Bifurcation and oscillatory dynamics of delayed CDK1-APC feedback loop.

Area of Science:

• Cell Biology
• Systems Biology
• Biophysics

Background:

• The CDK1-APC feedback loop is critical for cell cycle regulation.
• The precise dynamical mechanisms governing this loop remain incompletely understood.
• Understanding these dynamics is key to deciphering cell cycle control.

Purpose of the Study:

• To systematically investigate the stability and bifurcation criteria of a delayed CDK1-APC feedback loop.
• To elucidate the role of reaction rates and time delays in regulating loop dynamics.
• To provide a theoretical framework for understanding oscillations in cell cycle regulators.

Main Methods:

• Mathematical modeling of the CDK1-APC feedback loop.
• Analysis of stability and Hopf bifurcation criteria.
• Derivation of conditions for sustained oscillations.
• Numerical simulations to validate theoretical findings.

Main Results:

• The maximum reaction rate of CDK1 inactivation by APC can induce sustained oscillations in CDK1 and APC activity.
• Oscillation amplitude increases with the reaction rate.
• A specific range of CDK1 self-activation rates is necessary for oscillation generation.
• Time delays in CDK1 and APC activation can induce oscillations even in a stable steady state.

Conclusions:

• The dynamics of the CDK1-APC feedback loop are sensitive to reaction rates and time delays.
• Sustained oscillations are achievable under specific kinetic conditions, crucial for cell cycle progression.
• The study provides a theoretical basis for understanding cell cycle oscillations and identifies key regulatory parameters.