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Cell monolayers sense curvature by exploiting active mechanics and nuclear mechanoadaptation

Abstract

The early development of many organisms involves the folding of cell monolayers, but this behaviour is difficult to reproduce in vitro; therefore, both mechanistic causes and effects of local curvature remain unclear. Here we study epithelial cell monolayers on corrugated hydrogels engineered into wavy patterns, examining how concave and convex curvatures affect cellular and nuclear shape. We find that substrate curvature affects monolayer thickness, which is larger in valleys than crests. We show that this feature generically arises in a vertex model, leading to the hypothesis that cells may sense curvature by modifying the thickness of the tissue. We find that local curvature also affects nuclear morphology and positioning, which we explain by extending the vertex model to take into account membrane–nucleus interactions, encoding thickness modulation in changes to nuclear deformation and position. We propose that curvature governs the spatial distribution of yes-associated proteins via nuclear shape and density changes. We show that curvature also induces significant variations in lamins, chromatin condensation and cell proliferation rate in folded epithelial tissues. Together, this work identifies active cell mechanics and nuclear mechanoadaptation as the key players of the mechanistic regulation of epithelia to substrate curvature.

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Fig. 1: Wavy epithelial monolayers on corrugated polyacrylamide hydrogels.
Fig. 2: Theoretical modelling of epithelial thickness modulations from substrate curvature.
Fig. 3: Substrate curvature modulates the spatial distribution of nuclei.
Fig. 4: YAP curvature sensing is mediated by nuclear density modulation.
Fig. 5: Composition of nuclear lamina depends on substrate curvature.
Fig. 6: Concave curvature zones lead to lower cell proliferation rate and promote significant chromatin condensation in elongated nuclei.

Data availability

Source data are provided with this paper. Source data for Figs. 26 and Extended Data Figs. 2, 3 and 58 are available for this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The custom codes for modelling and simulation are available from the corresponding authors upon reasonable request.

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Acknowledgements

S.G. acknowledges funding from FEDER Prostem Research Project no. 1510614 (Wallonia DG06), F.R.S.-FNRS Epiforce Research Project no. T.0092.21 and Interreg MAT(T)ISSE project, which is financially supported by Interreg France-Wallonie-Vlaanderen (Fonds Européen de Développement Régional, FEDER-ERDF). This project was supported by the European Research Council under the European Union’s Horizon 2020 Research and Innovation Programme grant agreement 851288 (to E.H.), and by the Austrian Science Fund (FWF) (P 31639; to E.H.). L.R.M. acknowledges funding from the Agence National de la Recherche (ANR), as part of the ‘Investments d’Avenir’ Programme (I-SITE ULNE/ANR-16-IDEX-0004 ULNE). This work benefited from ANR-10-EQPX-04-01 and FEDER 12001407 grants to F.L. W.D.V. is supported by the Research Foundation Flanders (FWO 1516619N, FWO GOO5819N, FWO I003420N, FWO IRI I000321N) and is member of the Research Excellence Consortium µNEURO at the University of Antwerp. M.L. is financially supported by FRIA (F.R.S.-FNRS). M.S. is a Senior Research Associate of the Fund for Scientific Research (F.R.S.-FNRS) and acknowledges EOS grant no. 30650939 (PRECISION). Sketches in Figs. 1a and 5e and Extended Data Fig. 9 were drawn by C. Levicek.

Author information

Authors and Affiliations

Authors

Contributions

S.G. and M.L. conceived the project and S.G. and E.H. supervised the project. M.L. developed the corrugated hydrogels and performed cell experiments and imaging. S.-L.X. and E.H. developed the theoretical model. M.L., S.-L.X., E.H. and S.G. analysed the data. W.H.D.V. developed the image segmentation algorithm for nuclear detection. L.R.M., M.S. and M.L. performed and analysed the AFM experiments. F.L. contributed resources to the project. The article was written by M.L., S.-L.X., E.H. and S.G., read and corrected by all the authors, and all the authors contributed to the interpretation of the results.

Corresponding authors

Correspondence to Edouard Hannezo or Sylvain Gabriele.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Curvature of corrugated hydroxy-PAAm hydrogels.

