  To understand the nature of a cell, one needs to understand the structure of
its genome. For this purpose, experimental techniques such as Hi-C detecting
chromosomal contacts are used to probe the three-dimensional genomic structure.
These experiments yield topological information, consistently showing a
hierarchical subdivision of the genome into self-interacting domains across
many organisms. Current methods for detecting these domains using the Hi-C
contact matrix, i.e. a doubly-stochastic matrix, are mostly based on the
assumption that the domains are distinct, thus non-overlapping. For overcoming
this simplification and for being able to unravel a possible nested domain
structure, we developed a probabilistic graphical model that makes no a priori
assumptions on the domain structure. Within this approach, the Hi-C contact
matrix is analyzed using an Ising like probabilistic graphical model whose
coupling constant is proportional to each lattice point (entry in the contact
matrix). The results show clear boundaries between identified domains and the
background. These domain boundaries are dependent on the coupling constant, so
that one matrix yields several clusters of different sizes, which show the
self-interaction of the genome on different scales.
