  Chromosome conformation capture experiments such as Hi-C are used to map the
three-dimensional spatial organization of genomes. One specific feature of the
3D organization is known as topologically associating domains (TADs), which are
densely interacting, contiguous chromatin regions playing important roles in
regulating gene expression. A few algorithms have been proposed to detect TADs.
In particular, the structure of Hi-C data naturally inspires application of
community detection methods. However, one of the drawbacks of community
detection is that most methods take exchangeability of the nodes in the network
for granted; whereas the nodes in this case, i.e. the positions on the
chromosomes, are not exchangeable. We propose a network model for detecting
TADs using Hi-C data that takes into account this non-exchangeability. In
addition, our model explicitly makes use of cell-type specific CTCF binding
sites as biological covariates and can be used to identify conserved TADs
across multiple cell types. The model leads to a likelihood objective that can
be efficiently optimized via relaxation. We also prove that when suitably
initialized, this model finds the underlying TAD structure with high
probability. Using simulated data, we show the advantages of our method and the
caveats of popular community detection methods, such as spectral clustering, in
this application. Applying our method to real Hi-C data, we demonstrate the
domains identified have desirable epigenetic features and compare them across
different cell types.
