Shape Transition and Symmetry Breaking in Network Model of Active Elastic Shell Swollen by Hydrostatic Pressure

 Shape transition and symmetry breaking driven by active mechanical forces are hallmarks of living matter. How an embryo transforms itself from an initial spherical monolayer of homogeneous cells to a complex 3D shape in a programmed and robust manner is a central question in developmental biology.  Motivated by the body plan of hydra, which features a bilayer of orthogonally arranged parallel arrays of muscle-like actin fibres, we investigate a "globe" model geometry with elastic springs arranged along discrete lines of latitude and longitudes. We show with two minimal model ingredients, 1. curvature control of active forces, 2. hydrostatic pressure regulation , that an initially spheroidal elastic shell can autonomously transit to elongated ellipsoidal shapes.