Multi-contact 3C data reveal that the human genome is largely unentangled

The genome is organized into chromosome territories that are themselves spatially segregated in A and B compartments. The extent to which interacting compartment domains and chromosomes are topologically entangled is not known. We show that detection of series of co-occurring chromatin interactions using multi-contact 3C (MC-3C) reveals insights into the topological entanglement of compartment domains and territories. We find that series of co-occurring interactions and their order represent interaction percolation paths through nuclear space in single cells where fragment 1 interacts with fragment 2, which in turn interacts with fragment 3 and so on. Analysis of paths that cross two chromosome territories revealed very little mixing of chromatin from the two chromosomes. Similarly, paths that cross compartment domains show that loci from interacting domains do not mix. Polymer simulations show that such paths are consistent with chromosomes and compartment domains behaving as topologically closed polymers that are not catenated with one another. Simulations show that even low levels of random strand passage, e.g. through topoisomerase II activity, would result in entanglements and mixing of loci of different chromosomes and compartment domains with concomitant changes in interaction paths inconsistent with MC-3C data. Our results show that cells maintain a largely unentangled state of chromosomes and compartment domains.