I am interested in assigning genes to the domains defined in this paper by Rao et al. As I have little to no experience with HiC data, my approach so far has been rather simplistic: I downloaded the Arrowhead files containing the domains identified by the authors for a given cell line and then I extracted their coordinates to a BED file. Then I tried to determine to what domain each gene belongs based on its TSS.
However, domains defined in this way overlap each other, so a gene can be in multiple domains at once. I came across a paper where they use the inner-most domain, which seems a good idea, but it is not always entirely clear which one is the "inner-most". For instance, a gene with a TSS on 6259679 overlaps a domain comprising 6090000-6280000 and another one comprising 6050000-6540000.
Any ideas? Different approaches are also appreciated.