RT Journal Article
SR Electronic
T1 Aboave-Weaire’s law in epithelia results from an angle constraint in contiguous polygonal lattices
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 591461
DO 10.1101/591461
A1 Roman Vetter
A1 Marco Kokic
A1 Harold Gómez
A1 Leonie Hodel
A1 Bruno Gjeta
A1 Antonella Iannini
A1 Gema Villa-Fombuena
A1 Fernando Casares
A1 Dagmar Iber
YR 2019
UL http://biorxiv.org/content/early/2019/03/27/591461.abstract
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.