Title: Modeling and inferring cleavage patterns in proliferating epithelia
Description: A proliferating epithelium is a sheet of dividing cells that adhere to each other strongly. Understanding how these sheets divide is important both for development and for disease. The regulation of cell division is one of the key mechanisms that drive the development of living organisms. Abnormal divisions lead to cancer, of which most are epithelial in origin. Despite their importance, the specific local mechanisms that direct division in epithelia remain poorly understood. Several important questions arise: How does the local regulation of cleavage affect the global topology of proliferating epithelia? Conversely, can we infer properties of local cleavage by observing the global tissue architecture? My research attempts to answer these question and others by focusing on cell shape, defined here as a cell's number of neighbors. In this thesis, I propose a topological framework that yields new insights into the underlying mechanisms that govern cell shape dynamics in proliferating epithelia. Specifically, I formulate three distinct topological models, each of increasing complexity and detail. Using these models, I make several predictions, the most important of which has led to the discovery of a conserved distribution of cell shape in at least five disparate organisms. I also explain previously elusive phenomena, such as the problem of hexagonal dominance: Why are there so many hexagons in epithelia? I show that majority of hexagons seen empirically is a natural result of symmetric, charitable divisions, providing an answer to an old question.

Using more general simulation studies, I find that cleavage patterns generate signature distributions of cell shape that depend heavily on pattern of proliferation but are independent of initial conditions. These signatures enable the inference of local cleavage parameters such as neighbor impact, maternal influence, and division symmetry from simple observations of the distribution of cell shape. Applying these insights to the natural epithelia of five diverse organisms, I 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. And lastly, I present two distinct cleavage patterns that can reproduce the empirically observed distributions of cell shape with high accuracy. Together, my work strongly suggests that cell division planes are not chosen at random, but are instead actively regulated to suppress variation in cell shape within a proliferating epithelium.