Stress anisotropy in axisymmetric 3D active curved structures

Layers composed of lateral connections are ubiquitous in biological systems from subcellular membranes to epithelial sheets. Such layers are often found in nonflat environments, such as the ellipsoidal Drosophila embryo. Here we build on Lou et al. [Phys. Rev. Lett. 130, 108401 (2023)10.1103/PhysRevLett.130.108401] to provide a more complete description of the impact on three-dimensional (3D) cell shape of mechanical forces within a curved domain. We construct a generalizable model for the emergence of stress anisotropy as a function of depth in different curvature settings. We principally consider an epithelial monolayer to explain how the interplay between layer curvature and cell mechanics determines the stress anisotropy. We show that this can lead to irregular cellular shapes in 3D. Though here we principally focus on axisymmetric geometries, our framework is general and can be extended to a diverse set of biologically relevant systems.