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Z. Huang and M. Golubitsky

Classification of infinitesimal homeostasis in four-node input-output networks

*J. Math. Biol.*
submitted.

An input-output network has an input node i, an output node o, and regulatory
nodes j. Such a network is a core network if each j is downstream from I and up-
stream from o. Wang, Huang, Antonelli and Golubitsky [13] show that infinitesimal homeostasis can be classified in biochemical networks through infinitesimal
homeostasis in core subnetworks. Golubitsky and Wang [7] 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. [13]
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 help when calculating homeostasis in specific biochemical networks.