AI 中文总结
研究Goldbeter-Koshland环级联网络多稳态区域连通性问题，通过分析反应速率空间和全参数空间，发现n≥2且有共享磷酸酶时反应速率空间区域连通，n = 2时连通区域数量上下限有差距。
AI 中文摘要
反应网络的动力学通常由参数化多项式建模，描述系统达到多个正平衡态的参数集是一个具有挑战性的问题。在由反应速率常数和总浓度确定的全参数空间中，现有方法可以给出实现多稳态的区域连通分量数量的上限，这可为建立这些区域的路径连通性提供充分条件。本文聚焦于Goldbeter-Koshland环级联网络，表明对于具有n≥2个磷酸化位点且至少有一个共享磷酸酶进行去磷酸化的该网络，反应速率空间中的区域是连通的，而在全参数空间中可能并非如此。我们明确表明，当n = 2时，连通区域数量的上下限之间存在差距。
英文摘要
Dynamics of reaction networks is often modelled by parameterised polynomials and describing the set of parameters for which the system attains multiple positive equilibrium states is a challenging problem. In the full parameter space, determined by the reaction rate constants and the total concentrations, the existing methods can give an upper bound on the number of connected components of regions that enable multistationarity and this can give sufficient condition to establish path connectivity of these regions. In this article, we focus on cascade network of Goldbeter-Koshland loops and show that for this network, with $n\geq 2$ phosphorylation sites and at least one shared phosphatase for dephosphorylation, the region in the space of reaction rates is connected while it may not be true in the full parameter space. We explicitly show that there is a gap between the upper and lower bound for the number of connected regions for the case when $n=2$.
