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Stiffness-dependent active wetting enables optimal collective cell durotaxis


The directed migration of cellular clusters enables morphogenesis, wound healing and collective cancer invasion. Gradients of substrate stiffness direct the migration of cellular clusters in a process called collective durotaxis, but the underlying mechanisms remain unclear. Here we unveil a connection between collective durotaxis and the wetting properties of cellular clusters. We show that clusters of cancer cells dewet soft substrates and wet stiff ones. At intermediate stiffness—at the crossover from low to high wettability—clusters on uniform-stiffness substrates become maximally motile, and clusters on stiffness gradients exhibit optimal durotaxis. Durotactic velocity increases with cluster size, stiffness gradient and actomyosin activity. We demonstrate this behaviour on substrates coated with the cell–cell adhesion protein E-cadherin and then establish its generality on substrates coated with extracellular matrix. We develop an active wetting model that explains collective durotaxis in terms of a balance between in-plane active traction and tissue contractility and out-of-plane surface tension. Finally, we show that the distribution of cluster displacements has a heavy tail, with infrequent but large cellular hops that contribute to durotactic migration. Our study demonstrates a physical mechanism of collective durotaxis, through both cell–cell and cell–substrate adhesion ligands, based on the wetting properties of active droplets.

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Fig. 1: Epithelial cell clusters on E-cadherin-coated substrates show optimal motility in the neutral wetting regime.
Fig. 2: Collective durotaxis is optimal in the neutral wetting regime.
Fig. 3: A 3D model of active wetting explains non-monotonic tissue durotaxis.
Fig. 4: Wetting-based durotaxis also occurs on ECM substrates at high contractility.
Fig. 5: Sudden protrusion detachments give rise to long durotactic hops.

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The data that support the findings of this study are available at

Code availability

Analysis procedures and code for implementing the model are available at


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We thank all the members of our groups for their discussions and support. We thank A. Menéndez, S. Usieto and B. Martin for technical assistance and A. Le Roux for helping to produce and purify histidine-tagged mCherry. We also thank E. Sahai for sharing cell lines and plasmids used in this work. Finally, we thank J. F. Abenza, E. Dalaka and T. Golde for their feedback on the manuscript. This paper was funded by the Generalitat de Catalunya (AGAUR SGR-2017-01602 to X.T., AGAUR SGR-2017-1061 to J.C., the CERCA Programme and ‘ICREA Academia’ awards to P.R.-C. and J.C.); the Spanish Ministry for Science and Innovation MICCINN/FEDER (PGC2018-099645-B-I00 to X.T., PID2019-110298GB-I00 to P.R.-C., PID2019-108842GB-C21 to J.C., RTI2018-101256-J-I00 and RYC2019-026721-I to R.S., FPU19/05492 to I.P.-J., FPU15/06516 to M.-E.P.); Fondo Social de la DGA (grupos DGA) to V.G. and J.M.d.l.F.; European Research Council (Adv-883739 to X.T.); Fundació la Marató de TV3 (project 201903-30-31-32 to X.T.); the European Commission (H2020-FETPROACT-01-2016-731957 to P.R.-C. and X.T.); the European Union’s Horizon 2020 research and innovation programme (under the Marie Skłodowska-Curie grant agreement no. 797621 to M.G.-G.); the European Foundation for the Study of Chronic Liver Failure (EF-Clif); and the La Caixa Foundation (LCF/PR/HR20/52400004 to P.R.-C. and X.T.). IBEC is the recipient of a Severo Ochoa Award of Excellence from MINECO. R.S. is a Serra Húnter fellow.

Author information

Authors and Affiliations



M.-E.P., R.S. and X.T. conceived the project. M.-E.P., R.S. and I.C.F. performed experiments. V.G., J.M.d.l.F. and P.R.-C. contributed technical expertise, materials and discussion. I.P.-J., R.A. and J.C. developed the model. M.G.-G. and R.S. developed analysis software. M.-E.P., I.P.-J., R.A., R.S., J.C. and X.T. wrote the manuscript. All authors revised the completed manuscript. R.A., R.S., J.C. and X.T. supervised the project.

Corresponding authors

Correspondence to Ricard Alert, Raimon Sunyer, Jaume Casademunt or Xavier Trepat.

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The authors declare no competing interests.

