ArticleJournal of mathematical biology2021
The structure of infinitesimal homeostasis in input-output networks.
Article in Journal of mathematical biology, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
10 citing papers in PubMed.
- Automated Classification of Homeostasis Structure in Input-Output Networks.Bulletin of mathematical biology · 2026Article
- Infinitesimal homeostasis in mass-action systems.Journal of mathematical biology · 2026Article
- The adaptation property in non-equilibrium chemical systems.Journal of mathematical biology · 2026Article
- Topological criterion for robust perfect adaptation of reaction fluxes in biological networks.iScience · 2025Article
- Homeostasis in networks with multiple inputs.Journal of mathematical biology · 2024Article
- Advancing physiology education by understanding the multiple dimensions of homeostasis.Frontiers in physiology · 2023Review
- Universal structural requirements for maximal robust perfect adaptation in biomolecular networks.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Classification of infinitesimal homeostasis in four-node input-output networks.Journal of mathematical biology · 2022Article
- A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves.Journal of mathematical biology · 2022Article
- Discovering adaptation-capable biological network structures using control-theoretic approaches.PLoS computational biology · 2022Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Homeostasis refers to a phenomenon whereby the output [Formula: see text] of a system is approximately constant on variation of an input [Formula: see text]. Homeostasis occurs frequently in biochemical networks and in other networks of interacting elements where mathematical models are based on differential equations associated to the network. These networks can be abstracted as digraphs [Formula: see text] with a distinguished input node [Formula: see text], a different distinguished output node o, and a number of regulatory nodes [Formula: see text]. In these models the input-output map [Formula: see text] is defined by a stable equilibrium [Formula: see text] at [Formula: see text]. Stability implies that there is a stable equilibrium [Formula: see text] for each [Formula: see text] near [Formula: see text] and infinitesimal homeostasis occurs at [Formula: see text] when [Formula: see text]. We show that there is an [Formula: see text] homeostasis matrix [Formula: see text] for which [Formula: see text] if and only if [Formula: see text]. We note that the entries in H are linearized couplings and [Formula: see text] is a homogeneous polynomial of degree [Formula: see text] in these entries. We use combinatorial matrix theory to factor the polynomial [Formula: see text] and thereby determine a menu of different types of possible homeostasis associated with each digraph [Formula: see text]. Specifically, we prove that each factor corresponds to a subnetwork of [Formula: see text]. The factors divide into two combinatorially defined classes: structural and appendage. Structural factors correspond to feedforward motifs and appendage factors correspond to feedback motifs. Finally, we discover an algorithm for determining the homeostasis subnetwork motif corresponding to each factor of [Formula: see text] without performing numerical simulations on model equations. The algorithm allows us to classify low degree factors of [Formula: see text]. There are two types of degree 1 homeostasis (negative feedback loops and kinetic or Haldane motifs) and there are two types of degree 2 homeostasis (feedforward loops and a degree two appendage motif).
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.