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 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, i.e. not catenated. Simulations show that even low levels of random strand passage, e.g. 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.

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.3

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