Global stability of a class of futile cycles

2016/06/29 by Shodhan Rao · 1 citation
Biochemistry, Genetics and Molecular Biology · #Gene Regulatory Network Analysis #Microtubule and mitosis dynamics #Protein Structure and Dynamics

paper · pdf · doi:10.1007/s00285-016-1039-8

openalex publication_date 2016/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

Citations

• General mass action kinetics

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