From Semi-Flexible Polymers to Membranes: Anomalous Diffusion and Reptation

Granek, Rony

doi:10.1051/jp2:1997214

Cited by 200 publications

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“…In this limit, the growth of ͗d 2 ͑t͒͘ with time t at early times is limited by the finite transversal fluctuations of a wormlike chain, leading to an expected t 3/4 scaling. 70 This is indeed observed in the simulations as well ͑dashed line͒. With increasing network density ͑and hence decreasing mesh size͒ the displacement of the fibers become hindered by the presence of other fibers at smaller and smaller length scales.…”

Section: Influence Of Hydrodynamic Interactions and Uncrossability Ofsupporting

confidence: 67%

Efficient simulation of noncrossing fibers and chains in a hydrodynamic solvent

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2009

The Journal of Chemical Physics

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Waiting time dependence of T2 of protons in water suspensions of iron-oxide nanoparticles: Measurements and simulations J. Appl. Phys. 110, 073917 (2011) The effects of shape and flexibility on bio-engineered fd-virus suspensions J. Chem. Phys. 135, 144106 (2011) Quantitative measurement of scattering and extinction spectra of nanoparticles by darkfield microscopy Appl. Phys. Lett. 99, 131113 (2011) Implications of the effective one-component analysis of pair correlations in colloidal fluids with polydispersity J. Chem. Phys. 135, 124513 (2011) Single-walled carbon nanotubes and nanocrystalline graphene reduce beam-induced movements in highresolution electron cryo-microscopy of ice-embedded biological samples Appl. Phys. Lett. 99, 133701 (2011) Additional information on J. Chem. Phys. An efficient simulation method is presented for Brownian fiber suspensions, which includes both uncrossability of the fibers and hydrodynamic interactions between the fibers mediated by a mesoscopic solvent. To conserve hydrodynamics, collisions between the fibers are treated such that momentum and energy are conserved locally. The choice of simulation parameters is rationalized on the basis of dimensionless numbers expressing the relative strength of different physical processes. The method is applied to suspensions of semiflexible fibers with a contour length equal to the persistence length, and a mesh size to contour length ratio ranging from 0.055 to 0.32. For such fibers the effects of hydrodynamic interactions are observable, but relatively small. The noncrossing constraint, on the other hand, is very important and leads to hindered displacements of the fibers, with an effective tube diameter in agreement with recent theoretical predictions. The simulation technique opens the way to study the effect of viscous effects and hydrodynamic interactions in microrheology experiments where the response of an actively driven probe bead in a fiber suspension is measured.

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Section: Influence Of Hydrodynamic Interactions and Uncrossability Ofsupporting

confidence: 67%

Efficient simulation of noncrossing fibers and chains in a hydrodynamic solvent

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2009

The Journal of Chemical Physics

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“…(7), no decoupled bending regime exists, and the bending stiffness vanishes as the cross-link shear stiffness approaches zero [26]. The condition N delineating the remaining two regimes can be rewritten as E=G L=D 2 1, which reemphasizes the small value of cross-link shear stiffness in the intermediate regime.…”

Section: Functional Differentiation Of the Hamiltonian Results In Thementioning

confidence: 99%

Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

2007

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We demonstrate that a semiflexible bundle of wormlike chains exhibits a state-dependent bending stiffness that alters fundamentally its scaling behavior with respect to the standard wormlike chain. We explore the equilibrium conformational and mechanical behavior of wormlike bundles in isolation, in cross-linked networks, and in solution. DOI: 10.1103/PhysRevLett.99.048101 PACS numbers: 87.16.Ka, 82.35.Lr, 83.10.ÿy, 87.15.La In recent decades, the wormlike chain (WLC) has emerged as the standard model for the description of semiflexible polymers [1]. The defining property of a WLC is a mechanical bending stiffness f that is an intrinsic material constant of the polymer. Within this framework, numerous correlation and response functions have been calculated, providing a comprehensive picture of the equilibrium and dynamical properties of WLCs [2 -4]. A number of experimental studies have demonstrated the applicability of the WLC model to DNA [5] and F-actin [6], among other biological and synthetic polymers. Significant progress has also been made towards the description of the collective properties of WLCs, for example, in the form of entangled solutions. One of the hallmarks of this development is the scaling of the plateau shear modulus with concentration G c 7=5 [7][8][9], which is well established experimentally [10,11].Another important emerging class of semiflexible polymers consists of bundles of WLCs [12,13]. Semiflexible polymer bundles consisting of F-actin or microtubules are ubiquitous in biology [14] and have unique mechanical properties that may well be exploited in the design of nanomaterials [13]. As shown by Bathe et al. [15,16], wormlike bundles (WLBs) have a state-dependent bending stiffness B that derives from a generic interplay between the high stiffness of individual filaments and their rather soft relative sliding motion. In this Letter, we demonstrate that this state dependence gives rise to fundamentally new behavior that cannot be reproduced trivially using existing relations for WLCs. We explore the consequences of a state-dependent bending stiffness on the statistical mechanics of isolated WLBs, as well as on the scaling behavior of their entangled solutions and cross-linked networks.We consider the bending of ordered bundles with an isotropic cross section. A bundle consists of N filaments of length L and bending stiffness f . Filaments are irreversibly cross-linked to their nearest neighbors by discrete cross-links with mean axial spacing . Cross-links are modeled to be compliant in shear along the bundle axis with finite shear stiffness k and to be inextensible transverse to the bundle axis, thus fixing the interfilament distance b [17]. Bundle deformations are characterized by the transverse deflection r ? s of the bundle neutral surface at axial position s along the backbone and by the stretching deformation u i s of filament i. The torsional stiffness of the bundle is assumed to be of the same order as the bending stiffness. Thus, as long as transverse deflections remain sm...

