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A fluid-to-solid jamming transition underlies vertebrate body axis elongation


Just as in clay moulding or glass blowing, physically sculpting biological structures requires the constituent material to locally flow like a fluid while maintaining overall mechanical integrity like a solid. Disordered soft materials, such as foams, emulsions and colloidal suspensions, switch from fluid-like to solid-like behaviours at a jamming transition1,2,3,4. Similarly, cell collectives have been shown to display glassy dynamics in 2D and 3D5,6 and jamming in cultured epithelial monolayers7,8, behaviours recently predicted theoretically9,10,11 and proposed to influence asthma pathobiology8 and tumour progression12. However, little is known about whether these seemingly universal behaviours occur in vivo13 and, specifically, whether they play any functional part during embryonic morphogenesis. Here, by combining direct in vivo measurements of tissue mechanics with analysis of cellular dynamics, we show that during vertebrate body axis elongation, posterior tissues undergo a jamming transition from a fluid-like behaviour at the extending end, the mesodermal progenitor zone, to a solid-like behaviour in the presomitic mesoderm. We uncover an anteroposterior, N-cadherin-dependent gradient in yield stress that provides increasing mechanical integrity to the presomitic mesoderm, consistent with the tissue transiting from a wetter to a dryer foam-like architecture. Our results show that cell-scale stresses fluctuate rapidly (within about 1 min), enabling cell rearrangements and effectively ‘melting’ the tissue at the growing end. Persistent (more than 0.5 h) stresses at supracellular scales, rather than cell-scale stresses, guide morphogenetic flows in fluid-like tissue regions. Unidirectional axis extension is sustained by the reported rigidification of the presomitic mesoderm, which mechanically supports posterior, fluid-like tissues during remodelling before their maturation. The spatiotemporal control of fluid-like and solid-like tissue states may represent a generic physical mechanism of embryonic morphogenesis.

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We thank E. Sletten for sharing custom-made fluorinated dyes. We also thank all laboratory members and the UCSB Animal Research Center for support. P.R. thanks B. Aigouy for assistance with Tissue Analyzer. A.M. thanks EMBO (EMBO ALTF 509-2013), Errett Fisher Foundation and Otis Williams Fund for financial support. This work was partially supported by the National Science Foundation (CMMI-1562910) and the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health (R21HD084285; R01HD095797).

Reviewer information

Nature thanks J. Fredberg, P.-F. Lenne, O. Pourquié and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

A.M. and O.C. designed research; A.M., H.J.G., D.A.K. and F.S. performed experiments; A.M., H.J.G., P.R., E.S. and J.G. analysed the data; P.R. and O.C. performed theoretical interpretation of experiments; E.K.C. and P.R. performed simulations; A.A.L. assisted with droplet generation; A.M. and O.C. wrote the paper; O.C. supervised the project.

Competing interests

The authors declare no competing interests.

Correspondence to Otger Campàs.

Extended data figures and tables

  1. Extended Data Fig. 1 Loss of anteroposterior gradients of supracellular stresses and cell and nuclear shape anisotropy in N-cadherin mutants.

