Cell shape emerges from motion

We perform cell segmentation on images from experimental studies of confluent, mobile cells in epithelial monolayers and show that these systems possess a broad, positively-skewed shape parameter distribution P(A), where A=p²/4πa, p is the perimeter, and a is area of each cell. P(A) is peaked at a value higher than the typical shape parameter A^* ~ 1.15 that occurs for randomly packed, static confluent cell monolayers. The distribution does not arise from a heterogeneous population of cells with different fixed A, nor can it arise from cell shape fluctuations from strains below the elastic limit. Instead, we find that all cells in each monolayer sample A values that span the full shape parameter distribution. We develop a deformable particle model that allows cell perimeter to adapt to local forces during cell motion, and this model recovers P(A) to within $5%$ for both MDCK and HaCaT epithelial cell monolayers. These results emphasize that confluent epithelial monolayers of mobile cells generate a well-defined broad shape parameter distribution that is independent of the initial cell shapes.