Epithelial monolayers exhibit higher cell extrusion rates in negatively curved valleys of hemi-cylindrical wave substrates.

(A-C) SEM images of cylindrical wave structures with half-periods 200, 100 and 50 μm. Scale-bar: 100 μm. (D-F) Phase contrast images of confluent MDCK monolayers on 200, 100 and 50 μm waves, 24 hours after seeding. (G) Time-lapse excerpts demonstrating extrusion event registration (cyan objects) using our trained neural network. (H) Boxplot of extrusion events registered over 24 hours, on 200, 100 and 50 μm cylindrical waves, and on 200, 100 and 50 μm rectangular waves for comparison. Box shows the interquartile range (IQR) while whiskers are 1.5×IQR. Detailed statistics can be found in Supplementary File 2. (I) Multi-channel time-lapse excerpts of cells incubated with activated caspase 3/7 reporter (false green over phase contrast), on flat, hill and valley regions of a 100 μm wave: fluorescence indicate dying cells. Scale-bars (unless otherwise stated): 50 μm.

Osmosis induced basal hydraulic stress is linked to cell extrusions.

(A) Confluent MDCK II monolayers form fluid-filled domes (arrows) in wave valleys when cultured for over 48 hours. Scale-bar: 100 μm. (B) scatterplot of valley (green) and hill (orange) region dome-accumulation 24-48 hours into imaging for 3 independent samples (connecting lines are eye-guides). (C) Boxplot of extrusions per cell over 24 hours on 100 μm cylindrical waves, with monolayers subjected to osmolarity perturbations that included the addition of 4.1 wt. % sucrose, 1 % DMSO, 0.4 wt. % NaCl, 25 % water, and 25 % PBS. Boxes show the interquartile ranges (IQR) while whiskers represent 1.5×IQR. Detailed statistics can be found in Supplementary File 3. (D) Bright-field/RICM time-lapse excepts showing dynamic basal fluid spaces whose motion (direction encoded colored paths) corresponded with the direction of focal adhesion (dark streaks e.g. indicated by white arrow) disassembly. (E) Bright-field/RICM time-lapse excepts showing the accumulation of basal fluid (asterisks) when iso-osmolarity was reinstated (at 180 min) in hyper-osmotically pre-conditioned monolayers. (F) Plot of the image histograms against time showing an increase in grey values as iso-osmolarity was restored; this indicates a general increase in basal-to-substrate separations with decreasing apical media osmolarity. (G) Boxplot of histogram median grey-values from (F) averaged separately over the duration of hyper- and iso-osmolarity treatments. Detailed statistics can be found in Supplementary File 4-supplementary file 4a. (H) Representative max-projected RICM z-stacks of flat, hill and valley regions (before calibrating against blank substrate intensity differences). (I) Boxplot of histogram median grey values from images such as in (G) after calibrating against blank sample intensity differences and flat-region medians. Detailed statistics can be found in Supplementary File 4-supplementary file 4b. Scale-bars in (D), (E), (H): 20 μm.

Solute permeable hydrogel substrates reduce epithelial cell extrusions, and surface curvature induces symmetry breaking in collective cellular forces.

(A) Time-lapse excerpts showing cell extrusion accumulation on stiff PDMS (control), and on soft silicone (CY52-276) and PAM hydrogel of similar stiffness (scale bar: 50 μm). (B) Boxplot showing the cell extrusion rates from the 3 substrates in (A). Boxes show interquartile ranges (IQR) while whiskers represent 1.5×IQR. Detailed statistics can be found in table S5. (C) Fluorescence cross-section showing nuclei deforming against a wave-hill surface (scale bar: 10 μm). (D) Violin plot of nuclei deformation measure from cells in valleys, hills, and planar regions, and across the dimension conditions: values closer to 1.0 indicate less deviation from an ellipsoid. (E) 3D force-microscopy derived normal stress distribution from a 100 μm wave monolayer: wave profile plotted below. (F) Graph showing the bootstrapped magnitude of calculated stresses along the curved profile. (G) Mean bootstrapped normal stress vectors along the curved profile. In (F) and (G), bootstrapping was performed with 10000 re-samples and the 95 % confidence interval is indicated in the shaded region for each respective color.

Modulation of basal hydraulic stress through media osmolarity and substrate solute permeability regulate cell extrusion via FAK-Akt pathway.

