Modelling planar cell polarity in Drosophila melanogaster - Schamberg, Sabine (2009)
During development, polarity is a common feature of many cell types. One example is the polarisation of whole fields of epithelial cells within the plane of the epithelium, a phenomenon called planar cell polarity (PCP). It is widespread in nature and plays important roles in development and physiology. Prominent examples include the epithelial cells of external structures of insects like the fruit fly Drosophila melanogaster, polarised tissue morphogenesis in vertebrates and sensory hair cells in the vertebrate ear. In this work we focus on the wing and the abdomen of Drosophila, where PCP becomes obvious in the alignment of hairs and bristles. The underlying dynamics are not fully understood yet, but two distinct protein networks centred around the transmembrane proteins Frizzled and Dachsous, respectively, have been shown to play essential roles. We will present and analyse five models for different aspects of the process of planar cell polarisation. The first two models assess the nature of PCP in a generic setting, ensuring that the results are valid for whole classes of PCP models. Models three and four are existing more complex models that include detailed assumptions about the underlying protein interactions of the Frizzled system in the Drosophila wing. Model five considers the Dachsous system in the Drosophila abdomen. We describe the features of the different types of mechanisms and determine the conditions under which they can yield polarity. All five models can establish wild-type polarity for a wide range of parameter values. We find, however, that for model one, three and four an inhomogeneous pattern exists for the same parameter values as the polarised state. Therefore, in these cases either specific initial conditions, which are unlikely in nature, or a global bias are necessary to ensure correct polarisation. Furthermore, we present the effects of clonal clusters of cells on the polarity of the surrounding cells in our models and relate them to the phenotypes observed in experiments. Model one and five show the largest discrepance between the numerical and the experimental results. We discuss the biological relevance of these findings and indicate outstanding questions.