(A) Representation of a 3D volume view of a corrugated substrate with a tangent plane (xy, in blue) and two planes of principal curvatures: xz in green (k1 = 1/R) and yz in red (k2 = 0). The Gaussian curvature is k1.k2 = 0. The inset shows a 3D confocal view of a λ30 corrugated epithelial monolayer immunostained for actin (in green) and DNA (in blue). The scale bar is 30 µm. (B) Top: confocal view (xz) of the wavy profile of a corrugated epithelial monolayer (λ30) immunostained for actin (in green) and DNA (in blue). The scale bar is 10 µm. Bottom: Schematic representation of the wavy profile of a corrugated epithelial monolayer composed of concave (in blue), interm. (in green) and convex (in orange) zones. Convex zones correspond to the crest and concave zones to the valley. Interm. zones of zero curvature were located between concave and convex zones and the tangent to the interm. zones was used to determine borders with concave and convex zones. (C) The curvature, C, of convex (crest, in orange) and concave (valley, in blue) zones was determined along the substrate profile (xz, in black) as the reciprocal of the radius (C = 1/R) of the osculating circle having its center lying on the normal line. The substrate profile is characterized by a wavelength λ and an amplitude β.

Extended Data Fig. 2 Corrugations do not affect the actin intensity of epithelial monolayers.

(A) Maximum intensity projection of an epithelial monolayer grown on a flat, λ20 (in grey), λ30 (in red) and λ50 (in blue) hydrogel and stained for F-actin (in green) and nuclei (in blue). Scale bars are 20 µm for flat and λ20, 30 µm for λ30 and 50 µm for λ50. (B) High magnification confocal images of valley and crest zones for λ20, λ30 and λ50 corrugated hydrogels stained for actin (in green) with AlexaFluor 488. (C) 3D volume rendering of a MDCK monolayer grown on a flat hydroxy-PAAm hydrogel coated with FN. Actin is labeled in green with AlexaFluor 488 and DNA in blue with DAPI. The scale bar is 50 µm. (D) Total actin intensity in epithelial tissues grown on flat (dark grey), λ20 (light grey), λ30 (red) and λ50 (blue) hydrogels. n = 8 (flat in black), n = 10 (λ20 in grey), n = 12 (λ30 in red) and n = 5 (λ50 in blue). n.s. is not significant.

Source data

Extended Data Fig. 3 Mean epithelial cell area and polygon class.

Typical maximum intensity projection image of a MDCK monolayer stained for ß-catenin and grown on (A) λ20, (B) λ30 and (C) λ50 corrugated hydrogels and corresponding skeleton image of (D) λ20, (E) λ30 and (F) λ50. Scale bars correspond to 100 µm (λ20 and λ30) and to 50 µm (λ50). (G) Mean cell area and (H) distribution of polygon classes of epithelial tissues grown on flat (black), λ20 (grey), λ30 (red) and λ50 (blue) hydrogels. n = 1100 cells (flat in black), 1500 cells (λ20 in grey), 1700 cells (λ30 in red) and 1050 cells (λ50 in blue), obtained from n = 3, n = 6, n = 5 and n = 3 replicates respectively. (I) Mean cell area versus polygon class of epithelial monolayers grown on flat (black), λ20 (grey) and λ30 (red) hydrogels. n.s. is not significant.

Source data

Extended Data Fig. 4 Schematic of the model and sensitivity analysis.

Equilibrium configuration of a 2D vertex model representing apical and lateral surfaces of an epithelial monolayer attached to a curved substrate. (A) Increasing substrate amplitude, β, or (B) increasing apical tensions, Γa, increased thickness modulations. (C) Simulation of the vertex model on curved substrate with increasing density (4, 6, and 8 cells per wavelength, from top to bottom), showing that increasing density decreases thickness modulations. (D) Simulation of human keratocyte on curved substrate (see Supplementary Note for details), modelled with \(\frac{{{{{\mathrm{{\Gamma}}} }}_a}}{{{{{\mathrm{{\Gamma}}} }}_l}} \approx 5\), showing density modulations even for large wavelengths (top), which are amplified further to the point of crest/top dewetting when doubling the substrate amplitude (middle), or when doubling apical tensions \(\frac{{{{{\mathrm{{\Gamma}}} }}_a}}{{{{{\mathrm{{\Gamma}}} }}_l}} \approx 10\) (bottom). (E) Comparison for the thickness modulation Ω between analytical theory (thin lines) and vertex simulations (dots), for \(\frac{{{{{\mathrm{{\Gamma}}} }}_a}}{{{{{\mathrm{{\Gamma}}} }}_l}} = 5\) (purple), \(\frac{{{{{\mathrm{{\Gamma}}} }}_a}}{{{{{\mathrm{{\Gamma}}} }}_l}} = 2\) (green) and \(\frac{{{{{\mathrm{{\Gamma}}} }}_a}}{{{{{\mathrm{{\Gamma}}} }}_l}} = 1\) (purple), showing good agreement for large wavelengths λ (normalized by average cell thickness Δh, in all panels C–E, we have taken for simplicity average cell thickness Δh = 1and average cell side length 2d = 1), with corrections for small wavelengths. (F) Schematics of contact mechanics model of a nucleus subjected to apical compression, before (left) or after (right) lateral contact. (G–I) Sensitivity analysis of different model parameters/observations. Both full solutions (solid line) and analytic approximations (dashed line) are given (see Supplementary Note for details). We examine the influence of normalized cell height \(\bar h\) on aspect ratio Sn (G) for the nucleus (volume ratio of cell to nucleus \(\bar v = \frac{{V_c}}{{\pi r_0^2}} = 2\) and before lateral contact). We also examine the influence of local thickness gradient on aspect ratio (H) and nuclear offset (I), with \(\bar h = 0.5\), \(\bar d = 1.57\), and tension ratio \(\frac{{{{{\mathrm{{\Gamma}}} }}_a}}{{{{{\mathrm{{\Gamma}}} }}_{n0}}} = 5\). We find on both metrics a sharp transition above a critical value of thickness gradients, which occurs when the nucleus reaches lateral contact (and thus cannot increase its offset but start adopting distorted asymmetric shape because of the asymmetric contact).

