Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Emergence of bidirectional cell laning from collective contact guidance

Nature Physics volume 20, pages 1324–1331 (2024)Cite this article

Subjects

Abstract

Directed collective cell migration is central to morphogenesis, wound healing and cancer progression. Although the molecular anisotropy of the microenvironment guides this migration, its impact on cell flow patterns remains unexplored. Here we show that subcellular microgrooves elicit a polar mode of collective migration in bidirectional lanes, whose widths reach hundreds of micrometres. This directed form of flocking is observed in vitro with a confluent monolayer of human bronchial epithelial cells whose dynamics is chaotic on featureless substrates. A hydrodynamic theory of active polar fluids and corresponding numerical simulations account for this disorder-to-laning transition and further predict that anisotropic friction associated with the grooves lowers the transition threshold, which we confirm experimentally. Therefore, the microscopic anisotropy of the environment both directs collective cell motion along the substrate easy axis and shapes cell migration patterns. The flow patterns induced by this collective contact guidance are different from those resulting from supracellular confinement, demonstrating that collective migration is impacted by the different length scales of the microenvironment. Our findings offer a strategy for directing cells to specific geometries and functions in tissue engineering applications such as organoid morphogenesis.

Access through your institution
Buy or subscribe

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Flows within HBEC monolayers on grooved substrates self-organize in a bidirectional laning pattern.
Fig. 2: Development of the laning pattern.
Fig. 3: The laning pattern relies on cell polarity but not on cell–cell adhesion nor on cell contractility.
Fig. 4: Anisotropic friction results in bidirectional laning of active polar fluids.

Similar content being viewed by others

Data availability

The data that support the findings of this study and are not in the Article, Extended Data Figs. 1–10 or the Supplementary Information are available via Zenodo at https://doi.org/10.5281/zenodo.10887254 (ref. 62).

References

  1. Scarpa, E. & Mayor, R. Collective cell migration in development. J. Cell Biol. 212, 143–155 (2016).

    Article  Google Scholar 

  2. Friedl, P. & Gilmour, D. Collective cell migration in morphogenesis, regeneration and cancer. Nat. Rev. Mol. Cell Biol. 10, 445–457 (2009).

    Article  Google Scholar 

  3. Alexander, S., Weigelin, B., Winkler, F. & Friedl, P. Preclinical intravital microscopy of the tumour–stroma interface: invasion, metastasis, and therapy response. Curr. Opin. Cell Biol. 25, 659–671 (2013).

    Article  Google Scholar 

  4. Sarna, M., Wybieralska, E., Miekus, K., Drukala, J. & Madeja, Z. Topographical control of prostate cancer cell migration. Mol. Med. Rep. 2, 865–871 (2009).

    Google Scholar 

  5. Thrivikraman, G. et al. Cell contact guidance via sensing anisotropy of network mechanical resistance. Proc. Natl Acad. Sci. USA 118, e2024942118 (2021).

    Article  Google Scholar 

  6. Chanrion, M. et al. Concomitant Notch activation and p53 deletion trigger epithelial-to-mesenchymal transition and metastasis in mouse gut. Nat. Commun. 5, 5005 (2014).

    Article  ADS  Google Scholar 

  7. Erdogan, B. et al. Cancer-associated fibroblasts promote directional cancer cell migration by aligning fibronectin. J. Cell Biol. 216, 3799–3816 (2017).

    Article  Google Scholar 

  8. Sherwood, D. R. Basement membrane remodeling guides cell migration and cell morphogenesis during development. Curr. Opin. Cell Biol. 72, 19–27 (2021).

    Article  Google Scholar 

  9. Curtis, A. & Wilkinson, C. Topographical control of cells. Biomaterials 18, 1573–1583 (1997).

    Article  Google Scholar 

  10. Leclech, C. & Villard, C. Cellular and subcellular contact guidance on microfabricated substrates. Front. Bioeng. Biotechnol. 8, 551505 (2020).

