Theoretical Analysis of Stress Distribution and Cell Polarization Surrounding a Model Wound

A growing amount of experimental evidence shows that the local elastic field acting on cells governs their spatial organization and polarity in a tissue. Interestingly, experiments on wound healing reveal a universal formation of thick actomyosin bundles around the margins of epithelial gaps. Although the forces involved in this process have been measured, the mechanisms governing cellular alignment and contractile ring formation are still not fully understood. To theoretically investigate this process, we have carried out a self-consistent calculation of the elastic field that is actively generated around a circular gap in a contractile cell monolayer that is adhered to an elastic substrate, taking into account the responsiveness of actomyosin activity to the locally generated stress. We model actomyosin contractility by a radial distribution of point force dipoles that may alter in magnitude and orientation in response to the local elastic stress. In addition, the model takes into account the forces exerted by leader cells on the margins of the cell monolayer. Our model suggests that the presence of a hole in the center of a contractile cell monolayer creates a mechanical tendency for actomyosin forces to polarize tangentially around the hole margin. In addition, it predicts that this tendency optimizes with substrate rigidity, thickness, and strength of cell adhesion to the substrate. Our calculations support the view that the universal formation of a peripheral contractile ring is a consequence of actomyosin contractility in the bulk and its inherent responsiveness to the local stress.