Shear-driven solidification and nonlinear elasticity in epithelial tissues*

Biological processes, from  morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in  epithelia and the collective response of the tissue to bulk shear deformations remain, however, poorly understood.  Using  a minimal cell-based computational model, we investigate the constitutive relation of confluent tissues under simple shear deformation. We show that an initially undeformed fluid-like tissue    acquires finite rigidity above a critical applied strain.   This is akin to the shear-driven rigidity  observed in other soft matter systems. Interestingly,  shear-driven rigidity can be understood by a critical scaling analysis in the vicinity of the second order  critical point that governs the liquid-solid transition of the undeformed system. We further show that a solid-like tissue responds linearly only to small strains and but then switches to  a nonlinear response at larger stains, with substantial stiffening. Finally, we propose a mean-field formulation for cells under shear that offers a simple physical explanation of shear-driven rigidity and nonlinear response in a tissue.