Cytoskeletal networks are adaptive active elastic filamentous materials that design their own shape in response to system geometry
Living systems adopt a diversity of curved and highly dynamic shapes. These diverse morphologies appear on many length-scales, from cells to tissues and organismal scales. The common driving force for these dynamic shape changes are contractile stresses generated by myosin motors in the cell cytoskeleton, an intrinsically active filamentous material, while converting chemical energy into mechanical work. A good understanding of how contractile stresses in the cytoskeleton arise into different 3D shapes and what are the selection rules that determine their final configurations still lacks. Aiming to identify the selection rules governing the shapes formed by contractile forces in living systems, we recreate the actomyosin cytoskeleton in-vitro, with precisely controlled composition and initial geometry. A set of actomyosin gel discs, intrinsically identical but of variable initial geometry, spontaneously self-organize into a family of 3D shapes. This process occurs through robust distinct dynamical pathways, without specific pre-programming and additional regulation. Shape selection is encoded in the initial disc radius to thickness aspect ratio, and thus scale-free. This may indicate a universal process of shape selection, that works across scales, from cells to tissues and organelles. Finally, our results suggest that, while the dynamical pathways may depend on the detailed interactions of the different microscopic components within the gel, the final selected shapes obey the general theory of elastic deformations of thin sheets. Altogether, these results provide novel insights on the mechanically induced spontaneous shape transitions in active contractile matter and uncover new mechanisms that drive shape selections in living systems across scales. Significance statementLiving systems adopt a diversity of curved and highly dynamic shapes. These diverse morphologies appear on many length-scales, from cells to organismal scales, and are commonly driven by contractile stresses generated by myosin motors in the cell cytoskeleton. By recreating the actomyosin cytoskeleton in-vitro, with precisely controlled composition and initial geometry, we identify the shape selection rules that determine the final adopted configuration. Specifically, we find that shape selection is scale-free, which may indicate a universal process of shape selection, that works across scales, from cells to tissues and organelles. Altogether, our results provide novel insights on the mechanically induced spontaneous shape transitions in contractile active matter and uncover new mechanisms that drive shape selections in living systems.