Geometric and active control of anterior-posterior axis in Hydra.

We explore the possibility that the formation of the anterior-posterior axis in simple developing organisms, such as Hydra, is facilitated by mechanical processes. To this end, we consider an active spherical shell model where active nemato-dynamics, representing the activity of the muscle fibers, is coupled to the spherical Airy stress equation, representing the response of the tissue to stretching. We study the stress distribution due to elastic deformations tied to activity packaged as a conserved dynamical field. We find that this model undergoes a Jeans-like instability, controlled by curvature, to a state where elastic deformations are localized at a pole. This framework offers a mechanical route by which active solids can undergo global spontaneous symmetry breaking, an important step in many morphogenetic processes.