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Multiscale Topology of Chromatin Folding

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.