title: Hierarchical block matrices as efficient representations of chromosome topologies and their application for 3C data integration.
abstract: Recent advancements in molecular methods have made it possible to capture physical contacts between multiple chromatin fragments. The resulting association matrices provide a noisy estimate for average spatial proximity that can be used to gain insights into the genome organization inside the nucleus. However, extracting topological information from these data is challenging and their integration across resolutions is still poorly addressed. Recent findings suggest that a hierarchical approach could be advantageous for addressing these challenges.
  
  
  
  We present an algorithmic framework, which is based on hierarchical block matrices (HBMs), for topological analysis and integration of chromosome conformation capture (3C) data. We first describe chromoHBM, an algorithm that compresses high-throughput 3C (HiT-3C) data into topological features that are efficiently summarized with an HBM representation. We suggest that instead of directly combining HiT-3C datasets across resolutions, which is a difficult task, we can integrate their HBM representations, and describe chromoHBM-3C, an algorithm which merges HBMs. Since three-dimensional (3D) reconstruction can also benefit from topological information, we further present chromoHBM-3D, an algorithm which exploits the HBM representation in order to gradually introduce topological constraints to the reconstruction process. We evaluate our approach in light of previous image microscopy findings and epigenetic data, and show that it can relate multiple spatial scales and provide a more complete view of the 3D genome architecture.
  
  
  
  The presented algorithms are available from: https://github.com/yolish/hbm
  
  
  
  ys388@cam.ac.uk or pl219@cam.ac.uk
  
  
  
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Computer Laboratory, University of Cambridge, Cambridge CB3 0FD, UK.
authors.forename: Yoli
authors.initials: Y
authors.lastname: Shavit
authors.affiliation: University of Cambridge, Cambridge CB3 0FD, UK and Department of Life Sciences, Imperial College London, London SW7 2AZ, UK.
authors.forename: Barnabas James
authors.initials: BJ
authors.lastname: Walker
authors.affiliation: Computer Laboratory, University of Cambridge, Cambridge CB3 0FD, UK.
authors.forename: Pietro
authors.initials: P
authors.lastname: Lio'
mesh_terms: D000465:Algorithms; D002843:Chromatin; D002875:Chromosomes; D016678:Genome; D008968:Molecular Conformation
chemical_list: D002843:Chromatin