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：由双稳态引发的开关样响应与细胞信号传导过程及记忆密切相关。揭示导致双稳态的参数集合的形状与性质是理解潜在生物学机制的必要前提，但这是一个复杂的数学问题。我们提出了一种高效方法，用于判定多稳态参数区域的基本拓扑性质，即其是否连通。该区域的连通性可从双稳态背后的生物学机制及系统所能产生的开关样模式角度进行解读。我们提供了一种算法，旨在断言质量作用动力学反应网络的多稳态参数区域具有连通性。研究表明，多种此前被报道呈现双稳态的相关细胞信号基序均满足该性质。然而，我们发现在一个包含变构酶调控的磷酸化循环基序中，多稳态区域包含两个不同的连通分支，分别对应两种不同但对称的生物学机制。该方法基于线性规划，避免了直接研究参变量多项式系统通用方法的高昂计算成本，因而适用于反应网络的大规模筛选。