheinungsjahr:

2017

Erschienen:

2017

Enthalten in:

Zur Gesamtaufnahme - volume:74

Enthalten in:

Journal of mathematical biology - 74(2017), 3 vom: 30. Feb., Seite 709-726

Sprache:

Englisch

Beteiligte Personen:

Rao, Shodhan [VerfasserIn]

Links:

Volltext

Themen:

Futile cycles
Intermediate value property
Journal Article
LaSalle’s invariance principle
Mass action kinetics
Piecewise linear in rates Lyapunov functions
Processive multisite phosphorylation

Anmerkungen:

Date Completed 07.12.2017

Date Revised 02.12.2018

published: Print-Electronic

Citation Status MEDLINE

doi:

10.1007/s00285-016-1039-8

funding:

Förderinstitution / Projekttitel:

PPN (Katalog-ID):

NLM261881132