Dynamics of Wound Closure in Living Nematic Epithelia

We study theoretically the closure of a wound in a layer of epithelial cells in a living tissue after damage. Our analysis is informed by our recent experiments observing reepithelialization of pupae. On time and length scales such that the evolution of the epithelial tissue near the wound is well captured by that of a 2D active fluid with local nematic order, we consider the free-surface problem of a hole in a bounded region of tissue, and study the role that active stresses in the surrounding tissue play in the closure of the hole. For parallel anchored nematic order at the wound boundary (as we observe in our experiments), we find that closure is accelerated by contractile active stresses and is slowed down when the stresses are extensile. Parallel anchoring also leads to the appearance of topological defects that annihilate upon wound closure.