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Collective curvature sensing and fluidity in three-dimensional multicellular systems


Collective cell migration is an essential process throughout the lives of multicellular organisms, for example in embryonic development, wound healing and tumour metastasis. Substrates or interfaces associated with these processes are typically curved, with radii of curvature comparable to many cell lengths. Using both artificial geometries and lung alveolospheres derived from human induced pluripotent stem cells, here we show that cells sense multicellular-scale curvature and that it plays a role in regulating collective cell migration. As the curvature of a monolayer increases, cells reduce their collectivity and the multicellular flow field becomes more dynamic. Furthermore, hexagonally shaped cells tend to aggregate in solid-like clusters surrounded by non-hexagonal cells that act as a background fluid. We propose that cells naturally form hexagonally organized clusters to minimize free energy, and the size of these clusters is limited by a bending energy penalty. We observe that cluster size grows linearly as sphere radius increases, which further stabilizes the multicellular flow field and increases cell collectivity. As a result, increasing curvature tends to promote the fluidity in multicellular monolayer. Together, these findings highlight the potential for a fundamental role of curvature in regulating both spatial and temporal characteristics of three-dimensional multicellular systems.

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Fig. 1: MDCK cells grown on different curvatures and their individual and collective cellular behaviours.
Fig. 2: The multicellular flow field for MDCK cells is more dynamic with larger curvature.
Fig. 3: Alveolospheres derived from human iPSCs confirm that collective cellular behaviour is strongly affected by curvature.
Fig. 4: Curvature-induced bending energy causes higher dynamics in the multicellular flow field.

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Data availability

The data that support the findings are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

MATLAB scripts used in this paper are available from the corresponding author upon reasonable request.


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We acknowledge support from National Institute of General Medical Sciences grant number 1R01GM140108 and MathWorks. M.G. and D.B. are supported by the Sloan Research Fellowship. A.F.P. acknowledges NSERC Discovery and NSERC CRD grants to A. Stolow, the NRC-uOttawa Joint Centre for Extreme Photonics and the Max-Planck-University of Ottawa Centre for Extreme and Quantum Photonics. J.F. acknowledge supports from NHLBI under grant numbers 1R01HL148152 and PO1HL120839. D.N.K. acknowledge support from NIH grant numbers U01HL148692, U01HL134745, U01HL134766 and R01HL095993. iPSC distribution is supported by NIH grant numbers U01TR001810 and N01 75N92020C00005. A.D. and D.B. acknowledge support from the Northeastern University TIER 1 Grant and the Northeastern University Discovery Cluster, and the National Science Foundation DMR-2046683. A.D. also acknowledges support from the Centre for Theoretical Biological Physics at Northeastern University. We also thank C. Deng for helping plot the schematics figures in Fig. 1a,b.

Author information

Authors and Affiliations



W.T. and M.G. designed the experiments. M.G. supervised the project. W.T., J.H., D.A.R., Y.L.H. and H.Y. performed the experiments. W.T. analysed the experimental data. W.T., Y.L.H., A.D. and D.B. developed the MATLAB scripts for image processing and data analysis. A.D. and D.B. performed the simulation. W.T., A.F.P., A.D., J.J.F., D.N.K., D.B. and M.G. wrote the manuscript. All authors edited and approved the manuscript.

Corresponding author

Correspondence to Ming Guo.

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

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Supplementary information

Supplementary Information

Supplementary Figs. 1–10 and details of the simulation model.

Reporting Summary

Supplementary Video 1

Cell migration on fabricated curved and flat surfaces.

Supplementary Video 2

Cell migration in human iPSC-derived lung alveolosphere R= 38 μm.

Supplementary Video 3

Cell migration in human iPSC-derived lung alveolosphere, R = 53 μm.

Supplementary Video 4

Cell migration in human iPSC-derived lung alveolosphere, R= 75 μm.

Supplementary Video 5

Cell migration in human iPSC-derived lung alveolosphere, R = 96 μm.

Supplementary Video 6

Cell migration in human iPSC-derived lung alveolosphere, R = 116 μm.

Supplementary Video 7

Cell migration in human iPSC-derived lung alveolosphere, R = 144 μm.

Supplementary Video 8

Migration trajectories of MDCK cells on a fabricated concave well with a curvature radius of 225 μm.

Source data

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Statistical source data.

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3

Statistical source data.

Source Data Fig. 4

Statistical source data.

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Tang, W., Das, A., Pegoraro, A.F. et al. Collective curvature sensing and fluidity in three-dimensional multicellular systems. Nat. Phys. 18, 1371–1378 (2022).

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