Statistical mechanics and topology of polymer chains

Frank‐Kamenetskii, Maxim D.; Lukashin, A. V.; Vologodskii, Alexander

doi:10.1038/258398a0

Cited by 222 publications

(149 citation statements)

References 11 publications

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“…Correlation along the subchains was computed by using time-series analysis methods as described by Madras and Slade (33). Identification of the knotted polygons was achieved by computing the Alexander polynomial (14,34) …”

Section: Methodsmentioning

confidence: 99%

Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids

Arsuaga

Vázquez

Trigueros

et al. 2002

Proc. Natl. Acad. Sci. U.S.A.

244

307

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When linear double-stranded DNA is packed inside bacteriophage capsids, it becomes highly compacted. However, the phage is believed to be fully effective only if the DNA is not entangled. Nevertheless, when DNA is extracted from a tailless mutant of the P4 phage, DNA is found to be cyclic and knotted (probability of 0.95). The knot spectrum is very complex, and most of the knots have a large number of crossings. We quantified the frequency and crossing numbers of these knots and concluded that, for the P4 tailless mutant, at least half the knotted molecules are formed while the DNA is still inside the viral capsid rather than during extraction. To analyze the origin of the knots formed inside the capsid, we compared our experimental results to Monte Carlo simulations of random knotting of equilateral polygons in confined volumes. These simulations showed that confinement of closed chains to tightly restricted volumes results in high knotting probabilities and the formation of knots with large crossing numbers. We conclude that the formation of the knots inside the viral capsid is driven mainly by the effects of confinement.

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Section: Methodsmentioning

confidence: 99%

Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids

Arsuaga

Vázquez

Trigueros

et al. 2002

Proc. Natl. Acad. Sci. U.S.A.

244

307

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“…In particular, for all considered chain lengths the minimum overall ring size is obtained for D ≈ R The Monte Carlo strategy employed here and in other previous studies provides the means to characterize the occurrence of non-trivial knots in rings that are circularised in equilibrium. The knotting probability of unconstrained rings depends on several lengthscales such as the molecule's persistence length, its contour length and thickness [66,67]. Accordingly, the topological complexity of the circularised molecules can be tuned, to some extent, by varying these lengths, for example by intervening of the solution ionic strength [43,68].…”

Section: B Scaling Properties and The Degennes Regimementioning

confidence: 99%

Numerical Study of Linear and Circular Model DNA Chains Confined in a Slit: Metric and Topological Properties

2012

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Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2-4.8 µm range and slits widths spanning continuously the 50-1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is nonmonotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for threedimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.

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“…Much attention has been paid to the influence of topological constraints on ring polymers. The interaction between non-linked ring polymers without excluded volume has been investigated for chains of length up to N = 80 21 . In a recent study 14 out that while the dimensions of catenated rings show the same scaling behavior than their linear counterparts, the shape changes significantly.…”

Section: Topological Constraints Induce Additional Repulsionmentioning

confidence: 99%

“…While topological effects of rings have been considered in several studies 16,21,22 , the induced forces have not been quantitatively assessed. A system of two ring polymers can be viewed as a toy system for the influence of loop formation on chromatin folding.…”

Section: Introductionmentioning

confidence: 99%

Topological interactions between ring polymers: Implications for chromatin loops

Bohn

Heermann²

2010

The Journal of Chemical Physics

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Chromatin looping is a major epigenetic regulatory mechanism in higher eukaryotes. Besides its role in transcriptional regulation, chromatin loops have been proposed to play a pivotal role in the segregation of entire chromosomes. The detailed topological and entropic forces between loops still remain elusive. Here, we quantitatively determine the potential of mean force between the centers of mass of two ring polymers, i.e. loops. We find that the transition from a linear to a ring polymer induces a strong increase in the entropic repulsion between these two polymers. On top, topological interactions such as the non-catenation constraint further reduce the number of accessible conformations of close-by ring polymers by about 50%, resulting in an additional effective repulsion. Furthermore, the transition from linear to ring polymers displays changes in the conformational and structural properties of the system. In fact, ring polymers adopt a markedly more ordered and aligned state than linear ones. The forces and accompanying changes in shape and alignment between ring polymers suggest an important regulatory function of such a topology in biopolymers. We conjecture that dynamic loop formation in chromatin might act as a versatile control mechanism regulating and maintaining different local states of compaction and order.

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Statistical mechanics and topology of polymer chains

Cited by 222 publications

References 11 publications

Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids

Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids

Numerical Study of Linear and Circular Model DNA Chains Confined in a Slit: Metric and Topological Properties

Topological interactions between ring polymers: Implications for chromatin loops

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