Necking and failure of constrained 3D microtissues induced by cellular tension

In this paper we report a fundamental morphological instability of constrained 3D microtissues induced by positive chemomechanical feedback between actomyosin-driven 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" that lead to the failure of the tissue by narrowing and subsequent elongation. The magnitude of the instability is shown to be determined by the level of active contractile strain, the stiffness of the extracellular matrix, and the components of the tissue that act in parallel with the active component 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 tissue constrained in a loop-ended dog-bone geometry and cardiac microtissues constrained between microcantilevers. 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 how contractility can influence tissue morphology in complex 3D environments such as morphogenesis and organogenesis.