A current question in the high-order organization of chromatin is whether 
topologically associating domains (TADs) are distinct from other hierarchical 
chromatin domains. However, due to the unclear TAD definition in tradition, the 
structural and functional uniqueness of TAD is not well studied. In this work, 
we refined TAD definition by further constraining TADs to the optimal separation 
on global intra-chromosomal interactions. Inspired by this constraint, we 
developed a novel method, called HiTAD, to detect hierarchical TADs from Hi-C 
chromatin interactions. HiTAD performs well in domain sensitivity, replicate 
reproducibility and inter cell-type conservation. With a novel domain-based 
alignment proposed by us, we defined several types of hierarchical TAD changes 
which were not systematically studied previously, and subsequently used them to 
reveal that TADs and sub-TADs differed statistically in correlating chromosomal 
compartment, replication timing and gene transcription. Finally, our work also 
has the implication that the refinement of TAD definition could be achieved by 
only utilizing chromatin interactions, at least in part. HiTAD is freely 
available online.