  During embryonic development, structures with complex geometry can emerge
from planar epithelial monolayers and to study these shape transitions is of
key importance for revealing the biophysical laws involved in the morphogenesis
of biological systems. Here, using the example of normal proliferative monkey
kidney (COS) cell monolayers, we investigate global and local topological
characteristics of this model system in dependence on its shape. The obtained
distributions of cells by their valence demonstrate a previously undetected
difference between the spherical and planar monolayers. In addition, in both
spherical and planar monolayers, the probability to observe a pair of
neighboring cells with certain valences depends on the topological charge of
the pair. The zero topological charge of the cell pair can increase the
probability for the cells to be the nearest neighbors. We then test and confirm
that analogous relationships take place in a more ordered spherical system with
a larger fraction of 6-valent cells, namely in the non-proliferative epithelium
(follicular system) of ascidian species oocytes. However, unlike spherical COS
cell monolayers, ascidian monolayers are prone to non-random agglomeration of
6-valent cells and have linear topological defects called scars and pleats. The
reasons for this difference in morphology are discussed. The morphological
peculiarities found are compared with predictions of widely used vertex model
of epithelium.
