Modeling mechanochemical pattern formation in elastic sheets of biological matter

Self-assembled active actomyosin gels spontaneously curve and wrinkle similar to biological cells and tissues

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, that converts chemical energy into mechanical work. A good understanding of how contractile stresses in the cytoskeleton arise into different three-dimensional (3D) shapes and what are the shape selection rules that determine their final configurations is still lacking. To obtain insight into the relevant physical mechanisms, 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, dynamically self-organize into a family of 3D shapes, such as domes and wrinkled shapes, without the need for specific preprogramming or additional regulation. Shape deformation is driven by the spontaneous emergence of stress gradients driven by myosin and is encoded in the initial disc radius to thickness aspect ratio, which may indicate shaping scalability. Our results suggest that while the dynamical pathways may depend on the detailed interactions between the different microscopic components within the gel, the final selected shapes obey the general theory of elastic deformations of thin sheets. Altogether, our results emphasize the importance for the emergence of active stress gradients for buckling-driven shape deformations and provide insights on the mechanically induced spontaneous shape transitions in contractile active matter, revealing potential shared mechanisms with living systems across scales.

Shape transitions in a network model of active elastic shells

Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex 3D shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.