Reciprocal insulation analysis of Hi-C data shows that TADs represent a functionally but not structurally privileged scale in the hierarchical folding of chromosomes.

Understanding how regulatory sequences interact in the context of chromosomal architecture is a central challenge in biology. Chromosome conformation capture revealed that mammalian chromosomes possess a rich hierarchy of structural layers, from multi-megabase compartments to sub-megabase topologically associating domains (TADs) and sub-TAD contact domains. TADs appear to act as regulatory microenvironments by constraining and segregating regulatory interactions across discrete chromosomal regions. However, it is unclear whether other (or all) folding layers share similar properties, or rather TADs constitute a privileged folding scale with maximal impact on the organization of regulatory interactions. Here, we present a novel algorithm named CaTCH that identifies hierarchical trees of chromosomal domains in Hi-C maps, stratified through their reciprocal physical insulation, which is a single and biologically relevant parameter. By applying CaTCH to published Hi-C data sets, we show that previously reported folding layers appear at different insulation levels. We demonstrate that although no structurally privileged folding level exists, TADs emerge as a functionally privileged scale defined by maximal boundary enrichment in CTCF and maximal cell-type conservation. By measuring transcriptional output in embryonic stem cells and neural precursor cells, we show that the likelihood that genes in a domain are coregulated during differentiation is also maximized at the scale of TADs. Finally, we observe that regulatory sequences occur at genomic locations corresponding to optimized mutual interactions at the same scale. Our analysis suggests that the architectural functionality of TADs arises from the interplay between their ability to partition interactions and the specific genomic position of regulatory sequences.