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Positive and negative feedback: striking a balance between necessary antagonists
Olivier Cinquin1, Jacques Demongeot
1Faculty of Medicine, TIMC-IMAG-CNRS UJF-INPG, 38706 La Tronche, France. olivier.cinquin@imag.fr
Journal of Theoretical Biology
|June 25, 2002
Summary
Positive feedback circuits are essential for biological systems to achieve multiple stable states, challenging previous underestimations. This research provides a mathematical framework for understanding these crucial regulatory networks.
Area of Science:
- Systems Biology
- Mathematical Biology
- Biophysics
Background:
- Biological regulation heavily relies on feedback circuits.
- Negative feedback is well-understood and applied in engineering.
- Positive feedback circuits, often overlooked, play a critical role in biological complexity.
Purpose of the Study:
- To mathematically prove René Thomas's conjecture on the necessity of positive feedback for multiple steady states in biological systems.
- To derive constraints on the weights of positive and negative feedback circuits.
- To facilitate the reverse-engineering of biological regulatory networks.
Main Methods:
- Degree theory for vector fields.
- Analysis of autonomous differential systems.
- Modeling of multistable switches, e.g., in cellular differentiation.
Main Results:
- Demonstrated that positive feedback circuits are necessary for biological systems to exhibit multiple steady states.
- Derived qualitative (structural) and quantitative (numerical) constraints on feedback circuit weights.
- Illustrated the necessity of sufficient cooperativity using a cellular differentiation model.
Conclusions:
- Positive feedback is a fundamental requirement for multistability in biological regulatory systems.
- The derived constraints aid in reverse-engineering complex biological networks from experimental data.
- Findings have implications for understanding cellular differentiation and interpreting high-throughput biological experiments.
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