Motivation: Recent technological advances allow the measurement, in a single Hi-C experiment, of the frequencies of physical contacts among pairs of genomic loci at a genome-wide scale. The next challenge is to infer, from the resulting DNA-DNA contact maps, accurate 3D models of how chromosomes fold and fit into the nucleus. Many existing inference methods rely on multidimensional scaling (MDS), in which the pairwise distances of the inferred model are optimized to resemble pairwise distances derived directly from the contact counts. These approaches, however, often optimize a heuristic objective function and require strong assumptions about the biophysics of DNA to transform interaction frequencies to spatial distance, and thereby may lead to incorrect structure reconstruction. Methods: We propose a novel approach to infer a consensus 3D structure of a genome from Hi-C data. The method incorporates a statistical model of the contact counts, assuming that the counts between two loci follow a Poisson distribution whose intensity decreases with the physical distances between the loci. The method can automatically adjust the transfer function relating the spatial distance to the Poisson intensity and infer a genome structure that best explains the observed data. Results: We compare two variants of our Poisson method, with or without optimization of the transfer function, to four different MDSbased algorithms-two metric MDS methods using different stress functions, a non-metric version of MDS and ChromSDE, a recently described, advanced MDS method-on a wide range of simulated datasets. We demonstrate that the Poisson models reconstruct better structures than all MDS-based methods, particularly at low coverage and high resolution, and we highlight the importance of optimizing the transfer function. On publicly available Hi-C data from mouse embryonic stem cells, we show that the Poisson methods lead to more reproducible structures than MDS-based methods when we use data generated using different restriction enzymes, and when we reconstruct structures at different resolutions.
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