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# Active superelasticity in three-dimensional epithelia of controlled shape

## Abstract

Fundamental biological processes are carried out by curved epithelial sheets that enclose a pressurized lumen. How these sheets develop and withstand three-dimensional deformations has remained unclear. Here we combine measurements of epithelial tension and shape with theoretical modelling to show that epithelial sheets are active superelastic materials. We produce arrays of epithelial domes with controlled geometry. Quantification of luminal pressure and epithelial tension reveals a tensional plateau over several-fold areal strains. These extreme strains in the tissue are accommodated by highly heterogeneous strains at a cellular level, in seeming contradiction to the measured tensional uniformity. This phenomenon is reminiscent of superelasticity, a behaviour that is generally attributed to microscopic material instabilities in metal alloys. We show that in epithelial cells this instability is triggered by a stretch-induced dilution of the actin cortex, and is rescued by the intermediate filament network. Our study reveals a type of mechanical behaviour—which we term active superelasticity—that enables epithelial sheets to sustain extreme stretching under constant tension.

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## Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request.

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## Acknowledgements

We thank N. Castro for technical assistance; C. Pérez-González, A. Labernadie, R. Sunyer and A. Torres-Sánchez for discussions and G. Charras for providing cells; J. Colombelli, L. Bardia and A. Lladó (IRB) for assistance with laser ablation and photoactivation; N. Borges from Embryotools S.L. for fixation of mouse blastocysts. This work was supported by the Spanish Ministry of Economy and Competitiveness/FEDER (BFU2015-65074-P to X.T., DPI2015-71789-R to M.A., SAF2017-89782-R to N.M., SAF2015-72617-EXP to N.M., RYC-2014-16242 to N.M.), the Generalitat de Catalunya and CERCA program (2014-SGR-927 to X.T., 2017-FI-B1-00068 to E.L., 2014-SGR-1471 to M.A., 2017 SGR 1306 to N.M., ‘ICREA Academia’ award to M.A.), the European Research Council (CoG-616480 to X.T., CoG-681434 to M.A., CoG-617233 to B.L., StG-640525 to N.M.), European Commission (project H2020-FETPROACT-01-2016-731957 to M.A., A.d.C. and X.T.), LABAE16006 to N.M., Instituto de Salud Carlos III (CardioCell, TerCel to N.M.), the Deutsche Forschung Gemeinschaft (SFB 1027 to A.d.C.) and Obra Social ‘La Caixa’. IBEC is the recipient of a Severo Ochoa Award of Excellence from the MINECO.

### Reviewer information

Nature thanks U. Schwarz, M. Théry and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

### Affiliations

1. #### Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute for Science and Technology (BIST), Barcelona, Spain

• Ernest Latorre
• , Laura Casares
• , Manuel Gómez-González
• , Marina Uroz
• , Léo Valon
• , Elena Garreta
• , Nuria Montserrat
• , Marino Arroyo
•  & Xavier Trepat
2. #### LaCàN, Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain

• Ernest Latorre
• , Sohan Kale
•  & Marino Arroyo
3. #### INM-Leibniz Institut für Neue Materialien, Saarbrücken, Germany

• Roshna V. Nair
•  & Aránzazu del Campo
4. #### Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina, Barcelona, Spain

• Nuria Montserrat
•  & Xavier Trepat
5. #### Chemistry Department, Saarland University, Saarbrücken, Germany

• Aránzazu del Campo

8. #### Unitat de Biofísica i Bioenginyeria, Universitat de Barcelona, Barcelona, Spain

• Xavier Trepat
9. #### Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain

• Xavier Trepat

### Contributions

E.L., L.C., M.A. and X.T. conceived the study and designed experiments. E.L. and L.C. performed the experiments with the help of L.V., E.G. and N.M. E.L., M.G.-G. and M.U. developed the 3D traction microscopy algorithm. E.L. and M.G.-G. developed computational analysis tools. E.L. and L.C. processed and analysed the experimental data with the help of M.G.-G. S.K. and M.A. developed the theory and implemented the vertex model. B.L. contributed expertise in the implementation of the micropatterned substrates. R.V.N. and A.d.C. developed the photoactivatable derivative of Cytochalasin D. E.L., M.A. and X.T. wrote the manuscript. All authors helped with the interpretation of the results and commented on the manuscript. M.A. and X.T. supervised the study.

### Competing interests

The authors declare no competing interests.

### Corresponding authors

Correspondence to Marino Arroyo or Xavier Trepat.

