Classification of infinitesimal homeostasis in four-node input-output networks
The paper presents some new conclusions based on recent work from \textit{Y. Wang} et al. [J. Math. Biol. 82, No. 7, Paper No. 62, 43 p. (2021; Zbl 1467.92083)], describing in detail the twenty types of 4-node core networks and 17 types of infinitesimal homeostasis in 4 node core networks. The paper starts with an introduction that recapitulates the core concepts on input-output functions and infinitesimal homeostasis, on the definition of the homeostasis matrix, and on core networks and core equivalence classes, the latter described in detail with numerous examples. The introduction concludes with an overview of infinitesimal homeostasis types. Next, the authors present biochemical examples that support the subsequent enumeration of four-node core equivalent classes. The paper closes on the classification of infinitesimal homeostasis in four-node input-output networks on degree 1 (no cycle appendage homeostasis, null degradation and structural homeostasis, Haldane) and degree 2 (structural homeostasis, feed-forward loop and no cycle appendage homeostasis). All examples are thoroughly presented and discussed; the results are backed up with full proofs and richly decorated with references.
scientific article; zbMATH DE number 7488586
scientific article