Three-Dimensional Vertex Simulation on Smooth Surface Maintenance of Growing Epithelial Tissue Based on Intercellular Mechano-Feedback

Abstract

Shape of epithelial tissue is appropriately accomplished by a series of tissue deformation during morphogenesis. Therefore, driving forces of tissue deformation can be controlled not only by gene expressions but also by tissue shape at any instant. In this study we focused on the mechanosensitivity of alpha-catenin, an intercellular adhesion component, and suggested a mechano-feedback relationship between apical constriction and cell shape in which apical constriction induces a cell shape change, while the shape change in surrounding cells simultaneously modifies the apical constriction of a cell. Using a three-dimensional vertex model framework, we constructed a mathematical model expressing the feedback relationship in which the modification of the apical constriction force at the cell is achieved based on the difference in the circumferential length of its surrounding cells. We performed simulations on a growing spheroid-like tissue with and without mechano-feedback, in which cell proliferation occurs in a monolayer sheet of a spherical shell. Simulation results revealed that the apical surface of the growing tissue with mechano-feedback was a smooth spherical shape, whereas the apical surface without mechano-feedback was not smooth spherical. These results resembles the experimental results of spheroid formation in which a spherical tissue shape was formed in spheroids with wild-type alpha-catenin and not in spheroids with mutant alpha-catenin that lacked mechano-sensitivity. In the simulations, we found that the apical constriction force approached a certain range over time by mechano-feedback. Further analysis suggested that continuous modifications through mechano-feedback are necessary for maintaining a smooth apical surface by suppressing cells from becoming apically very narrow wedge-like shapes that contribute to disturbing the smoothness of the tissue surface. Consequently, we suggest that mechano-feedback plays a role in maintaining a smooth apical surface of the growing tissue.