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.España Ministerio de Ciencia y Tecnología BFU2013-48988-C2-1-P and BFU2016-8079

EpiGraph: an open-source platform to quantify epithelial organization

Here we present EpiGraph, an image analysis tool that quantifies epithelial organization. Our method combines computational geometry and graph theory to measure the degree of order of any packed tissue. EpiGraph goes beyond the traditional polygon distribution analysis, capturing other organizational traits that improve the characterization of epithelia. EpiGraph can objectively compare the rearrangements of epithelial cells during development and homeostasis to quantify how the global ensemble is affected. Importantly, it has been implemented in the open-access platform Fiji. This makes EpiGraph very user friendly, with no programming skills required.España Ministerio de Economia, Industria y Competitividad BFU2016-74975-PEspaña, Programa Ramón y Cajal (PI13/ 01347

EpiGraph: an open-source platform to quantify epithelial organization

Here we present EpiGraph, an image analysis tool that quantifies epithelial organization. Our method combines computational geometry and graph theory to measure the degree of order of any packed tissue. EpiGraph goes beyond the traditional polygon distribution analysis, capturing other organizational traits that improve the characterization of epithelia. EpiGraph can objectively compare the rearrangements of epithelial cells during development and homeostasis to quantify how the global ensemble is affected. Importantly, it has been implemented in the open-access platform Fiji. This makes EpiGraph very user friendly, with no programming skills required.L.M.E. and P.G.-G. were supported by the Ramón y Cajal program (PI13/01347); L.M.E, P.V.-M. and P.G.-G. work was funded by the Ministry of Economy, Industry and Competitiveness grant BFU2016-74975-P co-funded by FEDER funds. P.V.-M. was supported by a contract co-funded by the Asociación Fundación Española contra el Cáncer and the Seville University. A.T. and C.F. were supported by a contract from Sistema Nacional de Garantía Juvenil and Programa Operativo de Empleo Juvenil 2014-2020. R.J.T. was funded by a Medical Research Council Skills Development Fellowship (MR/N014529/1). Y.M. was funded by a Medical Research Council Fellowship (MR/L009056/1), a UCL Excellence Fellowship, a NSFC International Young Scientist Fellowship (31650110472) and a Lister Institute Research Prize Fellowship. This work was also supported by MRC funding to the MRC LMCB University Unit at UCL (award code MC_U12266B). M.T. was funded by a Sir Henry Wellcome Fellowship (Grant No: 103095)