Epithelial cell sheets form a fundamental role in the developing embryo, and also in adult tissues including the gut and the cornea of the eye. Soft and active matter provides a theoretical and computational framework to understand the mechanics and dynamics of these tissues. First, I will show, using both particle and vertex models, how the extended ’swirly’ velocity fluctuations seen in sheets on a substrate can be understood using a simple model that couples linear elasticity with disordered activity. We are able to quantitatively match experiments using
in-vitro corneal epithelial cells.
I will then show a direct application of this simple particle-based model to the steady-state flow pattern on the murine cornea. By engineering a balance between cell proliferation in the limbus and on the cornea with cell ablation (the ‘XYZ hypothesis’), we generate a spiral flow pattern as soon as there is alignment between cells present. Our numerical cornea is quantitatively consistent with the patterns observed on mouse corneas, and we are also able to accurately predict the response to in-vivo wounding.