    Article  Google Scholar 

  11. Nguyen, A. T., Sathe, S. R. & Yim, E. K. F. From nano to micro: topographical scale and its impact on cell adhesion, morphology and contact guidance. J. Phys.: Condens. Matter 28, 183001 (2016).

    ADS  Google Scholar 

  12. Provenzano, P. P. et al. Collagen density promotes mammary tumor initiation and progression. BMC Med. 6, 11 (2008).

    Article  Google Scholar 

  13. Clark, A. G. & Vignjevic, D. M. Modes of cancer cell invasion and the role of the microenvironment. Curr. Opin. Cell Biol. 36, 13–22 (2015).

    Article  Google Scholar 

  14. Paul, C. D., Mistriotis, P. & Konstantopoulos, K. Cancer cell motility: lessons from migration in confined spaces. Nat. Rev. Cancer 17, 131–140 (2017).

    Article  Google Scholar 

  15. Leclech, C. & Barakat, A. I. Is there a universal mechanism of cell alignment in response to substrate topography? Cytoskeleton 78, 284–292 (2021).

    Article  Google Scholar 

  16. Liu, R. et al. Diversity of collective migration patterns of invasive breast cancer cells emerging during microtrack invasion. Phys. Rev. E 99, 062403 (2019).

    Article  ADS  Google Scholar 

  17. Alexander, S., Koehl, G. E., Hirschberg, M., Geissler, E. K. & Friedl, P. Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model. Histochem. Cell Biol. 130, 1147–1154 (2008).

    Article  Google Scholar 

  18. Hakim, V. & Silberzan, P. Collective cell migration: a physics perspective. Rep. Prog. Phys. 80, 076601 (2017).

    Article  ADS  Google Scholar 

  19. Lee, G. et al. Contact guidance and collective migration in the advancing epithelial monolayer. Connect. Tissue Res. 59, 309–315 (2018).

    Article  Google Scholar 

  20. Dalton, B. A. et al. Modulation of epithelial tissue and cell migration by microgrooves. J. Biomed. Mater. Res. 56, 195–207 (2001).

    Article  Google Scholar 

  21. Lawrence, B. D., Pan, Z. & Rosenblatt, M. I. Silk film topography directs collective epithelial cell migration. PLoS ONE 7, e50190 (2012).

    Article  ADS  Google Scholar 

  22. Londono, C. et al. Nonautonomous contact guidance signaling during collective cell migration. Proc. Natl Acad. Sci. USA 111, 1807–1812 (2014).

    Article  ADS  Google Scholar 

  23. Leclech, C. et al. Topography-induced large-scale antiparallel collective migration in vascular endothelium. Nat. Commun. 13, 2797 (2022).

    Article  ADS  Google Scholar 

  24. Haga, H., Irahara, C., Kobayashi, R., Nakagaki, T. & Kawabata, K. Collective movement of epithelial cells on a collagen gel substrate. Biophys. J. 88, 2250–2256 (2005).

    Article  ADS  Google Scholar 

  25. Blanch-Mercader, C. et al. Turbulent dynamics of epithelial cell cultures. Phys. Rev. Lett. 120, 208101 (2018).

    Article  ADS  Google Scholar 

  26. Garcia, S. et al. Physics of active jamming during collective cellular motion in a monolayer. Proc. Natl Acad. Sci. USA 112, 15314–15319 (2015).

    Article  ADS  Google Scholar 

  27. Park, J.-A. et al. Unjamming and cell shape in the asthmatic airway epithelium. Nat. Mater. 14, 1040–1048 (2015).

    Article  ADS  Google Scholar 

  28. Guillamat, P., Ignés-Mullol, J. & Sagués, F. Control of active liquid crystals with a magnetic field. Proc. Natl Acad. Sci. USA 113, 5498–5502 (2016).

