Modeling and Inferring Cleavage Patterns in Proliferating Epithelia

The regulation of cleavage plane orientation is one of the key mechanisms driving epithelial morphogenesis. Still, many aspects of the relationship between local cleavage patterns and tissue-level properties remain poorly understood. Here we develop a topological model that simulates the dynamics of a 2D proliferating epithelium from generation to generation, enabling the exploration of a wide variety of biologically plausible cleavage patterns. We investigate a spectrum of models that incorporate the spatial impact of neighboring cells and the temporal influence of parent cells on the choice of cleavage plane. Our findings show that cleavage patterns generate “signature” equilibrium distributions of polygonal cell shapes. These signatures enable the inference of local cleavage parameters such as neighbor impact, maternal influence, and division symmetry from global observations of the distribution of cell shape. Applying these insights to the proliferating epithelia of five diverse organisms, we find that strong division symmetry and moderate neighbor/maternal influence are required to reproduce the predominance of hexagonal cells and low variability in cell shape seen empirically. Furthermore, we present two distinct cleavage pattern models, one stochastic and one deterministic, that can reproduce the empirical distribution of cell shapes. Although the proliferating epithelia of the five diverse organisms show a highly conserved cell shape distribution, there are multiple plausible cleavage patterns that can generate this distribution, and experimental evidence suggests that indeed plants and fruitflies use distinct division mechanisms. Author Summary: Cell division is one of the key mechanisms driving organismal growth and morphogenesis. Yet many aspects of the relationship between local cell division (how a cell chooses an orientation to divide) and global tissue architecture (e.g., regular versus irregular cells) remain poorly understood. We present a computational framework for studying topological networks that are created by cell division; this framework reveals how certain tissue statistics can be used to infer properties of the cell division model. Recently it has been observed that five diverse organisms show almost identical cell shape distributions in their proliferating epithelial tissues, yet how this conservation arises is not understood. Using our model we show that the low variation observed in nature requires a strong correlation between how neighboring cells divide and that although the statistics of plants and fruitflies are almost identical, it is likely that they have evolved distinct cell division methods.