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Embryonic tissues as active foams

Nature Physics volume 17, pages 859–866 (2021)Cite this article

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Abstract

The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but it is unclear how cells control these emergent tissue states and transitions, including tissue fluidization. Combining computational and experimental methods, here we show that tissue fluidization in posterior zebrafish tissues is controlled by the stochastic dynamics of tensions at cell–cell contacts. We develop a computational framework that connects cell behaviour to embryonic tissue dynamics, accounting for the presence of extracellular spaces, complex cell shapes and cortical tension dynamics. We predict that tissues are maximally rigid at the structural transition between confluent and non-confluent states, with actively generated tension fluctuations controlling stress relaxation and tissue fluidization. By directly measuring strain and stress relaxation, as well as the dynamics of cell rearrangements, in elongating posterior zebrafish tissues, we show that tension fluctuations drive active cell rearrangements that fluidize the tissue. These results highlight a key role of non-equilibrium tension dynamics in developmental processes.

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Fig. 1: Characteristics of multicellular systems and simulation framework.
Fig. 2: Equilibrium configurations and structural transitions.
Fig. 3: Tissue dynamics with finite tension fluctuations.
Fig. 4: Stress relaxation and structure in active multicellular systems.
Fig. 5: Stress relaxation and tissue fluidization in posterior tissues during body axis elongation.

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Data availability

Source data are provided with this paper.

Code availability

The code developed for this paper is available in Supplementary Software 1.

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Acknowledgements

We thank all members of the Campàs group for their comments and help, P. Rowghanian for help with cell segmentation, D. Kealhofer and E. Shelton for technical help, B. Shelby and the UCSB Animal Research Center for support with zebrafish, I. Lim and E. Sletten (University of California, Los Angeles) for sharing custom-made fluorinated dyes, and H. Knaut (New York University) and S. Megason (Harvard University) for kindly providing the Tg(hsp70:secP-mCherry)p1 and Tg(actb2:memCherry2)hm29 transgenic lines, respectively. The Tg(actb2:mem-neonGreen-neonGreen)hm40 line was generously provided before publication by T. Kawanishi and I. Swinburne in S. Megason’s lab (Harvard University). This work was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health (R01HD095797 to O.C.). We acknowledge support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1720256) and NSF CNS-1725797, as well as from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2068 - 390729961 - Cluster of Excellence Physics of Life of TU Dresden.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA

    Sangwoo Kim, Marie Pochitaloff, Georgina A. Stooke-Vaughan & Otger Campàs

  2. Center for Bioengineering, University of California, Santa Barbara, CA, USA

    Otger Campàs

  3. Department of Molecular, Cellular and Developmental Biology, University of California, Santa Barbara, CA, USA

    Otger Campàs

  4. California NanoSystems Institute, University of California, Santa Barbara, CA, USA

    Otger Campàs

  5. Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany

    Otger Campàs

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  1. Sangwoo Kim
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Contributions

S.K. and O.C. designed research; S.K. implemented and performed the simulations; M.P. and G.A.S.-V. performed experiments; S.K., M.P. and G.A.S.-V. analysed data; S.K. and O.C. wrote the paper; O.C. supervised the project.

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Correspondence to Otger Campàs.

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Extended data

Extended Data Fig. 1 Power law relation between NE rate and MSD at long timescales.

Power law relation between long time MSD values and NE rate when the systems are close to confluence for high adhesion levels. NE rate and longtime MSD show a power law relation with an exponent of 0.75.

Source data

Extended Data Fig. 2 Comparison of solid/fluid phase diagrams obtained from stress relaxation and from cell movements.

Solid/fluid phase diagrams determined by mechanical measurement of stress relaxation (left) and cell movements, MSD=1/2 (middle) and MSD=1/4 (right). Green region indicates confluent states.

Source data

Supplementary information

Supplementary Information

Supplementary Sections 1–5, Figs. 1–5 and video captions.

Reporting Summary

Supplementary Video 1

Simulations of equilibrium configurations showing the effect of decreasing the relative adhesion quasistatically from W/T0 = 0.6 to W/T0 = 0, both for low cell density (ρ = 0.81) and high cell density (ρ = 1.21).

Supplementary Video 2

Simulations of the system with an imposed strain step in the absence of tension fluctuations (ΔT/T0 = 0) for both non-confluent (ρ = 1, W/T0 = 0.2) and confluent (ρ = 1, W/T0 = 1) regimes. Cells that undergo topological transitions are colour-coded in red.

Supplementary Video 3

Simulations of the system dynamics in the non-confluent regime and in the presence of active tension fluctuations of small magnitude (ρ = 1, W/T0 = 0.2 and ΔT/T0 = 0.5) and large magnitude (ρ = 1, W/T0 = 0.2 and ΔT/T0 = 1.5). Trajectories of four cells are shown in different colours and cells that undergo topological transitions are colour-coded in red after t/τR = 150.

Supplementary Video 4

Simulations of the system dynamics in the non-confluent regime and in the presence of active tension fluctuations of small magnitude (ρ = 1, W/T0 = 1 and ΔT/T0 = 0.5) and large magnitude (ρ = 1, W/T0 = 1 and ΔT/T0 = 1.5). Trajectories of four cells are shown in different colours and cells that undergo topological transitions are colour-coded in red after t/τR = 150.

Supplementary Video 5

Simulations of the system with an imposed strain step in the presence of tension fluctuations (ΔT/T0 = 1) for both non-confluent (ρ = 1, W/T0 = 0.2) and confluent (ρ = 1, W/T0 = 1) regimes. Cells that undergo topological transitions are colour-coded in red..

Supplementary Video 6

Simulations of the system dynamics showing the spatiotemporal tension fluctuations for small magnitude of tension fluctuations (ρ = 1, W/T0 = 1 and ΔT/T0 = 0.5) and for large magnitude (ρ = 1, W/T0 = 1 and ΔT/T0 = 1.5): identical samples of Supplementary Video 3. A tension gradient colour scheme is rainbow coloured, with high tension as red and low tension as purple.

Supplementary Software 1

Source code used to perform all the simulations in the paper.

Source data

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Statistical source data.

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3

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Source Data Fig. 4

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Source Data Fig. 5

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Source Data Extended Data Fig. 1

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Source Data Extended Data Fig. 2

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Kim, S., Pochitaloff, M., Stooke-Vaughan, G.A. et al. Embryonic tissues as active foams. Nat. Phys. 17, 859–866 (2021). https://doi.org/10.1038/s41567-021-01215-1

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