Abstract
Mutations in multiple planar cell polarity (PCP) genes can cause swirling patterns indicated by whorls and tufts of hairs in the wings and the abdomen of Drosophila and in the skin of vertebrates. Damaged global directional cue caused by mutations in four-jointed, fat, and dachsous, impaired cellular hexagonal packing caused by mutations in frizzled, or weakened intracellular signaling caused by mutations in disheveled, inturned, and prickle all make hair patterns globally irregular yet locally aligned, and in some cases, typically swirling. Why and how mutations in different genes all lead to swirling patterns is unexplored. Although the mechanisms of molecular signaling remain unclear, the features of molecular distribution are evident-most PCP molecules develop the polarized distribution in cells and this distribution can be induced by intercellular signaling. Does this suggest something fundamental to swirling patterns beyond the particular functions of genes, proteins, and signaling? A simple model indeed indicates this. Disregarding detailed molecular interactions, the induced polarization of molecular distribution in an epithelial cell can be modeled as the induced polarization of positive and negative charge distribution in a dielectric molecule. Simulations reveal why and how mutations in different genes all lead to swirling patterns, and in particular, the conditions for generating typical swirling patterns. The results show that the anisotropic propagation of polarized molecular distribution may be the common mechanism of swirling patterns caused by different mutations. They also suggest that at the cell level, as at the molecular level, a simple mechanism can generate complex and diverse patterning phenotypes in different molecular contexts. The similarity between the induced polarization and its propagation in both the epithelial cells and the dielectric molecules also interestingly suggests some commonalities between pattern formation in the biological and physical systems.
