Three-dimensional Packing of Curved Epithelia: Biology and Topology meet Physics

Building and shaping tissues and organs relies on the ability of epithelial cells to efficiently pack together. In this context, we recently produced a major breakthrough by showing that epithelial cells display a previously undescribed geometrical shape when tissues are subjected to bending (curvature): the scutoid [1]. This discovery has opened the door to a deeper understanding of morphogenesis. Yet, the consequences of this new paradigm in terms of the 3D cellular organization remains largely uncharacterized. Here we address this problem using a combination of experiments, mathematical analyses, computer simulations, and biophysical approaches. In that context we derive the "Flintstones' Law" [2]: the thickness and curvature of epithelial tubes are linked to the cellular connectivity of the tissue via energetic cues. This principle explains how the topological and physical constraints inherent to living matter contribute to build functional complex shapes and lead to the self-organization of tissues.

[1] P. Gómez-Gálvez et al., Scutoids are a geometrical solution to three- dimensional packing of epithelia, Nature Comm. 9, 2960 (2018)
[2] P. Gómez-Gálvez et al., A quantitative principle to understand 3D self-organization in epithelial tubes, EMBO J (under review)