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Stoichiometric balance and sustained rhythms
Kuan-Wei Chen1,2, Chih-Wen Shih3
1Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano 4-21-1, Tokyo, 164-8525, Japan. kwchen0613@gmail.com.
Journal of Mathematical Biology
|June 16, 2026
Summary
Stoichiometric balance is key for oscillations in genetic feedback loops. This study defines stoichiometry and identifies the range for sustained oscillations using bifurcation analysis and simulations.
Area of Science:
- Systems Biology
- Biochemical Engineering
- Molecular Biology
Background:
- Genetic negative feedback loops are fundamental to cellular processes.
- Protein sequestration-based repression is a key regulatory mechanism.
- Understanding oscillation dynamics is crucial for gene circuit design.
Purpose of the Study:
- To investigate periodic solutions in a genetic negative feedback loop model with sequestration-based repression.
- To determine the role of stoichiometric balance in generating oscillations.
- To characterize the conditions for sustained oscillations.
Main Methods:
- Hopf bifurcation analysis to establish the existence of periodic solutions.
- Numerical simulations to analyze oscillation generation.
- Approximation of stoichiometry at the bifurcation point.
Main Results:
- Periodic solutions were established using Hopf bifurcation analysis.
- Stoichiometric balance critically influences oscillation emergence.
- A specific stoichiometric range for sustained oscillations was identified.
- Differential degradation rates affect oscillation stability and stoichiometry.
Conclusions:
- Stoichiometry is a precise predictor of oscillation generation in this model.
- The study provides a quantitative framework for understanding oscillations in genetic circuits.
- Findings offer insights into designing synthetic gene networks with desired dynamic properties.
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