PT - JOURNAL ARTICLE AU - Roman Vetter AU - Marco Kokic AU - Harold Gómez AU - Leonie Hodel AU - Bruno Gjeta AU - Antonella Iannini AU - Gema Villa-Fombuena AU - Fernando Casares AU - Dagmar Iber TI - Aboave-Weaire’s law in epithelia results from an angle constraint in contiguous polygonal lattices AID - 10.1101/591461 DP - 2019 Jan 01 TA - bioRxiv PG - 591461 4099 - http://biorxiv.org/content/early/2019/03/27/591461.short 4100 - http://biorxiv.org/content/early/2019/03/27/591461.full AB - It has long been noted that the cell arrangements in epithelia, regardless of their origin, exhibit some striking regularities: first, the average number of cell neighbours at the apical side is (close to) six. Second, the average apical cell area is linearly related to the number of neighbours, such that cells with larger apical area have on average more neighbours, a relation termed Lewis’ law. Third, Aboav-Weaire’s (AW) law relates the number of neighbours that a cell has to that of its direct neighbours. While the first rule can be explained with topological constraints in contiguous polygonal lattices, and the second rule (Lewis’ law) with the minimisation of the lateral contact surface energy, the driving forces behind the AW law have remained elusive. We now show that also the AW law emerges to minimise the lateral contact surface energy in polygonal lattices by driving cells to the most regular polygonal shape, but while Lewis’ law regulates the side lengths, the AW law controls the angles. We conclude that global apical epithelial organization is the result of energy minimisation under topological constraints.