Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks.

IF 2 4区 数学 Q2 BIOLOGY
Nidhi Kaihnsa, Máté L Telek
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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.

多位点磷酸化网络多态性参数区域的连接性
反应网络的多稳态参数区域包含相关动力系统表现出多稳态的所有参数。描述这一区域极具挑战性,目前仍是一个活跃的研究领域。在本文中,我们集中讨论了两个与生物相关的反应网络系列,它们模拟了底物在 n 个位点上的多位点磷酸化和去磷酸化。对于较小的 n 值,以前的研究表明,多态性参数区域是相连的。在这里,我们扩展了这些结果,并提供了适用于所有 n 值的证明。我们的技术基于对与这些反应网络相关的临界多项式以及该多项式符号支持的多面体几何条件的研究。
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来源期刊
CiteScore
3.90
自引率
8.60%
发文量
123
审稿时长
7.5 months
期刊介绍: The Bulletin of Mathematical Biology, the official journal of the Society for Mathematical Biology, disseminates original research findings and other information relevant to the interface of biology and the mathematical sciences. Contributions should have relevance to both fields. In order to accommodate the broad scope of new developments, the journal accepts a variety of contributions, including: Original research articles focused on new biological insights gained with the help of tools from the mathematical sciences or new mathematical tools and methods with demonstrated applicability to biological investigations Research in mathematical biology education Reviews Commentaries Perspectives, and contributions that discuss issues important to the profession All contributions are peer-reviewed.
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