Abstract

Epithelial cell sheets perform major biological functions by shaping the developing embryo, and they are equally important as barrier tissue in the adult, such as in the gut, or in the case of the corneal epithelium, the surface of the eye. This tissue consists of a thin layer of cells on a spherical cap, where cells are born at the edges (the limbus) and then migrate, divide, and are extruded in a steady-state spiral migration pattern with a vortex at the centre. In this talk, I will present a quantitative soft active matter model of this process. In a minimal approach, we model each cell as an active Brownian particle with a crawling speed, short-range interactions, orientational diffusion and alignment with other particles, as well as density-feedback division and death. First, we consider in in-vitro corneal cell sheets, where we identify a characteristic correlated velocity pattern that emerges from uncorrelated active persistent motion, a very general active effect. Using the fully fitted model to these in-vitro cells as well as corneal explants, we are able to simulate a full, spiralling cornea. The central spiral emerges as a +1 topological defect of the director and velocity fields, and is only present if the system crosses the flocking threshold in polar alignment. Thus we are able to identify the system as belonging to the class of polar systems without density conservation, and write a flux conservation equation for the spiral angle. We match the simulations with data obtained from tracing the stripes of dissected mouse eyes, from which we can infer the velocity field. We obtain good quantitative agreement on spiral angle, and renewal time of the tissue.