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Morphogenesis and mechanical instability of a prestressed tissue.

We consider the issue of whether purely mechanical properties of biological systems can, in principle, play a significant role in morphogenesis. As a simple example, we model a spherically arranged epithelium that is symmetrically prestressed under the action of cytoskeletal elements. A three-dimensional exact bifurcation analysis indicates the existence of a critical radius beyond which, for a physiologically attainable prestress, the spherical organoid is mechanically unstable and will buckle. We conclude that the purely mechanical aspects of biological tissues may indeed play a role in morphogenesis.