Manual Polymer Physics: A Molecular Approach

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To investigate the patterns of Hi-C matrices beyond the average contact probability, we next studied the mechanisms underlying the self-assembly of topological domains. The average pairwise contact matrix of our homopolymer is different in the different thermodynamics phases and, as expected, the contact network is strongly enhanced in the closed states Figure S4. Each polymer block can fold in the conformational states discussed for the homopolymer. As similar beads in different blocks can also interact with each other, the long time contact matrices have a more complex, chessboard-like pattern Fig.

By those principles, the combinatorial action of a few different types of binders and corresponding binding sites can produce and regulate an exponential number of 3D conformations and patterns, as we discuss below. While the molecular nature of the blocks envisaged within our SBS framework is yet to be identified in general, a recent study in Drosophila has shown that the blocks could be also linked to local epigenetic patterns In our view, chromosomal structures discovered in Hi-C data, such as TADs 6 , 7 and metaTADs 10 , and their differential re-wiring across tissues and cell types, emerge naturally by specialization of the involved molecular factors under general mechanisms of polymer physics.

The process is marked by a decrease of the gyration radius, R g t , in time bottom panel and by the formation of a hierarchy of higher-order domains, as reflected by the contact matrix pattern top. We also explored some additional, possibly functional consequences of the self-assembly of domains. As TAD boundaries have been associated to biological markers and, more specifically, to an insulating role, we focused on how they affect the physical distance of pairs of sites differently positioned relative to them.

Within our toy block-copolymer model, we focused on pairs of sites with the same contour separation: we considered two cases where the pair is located symmetrically or asymmetrically with respect to a domain boundary Fig. Within our toy homopolymer model, we measured the frequency of observing n sites in physical contact Figure S5a , see also Fig. As expected, in the closed states many-body contacts are exponentially more frequent than in the open state as n grows.

The contact probability of bead triplets on a same polymer at different genomic separations, P c s 1 , s 2 , is given in Figure S5b. Multiple interactions are currently not detected by Hi-C methods, yet our model highlights that they are likely to be an abundant structural component of chromatin. That hints towards an overseen functional role of closed chromatin domains whereby multiple regulatory regions enhancers can loop simultaneously onto a given target gene promoter with a much higher probability than in open regions.

Taken together our results support a view whereby basic mechanism of polymer folding could play key functional roles in the regulation of the genome by controlling the spatial organisation of chromatin. Bottom: the SBS polymer model that best explain the Hi-C contact map of the Sox9 region has the shown different types of binding sites, as seen in the zoom different colors ; their abundance is represented as an histogram over the genomic sequence.

The bar at the bottom highlights three main regional areas to help 3D visualization. Chromatin domains self-assemble hierarchically in higher-order structures, in approx. Next, we asked whether our polymer models can also explain the details of folding of specific DNA regions. To capture the details of Sox9 , we generalized our polymer model to accommodate different types of binding sites colors and molecular binders Fig.


We informed our polymer model with the obtained arrangement of binding sites and run full-scale Molecular Dynamics simulations to derive the ensemble of 3D conformations of the locus see Supplementary Materials and Methods. Figure 4a represents the histograms of the abundance of our inferred binding sites along the locus different types in different colors , ordered left-to-right according to the location of the domain center of mass.

Binding domains tend to overlap with the different TADs in the locus, but importantly they also overlap with each other producing higher-order interactions across TADs, i. A snapshot of a single typical configuration, in the closed state, is shown in Fig.

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The Sox9 locus is marked by many-body contacts that are exponentially more abundant than expected in a randomly folded conformation Fig. The self-assembly of the locus architecture from initial open states proceeds hierarchically, with early formed local domains folding into larger and larger 3D structures encompassing the entire locus Fig. The variety of information on Sox9 and its folding mechanisms that can be inferred from polymer physics extends well beyond the Hi-C pair-wise contact data used to infer the model. Finally, to test our model, we considered the Xist locus, an important 1.

In the above calculation there are no adjustable parameters. Such findings are in agreement with those of a similar interacting polymer model introduced for the Xist locus Summarizing, the binding domains identified in-silico by our model can describe the folding of Sox9 with high accuracy and predict the effects of genomic rearrangements based only on polymer physics. We have discussed a polymer model of chromatin where 3D conformations are shaped by the interactions of binding domains with their cognate binding molecular factors, such as DNA-binding molecules.

Genome-wide, and loci specific chromatin contact data can be explained by classical scaling concepts of polymer physics over orders of magnitude in genomic separation, up to chromosomal scales, across mammalian cell types. Contrary to previous approaches, our model does not require a previous knowledge of the molecular factors responsible for folding e. That supports the view that our model captures some of the key folding mechanisms of chromatin. By combining polymer models and Hi-C data, a quantitative scenario emerges of the large-scale features of chromatin architecture where chromatin folding is determined by a complex system of binding domains and molecular factors, regulated by general mechanisms of polymer physics.

As our polymer physics approach identifies the molecular determinants of folding and their mechanisms of action, it can help understanding the link between architecture and function, and the design of novel approaches to personalized diagnosis and treatment of human diseases.

A detailed description of the materials and methods is provided in the Supplementary Materials. All the details about the model and computational parameters, as well as on the analyses performed are reported in the Supplementary Materials and Methods. How to cite this article : Chiariello, A.

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Structural variations, the regulatory landscape of the genome and their alteration in human disease. Bioessays 35 , — Lupianez, D. Disruptions of topological chromatin domains cause pathogenic rewiring of gene-enhancer interactions. Nicodemi, M. Models of chromosome structure. Cell Bio. Sachs, R. USA 92 , —14 Marenduzzo, D. Entropy-driven genome organisation. Rosa, A. Structure and dynamics of interphase chromosomes. PLoS Comp. Kreth, G. Radial arrangement of chromosome territories in human cell nuclei: a computer model approach based on gene density indicates a probabilistic global positioning code.

Thermodynamic pathways to genome spatial organisation in the cell nucleus. Bohn, M. Diffusion-driven looping provides a consistent framework for chromatin organisation. Barbieri, M. USA , — Brackley, C. Nonspecific bridging-induced attraction drives clustering of DNA-binding proteins and and genome organisation.

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Polymer physics of chromosome large-scale 3D organisation

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