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.

The emergence of geometric order in proliferating metazoan epithelia

Abstract

The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues1, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays2. Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of in vivo analysis of mitotic cell junction dynamics in Drosophila imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Mitosis and the in vivo dynamics of epithelial topology.
Figure 2: A robust equilibrium topology in proliferating epithelial cell networks.
Figure 3: An emergent topological order in proliferating epithelia.

References

  1. Schwann, T. Microscopical Researches into the Accordance of Structure and Growth in Animals and Plants (Syndenham Society, London, 1847)

    Google Scholar 

  2. Thompson, D. W. On Growth and Form (Cambridge Univ. Press, Cambridge, 1942)

    MATH  Google Scholar 

  3. Hayashi, T. & Carthew, R. W. Surface mechanics mediate pattern formation in the developing retina. Nature 431, 647–652 (2004)

    Article  ADS  CAS  Google Scholar 

  4. Amonlirdviman, K. et al. Mathematical modeling of planar cell polarity to understand domineering nonautonomy. Science 307, 423–426 (2005)

    Article  ADS  CAS  Google Scholar 

  5. Weaire, D. & Rivier, N. Soap, cells and statistics—Random patterns in two dimensions. Contemp. Phys. 25, 59–99 (1984)

    Article  ADS  Google Scholar 

  6. Abbott, L. A. & Lindenmayer, A. Models for growth of clones in hexagonal cell arrangements: Applications in Drosophila wing disc epithelia and plant epidermal tissues. J. Theor. Biol. 90, 495–544 (1981)

    Article  CAS  Google Scholar 

  7. Lewis, F. T. The effect of cell division on the shape and size of hexagonal cells. Anat. Rec. 33, 331–355 (1926)

    Article  Google Scholar 

  8. Lewis, F. T. The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of Cucumis. Anat. Rec. 38, 341–376 (1928)

    Article  Google Scholar 

  9. Graustein, W. C. On the average number of sides of polygons of a net. Ann. Math. 32, 149–153 (1931)

    Article  MathSciNet  Google Scholar 

  10. Garcia-Bellido, A. & Merriam, J. R. Parameters of the wing imaginal disc development in Drosophila melanogaster. Dev. Biol. 24, 61–87 (1971)

    Article  CAS  Google Scholar 

  11. Bryant, P. J. & Levinson, P. Intrinsic growth control in the imaginal primordia of Drosophila, and the autonomous action of a lethal mutation causing overgrowth. Dev. Biol. 107, 355–363 (1985)

    Article  CAS  Google Scholar 

  12. Milan, M., Campuzano, S. & Garcia-Bellido, A. Cell cycling and patterned cell proliferation in the wing primordium of Drosophila. Proc. Natl Acad. Sci. USA 93, 640–645 (1996)

    Article  ADS  CAS  Google Scholar 

  13. Tepass, U., Tanentzapf, G., Ward, R. & Fehon, R. Epithelial cell polarity and cell junctions in Drosophila. Annu. Rev. Genet. 35, 747–784 (2001)

    Article  CAS  Google Scholar 

  14. Bertet, C., Sulak, L. & Lecuit, T. Myosin-dependent junction remodelling controls planar cell intercalation and axis elongation. Nature 429, 667–671 (2004)

    Article  ADS  CAS  Google Scholar 

  15. Zallen, J. A. & Zallen, R. Cell-pattern disordering during convergent extension in Drosophila. J. Phys. Condens. Matter 16, S5073–S5080 (2004)

    Article  ADS  CAS  Google Scholar 

  16. Classen, A. K., Anderson, K. I., Marois, E. & Eaton, S. Hexagonal packing of Drosophila wing epithelial cells by the planar cell polarity pathway. Dev. Cell 9, 805–817 (2005)

    Article  CAS  Google Scholar 

  17. Morin, X., Daneman, R., Zavortink, M. & Chia, W. A protein trap strategy to detect GFP-tagged proteins expressed from their endogenous loci in Drosophila. Proc. Natl Acad. Sci. USA 98, 15050–15055 (2001)

    Article  ADS  CAS  Google Scholar 

  18. Kelso, R. J. et al. Flytrap, a database documenting a GFP protein-trap insertion screen in Drosophila melanogaster. Nucleic Acids Res. 32, D418–D420 (2004)

    Article  CAS  Google Scholar 

  19. Bryant, P. J. Cell lineage relationships in the imaginal wing disc of Drosophila melanogaster. Dev. Biol. 22, 389–411 (1970)

    Article  CAS  Google Scholar 

  20. Garcia-Bellido, A., Ripoll, P. & Morata, G. Developmental compartmentalisation of the wing disk of Drosophila. Nat. New Biol. 24, 251–253 (1973)

    Article  Google Scholar 

  21. Resino, J., Salama-Cohen, P. & Garcia-Bellido, A. Determining the role of patterned cell proliferation in the shape and size of the Drosophila wing. Proc. Natl Acad. Sci. USA 99, 7502–7507 (2002)

    Article  ADS  CAS  Google Scholar 

  22. Struhl, G. & Basler, K. Organizing activity of wingless protein in Drosophila. Cell 72, 527–540 (1993)

    Article  CAS  Google Scholar 

  23. Cowan, R. & Morris, V. B. Division rules for polygonal cells. J. Theor. Biol. 131, 33–42 (1988)

    Article  CAS  Google Scholar 

  24. Taylor, H. M. & Karlin, S. An Introduction to Stochastic Modeling 3rd edn (Academic, Chestnut Hill, Massachusetts, 1998)

    MATH  Google Scholar 

  25. Edgar, B. A. & O'Farrell, P. H. The three postblastoderm cell cycles of Drosophila embryogenesis are regulated in G2 by string. Cell 62, 469–480 (1990)

    Article  CAS  Google Scholar 

  26. Halanych, K. M. & Passamaneck, Y. A brief review of metazoan phylogeny and future prospects in Hox-research. Am. Zool. 41, 629–639 (2001)

    CAS  Google Scholar 

Download references

Acknowledgements

We thank R. Ward, J. D. Lambert, B. Mathey-Prevot, E. Lieberman, R. Arnaout and M. Markstein for critical comments on the manuscript; the Bloomington Stock Center for fly stocks; and the Developmental Studies Hybridoma Bank for antibodies. This work was supported by a Microsoft New Faculty Fellowship to R.N., an NSF grant to R.N., and support from the Howard Hughes Medical Institute to N.P. A.B.P. is a fellow of the National Science Foundation and M.C.G. was supported by the Jane Coffin Childs Memorial Fund for Medical Research. Author Contributions R.N. and N.P. are senior authors. A.B.P. and M.C.G. contributed equally to the work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matthew C. Gibson.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Material

(PDF 284 kb)

Supplementary Movie 1

Imaginal disc cell division (MOV 8168 kb)

Supplementary Movie 2

Imaginal disc cell division (MOV 7465 kb)

Supplementary Movie 3

Imaginal disc cell division (MOV 6782 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gibson, M., Patel, A., Nagpal, R. et al. The emergence of geometric order in proliferating metazoan epithelia. Nature 442, 1038–1041 (2006). https://doi.org/10.1038/nature05014

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature05014

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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