"Mathematical modeling of planar cell polarity to understand domineering non-autonomy"
As the understanding of cellular regulatory networks grows, system dynamics and behaviors resulting from feedback effects of such systems have proven to be sufficiently complex as to prevent intuitive understanding. Often, only incomplete abstracted hypotheses exist to explain observed complex patterning and functions. The challenge has become to show that enough of a network has been understood to explain the behavior of the network. For example, only an incomplete understanding exists for the mechanisms that generate sub-cellular asymmetry along a tissue axis orthogonal to the apical-basal axis, termed planar cell polarity (PCP). Cell clones mutant for some PCP signaling components cause polarity disruptions of surrounding, wild-type cells, a phenomenon referred to as domineering non-autonomy. We propose that a contact dependent signaling hypothesis, derived from experimental results, is sufficient to explain domineering non-autonomy. However, intuition alone is insufficient to deduce that this model, which relies on a local feedback loop acting at the cell membrane, underlies the complex patterns observed in large fields of cells containing mutant clones, and others have argued that it cannot account for observed phenotypes. Here, we show, through reaction-diffusion, partial differential equation modeling and simulation, that the contact dependent signaling hypothesis can fully reproduce PCP phenotypes, including domineering non-autonomy, in the Drosophila wing. The sufficiency of this model argues that previously proposed diffusible factors need not be invoked to explain PCP signaling.