Heterogeneous loop model to infer 3D chromosome structures from Hi-C

Adapting a well-established formalism in polymer physics, we develop a minimalist approach to infer threedimensional (3D) folding of chromatin from Hi-C data. The 3D chromosome structures generated from our heterogeneous loop model (HLM) are used to visualize chromosome organizations that can substantiate the measurements from FISH, ChIA-PET, and RNA-Seq signals. We demonstrate the utility of HLM with several case studies. Specifically, the HLM-generated chromosome structures, which reproduce the spatial distribution of topologically associated domains (TADs) from FISH measurement, show the phase segregation between two types of TADs explicitly. We discuss the origin of cell-type dependent gene expression level by modeling the chromatin globules of α -globin and SOX2 gene loci for two different cell lines. We also use HLM to discuss how the chromatin folding and gene expression level of Pax6 loci, associated with mouse neural development, is modulated by interactions with two enhancers. Finally, HLM-generated structures of chromosome 19 of mouse embryonic stem cells (mESCs), based on single-cell Hi-C data collected over each cell cycle phase, visualize changes in chromosome conformation along the cell cycle. Given a contact frequency map between chromatic loci supplied from Hi-C, HLM is a computationally efficient and versatile modeling tool to generate chromosome structures, which can complement interpreting other experimental data.