    a, ActinRed staining of F-actin in the PSM of control (cdh2+/+ and cdh2+/−) and mutant (cdh2−/−) embryos at the 10-somite stage. Cell shapes are visibly elongated along the mediolateral (ML) direction in control embryos. Cell shape anisotropy is largely lost in cdh2−/− embryos. b, DAPI staining showing higher nuclear mediolateral elongation in the PSM of control embryos compared to cdh2 mutants. c, Frequency of nuclear major axis orientations in the MPZ and PSM (A-PSM and P-PSM). In control (cdh2+/+ and cdh2+/−) embryos, nuclei in the PSM are elongated along the mediolateral direction, whereas nuclei are oriented randomly in the MPZ. The observed nuclear anisotropy along the mediolateral direction in the PSM of control embryos is decreased in cdh2 mutants. d, A posterior-to-anterior increase in the extent of nuclear elongation (quantified by the nuclear aspect ratio; see inset and Methods) is observed in control (cdh2+/+ and cdh2+/−) embryos. No anteroposterior gradient in the extent of nuclear elongation (aspect ratio) is observed in cdh2 mutants (cdh2−/−). For c and d: control embryos, n = 695 (A-PSM), 752 (P-PSM), 732 (MPZ) nuclei, obtained in 6 embryos per region; cdh2−/−: n = 833 nuclei from 5 embryos (A-PSM), n = 538 nuclei from 6 embryos (P-PSM), n = 336 nuclei from 4 embryos (MPZ). Mean ± s.e.m. e, Relative change of cell–cell contact length along the anteroposterior axis and the mediolateral axis (n = 6,427 and 4,319 cell–cell contacts for PSM and MPZ, respectively, from 5 embryos). Cell junctions are longer along the mediolateral axis compared to the anteroposterior axis, both in the PSM and MPZ. Mean ± s.e.m. f, Supracellular stresses are uniform along the anteroposterior axis in cdh2 mutant embryos (n = 5 (A-PSM), 5 (P-PSM), 12 (MPZ)). Mean ± s.e.m.; Mann–Whitney U-test. The observed posterior-to-anterior increase in both supracellular stresses and nuclear elongation in control embryos (d and Fig. 1e), and the loss of both such gradients in cdh2 mutants (d and f), indicate the existence of a N-cadherin-dependent, posterior-to-anterior increase in supracellular stresses, consistent with a posterior-to-anterior increase in mediolateral constriction. Importantly, if the observed thinning of the body axis was caused by pulling forces from the MPZ on the PSM, as previously proposed18, both cells and nuclei would be elongated along the anteroposterior axis. Source Data

  2. Extended Data Fig. 2 Curvature changes along the droplet contour correlate with the locations of cell–cell contacts surrounding the droplet.

    Confocal section of a ferrofluid droplet (red) in the MPZ of a Tg(actb2:MA-citrine) embryo. The measured curvature values along the detected droplet contour are shown (colourcoded as in Fig. 1h) overlaid with the confocal image (left) and without it (right). White arrows point to locations of cell–cell contacts of cells surrounding the droplet, which correlate with maxima and minima of droplet curvature, consistent with the distance between maxima and minima being approximately the cell size (Fig. 1j).

  3. Extended Data Fig. 3 Increase of extracellular spaces and cell rounding in cdh2 mutants.

    2D confocal sections (inverted) of control (cdh2+/+ and cdh2+/−) and cdh2−/− Tg(actb2:MA-citrine) embryos showing an increase in extracellular space (cyan), as well as more cell rounding, in the PSM tissue of the mutant embryos.

  4. Extended Data Fig. 4 Example of neighbour exchanges induced in the tissue upon droplet actuation with a magnetic field.

    Confocal section showing the spatial arrangements of cells in the neighbourhood of a magnetically responsive droplet both in the absence of magnetic field (OFF) and after applying a magnetic field (ON) for 15 min (left). Several cell rearrangements are observed to be induced by droplet actuation (right). Some of the cells undergoing neighbour exchanges are coloured and numbered to highlight the rearrangements. Tg(actb2:MA-citrine) embryos were used to visualize cell membranes.

  5. Extended Data Fig. 5 Distribution of cell–cell contact length fluctuations in cdh2 mutants.

    Normalized frequency (distribution) of cell–cell contact length fluctuations in the PSM and MPZ of cdh2 mutants (red bars) compared to the control (violet and light blue lines). For PSM and MPZ, n = 13,212 and 13,634 cell–cell contacts obtained from 5 and 4 embryos, respectively. Source Data

