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Matrix viscoelasticity controls spatiotemporal tissue organization

Nature Materials volume 22, pages 117–127 (2023)Cite this article

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Abstract

Biomolecular and physical cues of the extracellular matrix environment regulate collective cell dynamics and tissue patterning. Nonetheless, how the viscoelastic properties of the matrix regulate collective cell spatial and temporal organization is not fully understood. Here we show that the passive viscoelastic properties of the matrix encapsulating a spheroidal tissue of breast epithelial cells guide tissue proliferation in space and in time. Matrix viscoelasticity prompts symmetry breaking of the spheroid, leading to the formation of invading finger-like protrusions, YAP nuclear translocation and epithelial-to-mesenchymal transition both in vitro and in vivo in a Arp2/3-complex-dependent manner. Computational modelling of these observations allows us to establish a phase diagram relating morphological stability with matrix viscoelasticity, tissue viscosity, cell motility and cell division rate, which is experimentally validated by biochemical assays and in vitro experiments with an intestinal organoid. Altogether, this work highlights the role of stress relaxation mechanisms in tissue growth dynamics, a fundamental process in morphogenesis and oncogenesis.

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Fig. 1: Matrix viscoelasticity determines symmetry breaking, tissue branching and EMT.
Fig. 2: Matrix viscoelasticity promotes EMT and tumour growth.
Fig. 3: Theoretical model predicts that spheroid–material physical interaction regulates tissue geometrical evolution.
Fig. 4: Stiffness intersects with matrix viscoelasticity to regulate growth and branching.
Fig. 5: Phase diagram predicts tissue morphological stability.
Fig. 6: Matrix viscoelasticity controls intestinal organoid growth, symmetry breaking, budding and cell patterning.

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Data availability

Digital data supporting the findings of this article are available at https://dataverse.harvard.edu/dataverse/EloseguiArtola_Gupta_2022. Source data are provided with this paper.

Code availability

The computational model code is available at https://github.com/anupamdata/ABM_VE_Matrix_Viscous_Tissue.git

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Acknowledgements

We thank M. Sobral, M. Dellacherie, J. Lou, M. Uroz and all the members of the Mooney lab for helpful discussions and comments on the manuscript. This work was supported by funding from the Wellcome Leap HOPE Program (D.J.M). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 851055) (A.E.-A.). A.E.-A. received funding for this work from the European Union’s Horizon 2020 research and innovation programme through a Marie Sklodowska-Curie grant agreement number 798504 (MECHANOSITY). A.J.N. acknowledges a Graduate Research Fellowship from the National Science Foundation. This work was partly supported by funding (R01 DK125817 and Tri-SCI grant) to QZ. I.d.L. was supported by the National Cancer Institute of the National Institutes of Health under award number U01CA214369. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or the Wyss Institute for Biologically Inspired Engineering at Harvard University.

Author information

Author notes

  1. These authors contributed equally: Alberto Elosegui-Artola, Anupam Gupta.

Authors and Affiliations

  1. Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Alberto Elosegui-Artola, Anupam Gupta, Alexander J. Najibi, Bo Ri Seo, Ryan Garry, Irene de Lázaro, Max Darnell, David A. Weitz, L. Mahadevan & David J. Mooney

  2. Wyss Institute for Biologically Inspired Engineering, Cambridge, MA, USA

    Alberto Elosegui-Artola, Alexander J. Najibi, Bo Ri Seo, Christina M. Tringides, Irene de Lázaro, Max Darnell & David J. Mooney

  3. Institute for Bioengineering of Catalonia, Barcelona, Spain

    Alberto Elosegui-Artola

  4. Cell and Tissue Mechanobiology Laboratory, Francis Crick Institute, London, UK

    Alberto Elosegui-Artola

  5. Department of Physics, King’s College London, London, UK

    Alberto Elosegui-Artola

  6. Department of Physics, Indian Institute of Technology Hyderabad, Hyderabad, India

    Anupam Gupta

  7. Harvard Program in Biophysics, Harvard University, Cambridge, MA, USA

    Christina M. Tringides

  8. Harvard–MIT Division in Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, USA

    Christina M. Tringides

  9. Weill Cornell Medicine, Cornell University, New York, NY, USA

    Wei Gu & Qiao Zhou

  10. Department of Physics, Harvard University, Cambridge, MA, USA

    David A. Weitz & L. Mahadevan

  11. Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA

    L. Mahadevan

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Contributions

A.E.-A. and D.J.M. conceived the study. A.E.-A., A.J.N., B.R.S., R.G., C.M.T., I.d.L., D.A.W. and D.J.M. designed the experiments. A.E.-A., A.J.N., B.R.S., R.G., C.M.T., I.d.L. and M.D. performed the experiments. A.G. and L.M. developed the computational model. W.G. and Q.Z. provided reagents. A.E.-A., A.G., L.M. and D.J.M. wrote the manuscript.