## Extended data figures and tables

1. ### Extended Data Fig. 1 The number of cells in the domes does not change significantly over time.

a-c, Confocal xy, yz and xz sections of domes of MDCK–CAAX cells, with rectangular basal shapes and varying size. Scale bar, 100 μm (representative of n = 3 micropatterned substrates). d, Time evolution (0, 60 and 120 min) of a representative dome with a star-shaped footprint. The patterned footprint (yellow) was obtained from images of the fibrinogen-labelled substrate. Each row shows a different z-plane (labelled by dotted yellow lines in the xy profiles in e (n = 3 micropatterned substrates). Scale bar, 50 μm. e, Time evolution (0, 60 and 120 min) of the same star-shaped dome, showing the rare delamination of a single cell (red rectangle) at one tip of the star. Images are maximum intensity projections with confocal xz and yz sections along the yellow dashed lines (n = 3 micropatterned substrates). Scale bar, 50 μm. f, Quantification of the number of cells in circular domes at two time points 12 h apart (n = 4 domes). NS, not significant (P = 0.4571), two-tailed Mann–Whitney test. Data are shown as mean ± s.d.

2. ### Extended Data Fig. 2 Dome response to inhibition of tension and weakening of cell–cell adhesion.

a, Time evolution of surface tension and volume of a representative dome in response to Y27632 (30 μM, added at t = 0 min). b, Cellular areal strain εc as a function of dome nominal areal strain εd during dome swelling. Only a subset of cells is represented and most cells with εc < εd have been omitted for clarity. Coloured lines represent the cells labelled in c. Dashed line represents the relation εc = εd. The inset represents the variance of εc within the dome as a function of εd. c, Maximum intensity projection and xz and yz confocal sections of an epithelial dome of MDCK–CAAX cells before (−1 min) and after (12 min and 26 min) addition of Y27632 (30 μM, added at t = 0 min). The time evolution of coloured cells is depicted in b using the same colour code. Scale bars, 50 μm. Data are representative of n = 3 experiments. d, Maximum intensity projection and corresponding xz and yz profiles, showing the collapse of a dome of MDCK–CAAX cells after treatment with 2 mM EGTA (30 min and 35 min after the addition of EGTA). Data are representative of n = 3 experiments. Scale bar, 50 μm. e, After dome collapse, gaps (red arrowheads) were apparent at tricellular junctions. Scale bar, 10 μm.

3. ### Extended Data Fig. 3 Dome volume dynamics during spontaneous fluctuations.

a, c, Time evolution of the dome volume in experiments that last 12 h (a) and 6 h (c). Cells are MDCK–LifeAct. b, d, Confocal xz sections of domes during these experiments. Data representative of n = 10 experiments. Scale bars, 50 μm.

4. ### Extended Data Fig. 4 Tension–strain relations in MDCK–CAAX and Caco2 cells.

a, Relation between surface tension and areal strain for MDCK–CAAX cells. Data include measurements at different time points from n = 9 domes. The tension–strain relation is qualitatively similar to the one obtained for MDCK–LifeAct cells (Fig. 3e), with small quantitative differences. The solid line and shaded area indicate the mean ± s.d. obtained by binning the data (n = 14 points per bin). b, Image of a representative Caco2-cell dome labelled with BODIPY FL C16 dye (n = 3 micropatterned substrates). Confocal xy, xz and yz sections are shown. Scale bar, 50 μm. c, Relation between surface tension and areal strain for Caco2 cells. Data include measurements at different time points from n = 6 domes. Caco2 cells show a tensional plateau throughout the probed strain range. The solid line and shaded area indicate the mean ± s.d. obtained by binning the data (n = 10 points per bin).

5. ### Extended Data Fig. 5 Dome cells exhibit large strain heterogeneity.

a, Cellular areal strain εc as a function of dome nominal areal strain εd during dome swelling. Only a subset of cells is represented and most cells with εc < εd have been omitted for clarity. Coloured lines represent the cells labelled in b. Dashed line represents the relation εc = εd. The inset represents the variance of εc within the dome as a function of εd. b, Maximum intensity projection of an epithelial dome of MDCK–CAAX cells at four different time points of the swelling event described in a. The time evolution of coloured cells is depicted in a using the same colour code. Scale bars, 50 μm. c, d, represent the same as a, b, for a different dome of MDCK–CAAX cells during slow deflation. e, Coefficient of variation (CV) (defined as standard deviation divided by mean) of MDCK–CAAX cells in a 2D adherent cell monolayer, in weakly inflated domes (20–100% areal strain), and in highly inflated domes (100–150%). The coefficient of variation is a non-dimensional indicator of heterogeneity. The coefficient of variation was calculated by measuring area of 10 cells in n = 7 cell monolayers, n = 7 weakly inflated domes and n = 7 highly inflated domes. **P = 0.0041 (left), **P = 0.0041 (right), two-tailed Mann–Whitney test. Data are shown as mean ± s.d. f, g, Mouse blastocysts (labelled with E-cadherin) exhibiting heterogeneity in cell area in the trophectoderm, particularly during hatching (g) (n = 4). Scale bars, 25 μm.

