Multi-contact 3C reveals that the human genome during interphase is largely not entangled

During interphase, the eukaryotic genome is organized into chromosome territories that are spatially segregated into compartment domains. The extent to which interacting domains or chromosomes are entangled is not known. We analyze series of co-occurring chromatin interactions using multi-contact 3C (MC-3C) in human cells to provide insights into the topological entanglement of chromatin. Multi-contact interactions represent percolation paths (C-walks) through three-dimensional (3D) chromatin space. We find that the order of interactions within C-walks that occur across interfaces where chromosomes or compartment domains interact is not random. Polymer simulations show that such C-walks are consistent with distal domains being topologically insulated, that is, not catenated. Simulations show that even low levels of random strand passage, for example by topoisomerase II, would result in entanglements, increased mixing at domain interfaces and an order of interactions within C-walks not consistent with experimental MC-3C data. Our results indicate that, during interphase, entanglements between chromosomes and chromosomal domains are rare.