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Nature Physics thanks Jennifer Mitchel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Characterization of cluster size and contact angle.

a, Distribution of the number of cells per cluster (n = 30 clusters). The high variability was intended in order to study the effect of cluster size on durotaxis. b, Contact angle as a function of stiffness for control cells (red) and for cells treated with 0.5 µg/ml of Y27632 (turquoise). Data are presented as median ± 95% CI estimated by bootstrapping (n = 4-9 clusters for control and n = 8-34 clusters for Y27632).

Extended Data Fig. 2 Functionalization of polyacrylamide gels with oriented E-cadherin extracellular domains (EC1-5).

a, Scheme showing the protocol to covalently attach E-cadherin extracellular domains on the surface of a polyacrylamide gel mimicking its oriented presentation on cell surfaces. Briefly, polyacrylamide gels containing acrylic acid and thus presenting free carboxyl groups were activated with EDC/NHS and incubated with a solution of NTA/Cu2+ complexes (1) aiming to form a covalent amide bond between carboxyl groups in the gels and amino groups from NTA/Cu2+ complexes. Next, gels were incubated with histidine-tagged E-cadherin extracellular domains EC1-5 (2), which spontaneously oriented along NTA/Cu2+ complexes through metal chelation of their poly-histidine tag. A covalent amide bond between histidine-tagged E-cadherin extracellular domains and NTA/Cu2+ complexes was formed upon a second round of EDC/NHS activation (3). Finally, a solution containing imidazole/EDTA was used to rinse/elute non-covalently bound histidine-tagged E-cadherin extracellular domains (4) prior to gel passivation with pLL-g-PEG (5). b, Fluorescence intensity as a readout of protein incorporation in polyacrylamide gels including (+) or omitting (–) steps in the protocol. First row indicates whether gels underwent a second EDC/NHS treatment to covalently bind histidine-tagged GFP to the gels; second row indicates concentration of acrylic acid; third row indicates whether gels were rinsed with imidazole/EDTA to remove non-covalently bound histidine-tagged GFP. c, Adhesion assay performed on A431 cells in the presence of E-Cadherin blocking antibody (DECMA). This assay validates the specificity of our coating. For panels b-c, data are presented as mean ± 95% CI. Differences in panel b were assessed by a post hoc permutational test (two-tailed). P values are shown in Supplementary Tables 5 and 6. Differences in panel d were assessed by a permutation test (two-sided). P value < 2.2 × 10–16. d-e, Fluorescence image of nuclei (labelled with Hoechst) of attached A431 single cells in controls and DECMA-treated A431 single cells, respectively. Scale bar, 500 µm.

Extended Data Fig. 3 3D cluster profile.

Z-stack of A431 clusters expressing LifeAct-mCherry for 0.2, 6, 24 and 200 kPa uniform stiffness gels coated with oriented E-cadherin. Slices are shown with a z-step size of 10 μm. Basal plane is z = 0 μm. Insets indicate zoomed areas of different planes.

Extended Data Fig. 4 Stiffness profile and protein incorporation of shallow and steep gradient gels.

a, Stiffness profile as a function of distance from soft edge for shallow (n = 12, orange) and steep (n = 12, blue) stiffness profiles. The stiffness profile was determined using AFM for every gel (see Methods). Data are presented as mean ± SD. b, Stiffness profile for individual gels (shallow in orange, steep in blue). Note the logarithmic scale on the Stiffness axis for the sake of visualization. c, Normalized fluorescence intensity of histidine-tagged mCherry signal as a readout of protein incorporation as a function of stiffness for shallow and steep gradient gels. Error bars are SE.

Extended Data Fig. 5 Dependence of durotactic velocity on stiffness for clusters within the 40 ± 10 kPa mm-1 gradient range.

Data analyzed include only the positions of the gels where the gradient was 40 ± 10 kPa mm−1, showing that the sharp increase of durotactic velocity with stiffness cannot be accounted for by changes in the gradient. Bin 1 (0 < E ≤ 20 kPa): n = 28 clusters (136 displacements), E’ = 36.8 kPa mm–1. Bin 2 (20 < E ≤ 40 kPa): n = 62 clusters (386 displacements), E’ = 40.5 kPa mm−1. Bin 3 (40 < E ≤ 80 kPa): n = 23 clusters (102 displacements), E’ = 47.8 kPa mm−1. Bin 4 (E > 80 kPa): n = 43 clusters (313 displacements), E’ = 48.8 kPa mm−1. Data includes clusters of all sizes. Data are presented as median ± 95% CI estimated by bootstrapping.

