Heterogeneous Loop Model to Infer 3D Chromosome Structures from Hi-C

Abstract

Adapting a well-established formalism in polymer physics, we develop a minimalist approach to infer three-dimensional folding of chromatin from Hi-C data. The three-dimensional chromosome structures generated from our heterogeneous loop model (HLM) are used to visualize chromosome organizations that can substantiate the measurements from fluorescence in situ hybridization, chromatin interaction analysis by paired-end tag sequencing, and RNA-seq signals. We demonstrate the utility of the HLM with several case studies. Specifically, the HLM-generated chromosome structures, which reproduce the spatial distribution of topologically associated domains from fluorescence in situ hybridization measurement, show the phase segregation between two types of topologically associated domains explicitly. We discuss the origin of cell-type-dependent gene-expression level by modeling the chromatin globules of a-globin and SOX2 gene loci for two different cell lines. We also use the HLM to discuss how the chromatin folding and gene-expression level of Pax6 loci, associated with mouse neural development, are modulated by interactions with two enhancers. Finally, HLM-generated structures of chromosome 19 of mouse embryonic stem cells, 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 that can complement interpreting other experimental data.

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

“…Therefore, the negative values are acceptable as repulsive forces in the polymer network model. This assumption is a unique point of our modeling, and different from the recently developed similar polymer modeling (23,24).…”

“…Recently, the quantitative significance of Hi-C contact matrix data was elucidated mathematically by several independent groups (23)(24)(25). We developed a polymer modeling and a simulation method called polymer dynamics deciphered from Hi-C data (PHi-C) to decipher Hi-C data into polymer dynamics (25).…”

Maximum parsimony interpretation of chromatin capture experiments

“…Such prospect is very promising, especially in light of the recent evidence (supported by computer simulations) suggesting that also in metazoans distinct cell populations may exist that realize specific structures of their topologically associated domains, and corresponding subpopulation-specific pattern of transcriptional activation of genes, see e.g. [16, 32, 33]. It is also important to note that our graph-coloring approach is not limited to distances and conflicts defined by Eqs (2) and (3) but it is a general framework that can be used with any method of assessing the distance and its error from the number of reads in the HiC dataset.…”

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

“…Here, the negative values are acceptable as repulsive forces in the polymer network model. This assumption is a unique point of our modeling and different from recently developed similar polymer modeling (23,24). As long as the Laplacian matrix of K is positive-semidefinite, the polymer organization does not break down (25).…”

“…Recently, the quantitative significance of Hi-C contact matrix data was elucidated mathematically by several independent groups (23)(24)(25). We developed a polymer modeling and a simulation method, called PHi-C (Polymer dynamics deciphered from Hi-C data), to decipher Hi-C data into polymer dynamics (25).…”