Active morphogenesis of patterned epithelial shells

Abstract

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.

Typos fixed in equations (165)-(168)

References in corpus (9)

• Topology and Dynamics of Active Nematic Vesicles
• Theory of defect-mediated morphogenesis
• Dynamics of a $Volvox$ Embryo Turning Itself Inside Out
• Defects in nematic membranes can buckle into pseudospheres
• Quantifying material properties of cell monolayers by analyzing integer topological defects
• Integer topological defects of cell monolayers -- mechanics and flows
• Theory of nematic and polar active fluid surfaces
• Vesicle shape, molecular tilt, and the suppression of necks
• Concise theory of chiral lipid membranes

Cited by in corpus (10)

• Patterning of morphogenetic anisotropy fields
• Morphodynamics of Active Nematic Fluid Surfaces
• Odd elasticity and topological waves in active surfaces
• Tuneable defect-curvature coupling and topological transitions in active shells
• Hydra morphogenesis as phase-transition dynamics
• Active Filaments on Curved Surfaces: From Single Filaments to Dilute Suspensions
• Elasticity tunes mechanical stress localization around active topological defects
• Passive defect driven morphogenesis in nematic membranes
• Spontaneous Bending of Hydra Tissue Fragments Driven by Supracellular Actomyosin Bundles
• Defect binding-unbinding transition in active nematic membranes