Spiral-eyes: A soft active matter model of in vivo corneal epithelial cell migration

Abstract

The mammalian cornea constantly regenerates its outer epithelial layer. Cells lost by abrasion are replaced by division of both corneal epithelial cells and stem cell populations around the corneal periphery, the limbus. Limbal-derived epithelial cells migrate into the cornea, maintaining equal rates of cell loss and replacement (the XYZ hypothesis). This process produces a striking stable spiral cell motion pattern across the corneal surface, with a central vortex. Here, we show that this spiral pattern can be explained by the interplay of limbus position, cell division, extrusion, and collective cell migration along the curved corneal surface. Using dissected LacZ mosaic murine corneas, we inferred the surface flow field by following stripe edges, revealing a tightening spiral. To explain these flow fields, we developed a cell-level in silico model treating corneal epithelial cells as soft, self-propelled particles with density-dependent proliferation and extrusion rates, and noisy alignment of migration direction. Even without global guidance cues, the model predicted stripes and spirals closely recapitulating experiment. A complementary continuum description generalised the XYZ hypothesis. Spiral formation was robust to curvature changes, but not topology, and sensitive to limbal stem cells and flocking alignment, showing how swarm physics on curved surfaces can explain tissue-scale biological processes.