  The three dimensional structure of DNA in the nucleus (chromatin) plays an
important role in many cellular processes. Recent experimental advances have
led to high-throughput methods of capturing information about chromatin
conformation on genome-wide scales. New models are needed to quantitatively
interpret this data at a global scale. Here we introduce the use of tools from
topological data analysis to study chromatin conformation. We use persistent
homology to identify and characterize conserved loops and voids in contact map
data and identify scales of interaction. We demonstrate the utility of the
approach on simulated data and then look data from both a bacterial genome and
a human cell line. We identify substantial multiscale topology in these
datasets.