    Article  ADS  Google Scholar 

  29. Thijssen, K., Metselaar, L., Yeomans, J. M. & Doostmohammadi, A. Active nematics with anisotropic friction: the decisive role of the flow aligning parameter. Soft Matter 16, 2065–2074 (2020).

    Article  ADS  Google Scholar 

  30. Hetrick, B., Han, M. S., Helgeson, L. A. & Nolen, B. J. Small molecules CK-666 and CK-869 inhibit actin-related protein 2/3 complex by blocking an activating conformational change. Chem. Biol. 20, 701–712 (2013).

    Article  Google Scholar 

  31. Lee, P. & Wolgemuth, C. Advent of complex flows in epithelial tissues. Phys. Rev. E 83, 061920 (2011).

    Article  ADS  Google Scholar 

  32. Blanch-Mercader, C. et al. Effective viscosity and dynamics of spreading epithelia: a solvable model. Soft Matter 13, 1235–1243 (2017).

    Article  ADS  Google Scholar 

  33. Brotto, T., Caussin, J. B., Lauga, E. & Bartolo, D. Hydrodynamics of confined active fluids. Phys. Rev. Lett. 110, 038101 (2013).

    Article  ADS  Google Scholar 

  34. Kumar, N., Soni, H., Ramaswamy, S. & Sood, A. K. Flocking at a distance in active granular matter. Nat. Commun. 5, 4688 (2014).

    Article  ADS  Google Scholar 

  35. Tamiello, C., Buskermolen, A. B. C., Baaijens, F. P. T., Broers, J. L. V. & Bouten, C. V. C. Heading in the right direction: understanding cellular orientation responses to complex biophysical environments. Cell. Mol. Bioeng. 9, 12–37 (2016).

    Article  Google Scholar 

  36. Maitra, A., Srivastava, P., Marchetti, M. C., Ramaswamy, S. & Lenz, M. Swimmer suspensions on substrates: anomalous stability and long-range order. Phys. Rev. Lett. 124, 28002 (2020).

    Article  ADS  Google Scholar 

  37. Heinrich, M. A. et al. Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia. eLife 9, e58945 (2020).

    Article  Google Scholar 

  38. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I. & Shochet, O. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  39. Giavazzi, F. et al. Flocking transitions in confluent tissues. Soft Matter 14, 3471–3477 (2018).

    Article  ADS  Google Scholar 

  40. Smeets, B. et al. Emergent structures and dynamics of cell colonies by contact inhibition of locomotion. Proc. Natl Acad. Sci. USA 113, 14621–14626 (2016).

    Article  ADS  Google Scholar 

  41. Zhao, Y., Ihle, T., Han, Z., Huepe, C. & Romanczuk, P. Phases and homogeneous ordered states in alignment-based self-propelled particle models. Phys. Rev. E 104, 044605 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  42. Vedula, S. R. K. et al. Emerging modes of collective cell migration induced by geometrical constraints. Proc. Natl Acad. Sci. USA 109, 12974–12979 (2012).

    Article  ADS  Google Scholar 

  43. Eckert, J., Ladoux, B., Mège, R.-M., Giomi, L. & Schmidt, T. Hexanematic crossover in epithelial monolayers depends on cell adhesion and cell density. Nat. Commun. 14, 5762 (2023).

  44. Friedl, P., Locker, J., Sahai, E. & Segall, J. E. Classifying collective cancer cell invasion. Nat. Cell Biol. 14, 777–783 (2012).

    Article  Google Scholar 

  45. Cetera, M. et al. Epithelial rotation promotes the global alignment of contractile actin bundles during Drosophila egg chamber elongation. Nat. Commun. 5, 5511 (2014).

    Article  ADS  Google Scholar 

  46. Duclos, G. et al. Spontaneous shear flow in confined cellular nematics. Nat. Phys. 14, 728–732 (2018).

    Article  Google Scholar 

  47. Deforet, M., Hakim, V., Yevick, H. G., Duclos, G. & Silberzan, P. Emergence of collective modes and tri-dimensional structures from epithelial confinement. Nat. Commun. 5, 3747 (2014).

