Self-Contact for Rods on Cylinders

Heijden, van der G.H.M.; Peletier, Mark A.; Planquè, Robert

doi:10.1007/s00205-006-0011-y

Cited by 11 publications

(13 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While the set of self-intersecting configurations may be of small measure in the configuration space C a , such configurations profoundly affect the topology of the configuration space. For, a WLC polymer can release link two units at a time by passing through itself [17,16,18]. This "topological untwisting" results in a collapse of link sectors.…”

Section: Theoretical Modelsmentioning

confidence: 99%

See 1 more Smart Citation

DNA elasticity: topology of self-avoidance

Samuel¹,

Sinha²,

Ghosh³

2006

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We present a theoretical treatment of DNA stretching and twisting experiments, in which we discuss global topological subtleties of self avoiding ribbons and provide an underlying justification for the worm like rod chain (WLRC) model proposed by Bouchiat and Mezard. Some theoretical points regarding the WLRC model are clarified: the "local writhe formula" and the use of an adjustable cutoff parameter to "regularise" the model. Our treatment brings out the precise relation between the worm like chain (WLC), the paraxial worm like chain (PWLC) and the WLRC models. We describe the phenomenon of "topological untwisting" and the resulting collapse of link sectors in the WLC model and note that this leads to a free energy profile periodic in the applied link. This periodicity disappears when one takes into account the topology of self avoidance or at large stretch forces (paraxial limit). We note that the difficult nonlocal notion of self avoidance can be replaced (in an approximation) by the simpler local notion of "south avoidance". This gives an explanation for the efficacy of the approach of Bouchiat and Mezard in explaining the "hat curves" using the WLRC model, which is a south avoiding model. We propose a new class of experiments to probe the continuous transition between the periodic and aperiodic behavior of the free energy.PACS numbers: 82.37. -j,36.20.-r,87.15.-V

show abstract

Section: Theoretical Modelsmentioning

confidence: 99%

“…It is easily checked that as σ → {0, L 0 },R → {t, −t} respectively. The Cȃlugȃreanu-White writhe is given by [18][19][20] …”

Section: Wreathe and Writhementioning

confidence: 99%

DNA elasticity: topology of self-avoidance

Samuel¹,

Sinha²,

Ghosh³

2006

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…Example: Rod on a cylinder. In [17,18] the present authors studied the deformation of an inextensible and unshearable rod constrained to lie on a cylinder. The rod is assumed to be loaded by an axial end force (tension) T and an end twisting moment M both of which are applied along the axis of the cylinder, which we take parallel to e 3 .…”

Section: λ) Cos θ(S λ)mentioning

confidence: 99%

“…In [18] this functional, under slightly different loading conditions, is studied subject to the constraint that the rod cannot pass through itself on the cylinder.…”

Section: λ) Cos θ(S λ)mentioning

confidence: 99%

On end rotation for open rods undergoing large deformations

2007

Self Cite

View full text Add to dashboard Cite

Abstract. We give a careful discussion of end rotation in elastic rods, focusing on ambiguities that arise if arbitrarily large deformations are allowed. By introducing a closure and restricting to a class of deformations we show that a rigorous treatment of end rotation can be obtained. The results underpin various non-rigorous discussions in the literature and serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations. As an example we discuss the application to the model of a rod lying on the surface of a cylinder.

show abstract

“…In other words, the solutions are consistent with the assumption. For a discussion of the balance equations of rods with self-contact we refer the reader to an article by van der Heijden et al [19]. Quantitative treatment of the contact force in DNA plectonemes has also been peformed by Clauvelin et al [3].…”

Section: Constructing the Plectonemic Solutionmentioning

confidence: 99%

Shape and Energetics of DNA Plectonemes

Purohit

2009

IUTAM Symposium on Cellular, Molecular and Tissue Mechanics

View full text Add to dashboard Cite

The mechanics of DNA at length scales of few hundred nanometers is described by a fluctuating elastic rod model. In this paper we couple the fluctuating rod model with a variational method for describing plectonemes to unravel the mechanics of some recent single molecule experiments. We are able to reproduce some features seen in these experiments which analyze plectoneme formation in DNA under tension by continuously twisting it and tracking its end-to-end distance, torque, etc., as a function of the added link. Our model accounts for configurational entropy and electrostatics in the plectoneme. We find that configurational entropy makes a significant contribution to the mechanics of the plectoneme while electrostatics (in the presence of monovalent counterions) plays a relatively minor role.

show abstract

Self-Contact for Rods on Cylinders

Cited by 11 publications

References 25 publications

DNA elasticity: topology of self-avoidance

DNA elasticity: topology of self-avoidance

On end rotation for open rods undergoing large deformations

Shape and Energetics of DNA Plectonemes

Contact Info

Product

Resources

About