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WIREs Comput Mol Sci
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A modern challenge of polymer physics: Novel ways to study, interpret, and reconstruct chromatin structure

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Abstract The constant development of sophisticated technologies is allowing to dissect three‐dimensional chromatin structure at high resolution level. The tremendous amount of quantitative experimental data available today requires a conceptual framework able to make sense of them. In this perspective, polymer physics offers a key tool to interpret chromatin architecture data and to unveil the basic mechanisms shaping its structure. In the very last years, several polymer models have been proposed and have allowed to capture complex features emerging from the data. The major peculiarity distinguishing the different models is represented by the more or less complicated physical mechanism used to explain chromatin folding. Here, we review very popular models which have been recently developed and which represent brilliant examples from this interdisciplinary research field. In order to highlight the wide range of practical applications they have, we discuss the cases of the murine Pitx1 and the human EPHA4 loci, showing that polymer physics allows to effectively study chromatin structure in different cell lines and to predict the impact of pathogenic structural variants on the genome three‐dimensional architecture. This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Statistical Mechanics
The Strings & Binders Switch (SBS) model can predict the impact of deletions and duplications in the human EPHA4 locus. (a) CHi‐C data for the healthy EPHA4 locus in human fibroblasts, and the model contact map reproduced from the SBS model. The schematic locus representation shows relevant genes related to limb development (WNT6, IHH, Epha4, Pax3), together with a known EPHA4 enhancer (Enh). On the top right corner of the model matrix an example of 3D structure, with the salient genomic elements marked by arrows. Data resolution is 10 kb. Region coordinates chr2:218,320,000–224,090,000, ref. genome hg19. (b) From the SBS healthy model, structural variants can be implemented in silico and their effect on the three‐dimensional structure evaluated. Top matrices show the predicted contact maps (deletion DelB/+ on the left and the duplication DupF/+ on the right) with the ectopic contacts highlighted by black arrows. The gray boxes highlight the coordinates of the variant. Bottom matrices are independent CHi‐C experiments performed on fibroblasts carrying the structural variants. In both cases, agreement between model prediction and experiment is very good. Examples of three‐dimensional configurations derived by the mutant SBS models are shown, with salient genomic elements indicated. (Reprinted with permission from Reference . Copyright 2018 Springer Nature)
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The Strings & Binders Switch (SBS) polymer model allows to explore chromatin structure of the murine Pitx1 locus in different tissues. (a) Schematic representation of the contact CHi‐C data in the Pitx1 locus in forelimb cells (left) and hindlimb cells (right). The coordinates of the modeled region are chr13:55,600,000–56,650,000 bp, ref. genome mm9, at 10 kb resolution. In forelimb Pitx1 gene results in contact with the repressed gene Neurog1, while no interaction is detected with the active enhancer Pen. The opposite holds for hindlimb, where a Pitx1‐Pen contact is observed, while none between Pitx1 and Neurog1. (b) Three‐dimensional structures of Pitx1 locus for forelimb (left) and hindlimb (right), obtained from the SBS model (Reprinted with permission from Reference . Copyright 2018 Springer Nature). In forelimb chromatin folds in two hubs, one containing Neurog1 and Pitx1, the other one Pen, which is thus physically separated by its target gene, consistently with contact maps and with expression data showing Pitx1 is silent in this tissue. In hindlimbs, three chromatin hubs are formed, one with Pitx1, another with Neurog1 and Pen. Pen is clearly closer to Pitx1 than in the forelimb configuration while Neurog1 is segregated away from it. These models give a structural rationale to the contact data and meaningfully link them with the expression changes
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Overview of four major polymer‐physics models of chromatin. (a) In the block‐copolymer model chromatin fiber is a self‐avoiding polymer made of differently colored domains. Colors are assigned according to epigenetic experimental tracks, so a block of colored beads along the chain is an epigenetic domain. Same‐colored beads interact attractively and specifically, thus the polymer folding occurs by a phase separation mechanism due to the formation of same‐colored blobs along the polymer chain. (b) In the SBS model chromatin fiber is a self‐avoiding polymer made of differently colored beads, which can interact with colored diffusive molecules, called binders. Only beads and binders having the same color can interact attractively, thus binders act as mediators between same colored distant beads. The polymer folding occurs via phase separation induced by such binder‐mediated interactions. The folded structures are in thermodynamic equilibrium. Binding sites can be assigned from the regulatory landscape of the locus or inferred by architectural data. (c) The loop extrusion model considers chromatin fiber a self‐avoiding polymer with a weak self‐interaction. Here, chromatin loops are thought to be formed via an extrusion process by a specific loop extruding factor (LEF), i.e., a molecular machinery (represented as two green rings) able to attach to the polymer and slide along it. Extruding process is stopped when LEFs meet specific convergent barriers along the polymer (green «directed» beads). Importantly, LEFs activity is assumed to be driven by an energy‐consuming motor. Therefore, in this scenario chromatin is an intrinsically off‐equilibrium system. Biologically, cohesin—a proteic complex—has been identified as possible ATP‐driven LEF and convergent CTCF sites as extrusion barriers. (d) The slip‐link model is analogous to the loop extrusion, but LEF sliding along the polymer is assumed to happen by simple diffusion rather than driven by an active motor. Again, the result is a nonequilibrium system
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The interplay between experimental technologies and polymer physics. In recent years, innovative technologies able to dissect the three‐dimensional chromatin structure have been invented. Such methods detect loci which are in close spatial proximity inside a cell nucleus, across a population of cells. To this aim, they employ different biochemical and physical approaches (ligation of fragments in Hi‐C, tagging in SPRITE and nucleus slicing in GAM). In turn, they return the number of contacts between the pairs of proximal loci and are usually arranged in a pairwise matrix. Importantly, GAM and SPRITE can also provide higher order contacts frequencies. These experimental data provide precious information to develop polymer physics models aiming to reconstitute the 3D chromatin organization underlying the observed contact pattern
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Theoretical and Physical Chemistry > Statistical Mechanics
Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods
Structure and Mechanism > Computational Biochemistry and Biophysics

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