The shape of the cells is defined by the lengths of apical a i ( red), basal b i ( blue), and lateral ℓ k ( green) surfaces. Each cell is represented by a polygon with four vertices denoted by solid circles. Morphogenesis of epithelial tissues in the absence of boundary constraints. The mechanical principles revealed in our model could potentially guide future studies on epithelial folding in diverse systems.Ĭopyright © 2017. Such cell deformation characteristics are verified via experimental measurements for a canonical folding process driven by apical modulation, indicating that our theory could be used to infer the underlying folding mechanisms based on experimental data. At the cellular scale, how cells change shape depends on their initial aspect ratios and the modulation mechanisms. These characteristic tissue shapes remain unchanged when subject to mechanical perturbations from the surroundings, illustrating that the autonomous folding is robust against environmental variabilities. Apical modulation sculpts epithelia into shallow and V-shaped folds, whereas basal-lateral modulation generates deep and U-shaped folds. We show that active modulation of intracellular mechanics along the basal-lateral as well as the apical surfaces is capable of inducing fold formation in the absence of buckling instability. Here we describe a simple and general theoretical model for the autonomous folding of monolayered epithelial sheets. Although substantial efforts have been devoted to identifying molecular mechanisms underlying epithelial folding, far less is understood about how forces deform individual cells to sculpt the overall sheet morphology. During embryonic development, epithelial sheets fold into complex structures required for tissue and organ functions.
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