Morphogenesis is driven by small cell shape changes that modulate tissue organization. Apical surfaces of proliferating epithelial sheets have been particularly well studied. Currently, it is accepted that a stereotyped distribution of cellular polygons is conserved in proliferating tissues among metazoans. In this work, we challenge these previous findings showing that diverse natural packed tissues have very different polygon distributions. We use Voronoi tessellations as a mathematical framework that predicts this diversity. We demonstrate that Voronoi tessellations and the very different tissues analysed share an overriding restriction: the frequency of polygon types correlates with the distribution of cell areas. By altering the balance of tensions and pressures within the packed tissues using disease, genetic or computer model perturbations, we show that as long as packed cells present a balance of forces within tissue, they will be under a physical constraint that limits its organization. Our discoveries establish a new framework to understand tissue architecture in development and disease.

Ataxia telangiectasia is caused by mutations in ATM and represents a paradigm for cancer predisposition and neurodegenerative syndromes linked to deficiencies in the DNA-damage response. The role of ATM as a key regulator of signalling following DNA double-strand breaks (DSBs) has been dissected in extraordinary detail, but the impact of this process on DSB repair still remains controversial. Here we develop novel genetic and molecular tools to modify the structure of DSB ends and demonstrate that ATM is indeed required for efficient and accurate DSB repair, preventing cell death and genome instability, but exclusively when the ends are irreversibly blocked. We therefore identify the nature of ATM involvement in DSB repair, presenting blocked DNA ends as a possible pathogenic trigger of ataxia telangiectasia and related disorders.