we report the discovery of a fundamental morphological instability of constrained 3D microtissues induced by a positive chemomechanical feedback between actomyosindriven contraction and the mechanical stresses arising from the constraints. Using a 3D model for mechanotransduction we find that perturbations in the shape of contractile tissues grow in an unstable manner leading to formation of "necks" where tensile stresses are sufficiently large to lead to the failure of the tissue by narrowing and subsequent elongation. The origin of the failure mechanism driven by active forces we report is distinct from the seemingly similar and well studied necking phenomena observed in "passive" materials due to elastic softening. Here the instability is caused by the active contraction (extension) of the regions of the tissue where the mechanical stresses are smaller (greater) than the characteristic actomyosin stall stress of the tissue. The magnitude of the instability is shown to be determined by the level of active contractile strain, the stiffness of the ECM and the stiffness of the boundaries that constrain the tissue. A phase diagram that demarcates stable and unstable behavior of 3D tissues as a function of these material parameters is derived. The predictions of our model are verified by analyzing the necking and failure of normal human fibroblast (NHF) tissue constrained in a loopended dogbone geometry and cardiac microtissues constrained between microcantilevers. In the former case, the tissue fails first by necking of the connecting rod of the dogbone followed by failure of the toroidal loops in agreement with our 3D finite element simulations. In the latter case we find that cardiac tissue is stable against necking when the density of the extra cellular matrix is increased and when the stiffness of the supporting cantilevers is decreased, also in excellent agreement with the predictions of our model. By analyzing the time evolution of the morphology of the constrained tissues we have quantitatively determined the chemomechanical coupling parameters that characterize the generation of active stresses in these tissues. More generally, the analytical and numerical methods we have developed provide a quantitative framework to study the biomechanics of cell to cellinteractions in complex 3D environments such as morphogenesis and organogenisis.
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