Extended Data Fig. 5 Modulation of wavelength and amplitude of corrugated substrates.

(A) Representative 3D confocal image of the spatial localization of the nuclei within an epithelial monolayer grown on a corrugated hydroxy-PAAm hydrogels of 100 µm in wavelength (λ100). The nuclear height is color-coded. (B) From top to bottom: typical confocal profile of an epithelial monolayer grown for 48 h on a corrugated λ100 substrates and stained for actin with phalloidin. Average height profiles along the x position obtained from Z-stack confocal imaging (n=5). Vertex model showing the thickness modulation of the epithelial monolayer with thicker cells on convex zones and thinner ones on concave zones. (C) Modulation of the corrugation amplitude for λ20 (in grey) and λ50 (in blue) substrates to match the amplitude of λ30 (in red) substrates of ~2.3 µm. The amplitude of l20 substrates was increased to ~2.3 µm (λ20/2.3, n=16 with N=3 replicates) and the amplitude of λ50 substrates was decreased to ~2.4 µm (λ20/2.4, n=18 with N=3 replicates) (B) Thickness modulation of the epithelial monolayer for λ20 (in grey) and λ50 (in blue) substrates of different amplitudes. **p < 0.01, ***p < 0.001, ****p < 0.0001 and n.s. not significant.

Source data

Extended Data Fig. 6 Substrate curvature modulates the nuclear area.

(A) Local nuclear projected area normalized by the mean nuclear area of each sample on convex (crest) and concave (valley) zones of λ20 (grey), λ30 (red) and λ50 (blue) substrates. (B) Nuclear density normalized by the mean nuclear density of each sample on convex and concave zones of λ20 (grey), λ30 (red) and λ50 (blue) substrates. 109 ≤ n ≤ 162 nuclei per sample with N=3 replicates for all conditions. **p < 0.01 and ***p < 0.001. (C–E) Local nuclear projected area (normalized by overall mean nuclear area) versus normalized position (x axis normalized by the wavelength, so that 0 and 1 correspond to top/concave regions and 0.5 to bottom/convex regions) for epithelial monolayers grown on (C) λ20, (D) λ30 and (E) λ50 hydrogels, for the best fit parameter of γ = 0.25 μm−1 (see Supplementaty Note for details). Grey squares (λ20), red circles (λ30) and blue triangles (λ50) are experimental data (mean ± S.D.) and plain lines the best fit model. 109 ≤ n ≤ 162 nuclei per sample with 3 replicates for all conditions.

Source data

Extended Data Fig. 7 Nuclear orientation and YAP nuclear export are modulated by substrate concave curvatures.

Mean orientation of the nuclei on (A) convex (crest) and (B) concave (valley) curvature zones of λ20 (in grey), λ30 (in red) and λ50 (in blue) wavy hydrogels. All data are shown as mean ± SD. The number of nuclei is indicated at the bottom of each bar: 170 ≤ n ≤ 368 for concave curvature and 109 ≤ n ≤ 405 for convex curvature. Nuclear to cytoplasmic YAP ratio of nuclei on interm., concave, convex zones of (C) λ20 in grey, (B) λ30 in red and (C) λ50 in blue corrugated hydrogels. Black bars correspond to flat hydrogels. For λ20 n=30 (interm.), n=16 (concave), 24 (convex) and n=50 (flat) obtained from 5 to 7 replicates, for λ30 n=18 (interm.), n=18 (concave), n=9 (convex) and n=50 (flat) obtained from 5 to 9 replicates and for λ50 n=6 (concave), n=7 (convex) and n=50 (flat) obtained from 3 to 5 replicates. All data are shown as mean ± SD. *p < 0.1, **p < 0.01, ***p < 0.001, ****p < 0.0001 and n.s. not significant.

