Department of Mathematics, University of Michigan, Ann Arbor, MI, 48104, USA.
Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.
J Math Biol. 2022 Feb 26;84(4):25. doi: 10.1007/s00285-022-01727-1.
An input-output network has an input node [Formula: see text], an output node o, and regulatory nodes [Formula: see text]. Such a network is a core network if each [Formula: see text] is downstream from [Formula: see text] and upstream from o. Wang et al. (J Math Biol 82:62, 2021. https://doi.org/10.1007/s00285-021-01614-1 ) show that infinitesimal homeostasis can be classified in biochemical networks through infinitesimal homeostasis in core subnetworks. Golubitsky and Wang (J Math Biol 10:1-23, 2020) show that there are three types of 3-node core networks and three types of infinitesimal homeostasis in 3-node core networks. This paper uses the theory developed in Wang et al. (2021) to show that there are twenty types of 4-node core networks (Theorem 1.3) and seventeen types of infinitesimal homeostasis in 4-node core networks (Theorem 1.7). Biological contexts illustrate the classification theorems and show that the theory can be an aid when calculating homeostasis in specific biochemical networks.
输入输出网络有一个输入节点[公式：见文本]，一个输出节点 o ，以及调节节点[公式：见文本]。如果每个[公式：见文本]都位于[公式：见文本]的下游和 o 的上游，那么这样的网络就是核心网络。Wang 等人（J Math Biol 82:62, 2021. https://doi.org/10.1007/s00285-021-01614-1 ）表明，可以通过核心子网中的微小稳态来对生化网络中的微小稳态进行分类。Golubitsky 和 Wang（J Math Biol 10:1-23, 2020）表明，在 3 节点核心网络中有三种类型的 3 节点核心网络和三种类型的微小稳态。本文利用 Wang 等人（2021 年）发展的理论，证明了在 4 节点核心网络中存在 20 种类型的 4 节点核心网络（定理 1.3）和 17 种类型的微小稳态（定理 1.7）。生物学背景说明了分类定理，并表明该理论在计算特定生化网络中的稳态时可以提供帮助。
