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.
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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.
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