Letter | Published:

The emergence of geometric order in proliferating metazoan epithelia


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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1

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

  2. 2

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

  3. 3

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

  4. 4

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

  5. 5

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

  6. 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)

  7. 7

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

  8. 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)

  9. 9

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

  10. 10

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

  11. 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)

  12. 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)

  13. 13

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

  14. 14

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

  15. 15

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

  16. 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)

  17. 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)

  18. 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)

  19. 19

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

  20. 20

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

  21. 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)

  22. 22

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

  23. 23

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

  24. 24

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

  25. 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)

  26. 26

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

Download references


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

Competing interests

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

Correspondence to Matthew C. Gibson.

Supplementary information

  1. Supplementary Material

    (PDF 284 kb)

  2. Supplementary Movie 1

    Imaginal disc cell division (MOV 8168 kb)

  3. Supplementary Movie 2

    Imaginal disc cell division (MOV 7465 kb)

  4. Supplementary Movie 3

    Imaginal disc cell division (MOV 6782 kb)

Rights and permissions

Reprints and Permissions

About this article

Further reading

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.


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.