Morphogenesis of active deformable shells

Inspired by observations of the morphogenesis of active thin layers of cells and tissues embedded in three dimensions, we derive an asymptotic theory for the low dimensional dynamics of active deformable shells. We then study simple instabilities associated with the dynamics of the governing equations, and show that tissues with start out flat or curved can become unstable to variations in thickness or undulations, resulting in the coupling of in-plane and out-of-plane flows and deformations. We study the role of the base geometry by calculating the growth rate of these instabilities for flat, cylindrical and spherical geometries, and attempt to link these to observations in gastrulation, neuralation and organoid morphogenesis.