Chromatin as self-returning walks: From population to single cell and back

With a growing understanding of the chromatin structure, many efforts remain focused on bridging the gap between what is suggested by population-averaged data and what is visualized for single cells. A popular approach to traversing these scales is to fit a polymer model to Hi-C contact data. However, Hi-C is an average of millions to billions of cells, and each cell may not contain all population-averaged contacts. Therefore, we employ a novel approach of summing individual chromosome trajectories-determined by our Self-Returning Random Walk model-to create populations of cells. We allow single cells to consist of disparate structures and reproduce a variety of experimentally relevant contact maps. We show that the amount of shared topology between cells, and their mechanism of formation, changes the population-averaged structure. Therefore, we present a modeling technique that, with few constraints and little oversight, can be used to understand which single-cell chromatin structures underlie population-averaged behavior.