Coupling Mechanical Deformations and Planar Cell Polarity to Create Regular Patterns in the Zebrafish Retina

Abstract

The orderly packing and precise arrangement of epithelial cells is essential to the functioning of many tissues, and refinement of this packing during development is a central theme in animal morphogenesis. The mechanisms that determine epithelial cell shape and position, however, remain incompletely understood. Here, we investigate these mechanisms in a striking example of planar order in a vertebrate epithelium: The periodic, almost crystalline distribution of cone photoreceptors in the adult teleost fish retina. Based on observations of the emergence of photoreceptor packing near the retinal margin, we propose a mathematical model in which ordered columns of cells form as a result of coupling between planar cell polarity (PCP) and anisotropic tissue-scale mechanical stresses. This model recapitulates many observed features of cone photoreceptor organization during retinal growth and regeneration. Consistent with the model's predictions, we report a planar-polarized distribution of Crumbs2a protein in cone photoreceptors in both unperturbed and regenerated tissue. We further show that the pattern perturbations predicted by the model to occur if the imposed stresses become isotropic closely resemble defects in the cone pattern in zebrafish lrp2 mutants, in which intraocular pressure is increased, resulting in altered mechanical stress and ocular enlargement. Evidence of interactions linking PCP, cell shape, and mechanical stresses has recently emerged in a number of systems, several of which show signs of columnar cell packing akin to that described here. Our results may hence have broader relevance for the organization of cells in epithelia. Whereas earlier models have allowed only for unidirectional influences between PCP and cell mechanics, the simple, phenomenological framework that we introduce here can encompass a broad range of bidirectional feedback interactions among planar polarity, shape, and stresses; our model thus represents a conceptual framework that can address many questions of importance to morphogenesis.

Author Summary

Many tissues and organs, including sensory organs like the vertebrate retina and inner ear, are built from sheets of connected cells called epithelia. The precise arrangement of different types of cells within these epithelia can be essential to their function. (For example, photoreceptor cells in eyes must be properly spaced to collect an optimal, undistorted signal.) We combine experimental observations with computational modeling to understand how a particular example of such epithelial organization—the planar crystalline packing of cone photoreceptor cells in the fish retina—is created. Specifically, we introduce a model where the strength of cell-cell adhesion along an interface depends on the orientation of that interface. When a global mechanical compression is applied along one direction, this model can recapitulate observed features of the cone packing and gives qualitatively correct predictions of the cone photoreceptor pattern observed in regenerated and mutant retinas. Our analysis shows that simple local interactions can direct the creation of regular, long-ranged order among epithelial cells, and it also clarifies the mechanical interactions needed to establish and maintain the integrity of the retinal epithelium. Our model may thus ultimately provide a foundation for insights into diseases in which epithelial integrity is lost.