title: Global stability of a class of futile cycles.
abstract: 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.
authors.affiliation: Ghent University Global Campus, Incheon Global Campus, 119 Songdomunhwa-ro, Yeonsu-gu, Incheon, 406-840, South Korea. Shodhan.Rao@ghent.ac.kr.
authors.forename: Shodhan
authors.identifier: 0000-0001-8840-6950
authors.initials: S
authors.lastname: Rao
mesh_terms: D008962:Models, Theoretical; D010766:Phosphorylation
keywords: Futile cycles; Intermediate value property; LaSalle’s invariance principle; Mass action kinetics; Piecewise linear in rates Lyapunov functions; Processive multisite phosphorylation