What is the length of a knot in a polymer?

Marcone, Boris; Orlandini, Enzo; Stella, Attilio L.; Zonta, Francesco

doi:10.1088/0305-4470/38/1/l03

Cited by 110 publications

(190 citation statements)

References 29 publications

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“…The particular focus of our interest is the size of the knotted domain, which in the case of torsionally relaxed DNA shows a strong correlation with the size of the entire molecule (19). If the tightness of the knotted domains facilitates unknotting, it may explain why only short, torsionally relaxed DNA molecules with relatively tight knotted domains are very efficiently unknotted by type IIA DNA topoisomerases.…”

Section: Resultsmentioning

confidence: 99%

“…If the tightness of the knotted domains facilitates unknotting, it may explain why only short, torsionally relaxed DNA molecules with relatively tight knotted domains are very efficiently unknotted by type IIA DNA topoisomerases. To measure the size of the knotted domains in individual configurations of simulated DNA molecules, we performed a systematic search for the shortest subchain which, upon closure, still had the same knot type as the original chain (19). Because the size of the knotted domain varies between individual configurations, many independent configurations must be analyzed to estimate the average length of the knotted domain for a given length of DNA molecule and a given level of supercoiling.…”

Section: Resultsmentioning

confidence: 99%

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Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

Witz

Dietler

Stasiak

2011

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

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Using numerical simulations, we compare properties of knotted DNA molecules that are either torsionally relaxed or supercoiled. We observe that DNA supercoiling tightens knotted portions of DNA molecules and accentuates the difference in curvature between knotted and unknotted regions. The increased curvature of knotted regions is expected to make them preferential substrates of type IIA topoisomerases because various earlier experiments have concluded that type IIA DNA topoisomerases preferentially interact with highly curved DNA regions. The supercoiling-induced tightening of DNA knots observed here shows that torsional tension in DNA may serve to expose DNA knots to the unknotting action of type IIA topoisomerases, and thus explains how these topoisomerases could maintain a low knotting equilibrium in vivo, even for long DNA molecules.Brownian dynamics | DNA topology | DNA structure | DNA configurations D uring normal cell growth, various DNA transactions are facilitated by topoisomerase-mediated passage of one DNA segment through another. These strand passages can inadvertently lead to the formation of DNA knots (1-3), which are highly deleterious for living cells if not removed efficiently (4, 5). Type IIA DNA topoisomerases can use the free energy of ATP hydrolysis (6) to decrease the knotting level significantly below the equilibrium value for DNA rings subject to random passages between colliding segments (7). This topoisomerase (topo) IIA ability has been often assumed to be a physiologically relevant mechanism ensuring efficient DNA unknotting and decatenation (7-10), but doubts on this relevance have been raised as well (11). Particularly problematic is the fact that the original study establishing that type IIA DNA topoisomerases actively unknot DNA also revealed that this ability decreases sharply with increasing DNA length. Although based on only two plasmid sizes, that study showed the generality of this length dependence for several topoisomerases (7) and, therefore, active unknotting would be doomed to be ineffective for long DNA molecules, where random passages lead to very frequent knotting (12). While trying to understand why earlier experimental studies predicted ineffectiveness of type IIA DNA topoisomerases in unknotting of long DNA molecules, we recognized that these studies were performed using torsionally relaxed DNA (7), whereas naturally occurring DNA is frequently under torsional tension (13), the best-known examples of this state being negatively supercoiled bacterial plasmids. To investigate the potential effects of torsional constraints on the activity of type IIA topoisomerases, we have performed Brownian dynamics simulations to examine how negative supercoiling affects the structure of knotted DNA molecules and whether DNA supercoiling can cause knotted regions to be recognized specifically and then unknotted by topoisomerases. We observed that DNA supercoiling results in the tightening of knots, which leads directly to an increase in curvature of the knotted regions, in turn re...

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

Witz

Dietler

Stasiak

2011

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

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“…The knot location along the ring was established using the bottom-up search of the smallest arc(s) that, after closure, has the same topology of the whole ring [57,71], see the example in Fig. 9.…”

Section: Knot Lengthmentioning

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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“…16 For example, when dealing with polymers in good solvent, we know that the prime components of a knot are weakly localized. [17][18][19] Each prime component of the knot behaves almost like a small bead sliding along the backbone. This makes it relatively simple to guess the gross structure of finite size corrections to the free energy expected for a knotted ring.…”

Section: Introductionmentioning

confidence: 99%

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature T , in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low T on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops (preserving their topology) which compete for the chain length, either in contact or separated by a wall as for translocation through a membrane pore. These findings suggest that in macromolecular environments there may be entropic forces with a purely topological origin, whence portions of polymers holding complex knots should tend to expand at the expense of significantly shrinking other topologically simpler portions. 1

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What is the length of a knot in a polymer?

Cited by 110 publications

References 29 publications

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

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

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

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