The ratio of lumen coalescence to cell division times controls the monolumen or multilumen phenotypes. (A) We treated cysts with aPKC-PSi to induce polarity disruption and spatially disordered spindle positioning. Cells were seeded in growth medium supplemented with 50 µM aPKC-PSi, and fixed 3 d later. Confocal scans for cysts treated with aPKC-PSi, which lack control over mitotic spindle positioning; stained for β-catenin (green), labeling cell membranes; and ZO-1 (white) and PCX/gp135 (red), labeling luminal interfaces. Notice the multilumen morphology. Time from seeding: 3 d. Bar, 10 µm. (B) 3D reconstructions of the cyst in A from the full set of confocal sections. Several disconnected lumens are visible in the cross-section (right). Bar, 10 µm. (C) Mean number of luminal volumes and fraction of cysts with single lumen/multiple lumen phenotypes (inset), obtained from numerical simulations as a function of the tightness of the control over orientation of the cleavage plane. ϕ = 0°, mitotic planes always orthogonal to the luminal surface. ϕ = 90°, division planes chosen isotropically in three dimensions. Note that even for ϕ = 0°, it is still possible to get more than one lumen. Simulated cysts have 32 cells. Error bars indicate standard deviations. (D) Numerical simulation of a multiple-lumen phenotype. The cleavage plane has been chosen at random, isotropically in 3D space. Equivalent time from seeding is around 5 d. (E) Mean fraction of cysts with single lumen/multiple lumen phenotypes (red/blue), obtained from numerical simulations as a function of the duplication time τ, for different levels of the control over the orientation of the cleavage plane. The dynamics of several cysts were simulated for four rounds of division, and the fraction of normal cysts in the population was measured at the end of the simulation (16 cells), corresponding approximately to day 3 in the experiments. The duplication time is rescaled with τ₀, which corresponds to normal MDCK cysts (20 degrees of error on spindle positioning and 30% of normal phenotype). For τ/τ₀ ≫ 1 (cell division slower than control), eventually 100% of the cysts are normal, regardless of cell division orientation. For τ/τ₀, slightly smaller than unity, the emergence of aberrant phenotypes is strongly increased, even in the case of perfect spindle positioning. (F) We numerically simulated the relaxation of a multiluminal cyst grown with aberrant spindle positioning to the monolumen configuration, with blocked cell divisions. Here we plot the time needed to reach the monolumen rescaled by the division time as a function of the number of cells, n_cells. As expected, this increases with the size of the aggregates, as more microlumens are generated. (G) Cartoon illustrating how the process of lumen coalescence can take place with no alteration in the total extent of lateral surfaces, and therefore without changing the energy defined in Eqs. 1 and 2. (H) To show the effect of cell division on lumen coalescence in numerical simulations, we grew cysts starting from a single cell with different division rates. Cysts are grown with normal, i.e., correctly oriented, cell divisions. During time, cells divide and form microlumens that tend to coalesce. Faster cell division rates do not allow lumens to coalesce, independently of polarity. Error bars indicate standard deviations. (I) Aphidicolin treatment rescues the multilumen phenotype induced by aPKC perturbation. To check whether the predictions of our model on the slowdown of cell division were correct, we fixed cysts at day 4 and experimented with several treatments. Cysts were grown with aPKC-PSi from seeding (aPKC-PSi), with both aPKC-PSi and Aphidicolin (aPKC-PSi+Aph), or were treated with aPKC-PSi for 2 d, then washed and either left untreated (aPKC-PSi WO d2) or treated with Aphidicolin (aPKC-PSi WO+Aph). Each percentage is obtained by means of the indicated number of independent experiments, for a total number of analyzed cysts reported in the top y axis. aPKC-PSi–treated cysts show a significant decrease in monoluminal cysts (aPKC-PSi [52.2 ± 6.1] vs. control [73.4 ± 3.8]; p-value, 1.5 × 10⁻¹²). Quadruplicate experiments of aPKC-PSi treatment and Aphidicolin show a significant shift toward the control situation, i.e., the number of monolumens increases (aPKC-PSi vs. aPKC-PSi+Aph [66.1 ± 1.4]; p-value, 9.8 × 10⁻¹⁰). Washing out aPKC-PSi restores the normal level of mono- versus multiluminal cysts (aPKC-PSi vs. aPKC-PSi WO [67.0 ± 3.7]; p-value, 7.5 × 10⁻⁷). Aphidicolin given for 2 d after the washout was similar to the washout alone (aPKC-PSi vs. aPKC-PSi WO+Aph [66.2 ± 4.7]; p-value, 1.5 × 10⁻⁵). Statistical significance was assessed by means of a two-tailed Fisher test on 2 × 2 contingency tables containing mono- and multilumen counts and indicated treatments. Values are indicated as percentage means of the independent experiments ± standard deviation. N indicates total number of analyzed cysts and n indicates number of biological replicates; n = 2 + 2 indicates two biological replicates and two technical replicates. In the legend, “Mixed polarity” indicates cysts with gp135/PCX localized to the exterior surface of the cyst, where the cell membrane contacts the ECM. “Lumen” refers to cysts with centrally localized lumens, scored on the basis of the localization of gp135/PCX. “AMIS” refers to cysts that exhibit an accumulation of gp135/PCX in vesicular structures that underlie the membrane where the lumen will develop.