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“…PACS numbers: 61.41.+e, 87.15.La, 87.15.He, 98.75.Da In tracing back the viscoelasticity of the cell to properties of its constituents, a detailed understanding of the mechanical response of single cytoskeletal filaments is indispensable. Due to their large bending stiffness, these filaments exhibit highly anisotropic static [1] and dynamic [2,3,4] features, such as the anomalous t 3 /4 -growth of fluctuation amplitudes in the transverse direction [5,6], i.e., perpendicular to the local tangent. The related response to a localized transverse driving force has so far been examined only by neglecting longitudinal degrees of freedom [6,7], although these polymers are virtually inextensible, and transverse and longitudinal contour deformations therefore coupled.…”

mentioning

confidence: 99%

“…The yet unknown time-dependent width ℓ ⊥ (t) of the bulge is controlled by the relaxation spectrum of bending deformations. In the weakly-bending limit, the transverse displacement field r ⊥ (s, t) of an overdamped inextensible rod with bending stiffness κ obeys [5] …”

mentioning

confidence: 99%

Coupling of Transverse and Longitudinal Response in Stiff Polymers

Obermayer

Hallatschek

2007

Phys. Rev. Lett.

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The time-dependent transverse response of stiff inextensible polymers is well understood on the linear level, where transverse and longitudinal displacements evolve independently. We show that for times beyond a characteristic time t f , longitudinal friction considerably weakens the response compared to the widely used linear response predictions. The corresponding feedback mechanism is explained by scaling arguments and quantified by a systematic theory. Our scaling laws and exact solutions for the transverse response apply to cytoskeletal filaments as well as DNA under tension. PACS numbers: 61.41.+e, 87.15.La, 87.15.He, 98.75.Da In tracing back the viscoelasticity of the cell to properties of its constituents, a detailed understanding of the mechanical response of single cytoskeletal filaments is indispensable. Due to their large bending stiffness, these filaments exhibit highly anisotropic static [1] and dynamic [2,3,4] features, such as the anomalous t 3 /4 -growth of fluctuation amplitudes in the transverse direction [5,6], i.e., perpendicular to the local tangent. The related response to a localized transverse driving force has so far been examined only by neglecting longitudinal degrees of freedom [6,7], although these polymers are virtually inextensible, and transverse and longitudinal contour deformations therefore coupled. In this Letter we show that longitudinal motion strongly affects the transverse response even for weakly-bending filaments and leads to relevant nonlinearities beyond a characteristic time t f .The physical key factors controlling the transverse response may be understood from Fig. 1, which shows a weakly-bending polymer (bending undulations are exaggerated for visualization) shortly after a transverse driving force f ⊥ has been applied in the bulk. In response to this force, the contour develops a bulge. Due to the backbone inextensibility, this bulge can continue growing only by pulling in contour length from the filament's tails. This effectively reduces the thermal roughness of the contour [8,9,10], at a rate substantially limited by longitudinal solvent friction. The resulting coupling to the longitudinal response tends to slow down the bulge growth. In order to describe this feedback mechanism, we start with a scaling analysis and treat the simpler athermal case first. To connect to the biologically important situations of prestressed actin networks [11] and prestretched DNA [12], we then extend a recent theory of tension dynamics [13] to calculate the nonlinear response for unstretched and prestretched initial conditions. Consider the overdamped dynamics of an initially straight stiff rod of total length L. Suddenly applying a transverse pulling force f ⊥ , for simplicity in the center of the rod, leads to the growth of a bulge deformation. The generated friction in the transverse and longitudinal direction needs to be balanced by corresponding driving forces. Viscous solvent friction is modeled via anisotropic friction coefficients (per length) ζ ⊥ and ζ = ζζ ⊥ with ζ ≈ ...

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From Semi-Flexible Polymers to Membranes: Anomalous Diffusion and Reptation

Cited by 200 publications

References 0 publications

Efficient simulation of noncrossing fibers and chains in a hydrodynamic solvent

Efficient simulation of noncrossing fibers and chains in a hydrodynamic solvent

Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

Coupling of Transverse and Longitudinal Response in Stiff Polymers

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