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Zusammenfassung:
The growth of tissue is an essential process controlling morphogenesis and regeneration of organs. In general tissue forming cells are interactive and motile, which can give rise to emergent physical properties such as viscous fluid behaviour as has been shown for epithelial monolayers during embryogenesis, and for cell-agglomerates with a measurable surface tension. However, the mechanical integrity of tissues is provided by extracellular matrices (ECM) that turn tissues into solids with well-defined elastic properties. Paradoxically, it has been shown by in-vitro experiments that even osteoid-like tissue with large amounts of ECM grows according to rules reminiscent of fluid behavior. Motivated by this conundrum, we show here quantitatively, by constraining growing tissues to surfaces of controlled mean curvature, that osteoid-like tissues, develop shapes similar to the equilibrium shapes of fluids. In particular, for geometries with rotational symmetry, the tissue stays bounded by Delaunay surfaces and grows with rates depending on surface curvature. Actin stress-fibre patterns at the tissue surface suggests that cell contractility is responsible for generating the necessary surface stresses. This indicates that continuous remodeling of the solid matrix combined with the contractility of bone forming cells provide sufficient effective fluidity and surface stress required for a fluid-like behavior of the growing tissue at the time scale of days to weeks. Our work demonstrates that morphogenesis shares fundamental physical principles with fluid droplets as first suggested in D'Arcy Thompson's seminal work 'On Growth and Form'.
