A binary segmentation method for detecting topological domains in Hi-C data

The three-dimensional (3D) architecture of chromosomes in nuclear space plays an important role in studying gene expression and regulation in cell biology. In particular, chromosome conformation capture (3C) techniques are used to study the spatial structure of chromosomes. Many such methods have been developed in the last two decades. Among them, Hi-C is a technology that uses a deep sequencing approach to detect the 3D spatial organization of a genome. That is, Hi-C allows us to evaluate spatial proximity between any pair of loci along the genome. This results in an interaction matrix with the frequency of interactions between genomic loci that physically interact in the nucleus. Highly self-interacting regions appear in the contact map of such interaction matrices. These regions are called topological domains and they play an important role in regulating gene expression and other genomic functions. Thus detecting such topological domains will provide new insights on chromosomal conformation in better understanding of cell functioning and various diseases.

The topological domains centered along a diagonal region in contact maps are more likely to exist and prominent in data. In this study, we focus on detecting such domains, and we approach this problem as a twodimensional segmentation problem. To solve this segmentation problem, we propose an algorithm based on the binary segmentation method, a well-known recursive partitioning technique used in change point detection problems. Our numerical experiments illustrate the usefulness of this approach. We obtain estimates for the number of diagonal blocks and their boundaries in an artificially generated data matrix and compare the results of these estimates to those obtained with the HiCSeg R package. We conclude that binary segmentation method works well in identifying such domains with easy implementation and a low computational cost.