    Article  ADS  Google Scholar 

  48. Gjorevski, N. et al. Tissue geometry drives deterministic organoid patterning. Science 375, eaaw9021 (2022).

    Article  Google Scholar 

  49. Karzbrun, E. et al. Human neural tube morphogenesis in vitro by geometric constraints. Nature 599, 268–272 (2021).

    Article  ADS  Google Scholar 

  50. Poujade, M. et al. Collective migration of an epithelial monolayer in response to a model wound. Proc. Natl Acad. Sci. USA 104, 15988–15993 (2007).

    Article  ADS  Google Scholar 

  51. Laurent, J. et al. Convergence of microengineering and cellular self-organization towards functional tissue manufacturing. Nat. Biomed. Eng. 1, 939–956 (2017).

    Article  Google Scholar 

  52. Sarkar, T. et al. Crisscross multilayering of cell sheets. PNAS Nexus 2, pgad034 (2023).

    Article  Google Scholar 

  53. Su, C. Y. et al. Engineering a 3D collective cancer invasion model with control over collagen fiber alignment. Biomaterials 275, 120922 (2021).

    Article  Google Scholar 

  54. Han, W. et al. Oriented collagen fibers direct tumor cell intravasation. Proc. Natl Acad. Sci. USA 113, 11208–11213 (2016).

    Article  ADS  Google Scholar 

  55. Duclos, G. et al. in Cell Migration: Methods and Protocols (ed. Gautreau, A.) 387–399 (Humana, 2018).

  56. Schindelin, J. et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012).

    Article  Google Scholar 

  57. Rasband, W. S. ImageJ v1.46b (US National Institutes of Health, 1997–2012).

  58. Preibisch, S., Saalfeld, S. & Tomancak, P. Globally optimal stitching of tiled 3D microscopic image acquisitions. Bioinformatics 25, 1463–1465 (2009).

    Article  Google Scholar 

  59. Petitjean, L. et al. Velocity fields in a collectively migrating epithelium. Biophys. J. 98, 1790–1800 (2010).

    Article  ADS  Google Scholar 

  60. Deforet, M. et al. Automated velocity mapping of migrating cell populations (AVeMap). Nat. Methods 9, 1081–1083 (2012).

    Article  Google Scholar 

  61. Sveen, J. K. An introduction to MatPIV v. 1.6.1 (Univ. of Oslo, 2004).

  62. Chen, H.-Y. et al. Emergence of bidirectional cell laning from collective contact guidance. Zenodo https://doi.org/10.5281/zenodo.10887254 (2024).

Download references

Acknowledgements

We thank the members of the Biology-inspired Physics at MesoScales (BiPMS) and the Physical Approach to Biological Problems (PABP) groups and, in particular, X. Wu for his help with the scanning electron microscopy. The BiPMS group is an associate member of the Institut Pierre-Gilles de Gennes and has benefited from the technical contributions of the joint service unit Unité d'Appui et de Recherche 3750 of the French National Centre for Scientific Research. The Molecular Biology and Cellular Biology platform of the UMR168 is gratefully acknowledged and in particular A. Battistella and F. Cayrac for their help with the transfection of the cells and J. Manzi for the western blots. We thank the Cell and Tissue Imaging core facility (PICT IBiSA), Institut Curie, member of the French National Research Infrastructure France-BioImaging (Grant No. ANR10-INBS-04). The BiPMS group and the PABP group are members of the LabEx Cell(n)Scale (Grant Nos. ANR-11-LABX-0038 and ANR-10-IDEX-0001-02). We acknowledge support from the French National Agency for Research (Grant No. ANR-18-CE30-0005). This study was supported by research funding from the Canceropôle Ile-de-France and the French National Cancer Institute. H.-Y.C. gratefully acknowledges funding from the Ministry of Science and Technology, Taiwan (Contract No. 109-2917-I-564-013), and from LabEx Cell(n)Scale. C.G. gratefully acknowledges funding from the Fondation pour la Recherche Médicale (Grant No. FDT202304016435). B.S. acknowledges support from the Research Foundation Flanders (Grant No. 12Z6118N), and KU Leuven internal funding (C14/18/055). S.B. and J.P. acknowledge funding from the Human Frontiers in Science Program (Grant No. HFSP RGP0038/2018).

