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Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

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Petridou, Nicoletta I., Corominas-Murtra, Bernat, Heisenberg, Carl-Philipp, Hannezo, Edouard·2021·Cell
DOI 10.1016/j.cell.2021.02.017PMC PMC8055543
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Abstract

Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.

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  • Embryonic tissue in its early stages lies close to the fluidization critical point, enabling the tissue to melt and thus induce a strong deformation to solidify again, to fix morphogenetic changes.

    “For example, it has been reported that the embryonic tissue in its early stages lies close to the fluidization critical point, enabling the tissue to melt and thus induce a strong deformation to solidify again, to fix the morphogenetic changes [406].”

    From Fundamental constraints to the logic of living systems (2024) · cites this paper as [406]

    The Results sections on zebrafish blastoderm fluidization and rigidity percolation report a transition near a critical connectivity threshold: the blastoderm briefly fluidizes at the onset of morphogenesis, then regains viscosity and rigidity. The paper does not establish that this sequence enables strong deformation or fixes morphogenetic changes, and its findings concern the central zebrafish blastoderm rather than embryonic tissue generally. The indexed passages provide section labels but no page numbers. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • Huge fluctuations due to proximity to the critical point may represent a serious drawback for the precision of tissue development.

    “In addition, huge fluctuations due to the proximity to the critical point may represent a serious drawback for the precision of tissue development [406].”

    From Fundamental constraints to the logic of living systems (2024) · cites this paper as [406]

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Cited by

Sorted by citations

Authors
Petridou, N. I., Corominas-Murtra, B., Heisenberg, C.-P., & Hannezo, E.
Affiliations
Institute of Science and Technology Austria (AT)
Corresponding author
Heisenberg, Carl-Philipp
ORCID
Venue
Cell
Publisher
Elsevier BV
Published
2021-04
Volume
184
Issue
7
Pages
1914-1928.e19
ISSN
0092-8674 (ISSN-L)
DOI
10.1016/j.cell.2021.02.017
PMC
PMC8055543
OpenAlex
W3138361816
Cited by
222
References
4
Citations by year
2026: 51 · 2025: 46 · 2024: 41 · 2023: 28 · 2022: 34 · 2021: 19 · 2020: 2 · 2019: 1
FWCI
15.92
Type
journal article
Language
en
Open access
Licence
Locations
  • Cell (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
Funders
  • European Research Council (742573, 851288)
  • Austrian Science Fund (V 736-B26)
  • European Commission
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Cell Biology › Cellular Mechanics and Interactions
  • Physical Sciences › Engineering › Mechanical Engineering › Advanced Materials and Mechanics
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
Keywords
rigidity percolation, cell connectivity, cell adhesion, tissue rheology, flow index, percolation theory, morphogenesis
MeSH terms
Animals, Blastoderm, Cell Adhesion, Embryo, Nonmammalian, Rheology, Viscosity, Zebrafish, Cadherins, Embryonic Development, Morpholinos

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