Source data

Extended Data Fig. 8 Finite element simulations of nuclei on curved substrates.

(A) Schematic of an axisymmetric compressed nucleus (in blue) with r and z the coordinates of the axisymmetric nucleus, θ the angle between the local tangent of the nuclear profile and r-axis, db the radius of the contact zone (the contact between nucleus and plane) and s the arclength of the nuclear profile (see Supplementary Note for details). (B) Snapshots of nuclear 3D morphologies in different regions, with the normalized average monolayer thickness \({{{\mathrm{{\Delta}}} }}\bar h = 0.3\). Dependence of (C) the normalized nuclear volume \(\bar V_n\) and (D) the nuclear aspect ratio in x-y plane on \({{{\mathrm{{\Delta}}} }}\bar h\). A nucleus in the concave region is either in contact with the neighboring nucleus (or cell membrane) on the right side, or confined on both sides, with cell side length (along x-axis) proportional to monolayer thickness.

Source data

Extended Data Fig. 9 Large-scale curvature sensing by epithelial monolayers depends on active cell mechanics and nuclear mechanoadaptation.

Schematic representation of the epithelial thickness modulation and the three main nuclear morphologies observed on crest (convex), interm. zones and valleys (concave). Composition of the nuclear lamina depends on substrate curvature, whereas YAP-curvature sensing is mediated by nuclear density modulation. Concave curvature zones lead to lower cell proliferation rate and promote significant chromatin condensation in elongated nuclei.

Extended Data Table 1 Dimensions of the corrugated hydrogels

Supplementary information

Supplementary Information

Supplementary Videos 1–9 and Note.

Reporting Summary

Supplementary Video 1

Three-dimensional confocal volume rendering of a wavy epithelial monolayer grown on a λ20 corrugated hydrogel. F-actin is stained in green with Alexa Fluor 488 and DNA in blue with DAPI.

Supplementary Video 2

Three-dimensional confocal volume rendering of a wavy epithelial monolayer grown on a λ30 corrugated hydrogel. F-actin is stained in green with Alexa Fluor 488 and DNA in blue with DAPI.

Supplementary Video 3

Three-dimensional confocal volume rendering of a wavy epithelial monolayer grown on a λ50 corrugated hydrogel. F-actin is stained in green with Alexa Fluor 488 and DNA in blue with DAPI.

Supplementary Video 4

Three-dimensional confocal volume rendering of a DAPI-stained nucleus (oblate morphology) at the concave zone (crest) of a λ20 corrugated hydrogel.

Supplementary Video 5

Rotated 3D confocal volume rendering of a DAPI-stained nucleus (oblate morphology) at the concave zone (crest) of a λ20 corrugated hydrogel.

Supplementary Video 6

Three-dimensional confocal volume rendering of a DAPI-stained nucleus (asymmetric morphology) at the interm. zone of a λ20 corrugated hydrogel.

Supplementary Video 7

Rotated 3D confocal volume rendering of a DAPI-stained nucleus (asymmetric morphology) at the interm. zone of a λ20 corrugated hydrogel.

Supplementary Video 8

Three-dimensional confocal volume rendering of a DAPI-stained nucleus (prolate morphology) at the convex (valley) zone of a λ20 corrugated hydrogel.

Supplementary Video 9

Rotated 3D confocal volume rendering of a DAPI-stained nucleus (prolate morphology) at the convex (valley) zone of a λ20 corrugated hydrogel.

Source data

Source Data Fig. 2

Experimental and theoretical data.

Source Data Fig. 3

Experimental and theoretical data.

Source Data Fig. 4

Experimental data.

Source Data Fig. 5

Experimental Data

Source Data Fig. 6

Theoretical and experimental data.

Source Data Extended Data Table. 1

Experimental data.

Source Data Extended Data Fig. 2

Experimental data.

Source Data Extended Data Fig. 3

Experimental data.

Source Data Extended Data Fig. 5

Experimental data.

Source Data Extended Data Fig. 6

Experimental and theoretical data.

Source Data Extended Data Fig. 7

Experimental data.

Source Data Extended Data Fig. 8

Theoretical data.

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Luciano, M., Xue, SL., De Vos, W.H. et al. Cell monolayers sense curvature by exploiting active mechanics and nuclear mechanoadaptation. Nat. Phys. 17, 1382–1390 (2021). https://doi.org/10.1038/s41567-021-01374-1

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