Mechanics of axis formation in $\textit{Hydra}$

Abstract

The emergence of a body axis is a fundamental step in the development of multicellular organisms. In simple systems such as $\textit{Hydra}$, growing evidence suggests that mechanical forces generated by collective cellular activity play a central role in this process. Here, we explore a physical mechanism for axis formation based on the coupling between active stresses and tissue elasticity. We analyse the elastic deformation induced by activity-generated stresses and show that, owing to the spherical topology of the tissue, forces globally condense toward configurations in which both elastic strain and nematic defect localise at opposite poles. These mechanically selected states define either a polar or apolar head-food axis. To characterize the condensed regime, we introduce a compact parametrization of of the active force and flux distributions, enabling analytical predictions and direct comparison with experiments. Using this framework, we calculate experimentally relevant observables, including areal strain, lateral pressure, and normal displacements during muscular contraction, as well as the detailed structure of topological defect complexes in head and foot regions. Together, our results identify a mechanical route by which active tissues can spontaneously break symmetry at the organismal scale, suggesting a general physical principle underlying body-axis specification during morphogenesis.