Dynamics of active defects under non-uniform Gaussian curvature

Living organisms are built from cells displaying a variety of shapes, morphologies and textures, which encode specific functions and physical behaviors. In this work, biomimmetic structural units are created by coating ellipsoidal droplets of a smectic liquid crystal with a protein-based active cytoskeletal gel, thus obtaining core-shell structures. We exploit the patterned texture and anisotropic shape of the core to mold the complex nematodynamics of the interfacial active material. New time-dependent states are identified in which topological defects periodically oscillate between a rotational and a translational regime. Nemato-hydrodynamic simulations of active nematics reveal that, beyond topology and activity, the dynamics of the active material is profoundly influenced by the local curvature and texture of the droplet, as well as by external hydrodynamic forces, which induce a solid-body rotation of the droplet. Our results illustrate how the incorporation of these constraints into active nematic shells orchestrates remarkable spatiotemporal motifs, providing new elements for the understanding of biological systems and fascinating perspectives for the design of bio-inspired micro-machines.