A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia.

Epithelial cell organization and the mechanical stability of tissues are closely related. In this context, it has been recently shown that packing optimization in bended or folded epithelia is achieved by an energy minimization mechanism that leads to a complex cellular shape: the "scutoid". Here, we focus on the relationship between this shape and the connectivity between cells. We use a combination of computational, experimental, and biophysical approaches to examine how energy drivers affect the three-dimensional (3D) packing of tubular epithelia. We propose an energy-based stochastic model that explains the 3D cellular connectivity. Then, we challenge it by experimentally reducing the cell adhesion. As a result, we observed an increment in the appearance of scutoids that correlated with a decrease in the energy barrier necessary to connect with new cells. We conclude that tubular epithelia satisfy a quantitative biophysical principle that links tissue geometry and energetics with the average cellular connectivity.

Author Correction: Scutoids are a geometrical solution to three-dimensional packing of epithelia.

The original version of this Article contained an error in ref. 39, which incorrectly cited 'Fristrom, D. & Fristrom, J. W. in The Development of Drosophila melanogaster (eds. Bate, M. & Martinez-Arias, A.) II, (Cold spring harbor laboratory press, 1993)'. The correct reference is 'Condic, M.L, Fristrom, D. & Fristrom, J.W. Apical cell shape changes during Drosophila imaginal leg disc elongation: a novel morphogenetic mechanism. Development 111: 23-33 (1991)'. Furthermore, the last sentence of the fourth paragraph of the introduction incorrectly omitted citation of work by Rupprecht et al. The correct citation is given below. These errors have now been corrected in both the PDF and HTML versions of the Article. Rupprecht, J.F., Ong, K.H., Yin, J., Huang, A., Dinh, H.H., Singh, A.P., Zhang, S., Yu, W. & Saunders, T.E. Geometric constraints alter cell arrangements within curved epithelial tissues. Mol. Biol. Cell 28, 3582-3594 (2017).

Scutoids are a geometrical solution to three-dimensional packing of epithelia.

As animals develop, tissue bending contributes to shape the organs into complex three-dimensional structures. However, the architecture and packing of curved epithelia remains largely unknown. Here we show by means of mathematical modelling that cells in bent epithelia can undergo intercalations along the apico-basal axis. This phenomenon forces cells to have different neighbours in their basal and apical surfaces. As a consequence, epithelial cells adopt a novel shape that we term "scutoid". The detailed analysis of diverse tissues confirms that generation of apico-basal intercalations between cells is a common feature during morphogenesis. Using biophysical arguments, we propose that scutoids make possible the minimization of the tissue energy and stabilize three-dimensional packing. Hence, we conclude that scutoids are one of nature's solutions to achieve epithelial bending. Our findings pave the way to understand the three-dimensional organization of epithelial organs.