Temporal variability in a system of coupled mitotic timers

Area of Science:

• Mathematical Biology
• Systems Biology
• Nonlinear Dynamics

Background:

• Cell proliferation is a fundamental biological process often modeled as periodic.
• Relaxation oscillators are key components in understanding oscillatory biological systems.
• Understanding the collective behavior of coupled oscillators is crucial for cell cycle dynamics.

Purpose of the Study:

• To numerically investigate the collective behavior of three identical relaxation oscillators.
• To explore dynamics under dominant slow-mode diffusion.
• To identify and characterize different periodic regimes and steady states.

Main Methods:

• Numerical simulation of a system of three coupled relaxation oscillators.
• Analysis of system dynamics under specific diffusion conditions.
• Identification of periodic regimes, phase relations, and steady states.

Main Results:

• Demonstrated the existence of three distinct periodic regimes with varying periods and phase relationships.
• Observed an unsymmetrical, stable steady-state (USSS) coexisting with in-phase oscillations.
• Identified the coexistence of multiple periodic attractors.
• Revealed the emergence of a two-loop limit cycle alongside in-phase oscillations and a stable steady-state.

Conclusions:

• The studied system exhibits rich dynamical behavior, including multiple coexisting attractors.
• The diversity of observed states provides a potential framework for understanding cell cycle variability.
• Dominant slow-mode diffusion significantly influences the collective dynamics of relaxation oscillators.