Abstract
An input–output network has an input node \(\iota \), an output node o, and regulatory nodes \(\rho _j\). Such a network is a core network if each \(\rho _j\) is downstream from \(\iota \) 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.
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Acknowledgements
We thank Fernando Antoneli, Janet Best, and Yangyang Wang for helpful discussions.
Funding
Funding for ZH was provided by an Undergraduate Research Scholarship from the College of Arts and Sciences of the Ohio State University.
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Huang, Z., Golubitsky, M. Classification of infinitesimal homeostasis in four-node input–output networks. J. Math. Biol. 84, 25 (2022). https://doi.org/10.1007/s00285-022-01727-1
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DOI: https://doi.org/10.1007/s00285-022-01727-1