Intrinsic linking of chromatin fiber in human cells

Motivation We propose a practical algorithm based on graph theory, with the purpose of identifying CTCF-mediated chromatin loops that are linked in 3D space. Our method is based finding clique minors in graphs constructed from pairwise chromatin interaction data obtained from the ChIA-PET experiments. We show that such a graph structure, representing a particular arrangement of loops, mathematically necessitates linking, if co-occurring in an individual cell. The presence of these linked structures can advance our understanding of the principles of spatial organization of the genome. Results We apply our method to graphs created from in situ ChIA-PET data for GM12878, H1ESC, HFFC6 and WTC11 cell lines, and from long-read ChIA-PET data. We look at these datasets as divided into CCDs - closely interconnected regions defined based on CTCF loops. We find numerous candidate regions with minors, indicating the presence of links. The graph-theoretic characteristics of these linked regions, including betweenness and closeness centrality, differ from regions without, in which no minors were found, which supports their non-random nature. We also look at the position of the linked regions with respect to chromatin compartments. Availability The implementation of the algorithm is available at Contact Dariusz.Plewczynski{at}pw.edu.pl ### Competing Interest Statement The authors have declared no competing interest.