engleski

Topology of dividing planar tilings: mitosis and ordering in epithelial tissues

Epithelial tissues can be well approximated as 2D polygon tilings of the plane. There are, however, infinitely many plane tilings, some ordered more than others and some seemingly “random”, consisting of a range of polygon types and sizes. Not all tilings which can be imagined represent epithelial tissues, but those which do still represent a rather varied class, consisting of several subclasses. The tissues are, furthermore, dynamical tilings, as the cells they consist of divide [1]. The ordering of the epithelial tissue is thus, in general, a consequence of two effects: (i) energetics of cell-cell contacts and (ii) dynamical effects related to mitosis [2]. Here we concentrate on the second of the two effects and explore the stationary configurations of the tissues governed exclusively by the rules of cell division in which the energetics plays a secondary role, implicitly encoded in the rules. Depending on the rules chosen, three different epithelial classes are identified – a completely ordered tiling, consisting only of hexagons, a “random” tiling, consisting of many different polygons with comparable occurrence frequencies, and a semi-disordered tiling, consisting mainly of pentagons, hexagons and heptagons. The latter structure is often observed in real tissues [3]. [1] A. Šiber and P. Ziherl, Cellular Patterns, Taylor & Francis (2017). [2] M. C. Gibson, A. B. Patel, R. Nagpal, and N. Perrimon, Nature 442, 1038 (2006). [3] M. Kokalj Ladan, A. Šiber and P. Ziherl, in preparation.

epithelium, tissue, tiling, mitosis, Markov, statistics

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