Abstract
The cross-section of a cell in a monolayer epithelial tissue can be modeled mathematically as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. A variety of mathematical models have been proposed for explaining this phenomenon. The highly parsimonious simulation model of (Patel et al., PLoS Comput. Biol., 2009) that takes into account only the number of sides of a given cell and cell division already achieves a remarkably good fit with empirical distributions from Drosophila, Hydra, Xenopus, Cucumber, and Anagallis. Within the same modeling framework as in that paper, we introduce additional options for the choice of the endpoints of the cleavage plane that appear to be biologically more realistic. By taking the same data sets as our benchmarks, we found that combinations of some of our new options consistently gave better fits with each of these data sets than previously studied ones. Both our algorithm and simulation data are made available as research tools for future investigations.
Highlights
Epithelia are sheets of tightly adherent cells that line both internal and external surfaces in a vast array of metazoans
Our refinement of the model of [3] is purely topological, which means that it takes into account only the number of sides of a given cell and the neighborhood relation
A variety of mathematical models have been proposed for explaining the polygonal distribution in developing epithelia that is fairly strongly conserved across evolutionarily distant species
Summary
Epithelia are sheets of tightly adherent cells that line both internal and external surfaces in a vast array of metazoans. A (cross-section of a) cell in an epithelial tissue can be modeled as a k-sided polygon. One class of models considers exclusively cell topology, that is the neighborhood relation between cells in the tissue. The other class of models, called here geometric models, considers such geometric features as size and shape of the polygon and permits the study of factors like the role of mechanical stresses. Another major distinction is between division-only models that consider only cell
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