Topological spectra and entropy of chromatin loop networks

Andrea Bonato, Michael Chiang, Dom Corbett, Sergey Kitaev, Davide Marenduzzo, Alexander Morozov, Enzo Orlandini

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Abstract

The 3D folding of a mammalian gene can be studied by a polymer model, where the chromatin fiber is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors and RNA polymerases. This physical model leads to the natural emergence of clusters of proteins and binding sites, accompanied by the folding of chromatin into a set of topologies, each associated with a different network of loops. Here, we combine numerics and analytics to first classify these networks and then find their relative importance or statistical weight, when the properties of the underlying polymer are those relevant to chromatin. Unlike polymer networks previously studied, our chromatin networks have finite average distances between successive binding sites, and this leads to giant differences between the weights of topologies with the same number of edges and nodes but different wiring. These weights strongly favor rosettelike structures with a local cloud of loops with respect to more complicated nonlocal topologies. Our results suggest that genes should overwhelmingly fold into a small fraction of all possible 3D topologies, which can be robustly characterized by the framework we propose here.

Original languageEnglish
Article number248403
Number of pages12
JournalPhysical Review Letters
Volume132
Issue number24
DOIs
Publication statusPublished - 14 Jun 2024

Keywords

  • chromatin
  • chromatin fibre
  • chromatin loop networks

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