Active Buckling and Shape Selection in Actomyosin Gels, Insight via Metric Elasticity

The mechanical behavior of the actomyosin cortex is crucial for determining animal cell shape and motility. Experimental work on disc-shaped extracts of actomyosin in solution with ATP demonstrated that the evolution of the shapes of the gels depends on the initial aspect ratio: thin gels tend to wrinkle, while thicker gels tend to form domes. Parallel efforts in our group suggest that the bound myosin concentration is higher near the boundary of the thin disks, while it is higher near the center of thicker disks. This is surprising because this is the opposite trend from what we would have expected. We address this via simulations of a modified plate theory inspired by metric elasticity, using the results of 2D poroelastic simulations as input for our 3D model. In the thick case, we find that the circumferential alignment of actomyosin fibers creates anisotropic contraction that is sufficient to create domes. For the thin case, poroelastic effects lead to a strain rate with a contractile band that moves inward, which, when interpreted as a change to the target metric, gives rise to wrinkles. These findings reveal the complex coupling of active stresses, elasticity, and solvent flow in determining shape evolution, emphasizing that active gels operate beyond the limits of classical elasticity.