Abstract
Pattern-dependent collective behaviors of cells have recently raised intensive attention. However, the underlying mechanisms that regulate these behaviors are largely elusive. Here, we report a quantitative study, combining experiment and modeling, on cell polarization and arrangement on a micropatterned substrate. We show that cells exhibit position-dependent collective behaviors that can be regulated by geometry and stiffness of the patterned substrate. We find that the driving force for these collective behaviors is the in-plane maximum shear stress in the cell layer that directs the arrangement of cells. The larger the shear stress, the more the cells preferentially align and polarize along the direction of the maximum principal stress. We also find that the aspect ratio of cell polarization shape and the degree to which cells preferentially align along the direction of maximum principal stress exhibit a biphasic dependence on substrate rigidity, corresponding to our quantitative predictions that the magnitude of the maximum shear stress is biphasically dependent on the stiffness of the substrate. As such, the driving force of these cell collective behaviors can be quantified using the maximum shear stress.