Extended Data Fig. 6 hEGF increases cell contractility and surface tension.

a, Time lapse evolution of the modulus of the traction forces upon addition of 10 ng ml−1 of hEGF and the subsequent addition of 5 µg ml−1 of Y27632 (indicated by vertical dashed lines). Gel stiffness is 6 kPa. b, Cluster area variation during the protocol described in (a). Data in panels a-b are median ± 95% CI estimated by bootstrapping (n = 15 clusters). c-f, In-plane traction forces exerted by a representative cluster before addition of hEGF (c), 1.5 min after the addition of hEGF (d), 3 min after the addition of hEGF (e), and 42 min after the addition of Y27632 (f). g, The normal traction component \(T_z\) increases 2 min after adding hEGF, indicating an increase in surface tension and Laplace pressure. A paired permutation test (two-tailed) indicated a significant increase (n = 13 clusters, P value= 0.0002441). h-i, \(T_z\) maps exerted by a representative cluster before (h) and after (i) the addition of hEGF. Scale bar is 50 µm.

Extended Data Fig. 7 Calculation of contact angle.

Measurement of contact angle θ as a function of the cluster radius (\(R_{{{{\mathrm{sphere}}}}}\)), the contact radius (R) and the cluster height (H). For low wettability (a) and high wettability (b) clusters the calculation varied. All parameters were estimated from high resolution z-stacks of LifeAct-mCherry A431 clusters seeded on E-cadherin substrates.

Supplementary information

Supplementary Information

Supplementary Note and Figs. 1–12.

Supplementary Table 1

Stiffness and corresponding acrylamide/bis-acrylamide concentrations for 1 ml gel premix.

Supplementary Table 2

Approximate experimental measures of the radial Tr and vertical Tz components of traction forces in cell clusters on top of uniform-stiffness substrates of 1 and 6 kPa (Fig. 1i,j) and surface tension estimates for clusters of an apparent size Rsphere ≈ 30 µm (Fig. 1g,h).

Supplementary Table 3

P values for Fig. 1d.

Supplementary Table 4

P values for Fig. 2g.

Supplementary Table 5

P values for Extended Fig. 2b. Groups are defined in Supplementary Table 6.

Supplementary Table 6

Definition of groups A, B, C and D in Supplementary Table 5.

Supplementary Video 1

Representative phase-contrast video of A431 cell cluster migration on uniform-stiffness gels of 0.2, 6, 24 and 200 kPa coated with E-cadherin.

Supplementary Video 2

Z stack movies of representative mCherry-Lifeact A431 cell clusters seeded on uniform-stiffness gels of 0.2, 6, 24 and 200 kPa coated with E-cadherin to illustrate the cluster wetting state.

Supplementary Video 3

Filopodia dynamics of representative A431 cell clusters seeded on uniform-stiffness gels of 6, 24 and 200 kPa coated with E-cadherin.

Supplementary Video 4

Actin retrograde flow of representative A431 cell clusters seeded on uniform-stiffness gels of 6, 24 and 200 kPa coated with E-cadherin.

Supplementary Video 5

Representative phase images of A431 cell cluster migration on a stiffness gradient coated with E-cadherin. Bottom numbers indicate stiffness in kPa.

Supplementary Video 6

Migration of representative mCherry-Lifeact A341 cell clusters on a stiffness gradient (local stiffness = 10 kPa) coated with E-cadherin.

Supplementary Video 7

Representative phase-contrast images of A431 cell cluster migration on a stiffness gradient coated with E-cadherin in controls and in the presence of 0.5 µM Y-27632 (ROCK inhibitor) to partially inhibit cell contractility.

Supplementary Video 8

Representative phase-contrast images of A431 cell cluster migration on uniform-stiffness gels of 0.2, 6, 24 and 200 kPa coated with fibronectin in controls and in the presence of 10 ng ml−1 hEGF to promote cell contractility.

Supplementary Video 9

Representative phase-contrast images of A431 cell cluster migration on a stiffness gradient coated with fibronectin in controls and in the presence of 10 ng ml−1 hEGF to promote cell contractility.

Supplementary Video 10

Phase-contrast video representing an example of a sudden retraction of filopodia triggering a long durotactic hop.

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Pallarès, M.E., Pi-Jaumà, I., Fortunato, I.C. et al. Stiffness-dependent active wetting enables optimal collective cell durotaxis. Nat. Phys. 19, 279–289 (2023).

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