{"title":"Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks","authors":"Nidhi Kaihnsa, Máté L. Telek","doi":"arxiv-2403.16556","DOIUrl":null,"url":null,"abstract":"The parameter region of multistationarity of a reaction network contains all\nthe parameters for which the associated dynamical system exhibits multiple\nsteady states. Describing this region is challenging and remains an active area\nof research. In this paper, we concentrate on two biologically relevant\nfamilies of reaction networks that model multisite phosphorylation and\ndephosphorylation of a substrate at $n$ sites. For small values of $n$, it had\npreviously been shown that the parameter region of multistationarity is\nconnected. Here, we extend these results and provide a proof that applies to\nall values of $n$. Our techniques are based on the study of the critical\npolynomial associated with these reaction networks together with polyhedral\ngeometric conditions of the signed support of this polynomial.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuanBio - Molecular Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.16556","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.