  6. Extended Data Fig. 6 Orientation of neighbour exchanges in the MPZ and PSM.

    a, Sketch of a dorsal view of the elongating body axis, with the anteroposterior and mediolateral directions defined (top). Sketch showing the orientation of a cell–cell contact (thick black line) before undergoing a neighbour exchange (bottom left). The angle θ corresponds to the angle between the cell–cell contact before undergoing the neighbour exchange and the anteroposterior axis (bottom). Four equal bins are defined (bin 1: 0 < θ < 22.5°; bin 2: 22.5° < θ < 45°; bin 3: 45° < θ < 67.5°; bin 4: 67.5° < θ < 90°) between the anteroposterior and mediolateral orthogonal directions (bottom right). b, Frequency of neighbour exchanges along different angular regions (n = 18 in 4 embryos for PSM and n = 23 in 3 embryos for MPZ, with n being the number of neighbour exchanges analysed). Data are mean ± s.d. Neighbour exchanges are largely randomly oriented in the MPZ. In the PSM, neighbour exchanges occur predominantly along either the mediolateral direction or along the anteroposterior axis, with neighbour exchanges occurring slightly less frequently for angles in between these orthogonal orientations. The more frequent occurrence of neighbour exchanges along the anteroposterior and mediolateral axes in the PSM is consistent with the measured directions and extent of ellipsoidal droplet deformation (Fig. 1f), as the persistent and larger supracellular stresses in the PSM may bias neighbour exchanges in these directions. Since neighbour exchanges occur equally frequently along the mediolateral and anteroposterior directions in the PSM, and are uniformly oriented in the MPZ, our results indicate no systematic alignment of neighbour exchanges along a single spatial direction that could potentially contribute to the elongation of the body axis. Source Data

  7. Extended Data Fig. 7 Energy landscape of neighbour exchanges.

    a, Schematic of key cellular configurations throughout a neighbour exchange and associated energy landscape. Changing neighbours requires overcoming an energy barrier. Large enough, active cell–cell contact length fluctuations enable neighbour exchanges. b, Measured energy landscape, E, for PSM and MPZ regions, normalized with the energy scale EA associated with cell–cell contact activity or effective temperature energy scale, namely EA = kBTEff, where kB is the Boltzmann constant and TEff is the effective temperature. n = 6,969, 7,896 cell–cell contacts obtained from 3, 4 embryos for PSM, MPZ, respectively. Source Data

  8. Extended Data Fig. 8 Dependence of posterior axis elongation speed and relative cellular movements in the MPZ on N-cadherin and non-muscle myosin-II activity.

    a, Sketch of a 10-somite stage embryo highlighting the mesodermal progenitor zone (MPZ, cyan) and the direction of posterior elongation (arrow). b, Comparison of posterior body elongation speeds between control (n = 6), cdh2 mutants (n = 7), and blebbistatin-treated embryos (n = 6 for 50 μM and n = 7 for 100 μM). Box plots representing median (red line) and second and third quartiles. Error bars indicate 95% confidence interval. Mann–Whitney U-test. c, Mean square relative displacement of cells in the MPZ region of control (n = 2,523 analysed cell pairs from 6 embryos), cdh2−/− (n = 1,154 analysed cell pairs from 4 embryos) and blebbistatin-treated embryos (n = 2,026 analysed cell pairs from 4 embryos). Source Data

  9. Extended Data Fig. 9 Cell density is uniform along the anteroposterior axis.

    a, Measured cell number density (cells per unit volume) in the MPZ, P-PSM and A-PSM. Mean ± s.e.m. Cell density does not vary significantly along the anteroposterior axis (within the 10% accuracy of our 3D measurements; Methods). b, 3D reconstructions of confocal stacks showing nuclei labelled with H2B::RFP, detected nuclei positions, and composition of both. Cell density was measured using 3D data of nuclear positions in the different regions (n = 7,866, 7,214, 11,537 detected cells in 694, 694, 833 defined boxes in 5, 5, 6 embryos, in A-PSM, P-PSM, MPZ, respectively; Methods). Source Data

  10. Extended Data Fig. 10 Yield stress values do not depend on the extent of droplet deformation before droplet relaxation.

