Homeostasis Patterns

Author(s)

Duncan, William ; Antoneli, Fernando ; Best, Janet ; Golubitsky, Martin ; Jin, Jiaxin ; Nijhout, H. . Frederik ; Reed, Mike ; Stewart, Ian

• Document type: Journal article
• Source: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 23, n. 3, p. 31-pg., 2024-01-01.

Abstract

Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when the model of interest is represented as an input-output network, with distinguished input and output nodes, and the dynamics of the network determines the corresponding input-output function of the system. In this context, homeostasis can be defined as an ``infinitesimal"" notion, namely, the derivative of the input-output function is zero at an isolated point. Combining this approach with graph-theoretic ideas from combinatorial matrix theory provides a systematic framework for calculating homeostasis points in models and classifying the different homeostasis types in input-output networks. In this paper we extend this theory by introducing the notion of a homeostasis pattern, defined as a set of nodes, in addition to the output node, that are simultaneously infinitesimally homeostatic. We prove that each homeostasis type leads to a distinct homeostasis pattern. Moreover, we describe all homeostasis patterns supported by a given input-output network in terms of a combinatorial structure associated to the input-output network. We call this structure the homeostasis pattern network. (AU)

• FAPESP's process: 19/21181-0 - New frontiers in Singularity Theory
• Grantee: Regilene Delazari dos Santos Oliveira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 19/12247-7 - Mathematical model for regulation of free intra-cellular cholesterol concentration in different cell types
• Grantee: Fernando Martins Antoneli Junior
• Support Opportunities: Regular Research Grants