Cell shapes

To measure individual cell shapes, nuclei and beta-catenin were imaged with a Leica DMI8 confocal fluorescence microscope using either a 40x or 63x oil objective (Leica). Cell-cell boundaries labelled by beta-catenin were traced using the semi-automatic, watershed-based SeedWater Segmenter (SWS), as previously described [55]. Briefly, SWS takes an edge-labeled image of a confluent cellular tissue and performs a watershed segmentation based on user-given seeds. Here as input seeds we use the nuclei markers from the DAPI channel. To characterize cell shape and shape variation from cell-to-cell we used the mean of aspect ratio, AR, which was obtained from the moment of inertia tensor, and the standard deviation of the aspect ratio SD(AR), as described previously [1,2]. For example, the more elongated cell shape profile, the higher its AR. In a previous study, we had also used as an index of shape the metric q, which is the cell perimeter divided by the square root of area [2]. Although AR and q were roughly correlated in the data set described here, the observed range of AR spanned roughly four-fold whereas that of q spanned less than two-fold (Supplementary Figure S2). To better resolve small changes in cell shape, here we used AR.