Geometric order in proliferating epithelia: impact of rearrangements and cleavage plane orientation.

Regulation of proliferation is required for normal development of tissues and prevention of cancer formation. Continuous control of proliferation leads to regular shaped cells forming characteristic tissue patterns. Epithelial tissues serve as a model system for studying tissue morphogenesis. Several groups have studied epithelial morphogenesis using topological or geometric models, with various assumptions. In this study, we have developed a method to simulate the dynamic process of proliferating epithelia using an off-lattice cellular model. Our method realistically models the shape, size, geometry, lineage, cleavage plane orientation as well as topological properties of individual cells. We find that cellular rearrangements and cleavage plane orientation are critical in the formation of the observed cellular pattern of epithelia, including a high percentage of hexagons in proliferating epithelial cells. It is likely that the rearrangements and orientation of the cleavage plane reduces the overall stress on the cell. We show that a high percentage of hexagons in proliferating epithelia can be obtained using uniform growth rates, which was considered unlikely in previous studies. Our off-lattice cellular model provides an improvement over existing topological for studying the dynamics of proliferating epithelium.