Instability of the steady state solution in cell cycle population structure models with feedback

Area of Science:

• Mathematical biology
• Systems biology
• Cell cycle dynamics

Background:

• Understanding cell cycle regulation is crucial for cell population dynamics.
• Agent-based models (ABMs) offer a framework for simulating complex biological systems.
• Cell-cell feedback mechanisms can significantly influence population-level behaviors.

Purpose of the Study:

• To investigate the impact of cell-cell feedback on the stability of cell cycle models.
• To analyze the conditions under which steady-state solutions become unstable.
• To explore the implications of feedback type (positive vs. negative) on model stability.

Main Methods:

• Development of a generic agent-based ordinary differential equation (ODE) model.
• Mathematical analysis of steady-state solutions under varying feedback conditions.
• Parameter space exploration to determine stability boundaries.

Main Results:

• Cell-cell feedback frequently leads to instability of the steady-state solution in large cell populations.
• Positive feedback generally causes instability across most parameter values.
• Negative feedback induces instability in approximately half of the parameter space, with further case-by-case analysis required for the remainder.

Conclusions:

• Cell-cell feedback is a critical factor destabilizing cell cycle models.
• The nature and extent of instability depend on the type and parameters of the feedback.
• These findings highlight the importance of considering feedback in predictive models of cell proliferation.