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Homeostasis and injectivity: a reaction network perspective.

Gheorghe Craciun1, Abhishek Deshpande2

  • 1Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison, Madison, USA.

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|November 15, 2022
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Summary
This summary is machine-generated.

Homeostasis, the ability of a system to maintain stability, is linked to network injectivity. A reaction network cannot achieve homeostasis if its associated network is injective, as demonstrated by analyzing network models.

Keywords:
Directed Species Reaction graphHomeostasisInjectivityReaction networks

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Area of Science:

  • Systems biology
  • Chemical kinetics
  • Mathematical modeling

Background:

  • Homeostasis is crucial for biological and chemical systems, maintaining stability despite environmental changes.
  • Understanding the mathematical underpinnings of homeostasis is key to predicting system behavior.
  • Reaction network models are widely used to study complex dynamic systems.

Purpose of the Study:

  • To establish a direct connection between the concept of homeostasis and network injectivity in reaction network models.
  • To determine conditions under which reaction networks can or cannot exhibit homeostasis.
  • To provide a theoretical framework for analyzing homeostasis in dynamical systems.

Main Methods:

  • Developing a modified network, termed the homeostasis-associated network.
  • Analyzing the injectivity property of these associated networks.
  • Applying these analytical methods to specific examples of reaction networks.

Main Results:

  • Demonstrated that a reaction network cannot exhibit homeostasis if its homeostasis-associated network is injective.
  • Provided criteria for identifying reaction networks that are incapable of homeostasis based on injectivity.
  • Illustrated with examples where homeostasis is possible and impossible.

Conclusions:

  • Injectivity of the homeostasis-associated network serves as a critical indicator for the absence of homeostasis in reaction networks.
  • This work offers a novel mathematical approach to understanding and predicting homeostasis in complex systems.
  • The findings have implications for designing and controlling biological and chemical systems to achieve desired stability properties.