Author information

Authors and Affiliations

  1. Laboratoire Physique des Cellules et Cancer UMR168, Institut Curie, Paris Sciences et Lettres, Centre National de la Recherche Scientifique, Sorbonne Université, Paris, France

    Mathilde Lacroix, Bart Smeets, Carles Blanch-Mercader, Samuel Bell, Caroline Giuglaris, Hsiang-Ying Chen, Jacques Prost & Pascal Silberzan

  2. BIOSYST-MeBioS, KU Leuven, Leuven (Heverlee), Belgium

    Bart Smeets

Authors
  1. Mathilde Lacroix
    View author publications

    Search author on:PubMed Google Scholar

  2. Bart Smeets
    View author publications

    Search author on:PubMed Google Scholar

  3. Carles Blanch-Mercader
    View author publications

    Search author on:PubMed Google Scholar

  4. Samuel Bell
    View author publications

    Search author on:PubMed Google Scholar

  5. Caroline Giuglaris
    View author publications

    Search author on:PubMed Google Scholar

  6. Hsiang-Ying Chen
    View author publications

    Search author on:PubMed Google Scholar

  7. Jacques Prost
    View author publications

    Search author on:PubMed Google Scholar

  8. Pascal Silberzan
    View author publications

    Search author on:PubMed Google Scholar

Contributions

M.L. and P.S. designed the research. M.L., C.G. and H.-Y.C. performed the experiments. M.L., B.S., C.B.M., C.G., H.-Y.C. and P.S. analysed the experimental data. C.B.M., S.B., B.S. and J.P. developed the theoretical model. B.S. performed the numerical simulations and analysed the simulation data. P.S. supervised the research. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to Pascal Silberzan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

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

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Experimental system.

a: Schematic and notations of the grooved PDMS substrate. 0<d < 2.5 µm. b: Representative Scanning Electron Microscopy image of a grooved substrate c: Confocal fluorescence image of the fibronectin coating on the grooves prior to seeding the cells (fluorescently labeled fibronectin). This image is an average over 40 µm along the x-axis. d: Phase contrast image of single HBECs on grooved substrates. Cells typically span over 2 to 3 motifs laterally while they migrate in the groove direction. e: Phase contrast image of a confluent HBEC monolayer on a grooved substrate (20 h post-confluence). The double arrow represents the grooves direction. Note the convention for the x and y axis, as well as for velocity angle measurements. In B and D, groove depth=1.75 µm.

Extended Data Fig. 2 Emergence of a laning pattern in HBEC monolayers on grooved substrates.

a: Representative vx laning pattern on a grooved substrate (t = 20 h post-confluence, d = 1.75 μm). The direction of the grooves is given by the double arrow. b: Profile of the x component of the velocity vx along y. vx(y) is aperiodic and varies between two opposite values. The profile shown is a representative profile acquired along the vertical black line in panel A. c: Close-up of the vx(y) profile. Within a lane, the velocity profile is flat, corresponding to a plug flow. Between antiparallel lanes, vx changes sign over less than 50 μm (~ two cell sizes). d: The histograms of vx in the two boxes drawn in panel (A) are symmetrical and well-peaked at opposite values.

