An Active Chemo-mechanical Model to Predict Adhesion and Microenvironmental Regulation of 3D Cell Shapes

Cell shapes are known to regulate cytoskeletal organization, stiffness and the ability of cells to migrate and proliferate. Yet a quantitative understanding of the fundamental biochemical and biophysical mechanisms that determine the cell shapes is currently not available. In this study, we developed a chemo-mechanical feedback model to predict how adhesions and the properties of the 3D microenvironment regulate cell shapes. We find that the cells in 3D collagen matrices remain round or adopt an elongated shape depending on the density of active integrins, the level of contractility regulated by mechanosensitive signaling pathways and the density and mechanics of the matrix. While the formation of actin fibers that run along the cell body mediated by integrins and matrix stiffness drive elongation of cells, the cortical and membrane tension resist elongation. Based on the competition between these mechanisms, we derive phase diagrams for cell shape in the space spanned by the density of active adhesions and the level of biochemical signaling that controls contractility. Our predictions are validated by studying the shapes of HT1080 cells cultured in collagen gels of varying densities and using pharmacological treatments to regulate adhesions and contractility. The predictions of the model are found to be in excellent agreement with our experiments and data reported on a number of cell types in the literature.