Effects of topological constraints on globular polymers

Imakaev, Maxim; Tchourine, Konstantin M.; Nechaev, Sergei; Mirny, Leonid A.

doi:10.1039/c4sm02099e

Cited by 65 publications

(84 citation statements)

References 43 publications

(146 reference statements)

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“…Simulations were initialized from a compact polymer conformation, as described in 64 , created on a cubic lattice a box of the size (PBC box – 2). Prior to a block of simulations, LEF dynamics were advanced by 500,000 steps.…”

Section: On-line Methodsmentioning

confidence: 99%

Two independent modes of chromatin organization revealed by cohesin removal

Schwarzer

Abdennur

Goloborodko

et al. 2017

Nature

1,020

114

1,115

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Imaging and chromosome conformation capture studies have revealed several layers of chromosome organization, including segregation into megabase-large active and inactive compartments, and partitioning into sub-megabase domains (TADs). Yet, it remains unclear how these layers of organization form, interact with one another and impact genome functions. Here, we show that deletion of the cohesin-loading factor Nipbl, in mouse liver, leads to a dramatic reorganization of chromosomal folding. TADs and associated peaks vanish globally, even in the absence of transcriptional changes. In contrast, compartmental segregation is preserved and even reinforced. Strikingly, the disappearance of TADs unmasks a finer compartment structure that accurately reflects the underlying epigenetic landscape. These observations demonstrate that the 3D organization of the genome results from the interplay of two independent mechanisms: 1) cohesin-independent segregation of the genome into fine-scale compartments, defined by chromatin state; 2) cohesin-dependent formation of TADs, possibly by loop extrusion, which contributes to guide distant enhancers to their target genes.

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Section: On-line Methodsmentioning

confidence: 99%

Two independent modes of chromatin organization revealed by cohesin removal

Schwarzer

Abdennur

Goloborodko

et al. 2017

Nature

1,020

114

1,115

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“…In 2015 we have performed in [50] extensive Monte-Carlo simulations for self-avoiding polymer chains in confined geometry in 3D space. The role of topological constraints in the equilibrium state of a single compact and unknotted polymer remains unknown.…”

Section: Crumpled Globule: Topological Correlations In Collapsed Umentioning

confidence: 99%

Concepts of polymer statistical topology

Nechaev

2017

Topology and Condensed Matter Physics

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I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called statistical (or probabilistic) topology. Contents I. Introduction: What we are talking about? II. Milestones A. Abelian epoch B. Non-Abelian epoch 1. Methods of algebraic topology in polymer statistics. Topology as quenched disorder 2. How to define the knot complexity? 3. Conformal methods in statistics of entangled random walks 4. Group-theoretic methods in statistics of entangled random walks 5. Conditional Brownian bridges in Hyperbolic spaces C. Crumpled globule: Topological correlations in collapsed unknotted rings III. Conclusion A. The King is dead, long live The King! B. Where to go? References

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“…A longlived, metastable state is obtained, due to the time-scale separation between the fast collapse process and further rearrangements that are much slower. (As noted above, other crumpled globule metastable states may also exist [4][5][6]22], at later times.) Now, let d …”

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confidence: 99%

“…However, they do not agree upon its fractal nature. In particular, the expected scaling r m ∼ m 1=d has not been conclusively confirmed, even with the largest size simulations (recently extended to polymers of up to 250 000 monomers [6,22]). This implies either a very large crossover scale before fractal behavior is clearly manifested, or else that the collapsed state is not strictly self-similar.…”

mentioning

confidence: 99%

“…This implies either a very large crossover scale before fractal behavior is clearly manifested, or else that the collapsed state is not strictly self-similar. The large finite-size effects are at least partly explained by partial mixing of short polymer segments, for which the topological constraints do not apply [1,[15][16][17][18][19][20]22]. More generally, various protocols for constructing crumpled globules have been suggested [2,[4][5][6]12,22], and it is not clear if the different procedures yield the same state.…”

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confidence: 99%

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Coalescence Model for Crumpled Globules Formed in Polymer Collapse

Bunin

Kardar

2015

Phys. Rev. Lett.

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The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived "crumpled globule." The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact. Distances between pairs of monomers are assigned upon their initial coalescence, and do not "equilibrate" subsequently. Surprisingly, the model reproduces quantitatively the dependence of distance on segment length, suggesting that the slow approach to scaling is related to the wide distribution of blob sizes. DOI: 10.1103/PhysRevLett.115.088303 PACS numbers: 82.35.-x, 68.43.Jk, 82.35.Pq The rapid collapse of a polymer into a dense globule is a long-standing problem [1][2][3][4][5][6][7][8][9][10][11][12]. Such a collapse may be triggered by changes in solvent quality, causing the polymer to reduce its solvent-exposed surface area by forming a dense globule. A polymer may also be condensed by active forces, as in the rearrangement of DNA by proteins in the cell nucleus [2]. The rapid collapse does not allow sufficient time for formation of topological entanglements, which abound in an equilibrated compact globule [1][2][3][4]6,13]. It is suggested [1] that during collapse segments of the polymer initially condense to spherelike "blobs," which coarsen upon contact to form larger blobs. At any given time during the process the state is then assumed to be characterized by a single length scale [1,[7][8][9], e.g., the typical size of the blobs or the width of the tube connecting the blobs [see, e.g., Fig. 1(a) [14]]. A central assumption is that when two blobs coalesce they remain more or less segregated within the newly formed structure. This is due to the slow relaxation processes within blobs, and due to topological constraints that prevent polymer segments forming the blobs from freely mixing-unlike a melt of independent polymer segments with open ends [1,[15][16][17][18][19][20]. The final configuration is thus predicted to be a constant density, self-similar, hierarchical structure, known as the "crumpled globule" or "fractal globule" [1-6,11]. The end-to-end distance r m of segments of length m in the resulting globule is predicted to scale as r m ∼ m 1=d in d space dimensions (throughout the Letter d ¼ 3). This is in contrast to the equilibrium state reached at much later times [10], where r m ∼ m 1=2 for small m, saturating at the globule size r max ¼ N 1=d , where N is the length of the polymer [21].These predictions have been tested in several simulations of polymer compaction [2,[4][5][6]11], which generally confirm that the rapidly collapsed state is not entangled, and is indeed different from the equilibrium globule. However, they do not agree upon its fractal nature. In particular, the expected scaling r m ∼ m 1=d has not been conclusively confirmed, even with the largest size simulations (recently extended to polymers of up to 250 ...

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Effects of topological constraints on globular polymers

Cited by 65 publications

References 43 publications

Two independent modes of chromatin organization revealed by cohesin removal

Two independent modes of chromatin organization revealed by cohesin removal

Concepts of polymer statistical topology

Coalescence Model for Crumpled Globules Formed in Polymer Collapse

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