Corresponding authors

Correspondence to L. Mahadevan or David J. Mooney.

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Nature Materials thanks Nuria Montserrat 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 Matrix Viscoelasticity regulates tissue growth and geometry.

Examples of growth of MCF10A spheroids in elastic versus viscoelastic hydrogels over 5 days. Phalloidin in cyan, Hoechst in magenta. b, c, Quantification of spheroids area (b) and circularity (c) after 5 days without or with focal adhesion kinase (FAK) inhibitor PF 573228. n = 56,27,41,23 spheroids per condition. Statistical analysis was performed using Kruskal–Wallis test followed by post hoc Dunn’s test. d, e, Representative examples (d) and quantification of pFAK (e) in spheroids in elastic and viscoelastic matrices. n = 9,12 images per condition. Statistical analysis was performed using two-sided Mann-Whitney U-test. f, g, Representative examples of emerin and nesprin staining in elastic and viscoelastic matrices. n = 15,9 (f) and n = 14,14 images per condition. No significant differences were observed between cells in elastic and viscoelastic matrices. h, Representative examples of phalloidin, Hoechst (left) and YAP (right) stainings of spheroids with thymidine treatment of cells in viscoelastic gels. n = 5 images. All data represent mean ± s.d.; all scale bars represent 100 µm.

Source data

Extended Data Fig. 2 Matrix viscoelasticity promotes epithelial to mesenchymal transition.

a-c, quantification of mean fluorescence intensity of Snail, Slug and Zeb1 in spheroids in elastic and viscoelastic matrices. n = 6 gels per condition. d, e, quantification of percentage of Zeb2 positive cells (d) and mean Zeb2 fluorescence intensity (e) in spheroids in elastic and viscoelastic matrices. n = 6 gels per condition. f, quantification of mean fluorescence intensity of Slug cells in elastic and viscoelastic matrices encapsulated in vivo (n = 9,10 gels per condition). g, quantification of number of Slug positive cells in spheroids in elastic and viscoelastic matrices encapsulated in vivo (n = 9,10 gels per condition). h, i, quantification of the area (h) and circularity (i) of MDA-MB-231 spheroids encapsulated in elastic and viscoelastic matrices. n = 40 spheroids per condition. Statistical analysis was performed using two-sided Mann-Whitney U-test. All data represent mean ± s.d.

Source data

Extended Data Fig. 3 3D model for stress dependent cell flux simulations.

a, The texts in light blue/light red colour boxes describe the matrix/cell property and interactions therein. The yellow boxes represent the parameters which we vary to probe the phase space of morphologies. In this case the cell proliferation is stress dependent, hence cell flux is material property dependent. b, Volume of the tissue as a function of time for the elastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 0.4,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 0.002,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.05\)) and viscoelastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 400,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 2,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.22\)) matrices (c) sphericity of the tissue as a function of time for elastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 0.4,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 0.002,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.05\)) and viscoelastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 400,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 2,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.22\)) matrices.

Extended Data Fig. 4 Cell motility regulates tissue growth, symmetry breaking and fingering.

a, b, Model prediction of spheroids projected area (a) and circularity (b) evolution with time when cell motility is suppressed, for stiff elastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 0.03,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 0.002,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}}\sim 0\)) and stiff viscoelastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 33.3,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 2,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}}\sim 0\)). c, Quantification of spheroids circularity after 5 days in hydrogels with and without cell adhesive ligand RGD. n = 52,52,51,54 spheroids per condition. Statistical analysis was performed using Kruskal–Wallis test followed by post hoc Dunn’s test. d, Representative images (upper row) and quantification of spheroids circularity (lower row) after 5 days in hydrogels in the presence of the indicated inhibitors. n = 52,50,51,51,51,50,51,50,51,46,41,51 spheroids per condition. Statistical analysis was performed using Kruskal–Wallis test followed by post hoc Dunn’s test. e, Representative images (upper row) and quantification of spheroid’s circularity (lower row) after 5 days hydrogels in the presence of the indicated inhibitor. n = 21,21,24,20,21,25 spheroids per condition. Statistical analysis was performed using Kruskal–Wallis test followed by post hoc Dunn’s test. f, g, Quantification of spheroids area (f) and circularity (g) of spheroids after 5 days in hydrogels in the presence of the indicated formins inhibitor. n = 29,26,32,26,27,28 spheroids per condition. No significant differences were observed in the presence of the inhibitor. Statistical analysis was performed using Kruskal–Wallis test followed by post hoc Dunn’s test. All data represent mean ± s.d.; all scale bars represent 200 µm.

