In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how cross-talk (coupling two or more pathways) or inhibiting molecular function (isolating one part of the pathway) affects systems-level behavior. However, the theory for tackling these larger systems in general has lagged behind. Here, we analyze how joining networks (e.g., cross-talk) or decomposing networks (e.g., inhibition or knock-outs) affects three properties that reaction networks may possess-identifiability (recoverability of parameter values from data), steady-state invariants (relationships among species concentrations at steady state, used in model selection), and multistationarity (capacity for multiple steady states, which correspond to multiple cell decisions). Specifically, we prove results that clarify, for a network obtained by joining two smaller networks, how properties of the smaller networks can be inferred from or can imply similar properties of the original network. Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.

中文翻译：

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加入和分解反应网络。

在系统和合成生物学中，许多研究都集中在单一途径的行为和设计上，而最近，实验工作集中在如何进行串扰（耦合两个或更多途径）或抑制分子功能（分离出一部分途径）上。途径）会影响系统级的行为。但是，解决这些较大系统的理论通常滞后。在这里，我们分析了加入网络（例如串扰）或分解网络（例如抑制或敲除）如何影响反应网络可能具有可识别性（从数据中恢复参数值），稳态不变量（稳态下物种浓度之间的关系，用于模型选择）和多平稳性（多个稳态下的容量，对应于多个细胞决策）。具体而言，我们证明了结果，对于通过连接两个较小的网络而获得的网络，可以弄清楚如何从原始网络的相似属性推论或暗示较小网络的属性。我们的证明使用来自计算代数几何的技术，包括消除理论和微分代数。