On the reaction rate constants that enable multistationarity in the two-site phosphorylation cycle

2018/09/18 by Elisenda Feliu, Feliu, Elisenda
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Algebraic Geometry (math.AG) #DNA and Nucleic Acid Chemistry #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Molecular Networks (q-bio.MN) #Origins and Evolution of Life #Protein Structure and Dynamics

paper · pdf · doi:10.48550/arxiv.1809.07275

openalex publication_date 2018/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualitative behavior of the solutions with respect to the parameter values gives rise to complex problems within real algebraic geometry, concerning the study of the signs of multivariate polynomials over the positive orthant. In this work we provide further insight into the number of positive steady states of a benchmark model, namely the two-site phosphorylation cycle. In particular, we provide new conditions on the reaction rate constants for the existence of one or three positive steady states, partially filling a gap left in previous works.

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