Mathematical Modeling of Planar Cell Polarity to Understand Domineering Nonautonomy

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Abstract
Planar cell polarity (PCP) signaling generates subcellular asymmetry along an axis orthogonal to the epithelial apical-basal axis. Through a poorly understood mechanism, cell clones that have mutations in some PCP signaling components, including some, but not all, alleles of the receptor frizzled, cause polarity disruptions of neighboring wild-type cells, a phenomenon referred to as domineering nonautonomy. Here, a contact-dependent signaling hypothesis, derived from experimental results, is shown by reaction-diffusion, partial differential equation modeling and simulation to fully reproduce PCP phenotypes, including domineering nonautonomy, in the Drosophila wing. The sufficiency of this model and the experimental validation of model predictions reveal how specific protein-protein interactions produce autonomy or domineering nonautonomy.