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  1. Home
  3. Stoichiometric Balance And Sustained Rhythms.
  1. Home
  3. Stoichiometric Balance And Sustained Rhythms.

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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

View abstract on PubMed

Summary
This summary is machine-generated.

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.

Keywords:
Biological rhythmHopf bifurcationStoichiometric balanceTight binding

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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.