(A) Cell extrusion rates on 100 μm waves in normal, sucrose, and sucrose + 3 μM FAKI14 media. (B) Adding 6 μM FAKI14 leads to cell death that compromised monolayers. Scale-bar: 50 μm. (C) Immunoblots of FAK and Akt proteins in MDCK cells subjected to treatments that lead to varying basal hydraulic stresses for 24 hours; namely, iso-osmotic (control), hyper-(4.1 wt. % sucrose), hypo- (25 % water), iso-osmotic with soft silicone and iso-osmotic with water/solute permeable PAM hydrogel. (D) and (E) Quantification of the relative expression levels of phosphorylated-FAK (tyr397) as a ratio of p-FAK to total FAK and phosphorylated-Akt (Ser473) as a ratio of p-Akt to total Akt, respectively. GAPDH was used as loading control (M ± SD, n = 5). Statistical analysis can be found in summary data in Supplementary File 8. (F) fluorescence images of cell nuclei (false blue), FAK (false red), and p-FAK at tyr397 (false green) on flat, hill and valley; the hill and valley images were unwrapped from 3D stacks. Scale-bar: 20 μm. (G) normalized p-FAK/FAK intensities from hill and valley cells. Statistical analysis can be found in summary data in Supplementary File 9. (H) and (I) Schematic of how osmolarity affect basal hydraulic stress and cell survival. (J) Schematic of how curvature induced force differences promote cell survival and death.

Schematic diagram showing the steps for microfabricating smooth periodic hemi-cylindrical wave substrates using glass rods and iterative molding.

Demonstration of achieving dimensions smaller than commercially available glass rods using an iterative stretching and molding method.

a, a stretchy silicone with wave pattern was held stretched for optical curable resin casting. b, a subsequent stretchy silicone was molded against the new resin template created from a; the whole process was repeated until the desired reduction in dimension was reached.

Dimensional characterization of cylindrical and rectangular waves through fluorescent collagen I z-stacks.

a-c, 50, 100, and 200 µm cylindrical waves. d-f, 50, 100, 200 µm rectangular waves. Scale-bars = 50 µm. g and h, dimensions measured: curvature (Xp and Vp); width (Xw and Vw); and height (H). Dimension summary data in Supplementary File 1.

Analysis of cell density 24 hours post seeding.

a-c, surface unwrapped fluorescent z-stacks of Hoechst stained MDCKs on 200, 100 and 50 µm waves. Hills: cyan boxes and Valleys: magenta boxes. Scale-bars: 50 µm. d, boxplot of overall cell densities, determined from nuclei staining, across wave dimensions at the initial time point. e, cell densities in d plotted according to curvature type.

Calculation of the normalized extrusion rate.

a, architecture of the attention-gated residual U-Net. b, example of a manually annotated extrusion event using the sequence of 5 timeframes above and the ground truth binary mask below. c confusion matrix of the machine learning network. d, examples of false negative and false positive registrations. e, Left: bright-field image; Center: prediction from StarDist; Right: overlay of the prediction outline on the bright-field image. Scale-bars: 50 µm.

Calibration of RICM intensities against geometric effects.

a, boxplot showing the reduction of reflected light intensities in hill regions on blank 100 and 200 µm wave substrates. b, boxplot of RICM intensities measured from monolayers over 100 and 200 µm wave substrates calibrated against the average reductions inferred from data in a. This latter result is then further normalized against flat region signals from each sample batch to remove cross-sample variations, giving the final result shown in main-text Figure 2I.

3D force microscopy.

a-c, schematic for the preparation of the gel as well as the cell seeding process. d, 3D-view showing the even distribution of fluorescent beads in the polyacrylamide gel. e, bright field image showing the cut get and the monolayer of cells on the curved substrate. Scale-bar: 500 µm. f, bright field images showing the removal of cells through the addition of 1 % SDS. g, maximum projected side profile of the polyacrylamide gel before (red) and after SDS treatment (green). h, Qualitative validation of the calculated displacements. Left: original fluorescent image showing the bead locations with cells (red) and without cells (green). Right: overlay of the mapped image (green) and the bead image with cells (red). i, 3D-view of the calculated displacements obtained using the two-frame 3D Farneback optical flow method. j, Representative 3D structure and mesh used in the finite element modelling of the polyacrylamide structure. Image used courtesy of ANSYS, Inc. k, 3D-view of the average nodal force obtained by solving the inverse problem. Scale-bars: 50 µm unless otherwise stated.

3D force microscopy validation.

a, shows simulated force field to generate simulated displacements on a 100 µm wave substrate. b, shows force field reconstructed from simulated displacements with noise of a. See MATERIALS AND METHODS for the quantitative comparison of the two force fields.