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

Kurzthaler, Christina; Franosch, Thomas

doi:10.1039/c8sm00366a

Cited by 7 publications

(6 citation statements)

References 68 publications

(144 reference statements)

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“…(3)] rather than on the distance between both ends. For the 2D analog of our model, clamped polymers assume an Sshaped and cantilevered polymers a hooked-shaped configuration at large compression forces [36], where the clamped ends remain aligned along the direction of the force (i.e. opposite to the compression).…”

Section: Discussionmentioning

confidence: 99%

“…Exact solutions for the force-extension relation of a wormlike chain in 2D have been provided for stretching [30] and only recently for compression forces [31], which complete previous approximate theories in the regime of stiff polymers [32][33][34][35]. Furthermore, the response of a wormlike chain in 2D has been elucidated using exact solutions for the associated probability densities [36]. For the 3D case, the force-extension relation of a semiflexible polymer under compression has been elaborated in Ref.…”

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confidence: 93%

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Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

Kurzthaler

2018

Soft Matter

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We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.

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Section: Discussionmentioning

confidence: 99%

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confidence: 93%

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

Kurzthaler

2018

Soft Matter

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“…In the limit of D = 0 and U (r) = 0, the above equation can be interpreted as that describing the probability distribution of the end-to-end separation r of a worm-like chain with bending rigidity κ ∼ 1/D r , interpreting the polymer contour length L ∼ t [29,39,[44][45][46]. For a harmonic trap, U (r) = (1/2)kr 2 , the equation (3) simplifies to…”

Section: The Langevin and Fokker-planck Equationsmentioning

confidence: 99%

Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition

Chaudhuri¹,

Dhar²

2021

J. Stat. Mech.

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We consider an active Brownian particle in a d-dimensional harmonic trap, in the presence of translational diffusion. While the Fokker–Planck equation cannot in general be solved to obtain a closed form solution of the joint distribution of positions and orientations, as we show, it can be utilized to evaluate the exact time dependence of all moments, using a Laplace transform approach. We present an explicit calculation of several such moments at arbitrary times and their evolution to the steady state. In particular we compute the kurtosis of the displacement, a quantity which clearly shows the difference of the active steady state properties from the equilibrium Gaussian form. We find that it increases with activity to asymptotic saturation, but varies non-monotonically with the trap-stiffness, thereby capturing recently observed active-to-passive re-entrant behavior.

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“…It is clear that the solution to

given in Equation ( 5 ) as a function of

has a periodicity of

. Quite often, this result is directly transferred from the quantum rotator to the WLC [ 18 , 19 , 20 , 21 , 22 ]. However, this mathematical analogy should not be carried too far.…”

Section: The Theoretical Modelmentioning

confidence: 99%

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

Cited by 7 publications

References 68 publications

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition

Orientational Fluctuations and Bimodality in Semiflexible Nunchucks

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