Transient topological entanglement of chromatin fiber in human cells during interphase

Topological entanglement of the chromatin polymer may influence its three-dimensional organization in ways that are not captured by pairwise chromatin contacts. We propose a practical method for detecting linking between Cohesin-mediated chromatin loops based on pairwise interaction data from ChIA-PET experiments. Our algorithm analyzes chromatin interaction networks and detects complete graph (K 6 ) graph minors that guarantee linking of the corresponding chromatin interaction graph. This implies the presence of linked chromatin loops provided that the interactions required to realize the minor coexist in a cell. We applied our algorithm to in situ ChIA-PET datasets from the GM12878, H1-hESC, HFFc6, and WTC11 cell lines, as well as to long-read ChIA-PET data for GM12878, with analyses performed separately for individual chromatin contact domains (CCDs). We found that 1–17% of CCDs contain K 6 minors, indicating potential linking. In GM12878, linked CCDs are enriched for multiplex ChIA-Drop interactions, 63% of which support the simultaneous spatial proximity of at least four loci. Loop extrusion simulations show an increased propensity for link formation in linked CCDs. Finally, linked CCDs are enriched at compartment boundaries and exhibit distinct compartment organization, lower CTCF occupancy, and slightly later replication timing.