Apico-basal cell intercalations (scutoids) optimize packing and energy expenditure in curved epithelia. Further consequences of this new paradigm of tissue packing remain uncharacterized. In particular, how scutoids modify the 3D cellular connectivity is an open question. This property is crucial for understanding epithelial architecture and is instrumental for regulating the biological function of tissues. Here, we address this problem by means of a computational model of epithelial tubes and a biophysical approach that links geometrical descriptors with the energetic cost required to increase the cellular connectivity. Our results predict that epithelial tubes satisfy a novel quantitative principle: the "Flintstones' law". In short, cellular connectivity increases with tissue thickness/curvature in a logistic way. We confirm experimentally the existence of this principle using Drosophila's salivary glands. Our study provides methodological advances to analyze tissue packing in 3D and, more importantly, unveils a morphogenetic principle with key biological consequences.

A quantitative principle to understand 3D cellular connectivity in epithelial tubes