MrTADFinder: A network modularity based approach to identify topologically associating domains in multiple resolutions

Genome-wide proximity ligation based assays such as Hi-C have revealed that eukaryotic genomes are organized into structural units called topologically associating domains (TADs). From a visual examination of the chromosomal contact map, however, it is clear that the organization of the domains is not simple or obvious. Instead, TADs exhibit various length scales and, in many cases, a nested arrangement. Here, by exploiting the resemblance between TADs in a chromosomal contact map and densely connected modules in a network, we formulate TAD identification as a network optimization problem and propose an algorithm, MrTADFinder, to identify TADs from intra-chromosomal contact maps. MrTADFinder is based on the network-science concept of modularity. A key component of it is deriving an appropriate background model for contacts in a random chain, by numerically solving a set of matrix equations. The background model preserves the observed coverage of each genomic bin as well as the distance dependence of the contact frequency for any pair of bins exhibited by the empirical map. Also, by introducing a tunable resolution parameter, MrTADFinder provides a self-consistent approach for identifying TADs at different length scales, hence the acronym "Mr" standing for Multiple Resolutions. We then apply MrTADFinder to various Hi-C datasets. The identified domain boundaries are marked by characteristic signatures in chromatin marks and transcription factors (TF) that are consistent with earlier work. Moreover, by calling TADs at different length scales, we observe that boundary signatures change with resolution, with different chromatin features having different characteristic length scales. Furthermore, we report an enrichment of HOT (high-occupancy target) regions near TAD boundaries and investigate the role of different TFs in determining boundaries at various resolutions. To further explore the interplay between TADs and epigenetic marks, as tumor mutational burden is known to be coupled to chromatin structure, we examine how somatic mutations are distributed across boundaries and find a clear stepwise pattern. Overall, MrTADFinder provides a novel computational framework to explore the multi-scale structures in Hi-C contact maps.Author summary: The accommodation of the roughly 2m of DNA in the nuclei of mammalian cells results in an intricate structure, in which the topologically associating domains (TADs) formed by densely interacting genomic regions emerge as a fundamental structural unit. Identification of TADs is essential for understanding the role of 3D genome organization in gene regulation. By viewing the chromosomal contact map as a network, TADs correspond to the densely connected regions in the network. Motivated by this mapping, we propose a novel method, MrTADFinder, to identify TADs based on the concept of modularity in network science. Using MrTADFinder, we identify domains at various resolutions, and further explore the interplay between domains and other chromatin features like transcription factors binding and histone modifications at different resolutions. Overall, MrTADFinder provides a new computational framework to investigate the multiple length scales that are built inside the organization of the genome.