Modelling and analysis of planar cell polarity

Area of Science:

• Developmental Biology
• Biophysics
• Mathematical Biology

Background:

• Planar cell polarity (PCP) governs the alignment of cellular structures like hairs and feathers in animal epithelia.
• Understanding the fundamental mechanisms of PCP is essential for comprehending tissue organization and development.

Purpose of the Study:

• To develop mathematically tractable models for planar cell polarity (PCP).
• To identify core mechanisms driving PCP phenomena in epithelial tissues.

Main Methods:

• A feedback and diffusion model coupling neighboring cell sides via negative feedback and intracellular diffusion.
• A conservative model involving protein redistribution between cells and intracellular diffusion.

Main Results:

• The feedback-diffusion model generates polarity through instability when feedback is strong and diffusion is weak, also producing period-two patterns.
• The conservative model achieves polarity from weak initial conditions or waves, contingent on sufficiently weak diffusion.
• Both models demonstrate robustness against minor initial condition anomalies.

Conclusions:

• Mathematical modeling provides insights into the fundamental drivers of planar cell polarity (PCP).
• Feedback, diffusion strength, and initial cues significantly influence PCP establishment and robustness in epithelial systems.