J Theor Biol 2014 Apr 07;346:1-7. doi: 10.1016/j.jtbi.2013.12.029.

Quantitative analysis of cell arrangement indicates early differentiation of the neural region during Xenopus gastrulation.

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Cell adhesion properties change with the state of cell differentiation, causing specific rearrangements of cells within the tissue during morphogenesis. Any such differing cell arrangements must be a result of change of the adhesion properties. Thus, cell arrangement is expected to be an indication of differentiation and phenotype. However, there is no established system, theoretical or experimental, to describe general cell arrangements. In order to evaluate cell arrangement quantitatively, we used a mathematical graph model in which cell arrangement is simplified to an adjacency relationship. We introduce a new index of cell arrangement defined in terms of how much of different particular small graphs are included in the graph of cells. The index, represented by vectors, enables the comparison of areal cell arrangements. In an analysis of Xenopus ectoderm, the site where the vector changed was detected in an area between the dorsal and ventral regions at late gastrula, and this site moved toward the dorsal midline at early neurula, similar to the behavior of a prospective neural region. Interestingly, the border between areas with different cell arrangements corresponded to the neural-epithelial boundary. The graph model of cell arrangement was shown to be able to distinguish difference in cell arrangements which are hard to tell by intuitive analysis of microscopic images. The behavior of cell arrangement border suggests that it corresponds to a neural-epithelial border, and the neural differentiation at late gastrula.

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