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 tissues, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays. 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.

On the mechanism of wing size determination in fly development

“…Adherens junctions involve cadherins that bind apposing cell surfaces and link to the cortical actin cytoskeleton on the intracellular side (34)(35)(36). Recent experiments visualizing cell division in ex vivo late third-instar imaginal discs have demonstrated a remarkable lack of cell rearrangement (37). This fact strongly suggests that imaginal disk tissue behaves more like an elastic ''solid,'' than a ''fluid'' where cells would be free to rearrange rapidly.…”

Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures

“…In this case, for a 2D monolayer, our model predicts that the probability distribution of cell-cell contacts should reduce to that found in Gibson et al (2006) and Dubertret et al (1998), as mechanical relaxations become negligible compared with cell division. Indeed, the models described in Gibson et al (2006) and Dubertret et al (1998) consider the topological distribution of polygonal tilings emerging as a sole effect of random cell divisions, without taking into account mechanical relaxation.…”

“…Luminal surfaces were measured from segmented stacks by fitting the data with triangulated surfaces and calculating their areas. In Figs neq and x i eq of the theoretically predicted frequencies for nonequilibrium (Gibson et al, 2006) and equilibrium (Cox and Flikkema, 2010), respectively.…”

“…Conversely, if cysts grow out of mechanical equilibrium, their surface topology has to be the one predicted in Gibson et al (2006).…”

Que faire de la membrane plasmique d’une cellule pendant la mitose ?

“…Elles forment alors chacune une boule compacte lors de la métaphase, que ce soit dans des conditions de culture cellulaire ou dans les tissus vivants [1][2][3][4]. Puis, au cours de l'anaphase et de la cytokinèse, les deux cellules filles en formation reprennent leurs formes étalées (Figure 1).…”