Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Nice Nature paper on cell packing
In the August 31 Nature there is a fine paper on the neighbor relationships of skin cells, whether they form hex grids for minimization reasons or not, that sort of subject. It makes a very convincing case that minimization has nothing to do with it and the patterns seen are purely a result of the effect of cell division on the number of neighbors. A simple markov model yields a stable distribution of neighbor number, clustered around 5 to 8 neighbors, that fits remarkably well with their empirical data. I found it an excellent NKS-esque model, because it is an example of a simple combinatoric-based underlying driver giving a complex emergent pattern effortlessly.
The article is entitled "The emergence of geometric order in proliferating metazoan epithelia", and the authors (from various groups at Harvard) are Matthew C. Gibson, Ankit B. Patel, Radhika Nagpal, and Norbert Perrimon. Here is their 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.
Here is a link to the article at Nature online -
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