Elasticity of semiflexible polymers in two dimensions

Prasad, Ashok; Hori, Yûko; Kondev, Jané

doi:10.1103/physreve.72.041918

Cited by 39 publications

(66 citation statements)

References 26 publications

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“…Concurrently, characteristics of semi-flexible polymer networks have been studied theoretically and computationally [24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of a Cross-linked Actin-like Network

2007

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Mechanical force plays an important role in the physiology of eukaryotic cells whose dominant structural constituent is the actin cytoskeleton composed mainly of actin and actin crosslinking proteins (ACPs). Thus, knowledge of rheological properties of actin networks is crucial for understanding the mechanics and processes of cells. We used Brownian dynamics simulations to study the viscoelasticity of crosslinked actin networks.Two methods were employed, bulk rheology and segment-tracking rheology where the former measures the stress in response to an applied shear strain, and the latter analyzes thermal fluctuations of individual actin segments of the network. Bulk rheology demonstrates that the storage shear modulus (G') increases more by the addition of ACPs that form orthogonal crosslinks than for those that form parallel bundles. In networks with orthogonal crosslinks, as crosslink density increases, the power law exponent of G' as a function of the oscillation frequency decreases from 0.75, which reflects the transverse thermal motion of actin filaments, to near zero at low frequency. Under increasing prestrain, the network becomes more elastic, and three regimes of behavior are observed, each dominated by different mechanisms: bending of actin filaments, bending of ACPs, and at the highest prestrain tested (55%), stretching of actin filaments and ACPs. In the last case, only a small portion of actin filaments connected via highly stressed ACPs support the strain. We thus introduce the concept of a 'supportive framework,' as a subset of the full network, which is responsible for high elasticity. Notably, entropic effects due to thermal fluctuations appear to be important only at relatively low prestrains and when the average crosslinking distance is comparable to or greater than the persistence length of the filament. Taken together, our results suggest that viscoelasticity of the actin network is attributable to different mechanisms depending on the amount of prestrain. Author SummaryThe actin cytoskeleton provides structural integrity to a cell, is highly dynamic, and plays a central role in a wide variety of essential biological phenomena. For years, researchers have studied the mechanics of the cytoskeleton by creating reconstituted actin gels with one or more of the crosslinking proteins found in cells. These reconstituted gels, however, failed to replicate many aspects of cell behavior. Recent studies have shown that tension, or prestrain, on the cytoskeleton due to actomyosin contractility contributes to the observed stiffness. Still, our understanding of cytoskeletal mechanics is incomplete, and 3 many observed phenomena cannot be explained by existing models. Here, we introduce a Brownian dynamics simulation of a three-dimensional network containing actin filaments and crosslinking proteins. By varying model parameters, we show relative contributions of thermal fluctuations and the stiffness of filaments and crosslinks. Under conditions that replicate those in a cell, properties of the cro...

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“…Concurrently, characteristics of semi-flexible polymer networks have been studied theoretically and computationally [24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of a Cross-linked Actin-like Network

2007

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“…This equation is reminiscent of the Schrödinger equation of a quantum pendulum [48] and evaluates to an expansion in even and odd Mathieu functions, as has been elaborated for stretching forces, f > 0, in Ref. [45] and for compression forces, f < 0, in Ref. [44], respectively.…”

Section: Wormlike Chain Modelmentioning

confidence: 99%

“…The partition sums for clamped, Z(ϕ L , L|ϕ 0 , 0), cantilevered, Z(L|ϕ 0 , 0), and free polymers, Z(L), subject to external forces have been computed in Refs. [44,45]. These are now used to normalize the characteristic functions (instead of Z 0 ).…”

Section: Free Polymermentioning

confidence: 99%

“…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. the variance) [44], thereby, complementing theoretical and simulation studies on the stretching behavior [45] and the response of single semiflexible polymers upon compression in the weakly-bending approximation [10,19]. The smearing of the classical Euler buckling instability by thermal fluctuations leads to a rapid decrease of the forceextension relation and a strongly peaked susceptibility, reminiscent of a smeared discontinuous phase transition in a finite system.…”

Section: Introductionmentioning

confidence: 99%

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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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“…It is known that the force versus extension curve of an isotropic chain (i.e. A 1 = A 2 = P ) in 2D is given by [70] …”

Section: B Stretching Anisotropic Chain In 2dmentioning

confidence: 99%

Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy

Salari¹,

Eslami-Mossallam²,

Ranjbar³

et al. 2016

Phys. Rev. E

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Using analytical approach and Monte-Carlo (MC) simulations, we study the elastic behaviour of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than 3D conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in 2D, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-bend coupling, which leads to the kink formations with a half helical turn periodicity along the bent polymer.

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Elasticity of semiflexible polymers in two dimensions

Cited by 39 publications

References 26 publications

Computational Analysis of a Cross-linked Actin-like Network

Computational Analysis of a Cross-linked Actin-like Network

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

Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy

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