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En Face Endocardial Cushion Preparation for Planar Morphogenesis Analysis in Mouse Embryos

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Modelling and analysis of planar cell polarity.

S Schamberg¹, P Houston, N A M Monk

¹School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. pmxscs@nottingham.ac.uk

Bulletin of Mathematical Biology

|January 29, 2010

Summary

Two models explore how planar cell polarity (PCP) arises in animal epithelia. Mathematical models reveal feedback and diffusion mechanisms driving cell alignment, crucial for tissue development and function.

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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.