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Oscillator death in coupled biochemical oscillators.
Tomáš Gedeon1, Breschine Cummins1
1Department of Mathematical Sciences, Montana State University, Bozeman, MT 59715, USA.
Mathematics of Control, Signals, and Systems : MCSS
|November 3, 2025
Summary
Coupled biochemical oscillators, modeled as repressilators, can stop oscillating when mutually coupled. This study explores conditions for stable, rhythmic cellular behaviors in biological networks.
Area of Science:
- Systems Biology
- Biochemical Oscillations
- Cellular Dynamics
Background:
- Rhythmic cellular behaviors like circadian rhythms, cell division, and metabolic oscillations require robustness and environmental responsiveness.
- Biochemical networks often exhibit dynamics governed by switching mechanisms, necessitating appropriate modeling approaches.
Purpose of the Study:
- To investigate the emergent behavior of coupled biochemical oscillators, specifically repressilators, using a switching systems model.
- To understand how coupling configurations affect the stability and continuation of oscillations in biological networks.
Main Methods:
- Modeling coupled biochemical oscillators as repressilators.
- Utilizing switching systems to represent cellular network dynamics.
- Analyzing parameter regimes for one-directional and mutual coupling.
Main Results:
- One-directional coupling of repressilators maintains stable individual oscillations.
- Specific parameter regimes of mutual coupling lead to the cessation of oscillations.
- Other parameter regimes of mutual coupling sustain joint oscillations.
Conclusions:
- The coupling configuration significantly impacts the oscillatory behavior of repressilators.
- Findings offer insights into condition-dependent network coupling and un-coupling in biological systems.
- Switching systems provide a suitable framework for modeling synchronized cellular behaviors.
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