Establishment and maintenance of planar epithelial cell polarity by asymmetric cadherin bridges: a computer model.

Animal scales, hairs, feathers, and cilia are oriented due to cell polarization in the epithelial plane. Genes involved have been identified, but the signal and mechanism remain unknown. In Drosophila wing polarization, the action of a gradient of Frizzled activity is widely assumed; and cell-cell signalling by cadherins such as Flamingo surely plays a major role. We present a computer model where reading the Frizzled gradient occurs through biased, feedback-reinforced formation of Flamingo-based asymmetric intercellular complexes. Through these complexes neighboring cells are able to compare their Frizzled activity levels. Our computations are highly noise-resistant and reproduce both wild-type and all known mutant wing phenotypes; other phenotypes are predicted. The model puts stringent limits on a Frizzled activation signal, which should exhibit unusual properties: (1) the extracellular Frizzled signalling gradient should be counterdirectional--decreasing from proximal (P) to distal (D), whereas during polarization, the intracellular Frizzled gradient builds up from P to D; (2) the external gradient should be relatively weak and short-lived, lest it prevent inversion of intracellular Frizzled. These features, largely independent of model details, may provide useful clues for future experimental efforts. 2005 Wiley-Liss, Inc.