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A conceptual framework for modeling a latching mechanism for cell cycle regulation.
1Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, 23226, VA, USA.
Mathematical Biosciences
|February 12, 2025
Summary
This study models cell cycle regulation using coupled van der Pol oscillators. A homoclinic bifurcation explains the switch from normal cell cycles to endocycles.
Area of Science:
- Mathematical Biology
- Dynamical Systems Theory
- Cell Cycle Regulation
Background:
- Cell cycle progression relies on complex regulatory networks.
- Oscillatory dynamics are fundamental to understanding cell cycle control.
- Latching mechanisms ensure proper cell cycle transitions.
Purpose of the Study:
- To model cell cycle regulation using coupled van der Pol oscillators.
- To investigate the transition from normal cell cycling to endocycles.
- To identify the bifurcation mechanism underlying this transition.
Main Methods:
- Utilized two identical van der Pol oscillators with mutual inhibition.
- Biased oscillators to a latched state with a steady-state equilibrium.
- Analyzed the effect of inhibitory coupling on oscillatory behavior.
- Investigated homoclinic bifurcations within the model.
Main Results:
- Inhibitory coupling induced stable, alternating large-amplitude oscillations, modeling normal cell cycles.
- A homoclinic bifurcation was identified as the key mechanism for transition.
- The bifurcation leads to endocycles where only one oscillator exhibits large-amplitude oscillations.
Conclusions:
- The coupled van der Pol oscillator model provides a framework for cell cycle regulation.
- Homoclinic bifurcations are critical for understanding cell cycle state transitions.
- The model elucidates the switch from normal cycling to endocycles.
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