Source data

Extended Data Fig. 5 Cell proliferation is required for tissue growth, symmetry breaking and fingering.

a, b, Quantification from the simulations of the projected area (a) and circularity (b) of the spheroids, respectively, over time when proliferation is inhibited, for stiff elastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 0.4,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 0.002,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0\)) and stiff viscoelastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 400,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 2,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0\)) matrices. c, Quantification of the circularity of spheroids without or in the presence of thymidine to inhibit cell proliferation. n = 52,53,51,53 spheroids per condition. Statistical analysis was performed using Kruskal–Wallis test followed by post hoc Dunn’s test. All data represent mean ± s.d.

Source data

Extended Data Fig. 6 Cell proliferation is required for tissue growth, symmetry breaking and fingering.

a, Simulation and Experimental results for the distribution of proliferating cells across spheroids in elastic (upper row) and viscoelastic gels (lower row): left, simulation example of the daughter cells (cyan) and the cells in the tissue spheroid (yellow elastic and cyan viscoelastic); centre, representative examples of experimental spheroids showing EdU-positive cells (cyan) and cell nuclei (Hoechst, magenta) for spheroids; right, colormaps showing the local percentage of Edu positive cells across the spheroid. b-c, Experimental (b) and simulation results (c) showing the density proliferating cells depending of distance from the spheroid edge. n = 3,4 spheroids per condition. Error bars are s.e.m. All scale bars are 200 µm. d, The normalized stress energy estimated from the simulations depending on the distance from the spheroid edge. The dimensionless parameter in the model for stiff elastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 0.4,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 0.002,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.05\)) and stiff viscoelastic (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 400,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 2,\) \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.22\)) matrices.

Source data

Extended Data Fig. 7 Development of a microfluidic device to study the influence of pressure in tissue morphological stability.

a, Pillars are distributed across the petri dish and an unpolymerized alginate solution is loaded. b, A PDMS slab is placed on top of the pillars and alginate is allowed to polymerize for 45 min. c, cells are loaded at a constant rate (1 µl/min) with a syringe pump through a hole in the PDMS slab. Due to the pressure (∼19 kPa), cells displace the material. d, Model prediction for cell flux driven experiments for elastic \(({A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 0.003,\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 0.002,j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 5})\) and viscoelastic \(({A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 3.33,\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 2,j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 5})\) matrices. e, Examples of Hoechst staining of cells in elastic and viscoelastic matrices. Scale bar is 2000 µm. f, Quantification of the circularity in elastic and viscoelastic hydrogels. n = 5,5 experiments per condition. g, Quantification of single cells circularity inside tissues in elastic and viscoelastic hydrogels. n = 100,100 cells per condition. Statistical analysis was performed using two-sided Mann-Whitney U-test. Data represent mean ± s.d.

Source data

Extended Data Fig. 8 Phase diagram simulations.

a, 3D phase diagram including the results of multiple simulation runs utilized to determine the phase boundaries. Each dot represents the final result of a single simulation run under specific condition, and they are colour coded (blue = stable tissue growth; red = unstable tissue growth). b, A two-dimensional phase diagram for low motility case as a consequence of slow addition of cells, always leading to a stable spheroid (all blue). c, Two-dimensional phase diagram for the controlled cell-flux driven case where the addition of cells is fast. This leads to an inverted behaviour, the growth of tissue in elastic matrix (close to origin) is branched (red) and in viscoelastic matrix (away from origin) is a stable (blue). In b and c, the red and blue dots against represent data points extracted from individual simulations. When the scaled proliferation pressure \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} \ll 1\), the tissue grows as a stable spheroid (Fig. 3i, j and Supplementary Figs. 7, 8). Additionally, when the scaled matrix relaxation time \(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} \ll 1\), the tissue remains spheroidal and is morphologically stable as long as the scaled proliferation pressure \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} \sim O(1)\) (top panel of Figs.1d, 3b, 4b). When the scaled matrix relaxation time \(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} \gg 1\): if the scaled proliferation pressure \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} \ll 1\), the tissue grows as a stable spheroid (bottom right of Fig. 3i and bottom panel of Supplementary Fig. 8b); if the scaled proliferation pressure \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} \sim O\left( 1 \right)\), the growth is unstable and the tissue breaks symmetry and develops fingers (bottom panel of Fig. 1d and bottom panel of Figs. 3b, 4b); if the scaled proliferation pressure \(j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} \gg 1\), the morphological stability of the tissue depends on \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}}\) (see Extended Data Figs 7d, e, 8c); for \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} \ll 1\), the tissue remains spheroidal (Extended Data Figs. 7d, e, 8c); for \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} \gg 1\), growth is unstable and the tissue breaks symmetry and develops fingers (Extended Data Figs. 7d, e, 8c). viscoelastic limit are (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 0.017,\) \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 0.002,\;j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.05\)) and (\(A = \frac{{\tau _{{{\mathrm{a}}}}}}{{\tau _{{{\mathrm{m}}}}}} = 133,\), \(\mu = \frac{{\mu _{{{\mathrm{t}}}}}}{{\mu _{{{\mathrm{m}}}}}} = 2,j = \frac{{\tau _{{{\mathrm{g}}}}}}{{\tau _{{{\mathrm{t}}}}}} = 0.16\)) respectively.