    Measured values of the yield stress plotted against the maximal droplet deformation (maximal applied strain, εM; Fig. 2a, b) before starting droplet relaxation. The measured yield stress values do not correlate with the maximal applied strain, neither in control (cdh2+/+ and cdh2+/−, grey dots, n = 53 embryos) or mutant embryos (cdh2−/−, red dots, n = 27 embryos). Correlation coefficient, r = −0.34 (control), r = −0.04 (cdh2−/−). Source Data

Supplementary Information

  1. Supplementary Information

    Supplementary Fig. 1 explains the concept of yield stress in aqueous foams and its dependence on the volume fraction of fluid between bubbles. Supplementary Figure 2 reports the tissue mechanical properties in the PSM and MPZ beyond the yield stress. Supplementary Figure 3 includes key detains of the simulations and is associated with the Supplementary Note 1, which describes the theoretical approach to simulate body axis elongation. Supplementary Video 1 shows a representative example of cellular ‘jiggling’ in the tissue, and Supplementary Videos 2 and 3 show the simulated tissue morphogenesis in the presence and absence of a jamming transition in the tissue state. The Supplemental Data files include the source data for all the main figures and Extended Data Figures in the paper.

  2. Reporting Summary

  3. Supplementary Data

    Source data for Supplementary Fig. 2.

  4. Supplementary Video 1

    Confocal time-lapse (30 min total time) of a portion of the A-PSM region of Tg(actb2:MA-Citrine) embryos (membrane label), showing cellular ‘jiggling’ caused by non-persistent actomyosin-driven cortical contractions (or cell-scale stresses).

  5. Supplementary Video 2

    Simulated time evolution of morphogenesis of the posterior tissues (PSM and MPZ; dorsal-ventral projection) in the presence of the reported fluid-to-solid jamming transition, as the fluid-like MPZ transits to a solid-like PSM. The solid-like state of the PSM mechanically supports the extending, fluid-like end of the posterior body, as cells from the DM region are added to the MPZ and progressively elongate the body axis (see Fig. 4d in the main text and Supplementary Note 1 for details). The magnitude of the tissue velocity (speed) is color coded. The vertical line on the left indicates the position of a fixed wall.

  6. Supplementary Video 3

    Simulated time evolution of morphogenesis of the posterior tissues (PSM and MPZ; dorsal-ventral projection) in the absence of a fluid-to-solid jamming transition, so that the PSM tissue never rigidifies and has the same tissue viscosity as the posterior MPZ tissue (see Fig. 4e in the main text and Supplementary Note 1 for details). The magnitude of the tissue velocity (speed) is color coded. The vertical line on the left indicates the position of a fixed wall.

Source data

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  3. Source Data Fig. 3

  4. Source Data Extended Data Fig. 1

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  6. Source Data Extended Data Fig. 6

  7. Source Data Extended Data Fig. 7

  8. Source Data Extended Data Fig. 8

  9. Source Data Extended Data Fig. 9

  10. Source Data Extended Data Fig. 10

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Further reading

Fig. 1: Supracellular and cell-scale mechanical stresses during body axis elongation.
Fig. 2: Mechanical integrity of the extending body axis.
Fig. 3: Cell–cell contact length fluctuations and cellular movements along the anteroposterior axis.
Fig. 4: Physical mechanism of vertebrate body axis elongation.
Extended Data Fig. 1: Loss of anteroposterior gradients of supracellular stresses and cell and nuclear shape anisotropy in N-cadherin mutants.
Extended Data Fig. 2: Curvature changes along the droplet contour correlate with the locations of cell–cell contacts surrounding the droplet.
Extended Data Fig. 3: Increase of extracellular spaces and cell rounding in cdh2 mutants.
Extended Data Fig. 4: Example of neighbour exchanges induced in the tissue upon droplet actuation with a magnetic field.
Extended Data Fig. 5: Distribution of cell–cell contact length fluctuations in cdh2 mutants.
Extended Data Fig. 6: Orientation of neighbour exchanges in the MPZ and PSM.
Extended Data Fig. 7: Energy landscape of neighbour exchanges.
Extended Data Fig. 8: Dependence of posterior axis elongation speed and relative cellular movements in the MPZ on N-cadherin and non-muscle myosin-II activity.
Extended Data Fig. 9: Cell density is uniform along the anteroposterior axis.
Extended Data Fig. 10: Yield stress values do not depend on the extent of droplet deformation before droplet relaxation.


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