ArticleBulletin of mathematical biology2024
Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks.
Article in Bulletin of mathematical biology, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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- Positive equilibria in mass action networks: geometry and bounds.Journal of mathematical biology · 2026Article
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Abstract
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of research. In this paper, we concentrate on two biologically relevant families of reaction networks that model multisite phosphorylation and dephosphorylation of a substrate at n sites. For small values of n, it had previously been shown that the parameter region of multistationarity is connected. Here, we extend these results and provide a proof that applies to all values of n. Our techniques are based on the study of the critical polynomial associated with these reaction networks together with polyhedral geometric conditions of the signed support of this polynomial.
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