Cancer cell hyper-proliferation disrupts the topological invariance of epithelial monolayers

Although the polygonal shape of epithelial cells has drawn the attention of scientists for several centuries, only recently, it has been demonstrated that distributions of polygon types (DOPTs) are similar in proliferative epithelia of many different plant and animal species. In this study we show that hyper-proliferation of cancer cells disrupts this universality paradigm and results in random epithelial structures. Examining non-synchronized and synchronized HeLa cervix cells, we suppose that the cell size spread is the single parameter controlling the DOPT in these monolayers. We test this hypothesis by considering morphologically similar random polygonal packings. By analyzing the differences between tumoral and non-tumoral epithelial monolayers, we uncover that the latter have more ordered structures and argue that the relaxation of mechanical stresses associated with cell division induces more effective ordering in the epithelia with lower proliferation rates. The proposed theory also explains the specific highly ordered structures of some post-mitotic unconventional epithelia.