Cell cycle dynamics: clustering is universal in negative feedback systems

Area of Science:

• Mathematical Biology
• Systems Biology
• Nonlinear Dynamics

Background:

• Cell cycle regulation involves complex interactions and feedback mechanisms.
• Understanding ensemble dynamics is crucial for comprehending cell population behavior.
• Cell-cell communication influences developmental rates and synchronization.

Purpose of the Study:

• To analyze the stability of k-cyclic solutions in a cell cycle model with cell-cell feedback.
• To characterize parameter space for k-cyclic solution stability under general nonlinear feedback.
• To investigate the impact of negative versus positive feedback on emergent cyclic behaviors.

Main Methods:

• Development of a mathematical model for cell cycle ensemble dynamics.
• Analysis of periodic solutions, termed k-cyclic or clustered solutions.
• Characterization of stability within a 2D parameter space (triangle T).
• Investigation of stability types across sub-triangles of T.

Main Results:

• For a fixed k, k-cyclic solution stability is fully characterized in parameter space T.
• Parameter space T is partitioned into sub-triangles, each with a unique stability type for k-cyclic solutions.
• Negative feedback leads to unstable synchronous solutions (k=1) but stable k ≥ 2 clustered solutions across T.
• Negative feedback systems exhibit bi-stability or multi-stability.
• Positive feedback systems show only the synchronous solution (k=1) as asymptotically stable.

Conclusions:

• Negative feedback systems are expected to exhibit k-cyclic solutions for k ≥ 2.
• The stability landscape of cell cycle dynamics is highly dependent on feedback type.
• Clustered cell cycle solutions are a significant emergent property in systems with negative feedback.