Modelling and analysis of planar cell polarity

Schamberg, Sabine; Houston, Paul; Monk, Nick A.M.; Owen, Markus R.

Abstract

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion.

Citation

Schamberg, S., Houston, P., Monk, N. A., & Owen, M. R. Modelling and analysis of planar cell polarity. Manuscript submitted for publication

• Journal Article Type: Article
• Deposit Date: Nov 19, 2008
• Journal: Bulletin of Mathematical Biology
• Print ISSN: 0092-8240
• Electronic ISSN: 0092-8240
• Publisher: Springer Verlag
• Peer Reviewed: Not Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/1016116
• Publisher URL: http://www.springerlink.com/content/119979/?p=96f6d5a3afbd4550a22038fe24ce2763&pi=1