Winding angle distribution for planar random walk, polymer ring entangled with an obstacle, and all that: Spitzer–Edwards–Prager–Frisch model revisited

Grosberg, Alexander Y.; Hl, Frisch

doi:10.1088/0305-4470/36/34/303

Cited by 47 publications

(90 citation statements)

References 35 publications

(136 reference statements)

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“…In the continuous approximation, the statistical weight W of the Gaussian chain comprising N segments is described by the diffusionlike equation ( [2] and references therein),…”

Section: A Ideal Gaussian Chain Wound Around a Cylindermentioning

confidence: 99%

“…where the parameter κ for an ideal Gaussian chain = 1 (reviewed in [2]). For two-dimensional chains with excluded volume κ = 0.5 (reviewed in [33]); for three-dimensional chains with excluded volume, the analytically predicted value is also 0.5 [34], but computer modeling produced κ = 0.75 [35].…”

Section: B Simplified Analysis Of the Nonideal Chains With Excluded mentioning

confidence: 99%

“…The winding of random walk trajectories around a given domain in space, for example, an impenetrable obstacle, has received significant attention and has multiple implications for polymer physics ( [1,2], and references therein). In general, the winding of a polymer chain around an obstacle decreases the chain entropy and consequently creates forces directed to unwinding; if the unwinding is impossible (for example, due to anchoring of the chain's ends), these forces would create mechanical strains and deformations within the system.…”

Section: Introductionmentioning

confidence: 99%

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Relationships between the winding angle, the characteristic radius, and the torque for a long polymer chain wound around a cylinder: Implications for RNA winding around DNA during transcription

Belotserkovskii

2014

Phys. Rev. E

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Long polymer chains are ubiquitous in biological systems and their mechanical properties have significant impact upon biological processes. Of particular interest is the situation in which polymer chains are wound around each other or around other objects. We have analyzed the parameters of a long Gaussian polymer chain wound around a cylinder as a function of the torque applied to the ends of the chain. We have shown that for sufficiently long polymer chains, an average winding angle and a characteristic radius of the chain can be determined from a modified Bessel function of purely imaginary order, in which the value of the order is equivalent to the applied torque, normalized to the product of the absolute temperature and the Boltzmann constant. The obtained results are consistent with a simplified interpretation in terms of "torsional blobs," and this could be extended to nonideal chains with excluded volumes. We have also extended our results to the case of a polymer chain rotating in viscous medium. Our results could be used to estimate the mechanical strains that appear in DNA and RNA during transcription, as these might initiate formation of unusual DNA structures, invasion of RNA into the DNA duplex (R-loop formation), and modulation of the interactions of DNA and RNA with proteins.

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“…In the continuous approximation, the statistical weight W of the Gaussian chain comprising N segments is described by the diffusionlike equation ( [2] and references therein),…”

Section: A Ideal Gaussian Chain Wound Around a Cylindermentioning

confidence: 99%

Section: B Simplified Analysis Of the Nonideal Chains With Excluded mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Relationships between the winding angle, the characteristic radius, and the torque for a long polymer chain wound around a cylinder: Implications for RNA winding around DNA during transcription

Belotserkovskii

2014

Phys. Rev. E

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“…The winding sectors of a closed curve are displayed in figure 9. The random variable S n scales like t. In particular, we know [62,118] its expectation S n = t 2πn 2 . Moreover, it has been shown in [223] that the variable n 2 S n becomes more and more peaked when n grows: P (n 2 S n = X) −→ n→∞ δ(X − t 2π ) (the average area of the n = 0-sector has been recently studied in ref.…”

Section: Occupation Time and Local Time Distribution On A Graphmentioning

confidence: 99%

Functionals of Brownian motion, localization and metric graphs

Comtet¹,

Desbois²,

Texier³

2005

J. Phys. A: Math. Gen.

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We review several results related to the problem of a quantum particle in a random environment.In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization).Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues).Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schrödinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated.Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.

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“…Three characteristics of long chain molecules (including polymers or oligomers) are as follows: (i) Some form entangled loops and knots [1], [2]. (ii) Some can be electrically conducting [3].…”

mentioning

confidence: 99%

Aharonov-Bohm Effects in Entangled Molecules

Kimball

Frisch

2004

Phys. Rev. Lett.

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Molecules which are magnetic and conducting, if suitably entangled (e.g., catenanes and knots) could exhibit Aharonov-Bohm effects which can be viewed as particular examples of a Berry phase. The corrections to the quantum energy levels reflect the entangled geometry of the molecules and, while small (they are proportional to the square of the fine structure constant), may be observable. We illustrate these corrections for a number of catenated and knotted structures. For couplings between the components of a catenane (link), the Aharonov-Bohm corrections are determined by integer-valued linking numbers. For knots, the Aharonov-Bohm correction is proportional to the geometric writhe of the knot.

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Winding angle distribution for planar random walk, polymer ring entangled with an obstacle, and all that: Spitzer–Edwards–Prager–Frisch model revisited

Cited by 47 publications

References 35 publications

Relationships between the winding angle, the characteristic radius, and the torque for a long polymer chain wound around a cylinder: Implications for RNA winding around DNA during transcription

Relationships between the winding angle, the characteristic radius, and the torque for a long polymer chain wound around a cylinder: Implications for RNA winding around DNA during transcription

Functionals of Brownian motion, localization and metric graphs

Aharonov-Bohm Effects in Entangled Molecules

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