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

TL;DR
This paper develops a mathematical framework using graph theory and matrix analysis to identify and classify homeostasis points and patterns in input-output networks, extending previous models to include sets of nodes with simultaneous homeostasis.
Contribution
It introduces the concept of homeostasis patterns and the homeostasis pattern network, providing a systematic way to analyze multiple nodes' simultaneous homeostasis in complex systems.
Findings
Defined homeostasis patterns as sets of nodes with infinitesimal homeostasis.
Proved each homeostasis type corresponds to a unique pattern.
Characterized all patterns via the homeostasis pattern network.
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…
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Taxonomy
TopicsGene Regulatory Network Analysis · Bioinformatics and Genomic Networks
