多位点磷酸化网络多态性参数区域的连接性

Nidhi Kaihnsa, Máté L. Telek
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引用次数: 0

摘要

反应网络的多稳态参数区域包含相关动力系统呈现多稳态的所有参数。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学相关的反应网络家族,它们模拟了一个底物在 $n$ 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,多稳态的参数区域是相连的。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有符号支持的多面体几何条件的研究。
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Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks
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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