Extended Data Fig. 3 Emergence of a laning pattern in HBEC monolayers on micro-patterned substrates.

a: Compared to the grooved substrates, the micropatterned substrates have no topography but present an alternation of adhesive (fibronectin, cyan)/non-adhesive (PEG, pink) lines whose lateral dimensions are the same as the grooved substrates. b: vx cartography for an HBEC monolayer plated on a micropatterned substrate t = 20 h post-confluence. Cell flows self-organize in bilateral laning similar to the one obtained on grooved substrates (see Fig. 1j for comparison). On these micropatterned substrates, anisotropic friction does not result from grooves but from the contrast in cell-substrate adhesion between the fibronectin lines and PEG lines.

Extended Data Fig. 4 Dynamics of apparition of a laning pattern.

a: Time evolution of vx in a HBEC monolayer on flat and on grooved substrates. The double-headed arrow indicates the groove orientation. Note that the system progressively jams with time. When normalized by vrms (bottom row), the laning pattern coarsens more and more slowly until t = 45 h and is lost only at long timescales when the system freezes and velocities approach 0. b: The time evolutions of the rms velocities are comparable on grooved (blue line) and flat (black line) substrates and the systems jam similarly in both cases. See also Extended Data Fig. 9a. Lines are mean values, coloured areas are standard deviations of the mean values distribution (n = 10 (resp. 7) on a flat (resp. grooved) substrate). d = 1.75 μm for the grooved substrates. All panels: t = 0 corresponds to confluence.

Extended Data Fig. 5 The emergence of a laning pattern is independent of E-cadherin based cell-cell adhesion.

a: HBECs are not cohesive and scatter at the front edge of a collectively migrating monolayer in a wound healing barrier assay. The monolayer is initially confined by a barrier (Ibidi chamber) that is removed at t = 0. The snapshot at t = 10 h shows the cells scattering individually on the substrate. Experiments are performed on a flat fibronectin-coated substrate. b: E-cadherin immunostaining of a HBEC confluent monolayer on a grooved substrate shows that E-cadherins are mainly cytoplasmic 15 h after confluence although bilateral laning is already well-established. By contrast, after 3 days, the cells jam and E-cadherins localize at cell-cell junctions. Of note, cadherin localization is unaffected by the presence of the grooves (see ref. 26 for images on flat substrates). Representative images, 3 repeats. c: Representative vx laning pattern of E-cadherin knocked-down HBECs on a grooved substrate. Cell-cell adhesion is therefore dispensable for the emergence of the laning pattern.

Extended Data Fig. 6 The emergence of a laning pattern is independent from cell contractility.

A laning pattern develops even when cell contractility is impaired by inhibiting myosin II with blebbistatin. The double arrow shows the direction of the grooves. Myosin II inhibition does not prevent collective cell guidance by the grooves and does not impair the emergence of a laning pattern. t = 20 h post-confluence, groove depth=1.45 μm.

Extended Data Fig. 7 Distribution of the lane widths in simulations and experiments.

\(\tilde{p}(w)\) is the probability for a lane to be wider than w. a) Simulations; b) Experiments. hs = 1 in (A) and d = 0 in (B) correspond to isotropic (flat) substrates (blue curves). Simulations with anisotropic friction (A) and experiments with finite groove depth (B) are plotted in red. These distributions are not peaked, meaning unambiguously that the laning pattern is aperiodic in both simulations and experiments. Panel A: Parameters of the simulations are listed in Supplementary Table 1. ks = 6. Panel B: n = 10 (flat substrates), n = 15 (grooved substrates); t = 20 h post-confluence.

Extended Data Fig. 8 The disorder-to-laning transition is mediated by friction anisotropy.

