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Infinitesimal homeostasis in mass-action systems.

Jiaxin Jin1, Grzegorz A Rempala2,3

  • 1Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504, USA.

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|February 17, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces infinitesimal homeostasis for biological systems modeled as chemical reaction networks. It provides methods to verify homeostasis, even with conservation laws, enhancing our understanding of biological robustness.

Keywords:
BiochemistryChemical Reaction NetworkHomeostasisInput-Output Network

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Area of Science:

  • Biochemistry
  • Systems Biology
  • Chemical Kinetics

Background:

  • Homeostasis is crucial for biological systems, maintaining stable internal conditions.
  • Chemical reaction networks are fundamental models for biological processes.
  • Conservation laws in these networks complicate traditional homeostasis analysis.

Purpose of the Study:

  • To define and analyze infinitesimal homeostasis in chemical reaction networks.
  • To develop methods for verifying homeostasis under conservation laws.
  • To introduce and explore infinitesimal concentration robustness.

Main Methods:

  • Mathematical derivation of conditions for infinitesimal homeostasis.
  • Analysis of input-output relationships in chemical reaction networks.
  • Incorporation of conservation laws into homeostasis analysis.
  • Development of the concept of infinitesimal concentration robustness.

Main Results:

  • Established methods to verify infinitesimal homeostasis in chemical reaction networks.
  • Demonstrated that conserved quantities can act as input parameters for homeostasis.
  • Introduced and defined infinitesimal concentration robustness.
  • Illustrated findings with examples in both deterministic and stochastic settings.

Conclusions:

  • Infinitesimal homeostasis analysis is applicable to chemical reaction networks, even with conservation laws.
  • Conservation laws do not preclude homeostasis and can be integrated into its analysis.
  • The concept of infinitesimal concentration robustness offers a new perspective on biological stability.