Healing regimes for microscopic wounds in the vertex model of cell tissues

Wounds in epithelial tissues compromise their vital role in homeostasis. A rapid and efficient wound healing encompasses different mechanisms, which includes the formation of a contractile actin-myosin cable around its edge, known as the purse-string mechanism. We combine mean-field calculations and numerical simulations of the Vertex model to study the interplay between tissue properties and the purse-string mechanism and its impact on the healing process. We find different regimes, where the wound opens or closes partially or completely. We also derive an analytic expression for the closure time which is validated by numerical simulations. This study establishes under which conditions the purse-string mechanism suffices for closure, providing an analytical mean-field expression for the respective thresholds.