The Harvard group first confirmed that epithelial neighbors did not easily reassort their contacts, even during a cell division. They then constructed a model that predicted the probability that a daughter cell would have a particular number of sides after assigning a cell division plane randomly.
Where the division plane hit the side of a neighboring cell, that neighboring cell gained an extra side. This gain was balanced in the dividing cell: typically its two progeny had less than twice the number of sides than the parent. This to-and-fro of sides drives the system to an equilibrium with a very specific distribution of cells, with hexagons the most abundant. The relative numbers of these shapes as predicted by the model was matched almost precisely by the shapes seen in real epithelia.
“If it didn't [emerge this way], maybe it would be very difficult for the cell to proliferate rapidly,” says Nagpal, because the cells would have to reassort to regain stable topologies. The Harvard group now plans to add assumptions about cell volume and side lengths to the model, which will allow predictions about how changes in cell proliferation can change the shape of a tissue.