The fingering patterns in the epithelial layer control the gap closure rate via curvature-mediated force

Closing gaps in cellular monolayers is a fundamental aspect of both morphogenesis and wound healing. This closure can be achieved through leader cell crawling or actomyosin-based contraction, depending on the size of the gap. Here, we focus on wounds whose closure is driven by interfacial instabilities, featuring both leader cell-driven fingers and actin-mediated contraction. Our proposed model predicts a positive correlation between the frequency of fingering and the overall speed of boundary closure. This fingering frequency is precisely regulated through the orchestration of cell density-driven pressure, cell-cell repulsions, and the initial curvature of the wound boundary. Our findings demonstrate an inverse correlation between fingering frequency and boundary curvatures, indicating a "self-control" mechanism for closure rates independent of the initial curvatures of the wound periphery. Notably, changes in curvature caused by fingering formation generate force that aids in the healing process.