6. ### Extended Data Fig. 6 Superstretched cells display a lower density of F-actin at the cortical surface.

af, Sum of intensity projection of epithelial domes stained with phalloidin for F-actin. n = 5. Scale bars, 50 μm.

7. ### Extended Data Fig. 7 Inhibition of ARP2/3 does not affect area heterogeneity in domes of MDCK cells.

a, Coefficient of variation of the cell area in domes of MDCK–CAAX cells, treated with CK666 (100 μM for 60 min), compared to control domes. The coefficient of variation is a non-dimensional indicator of heterogeneity. The coefficient of variation was calculated by measuring area of 10 cells in n = 6 domes treated with CK666 and in n = 14 control domes. NS, not significant (P = 0.1256). Two-tailed Mann–Whitney test. Data are shown as mean ± s.d. b, Dome nominal areal strain in domes of MDCK–CAAX cells, treated with CK666 (100 μM for 60 min, n = 6), compared to control domes (n = 14). NS, not significant (P = 0.7043). Two-tailed Mann–Whitney test. Data are shown as mean ± s.d. c, Maximum intensity projections and xz sections of a representative control dome (left) and the same dome treated with CK666 100 μM (60 min). Scale bar, 25 μm.

8. ### Extended Data Fig. 8 Local perturbation of the actin cortex using photoactivatable cytochalasin D increases cell area.

a, Time evolution of the normalized cell area in response to local photoactivation of cytochalasin D (black line, activation at t = 0 min, n = 5 domes; see Methods). The blue line shows the time evolution of control cells (same illumination protocol but no photoactivatable cytochalasin D in the medium, n = 8 domes). The area was normalized to the first time point. Solid lines and shaded areas indicate mean ± s.d. At t = 21 min, normalized cell areas were significantly different (*P = 0.0159, two-tailed Mann–Whitney test). b, Normalized cell area 21 min after photoactivation in three experimental conditions: photoactivated cells (black circles, n = 19 cells from 5 domes), cells subjected to the same illumination protocol but without photoactivatable cytochalasin D in the medium (blue squares, n = 19 cells from 8 domes) and cells with photoactivatable cytochalasin D in the medium but without illumination (red triangles, n = 24 cells from 9 domes). Data include the immediate neighbours of the targeted cells because cytochalasin D quickly diffused after activation. ****P < 0.0001, NS, not significant (P = 0.4130), two-tailed Mann–Whitney test. Data are shown as mean ± s.d. c, Representative photoactivation experiments showing the apex of one dome before (−12 min) and after (6 min and 21 min) photoactivation of the cell marked with a yellow dashed rectangle (n = 5). Top panels show the fluorescently labelled membrane and bottom panels show the SiR–actin channel. Note the increase in cell area and granulation in the SiR–actin channel (white arrowheads), which indicates disruption of the actin cortex. Scale bar, 15 μm. d, Control experiment in which one cell at the apex of the dome (yellow dashed line) was subjected to the illumination protocol of c without photoactivatable cytochalasin D in the medium (n = 8). Top panels show the fluorescently labelled membrane and bottom panels show the SiR–actin channel. Scale bar, 15 μm. See also Supplementary Video 9.

9. ### Extended Data Fig. 9 Intermediate filaments reorganize in superstretched cells.

af, Immunofluorescence micrographs (see Methods)—represented using maximum intensity projection—of domes of MDCK keratin-18–GFP (in green) cells stained for F-actin (phalloidin, red), and nuclei (Hoechst, blue), n = 3. Scale bars, 50 μm. a, d, Zoomed-in area (marked with a dashed white square in b, e) showing that the keratin-18 filament network links neighbouring cells and localizes at cell boundaries (white arrowheads). Scale bars, 10 μm. c, f, Zoomed-in area (marked with a dashed white square in be) showing that keratin-18 filaments are taut (white arrowheads) and have reorganized, with nodes at the cell centre connecting different cells. Scale bars, 10 μm.

10. ### Extended Data Fig. 10 Intermediate filaments stabilize cell shape in superstretched cells.

a, Representative MDCK keratin-18–GFP superstretched cell at the apex of a dome before (0 s) and after (90 s) laser cutting the keratin filament bundle marked in b with a white arrowhead. The yellow line marks the outline of the cell measured with bright-field imaging. Scale bar, 10 μm. b, Magnified view of the region labelled in a with a dotted magenta rectangle. Scale bar, 5 μm. c, Representative MDCK keratin-18–GFP weakly stretched cell at the apex of a dome before (0 s) and after (90 s) laser cutting the keratin filament bundle shown in d. The yellow line marks the outline of the cell measured with bright-field imaging. Scale bar, 10 μm. d, Magnified view of the region labelled in c with a dotted magenta rectangle. The same laser cutting protocol and laser power were used to cut filaments in superstretched and weakly stretched cells. n = 5. Scale bar, 5 μm. See Fig. 4o, p for quantification and statistics.

