Deformation Dynamics of Active Shells: Polar v Nematic

Recent observations suggest that topology enters biology in subtle ways that are only now beginning to be appreciated. In the last few years the framework of active liquid crystals has been used to gain insight into tissue dynamics. While much of this work was focused on flat geometries, more recently the focus has also moved to non-flat geometries, where the complex interaction of topological defects, hydrodynamics, and geometry is studied, trying to understand, e.g., morphogenesis better.

However, so far geometry has mostly been considered as a fixed background rather than coupled to the dynamics. We lift this constraint and consider, analytically and with simulations, active liquid crystals coupled to an elastic, initially spherical, surface. Due to topological constrains there are always defects present. Building on our model of defect-driven active buckling [arXiv:2105.15200] we show that in the polar system with extensile activity the sphere flattens, eventually leading to a genus transformation from a sphere to a torus in the turbulent regime. For the nematic case we observe periodic deformations of the shell and the formation of protrusions. This work thus clarifies the interaction of active defects and geometry and provides potentially new insight into morphogenesis.