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WIREs Syst Biol Med
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Models of polymer physics for the architecture of the cell nucleus

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The depth and complexity of data now available on chromosome 3D architecture, derived by new technologies such as Hi‐C, have triggered the development of models based on polymer physics to explain the observed patterns and the underlying molecular folding mechanisms. Here, we give an overview of some of the ideas and models from physics introduced to date, along with their progresses and limitations in the description of experimental data. In particular, we focus on the Strings&Binders and the Loop Extrusion model of chromatin architecture. This article is categorized under: Analytical and Computational Methods > Computational Methods
Schematic representation of polymer models describing chromatin folding. (a) The Strings&Binders Switch (SBS) model quantifies the biological scenario where diffusing transcription factors mediate DNA looping and folding. Its stable conformations can be derived by equilibrium thermodynamics. (b) The Loop Extrusion (LE) model quantifies the off‐equilibrium folding scenario where an active motor binds to DNA and actively extrude a DNA loop. (c) The Slip‐Link (SL) model is a variant without active, energy burning mechanisms, where DNA diffusively slips through a bridging factor
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Microphase separation and domain formation. (a) In the SBS view, stable architectural classes of polymer physics correspond to different thermodynamics phases. The SBS toy model with only one type of binders and binding sites, exhibits a coil‐globule phase transition, where its 3D conformation switches from being open to compact. (Reprinted with permission from Chiariello et al., . Copyright 2016 Nature). (b) In the SBS mixture model, the regions with red and green binding sites fold into distinct domains by microphase separation, as visible in the pairwise contact map. (Reprinted with permission from Barbieri et al., . Copyright 2012 Proceedings of the National Academy of Sciences of the United States of America)
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Polymer models can reproduce Hi‐C data. (a) The folding of the Sox9 locus in mESC is described by the SBS model with good accuracy: Hi‐C (Dixon et al., ) and model derived contact data have a Pearson correlation r = 0.95. A single‐molecule 3D conformation of the locus derived from the SBS is also shown to visualize the 3D structure corresponding to Hi‐C patterns. (Reprinted with permission from Chiariello et al., . Copyright 2016 Nature). (b) The LE model has been used to successfully explain the architecture of chromosomal loci where Cohesin/CTCF is the key driving force of folding, as the one in GM12878 cells shown in the example. (Reprinted with permission from Sanborn et al., . Copyright 2015 Proceedings of the National Academy of Sciences of the United States of America)
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