Extended Data Fig. 9 Organoids grow, break symmetry and form buds with time.

a, Examples of growth of intestinal organoids in elastic versus viscoelastic hydrogels over 7 days. Phalloidin in cyan, Hoechst in magenta. Scale bar is 100 µm. b, Quantification of organoid circularity in different stiffness elastic and viscoelastic hydrogels. n = 32,32,38,37 organoids per condition. Statistical analysis was performed using Kruskal–Wallis test followed by post hoc Dunn’s test. Data represent mean ± s.d.

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Extended Data Fig. 10 Organoids present differentiated cell types.

a, Quantification of the percentage of Sox9 positive cells in low and high-curvature areas in organoids. n = 9,12 images per condition. Statistical analysis was performed using two-sided Mann-Whitney U-test. b, Representative examples. c, Organoid buds have lysozyme positive cells intercalated in between Sox9 positive cells (n = 15 images). d–f, Organoids cultured in interpenetrating networks contain also (d) enteroendocrine (n = 7 images), (e) goblet cells (n = 8 images) and (f) enterocytes (n = 5 images). Data represent mean ± s.d. Scale bars are 20 µm.

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Supplementary information

Supplementary Information

Supplementary Note 1, Figs. 1–23, text describing the model, and Tables 1–3.

Reporting Summary

Supplementary Video 1

Examples of spheroids growth in elastic (left) and viscoelastic (right) matrices.

Supplementary Video 2

Examples of simulated tissue growth in elastic (left) and viscoelastic (right) matrices.

Supplementary Video 3

Examples of simulated tissue growth when cell motility is inhibited in elastic (left) and viscoelastic(right) matrices.

Supplementary Video 4

Examples of simulated tissue growth when cell proliferation is inhibited in elastic (left) and viscoelastic(right) matrices.

Supplementary Video 5

Examples of simulated tissue growth in elastic (upper row) and viscoelastic (lower row) in matrices of increasing stiffness.

Supplementary Video 6

Examples of simulated tissue growth when cell migration is inhibited in elastic (upper row) and viscoelastic (lower row) in matrices of increasing stiffness.

Supplementary Video 7

Examples of simulated tissue growth when cell proliferation is inhibited in elastic (upper row) and viscoelastic (lower row) in matrices of increasing stiffness.

Supplementary Video 8

Example of simulated tissue growth when cells are continuously added to the tissue in elastic (left) and viscoelastic (right) matrices.

Supplementary Video 9

Example of simulated tissue growth when the matrix property changes from elastic to viscoelastic.

Supplementary Video 10

Example of simulated tissue growth when the matrix property changes from viscoelastic to elastic.

Supplementary Video 11

Examples of simulated organoid tissue growth in elastic (upper row) and viscoelastic (lower row) in matrices of increasing stiffness.

Supplementary Video 12

Examples of simulated organoid tissue growth in viscoelastic matrices where two black cells have higher motility compared to the rest.

Supplementary Video 13

Examples of simulated organoid tissue growth in viscoelastic matrices where an increasing number of cells (black) have 4 times higher motility compared to the rest.

Supplementary Video 14

Examples of simulated organoid tissue growth in viscoelastic matrices where four black cells have an increasing probability to divide compared to the rest.

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Elosegui-Artola, A., Gupta, A., Najibi, A.J. et al. Matrix viscoelasticity controls spatiotemporal tissue organization. Nat. Mater. 22, 117–127 (2023). https://doi.org/10.1038/s41563-022-01400-4

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