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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.
Journal of Mathematical Biology
|February 17, 2026
Summary
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.
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.
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