G.A. Savostyanov, N.M. Grefner and O.F. Lutskaja

The 3 - dimensional structure of normal and pathological tissues is poorly studied and its reconstruction is rather complicated. Thus a new approach to the investigation of 3 - dimensional shape and spatial arrangement of cells in epithelial sheets has been developed. This approach made it possible to show that this symmetry is typical for epithelial tissues. The approach is based on an assumption that tissues consist of cell groups rather that cells itself. The groups are originated due to the division of functions between cells and local cells interactions. The groups represent an overlooked level of biological organization that situated between cell`s and tissue`s levels. Therefore one may consider tissues as polymeric cell`s groups. There are natural set of groups polymerization rules. So the periodic cell mosaics with translational symmetry should be typical to epithelia. According to this hypothesis, theoretical evidences shows that as many as 11 topological variants of cells arrangement (cell mosaic patterns) are possible for simple epithelium but not the only one as it was assumed before. All these mosaics are known in mathematics as Kepler`s regular parquets and characterized by the translation symmetry. The mosaics limit the directions of epithelia development in onto- and phylogenesis making the prediction of the tissue development possible. Up to now 8 variants of such epithelial mosaics in different animals have been already experimentally found. The discovery of other ones is possible in future.

According to the results a model of 3 - dimensional shape and spatial arrangement of cells in pseudostratified epithelial sheets were developed. Preliminary data seem to confirm the models and stress up the importance of the investigation.

The present investigation brings us to the conclusion that tissue topology transformation during carcinogenesis may be compared with phase transformation in physics and described quite accurately. The analysis of transformation of cell mosaics symmetry may serve as the key to understanding of carcinogenesis and the role of cell`s groups (or tissue elementary units) in these processes.

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