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

The mammalian cornea constantly regenerates its outer epithelial layer. Cells lost by abrasion are replaced by division of both corneal epithelial cells and populations of stem cells around the corneal periphery, the limbus. Limbal-derived epithelial cells migrate into the cornea, retaining equal cell loss and replacement rates (the 'XYZ hypothesis'). This process leads to a striking stable spiral cell motion pattern across the corneal surface, with a central vortex. Here, we show that the emergence of the spiral pattern can be explained by the interplay of the position of the limbus, cell division, extrusion, and collective cell migration along the curved surface of the cornea. Using dissected LacZ mosaic murine corneas, we inferred the flow field on the curved surface by following stripe edges, revealing a tightening spiral. To explain the flow fields, we developed a cell-level, in silico model of the mouse cornea. Corneal epithelial cells were treated as mechanically soft, self-propelled particles with density-dependent proliferation and extrusion rates, and noisy alignment of the direction of migration. Even without any global guidance cues, the model predicted that migration patterns form stripes and spirals closely recapitulating those in the experiment. To understand the origin and properties of this flow field, we complemented the particle-based model with a continuum description of cell flux on the cornea that generalises the XYZ hypothesis of steady-state balance between cell divisions and extrusions. The work, therefore, demonstrates how the physics of swarms on curved surfaces can provide quantitative explanations of biological processes at the tissue scale.