## Supplementary information

1. ### Supplementary Information

This file contains Supplementary Table 1, Supplementary Notes 1–4 and Supplementary References. Supplementary Table 1: Cell cultures reported to exhibit domes. Supplementary Note 1: Mechanics of a thin axisymmetric membrane under uniform pressure. Supplementary Note 2: Dome hydraulics. Supplementary Note 3: 3D vertex model of epithelial domes. Supplementary Note 4: Surface calculations.

3. ### Video 1 | Dome mechanics during tension inhibition.

Time evolution of tractions on epithelial domes of MDCK–LifeAct cells before (CT) and after 5 min incubation with 30 µM Y-27632, known to reduce tissue tension (n = 3). Time step is 15 min. Scale arrows, 100 Pa. Scale bar, 50 µm.

4. ### Video 2 | Dome mechanics during spontaneous fluctuations.

Time evolution of tractions on epithelial domes of MDCK–LifeAct cells during spontaneous volume fluctuations (n = 13). Time step is 30 min. Scale arrows, 150 Pa. Scale bar, 50 µm.

5. ### Video 3 | Spontaneous fluctuations of an epithelial dome.

Projected view (maximum intensity) of a dome of MDCK–CAAX cells during spontaneous volume fluctuations (= 10). Dome footprint was circular. Time step is 2.5 min. Scale bar, 50 µm.

6. ### Video 4 | Spontaneous fluctuations of an epithelial dome.

Projected view (maximum intensity) of a dome of MDCK–CAAX cells during spontaneous volume fluctuations. Time step is 1 h. Dome footprint was star-shaped (n = 3). Scale bar, 50 µm.

7. ### Video 5 | Strain heterogeneity during spontaneous deswelling of an epithelial dome.

Projected view (maximum intensity) of a dome of MDCK–CAAX cells during spontaneous deswelling (n = 10). Time step is 10 min. Scale bar, 50 µm.

8. ### Video 6 | Strain heterogeneity during spontaneous swelling of an epithelial dome.

Projected view (maximum intensity) of a dome of MDCK–LifeAct cells during spontaneous swelling (n = 6). Time step is 30 min. Scale bar, 50 µm.

9. ### Video 7 | Strain heterogeneity during spontaneous deswelling of an epithelial dome.

Projected view (maximum intensity) and lateral view of a dome of MDCK–CAAX cells during dome deswelling (n = 10). Time step is 10 min. Scale bar, 50 µm.

10. ### Video 8 | Reversible cortical dilution during dome fluctuations.

Projected view (sum of intensity) of a dome of MDCK cell labelled with SiR–actin cells during spontaneous volume fluctuations (n = 3). Time step is 30 min. Scale bar, 25 µm.

11. ### Video 9 | Local perturbation of the actin cortex using photoactivatable Cytochalasin D.

Projected view (maximum intensity) of the apex of a dome of MDCK–CAAX cells (green) labelled with SiR–actin (red) before and after local photoactivation of Cytochalasin D (n = 5). Activation was produced by illumination (405 nm) of the region marked with a white square at t = 0 min. Time step is 3 min. Scale bar, 15 µm.

12. ### Video 10 | Vertex model simulation showing sudden localization of the areal strain during dome swelling.

Computational vertex model simulation accounting for strain-softening due to cortical depletion but not re-stiffening due to intermediate filaments leads to sudden localization of the areal strain in a single cell. The simulation is performed for $${\gamma }_{l,0}/{\gamma }_{ab,0}=0.25$$ and $$\omega =10$$.

13. ### Video 11 | Vertex model simulation of swelling-deswelling events in an epithelial dome.

The enclosed volume was increased to reach a nominal dome strain of 400%, and then decreased until the dome flattens. The simulation parameters are those used in Fig. 4k, q, r and described in Supplementary Note 3. The network of intermediate filaments that re-stiffen the superstretched cells are also shown.

14. ### Video 12 | Vertex model simulation of equibiaxial stretching of a biperiodic epithelial sheet beyond the superelastic transition.

The nominal areal strain of the sheet is increased beyond the high strain phase of individual cells, thus leading to the progressive transition of all cells from low-strain phase to high-strain phase. The intermediate filaments surpassing the activation threshold appear in the superstretched cells. The simulation parameters are those used in Fig. 4k, q, r.

### DOI

https://doi.org/10.1038/s41586-018-0671-4