How do multiple active cellular forces co-regulate wound shape evolution?

Wound closure is a fundamental procedure in many physiological and pathological processes, driven by multiple active cellular forces. In the closure process the wound shape can evolve into round, oval, or slit. However, the underlying mechanisms that determine the mechanical strategies of wound shape evolution are unclear. To understand how these active forces co-regulate wound shapes, we constructed a novel complex variable method-based mechanical model and obtained the stress field and free energy of cell layer with arbitrary wound shape. Our results revealed that there was a stress-driven cell polarization and arrangement around the wound under the cooperative regulation of the tissue pretension, cell protrusion stress and actomyosin ring tension that drove the direction of cell polarization and arrangement for the wound closure. In addition, a 3D phase diagram was obtained from minimizing the free energy of the cell layer that illustrates how the different active cellular forces co-regulate the wound shape evolution. In general, large cellular protrusion induces the evolution of the wound toward slit shape, and strong and medium contractions of the actomyosin ring correspond to the evolution toward oval shape and round shape, respectively. This study reveals a critical mechanism by which living organisms actively control complex processes via the coordination of multiple active cellular forces in tissue repair and development.