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.

Tuneable defect-curvature coupling and topological transitions in active shells

“…6 Furthermore, at large extensile activity, such a vortices-mediated flattening can result in a fusion of the internal leaflet of the shell, which eventually drives a transition from spherical to toroidal topology. Something related has recently be observed by Khoromskaia and Salbreux 72 and in the context of elastic sheets by Pearce et al 22…”

“…6 Furthermore, at large extensile activity, such a vortices-mediated flattening can result in a fusion of the internal leaflet of the shell, which eventually drives a transition from spherical to toroidal topology. Something related has recently be observed by Khoromskaia and Salbreux 72 and in the context of elastic sheets by Pearce et al 22 To better understand the pathway leading to the formation of protrusions, we focused on active nematic shells and showed that, for large extensile activity and after two oscillatory regimes (Fig. 6), protrusions appears as the result of the merging of pairs of +1/2 disclinations into asters.…”

Hydramorphogenesis as phase-transition dynamics

“…To understand these results, we consider a simplified model of the Hydra's tissue, ignoring its bilayer structure and regarding the tissue as a closed 2D surface 38 with a minimal coupling of its curvature to the Ca 2+ field,  , given by the Jackiw-Teitelboim action 39,40 :…”

Morphodynamics of active nematic fluid surfaces

“…Mathematically, the development of theory that couples hydrodynamics to surface geometry has led to many interesting predictions on the role of viscous forces in the ordering and shaping of membranes in both isotropic (Steigmann 1999;Hu, Zhang & Weinan 2007;Arroyo & DeSimone 2009;Rangamani et al 2013;Sahu et al 2020a;Tchoufag, Sahu & Mandadapu 2022) and ordered (Napoli & Vergori 2016;Nestler & Voigt 2022) fluids. Of particular note has been the inclusion of activity, leading to a variety of interesting morphodynamical phenomena and instabilities (Salbreux & Jülicher 2017;Bächer et al 2021;Khoromskaia & Salbreux 2023;Rank & Voigt 2021;Alert 2022;Bell et al 2022;Hoffmann et al 2022;Nestler & Voigt 2022;Salbreux et al 2022;Vafa & Mahadevan 2022) and even some attempts to construct rigorous shell theories of active materials (da Rocha, Bleyer & Turlier 2022). Much of this work has been driven by the desire to develop theories capable of describing the dynamics and morphogenesis of biological tissues and organisms (Jülicher, Grill & Salbreux 2018;Al-Izzi & Morris 2021).…”

“…Of particular note has been the inclusion of activity, leading to a variety of interesting morphodynamical phenomena and instabilities (Salbreux & Jülicher 2017; Bächer et al. 2021; Khoromskaia & Salbreux 2023; Rank & Voigt 2021; Alert 2022; Bell et al. 2022; Hoffmann et al.…”