University of Copenhagen, Copenhagen, Denmark.
Bull Math Biol. 2024 Nov 4;86(12):144. doi: 10.1007/s11538-024-01368-z.
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.
参数区域的多稳定性的反应网络包含所有的参数,关联的动力系统表现出多个稳定状态。描述这个区域是具有挑战性的,仍然是一个活跃的研究领域。在本文中,我们集中在两个生物学相关的反应网络模型家族多站点磷酸化和去磷酸化的一个底物在 n 个站点。对于小值的 n,以前已经表明参数区域的多稳定性是连接的。在这里,我们扩展这些结果并提供一个证明适用于所有值的 n。我们的技术是基于研究的关键多项式与这些反应网络结合一起带符号的支撑的多面体几何条件的这个多项式。
