Relaxation of cortical tension via inhibition of ROCK drives topology toward equilibrium, independent of cell division rate. (A) The table reports the experimentally observed and theoretically predicted topological configurations of a subset of control (top) and (bottom) MDCK cysts treated with Y-27632 to inhibit ROCK activity. Each line of the table represents, for a given number of cells in the cyst (top rows), the number of cells displaying four, five, six, seven, and eight neighbors. The topology of control cysts is never consistent with equilibrium and approaches the nonequilibrium topology for increasing numbers of cells, as expected from the theory. (B) After reconstructing the 3D structure of treated and untreated cysts, we calculated the distance from equilibrium and plotted it as a function of the number of cells. The topology of control cysts (closed blue triangles) is clearly closer to the nonequilibrium distribution, whereas Y-27632–treated cysts (closed red squares) are closer to equilibrium, especially when the number of cells is small. Here Y-27632 is given right after seeding. Open symbols are medians on series of data (n = 0–20, 20–40, 40–80, and 80–100), and lines are a guide to the eye. The data shown are from a total of n = 34 cysts, each containing between 10 and 90 cells, coming from a single experiment. (C) Topology of cysts at different times: untreated (top right), Y-27632 given from seeding (top left), Y-27632 given from day 3 (bottom left), and Aphidicolin given from day 3 (bottom right). Labels: c, control; Y, Y-27632; A, Aphidicolin; 1d/2d/3d, 1/2/3 d; and c3dY1d, untreated for 3 d, then treated with Y-27532 for 1 d; c3dA2d, untreated for 3 d, then treated with Aphidicolin for 2 d. Y-27632–treated cysts (top left) lie systematically in the half plane closer to equilibrium with respect to control cysts (top right) and contain on average a smaller number of cells (at a given time from seeding), due to the slowdown of cell division induced by Y-27632. Each point corresponds to the topology of a single cyst. (D) To account for the differences in topology, different groups of cysts were compared by means of a one-tailed Welch’s test to assess for statistical significance, where the existence of a difference in the mean value of the topology was used as a null hypothesis. Cysts with 20–40 cells (left) and 40–60 cells (right) were grouped and compared. A statistically significant difference is seen between Y-27632–treated (left, n = 7; right, n = 6) and control (left, n = 7; right, n = 4) for any number of cells. As for other treatments, such as Aphidicolin (left, n = 5; right, n = 3) or Y-27632 given from day 3 (left, n = 1; right, n = 2), the topology is different from the Y-27632–treated cysts, resembling the untreated case, albeit not significantly. Asterisks indicate statistical significance: *, P < 0.05; **, P < 0.01; ***, P < 0.001, etc. Error bars indicate standard deviations. (E) The effect of the different treatments on cell division was assessed by means of statistical comparison (Welch’s Test) of different groups. The number of cells in the cysts at day 5 was compared in the different populations. All cases have n = 5 samples. Error bars indicate standard deviations.