title: A statistical approach for inferring the 3D structure of the genome.
abstract: BACKGROUND
  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 MDS-based 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.
  
  
  METHODS
  A Python implementation of the proposed method is available at http://cbio.ensmp.fr/pastis.
authors.affiliation: Centre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USACentre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USACentre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USA.
authors.forename: Nelle
authors.initials: N
authors.lastname: Varoquaux
authors.affiliation: Centre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USA.
authors.forename: Ferhat
authors.initials: F
authors.lastname: Ay
authors.affiliation: Centre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USACentre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USA.
authors.forename: William Stafford
authors.initials: WS
authors.lastname: Noble
authors.affiliation: Centre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USACentre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USACentre for Computational Biology, Mines ParisTech, Fontainebleau F-77300, Institut Curie, U900, INSERM, Paris, F-75248, France, Department of Genome Sciences and Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USA.
authors.forename: Jean-Philippe
authors.initials: JP
authors.lastname: Vert
mesh_terms: D000465:Algorithms; D000818:Animals; D002875:Chromosomes / Q000737:chemistry*; D004247:DNA / Q000737:chemistry; D016678:Genome; D023281:Genomics / Q000379:methods; D051379:Mice; D008958:Models, Molecular; D015233:Models, Statistical; D009690:Nucleic Acid Conformation; D016012:Poisson Distribution
chemical_list: D004247:DNA