Fig. 2: Misalignment between cell orientation and stress in experiments and simulations.
a Definition of the misalignment angle θ between the shape orientation axis n, and the principal axis of contractile stress m. b Distribution of the misalignment angle θ. Red/blue colouring denotes contractile (θ < 45o)/extensile (θ > 45o) values. The distribution contains data from 11 independent MDCK islands and all time points. The black dotted line shows the result from the simulation. c Left: Tissue snapshot with the cell orientation field n shown as black lines on top of a colour map distinguishing contractile (red) and extensile (blue) regions. Topological defects in the cell orientation are indicated by yellow (+1/2) and green (−1/2) symbols. Right: Snapshots of a region of the same tissue taken 15 min apart showing the evolution of extensile clusters. The time axis is from left to right. d Experimental time average of the area fraction of contractile (red) and extensile (blue) cells. The crosses show the results from simulations. The time-averaged area fraction of extensile cells is 27 ± 4% (28 ± 2%) in experiments (simulations). e Defects are preferentially found in the vicinity of boundaries between extensile and contractile regions. A spatial and temporal average on all frames of the experiments and simulations show that interface domains make up about 18 ± 2% of the tissue area fraction in the experiments and about 21 ± 3% of the area fraction in simulations. However, 86 ± 2% (82 ± 7.9%) of defects lie within interface domains in experiments (simulations). In (d, e) the experimental data shows the behaviour over 11 different experiments over 12 h (48 data points in each experiment). The simulation data is calculated over all frames of the simulations after the steady state is reached (150 data points). The error bars represent the standard deviation. f Snapshot from simulations with the cell orientation field n shown as black lines on top of a colour map distinguishing contractile (red) and extensile (blue) regions. Topological defects in the cell orientation are indicated by yellow arrow (+1/2) and green trefoil (−1/2) symbols. The time axis is from left to right. Source data are provided as a Source Data file in ref. 45.
