Stress anisotropy in 3D active curved structures

Abstract

Layers composed of lateral connections prevail in biological systems from subcellular membranes to epithelial sheets. This work presents a continuum framework to describe the effects of mechanical forces within a 3D curved layer with supporting lateral mesh. We provide detailed discussion on the emergence of stress anisotropy as a function of depth in different curvature settings, building on Lou et al. Phys. Rev. Lett. 130, 108401 (2023). 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, including scutoid-like geometries. Our framework is general, and can be extended to a diverse set of biologically relevant systems.