Statistical mechanics of triangulated ribbons

Mergell, Boris; Ejtehadi, Mohammad Reza; Everaers, Ralf

doi:10.1103/physreve.66.011903

Cited by 13 publications

(18 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1. In that model, the anisotropic bundle cross section leads to a coupling of inplane and out-of-plane bending modes [20] that is absent in the present model because it has a symmetric cross section.…”

mentioning

confidence: 76%

Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

2007

View full text Add to dashboard Cite

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...

show abstract

mentioning

confidence: 76%

Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

2007

View full text Add to dashboard Cite

show abstract

“…A more general description is obtained by the classical elastic ribbon [8], which accounts for three parameters concerning bending and twisting. There are also advances to describe polymer bundles as a set of interconnected semiflexible polymers, starting out with railway track models of two coupled filaments in two [9] and three [10,11,12] dimensions, whose exact implementation and results were much in debate [12]. Recently, a model for wormlike bundles with isotropic cross-section, consisting of a finite number of semiflexible polymers, has been introduced and analyzed [13,14].…”

Section: Introductionmentioning

confidence: 99%

Fluctuating semiflexible polymer ribbon constrained to a ring

Alim

Frey

2007

Eur. Phys. J. E

View full text Add to dashboard Cite

Abstract. Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.

show abstract

“…Supercoiling plays an important role in determining the large-scale structure of DNA in both prokaryotic and eukaryotic cells, 1 and a lot of effort has gone into developing algorithms for Monte Carlo, [2][3][4][5] Brownian Dynamics, 6,7 and Molecular Dynamics 8 simulations of supercoiled DNA. At a mesoscopic level, the DNA chain can be viewed as a ribbon ͕r͑s͒ , n͑s͖͒ consisting of a spacecurve r͑s͒ and a local normal n͑s͒ pointing, for example, in the direction of the major groove.…”

Section: Introductionmentioning

confidence: 99%

Evaluating changes of writhe in computer simulations of supercoiled DNA

Vries

2005

The Journal of Chemical Physics

View full text Add to dashboard Cite

We compute changes in the writhe of a polygonal space curve when one of the vertices is displaced. The resulting expressions can be used in simulations of supercoiled DNA. For Brownian dynamics simulations, the expressions can be used to eliminate the explicit twisting degree of freedom. For Monte Carlo simulations, they can be used in fast local moves. Preliminary Monte Carlo simulations using only such fast local moves show that these can be used to efficiently simulate small DNA supercoils.

show abstract

Statistical mechanics of triangulated ribbons

Cited by 13 publications

References 35 publications

Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

Fluctuating semiflexible polymer ribbon constrained to a ring

Evaluating changes of writhe in computer simulations of supercoiled DNA

Contact Info

Product

Resources

About