Bimodal distribution function of a three-dimensional wormlike chain with a fixed orientation of one end

Semeriyanov, F. F.; Stepanow, S.

doi:10.1103/physreve.75.061801

Cited by 5 publications

(12 citation statements)

References 41 publications

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“…This peculiar behavior arising in semiflexible polymers has already been observed earlier for polymers in 2D in terms of computer simulations [41] and an approximate theory [42]. Similar behavior has been observed in the distribution function of a cantilevered polymer in 3D, which has been elaborated formally exactly in Fourier-Laplace space by an expansion in Legendre polynomials [43].…”

Section: End-to-end Distance Transverse To the Clamped Endssupporting

confidence: 80%

“…The force-free behavior of a wormlike chain with free ends has been elaborated analytically for the end-toend probability density in the weakly-bending approximation [34] and, furthermore, evaluated numerically for polymers of arbitrary stiffness using an inverse (Fourier) Laplace transform [39,40]. In addition, the probability density for the transverse fluctuations of the free end of a cantilevered polymer has been extracted from computer simulations [41] and qualitatively confirmed by an approximate theory [42] in 2D and computed formally exactly in 3D by inverting an infinite matrix [43]. To explore the response of semiflexible polymers to external forces, we have recently provided exact expressions arXiv:1911.03431v1 [cond-mat.soft] 8 Nov 2019 for the two lowest-order moments, namely, the forceextension relation and the susceptibility (i.e.…”

Section: Introductionmentioning

confidence: 86%

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Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

Kurzthaler

Franosch

2018

Soft Matter

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We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density for the transverse fluctuations of the free end of a cantilevered polymer as fingerprint of its semiflexibility. In contrast to clamped polymers, free polymers display a circularly symmetric probability density and their distributions are identical for compression and stretching forces.

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Section: End-to-end Distance Transverse To the Clamped Endssupporting

confidence: 80%

Section: Introductionmentioning

confidence: 86%

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

Kurzthaler

Franosch

2018

Soft Matter

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“…Even though the three-dimensional case is beyond the scope of this article, we do not expect a qualitative case. This bimodality is similar to that in grafted wormlike chains, and Reference [ 33 ] shows that it persists in three dimensions.…”

Section: Conformational Probabilities Of Kinked and Hinged Stiff Chainssupporting

confidence: 74%

“…As we see from Equation ( 14 ), if we set

is peaked at

and the variance of y is

. It is known that, as the stiffness of the WLC (given by

) decreases,

changes from its original Gaussian form and develops a bimodality, which can be viewed as the hallmark of semiflexibility (

) [ 22 , 30 , 31 , 32 , 33 ]. Bimodality has also been observed in molecular dynamics simulations of semiflexible polymers in two dimensions under shear flow [ 34 ].…”

Section: Conformational Probabilities Of Kinked and Hinged Stiff Chainsmentioning

confidence: 99%

Orientational Fluctuations and Bimodality in Semiflexible Nunchucks

Benetatos

Razbin

2021

Polymers

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Semiflexible nunchucks are block copolymers consisting of two long blocks with high bending rigidity jointed by a short block of lower bending stiffness. Recently, the DNA nanotube nunchuck was introduced as a simple nanoinstrument that mechanically magnifies the bending angle of short double-stranded (ds) DNA and allows its measurement in a straightforward way [Fygenson et al., Nano Lett. 2020, 20, 2, 1388–1395]. It comprises two long DNA nanotubes linked by a dsDNA segment, which acts as a hinge. The semiflexible nunchuck geometry also appears in dsDNA with a hinge defect (e.g., a quenched denaturation bubble or a nick), and in end-linked stiff filaments. In this article, we theoretically investigate various aspects of the conformations and the tensile elasticity of semiflexible nunchucks. We analytically calculate the distribution of bending fluctuations of a wormlike chain (WLC) consisting of three blocks with different bending stiffness. For a system of two weakly bending WLCs end-jointed by a rigid kink, with one end grafted, we calculate the distribution of positional fluctuations of the free end. For a system of two weakly bending WLCs end-jointed by a hinge modeled as harmonic bending spring, with one end grafted, we calculate the positional fluctuations of the free end. We show that, under certain conditions, there is a pronounced bimodality in the transverse fluctuations of the free end. For a semiflexible nunchuck under tension, under certain conditions, there is bimodality in the extension as a function of the hinge position. We also show how steric repulsion affects the bending fluctuations of a rigid-rod nunchuck.

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“…Thus, the probability evolution can be described through a Focker-Planck dynamics [1][2][3][4]. Some examples where multimodality can be found in a stationary regime are diffusion driven by a random shear flow [5,6], and grafted polymers [7][8][9][10], just to name a few [1]. The developing of transient multimodality in Focker-Planck dynamics has also been of interest [11].…”

Section: Introductionmentioning

confidence: 99%

Emergence of stationary multimodality under two-timescaled dichotomic noise

et al. 2020

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We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic noise. It is shown that when the statistics of the time intervals between noise transitions is characterized by two well differentiated timescales, the stationary distribution may develop multimodality (bi-and trimodality). The underlying effects that lead to a probability concentration in different points include intermittence and also a dynamical locking of realizations. Our results are supported by numerical simulations as well as by an exact treatment obtained from a Markovian embedding of the full dynamics, which leads to a third-order differential equation for the stationary distribution.

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Bimodal distribution function of a three-dimensional wormlike chain with a fixed orientation of one end

Cited by 5 publications

References 41 publications

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

Orientational Fluctuations and Bimodality in Semiflexible Nunchucks

Emergence of stationary multimodality under two-timescaled dichotomic noise

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