a: In particle-based simulations, friction anisotropy hs guides the particles along the x axis and gives rise to patterns very similar to the ones observed in experiments. Bivariate histograms of \(({\hat{v}}_{x},{\hat{v}}_{y})\) for increasing values of hs show a transition from a ring distribution (preferred speed and random orientations) to a bimodal distribution (preferred speed and orientation along the easy axis). See Extended Data Fig. 9 for a comparison with experiments. b: Velocity profile along the line drawn in panel A, for hs = 3. The profile is square and aperiodic, as it is in the experiments (Figure 1g, Extended Data Fig. 2b, c). c: Cumulative probability distribution function of the lane width w for various values of the friction anisotropy hs. For each value of hs, the distribution is obtained from 5 repeats of the simulation. For the sake of clarity, only the average values have been plotted. Black line: isotropic friction (hs = 1). d: Average lane width \(\bar{w}\) as a function of the guidance order parameter S. As the order increase, \(\bar{w}\) sharply increases at the transition (\(S\) ~ 0.4) and then decreases. Data are presented as mean values +/- SD (5 repeats). Parameters used in the numerical simulations are listed in Supplementary Table 1. ks = 6.

Extended Data Fig. 9 The groove depth is a good proxy of the friction anisotropy.

a: vrms. as a function of groove depth. vrms. is practically independent from the substrate topography. Data are presented as mean values ± SD. See Methods section for n values. b: Antiparallel laning emerges when grooves are sufficiently deep. The bivariate histograms of (vx, vy). corresponding to these patterns evolve from a ring to a bimodal distribution of vx with very small fluctuations of vy (data from all the analyzed FOVs, n = 54, N = 32 (see table in Methods section)) are concatenated in these histograms). See Extended Data Fig. 8a for comparison with numerical simulations. c: Cumulative probability distribution function of lane width \(\tilde{p}(w)\) for different groove depths. See Extended Data Fig. 8c for comparison with numerical simulations. d: Evolution of the average lane width \(\bar{w}\) with the guidance order parameter S. \(\bar{w}\) is larger on deep grooves compared to flat or shallow substrates. See Extended Data Fig. 8d for comparison with numerical simulations. Data are presented as mean values ± SD. t = 20 h post-confluence.

Extended Data Fig. 10 Velocity dependency on friction anisotropy.

The experimental evolution of the velocity with respect to groove depth (a) is well captured by the corresponding simulations (C, ks = 6). Except for very small anisotropies, this value of the velocity-reinforcement (ks = 6) corresponds to the laning regime (see Fig. 4c) and therefore the continuum theory is not expected to quantitatively describe the experiments. Yet, it qualitatively gives the trend of evolution of the two components of the velocity vs groove depth for shallow grooves (b). By contrast, in the disordered regime, the theoretical evolution of the velocity with friction anisotropy in the disordered regime (panel B) accounts well for the corresponding simulation (panel C, ks = 3). Panel A: t = 20 h post confluence. Data are presented as mean values ± SD. Panel C: Parameters are listed in Supplementary Table 1.

Supplementary information

Supplementary Information

Supplementary Notes, Fig. 1, Tables 1 and 2 and Videos 1–3.

Reporting Summary

Supplementary Video 1

Emergence of lanes in a HBEC monolayer. t = 0 corresponds to confluence. The blue and red colours code for the x component of the velocity. They are superimposed on the phase contrast video. Groove depth, d = 1.75 µm.

Supplementary Video 2

Particle-based simulation of bidirectional laning through velocity self-reinforcement and anisotropic friction. Individual cells are indicated by their centre position (points) and their corresponding Voronoi region. This video shows a domain smaller than the ones used in the results reported in Fig. 4 to visualize individual cells. The colour codes for the scaled x component of the velocity. The scale bar is 50 cell radii. The simulation parameters are reported in Supplementary Table 1. ks = 4.5, and hs = 3

Supplementary Video 3

Particle-based simulations with varying substrate anisotropy hs and velocity reinforcement ks. The colour codes for the scaled x component of the velocity. The scale bar is 50 cell radii. Other simulation parameters are reported in Supplementary Table 1.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lacroix, M., Smeets, B., Blanch-Mercader, C. et al. Emergence of bidirectional cell laning from collective contact guidance. Nat. Phys. 20, 1324–1331 (2024). https://doi.org/10.1038/s41567-024-02510-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41567-024-02510-3

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing