Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bistability is necessary to understand the underlying biological mechanisms, but is a complex mathematical problem. We present an efficient approach to determine a basic topological property of the parameter region of multistationary, namely whether it is connected or not. The connectivity of this region can be interpreted in terms of the biological mechanisms underlying bistability and the switch-like patterns that the system can create. We provide an algorithm to assert that the parameter region of multistationarity is connected, targeting reaction networks with mass-action kinetics. We show that this is the case for numerous relevant cell signaling motifs, previously described to exhibit bistability. However, we show that for a motif displaying a phosphorylation cycle with allosteric enzyme regulation, the region of multistationarity has two distinct connected components, corresponding to two different, but symmetric, biological mechanisms. The method relies on linear programming and bypasses the expensive computational cost of direct and generic approaches to study parametric polynomial systems. This characteristic makes it suitable for mass-screening of reaction networks.
翻译:多静站参数区域的拓扑描述:决定连通性
摘要:双稳态中产生的开关响应已经与细胞信号传递过程和记忆联系起来。揭示导致双稳态的参数集的形状和属性对于理解潜在的生物机制是必要的,但是这是一个复杂的数学问题。我们提出了一种有效的方法来确定多目标参数区域的基本拓扑性质,即它是否连通。该区域的连通性可以从生物机制和系统可能创建的开关模式的角度来解释。我们提供了一种算法来确认其中的多静态参数区域是连通的,以反应具有质量作用动力学的网络为目标。我们表明,对于以前被描述为展现双稳态的许多相关细胞信号路由图案,该情况是成立的。但是,对于显示具有调节酶的磷酸化循环的构图,我们表明多静态参数区域具有两个不同的连通分量,对应于两个不同但对称的生物机制。该方法依赖线性规划,并绕过直接和通用方法研究参数多项式系统的昂贵计算成本。这一特点使其适用于反应网络的大规模筛查。