Shapes of Semiflexible Polymer Rings

Alim, Karen; Frey, Erwin

doi:10.1103/physrevlett.99.198102

Cited by 78 publications

(120 citation statements)

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“…From our results for the correlation function, ring polymers in classes I and II are clearly described very well by the LSF model, and thus we pursue our comparison with the results of Fisher and coworkers who extensively studied the shape parameters of vesicles. As the correlation function, these shape parameters are convenient measures characterizing the different polymer classes because they depend on the type of polymer (Gaussian, self-avoiding), its dimensionality, its topology, and its rigidity [4,5,27,28]. Typical shape measures include the anisotropy AE and the asphericity A, which are defined as combinations of R 2 G1 and R 2 G2 , the small and large principal axes of the radius-of-gyration tensor R G , by AE ¼ hR 2 G1 =R 2 G2 i and…”

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“…Ring closure of a polymer is one of the important factors influencing its statistical mechanical properties [1], e.g., scaling [2,3], shape [4,5], and diffusion [6][7][8], because it restrains the accessible phase space. The theoretical description of circular chains (knots or catenanes) is a challenging problem, owing to the difficulties inherent to a systematic theoretical analysis of such objects constrained to a unique topology.…”

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“…Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box. DOI: 10.1103/PhysRevLett.106.248301 PACS numbers: 82.35.Gh, 87.64.Dz, 36.20.Ey, 87.14.gk Ring closure of a polymer is one of the important factors influencing its statistical mechanical properties [1], e.g., scaling [2,3], shape [4,5], and diffusion [6][7][8], because it restrains the accessible phase space. The theoretical description of circular chains (knots or catenanes) is a challenging problem, owing to the difficulties inherent to a systematic theoretical analysis of such objects constrained to a unique topology.…”

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Conformation of Ring Polymers in 2D Constrained Environments

et al. 2011

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The combination of ring closure and spatial constraints has a fundamental effect on the statistics of semiflexible polymers such as DNA. However, studies of the interplay between circularity and constraints are scarce and single-molecule experimental data concerning polymer conformations are missing. By means of atomic force microscopy we probe the conformation of circular DNA molecules in two dimensions and in the concentrated regime (above the overlap concentration c Ã ). Molecules in this regime experience a collapse, and their statistical properties agree very well with those of simulated vesicles under pressure. Some circular molecules also create confining regions in which other molecules are trapped. Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box. DOI: 10.1103/PhysRevLett.106.248301 PACS numbers: 82.35.Gh, 87.64.Dz, 36.20.Ey, 87.14.gk Ring closure of a polymer is one of the important factors influencing its statistical mechanical properties [1], e.g., scaling [2,3], shape [4,5], and diffusion [6][7][8], because it restrains the accessible phase space. The theoretical description of circular chains (knots or catenanes) is a challenging problem, owing to the difficulties inherent to a systematic theoretical analysis of such objects constrained to a unique topology. The problem is particularly evident for systems of interacting chains, for example, in semidilute or confined states. Cates and Deutsch [9] pointed out that topological constraints act to alter quite dramatically the behavior of chains in a melt. This has been confirmed by experiments and simulations for the three-dimensional (3D) system [10], but to our knowledge not for the 2D case where studies are limited to the linear case [11].The behavior of confined circular chains remains also poorly understood, and only a few experiments explored this system [12]. Ring closure, and more generally topology, plays a key role in a wide range of biophysical contexts where DNA is constrained: segregation of the compacted circular genome of some bacteria [13], formation of chromosomal territories [14] in cell nuclei, compaction and ejection of the knotted DNA of a virus [15,16], migration of a circular DNA in an electrophoresis gel [17] or in a nanodevice such as a nanochannel [18], or localization of knots [3,19]. Therefore a better understanding of the basic properties of such systems is highly needed.In the present Letter, we would like to present experimental findings on ring polymers in the concentrated phase and in a confined environment obtained at the singlemolecule level by means of the atomic force microscope (AFM) as depicted in Fig. 1.A 10 l drop of nicked circular-plasmid DNA pBR322 (4361 base pairs) at a concentration of 0:5 mg=ml in 1 mM MgCl 2 was deposited for 5 minutes on a freshly cleaved mica surface, then rinsed with 10 ml of ultrapure water and dried. The samples were then imaged in tapping mode wit...

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Conformation of Ring Polymers in 2D Constrained Environments

et al. 2011

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“…For the targeted search by proteins along genomic DNA [3,4], long-range spatial and temporal interactions arising from such interplay are known to be crucial. While physical properties of circular polymers are significantly different from those of linear polymers, an understanding comparable to that of open polymers is still lacking [5][6][7][8][9][10][11][12][13][14]. A central complication lies in the topological constraint that severely restricts a rigorous theoretical treatment.…”

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Universal bond correlation function for two-dimensional polymer rings

Sakaue¹,

Witz²,

Dietler³

et al. 2010

EPL

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-The bond orientational correlation function (BCF) of a semiflexible ring polymer on a flat surface is studied theoretically. For a stiff chain, we give an exact analytic form of BCF with perturbation calculations. For a chain sufficiently longer than its persistence length, the conventional exponential decay vanishes and a long-range order along the chain contour appears. We demonstrate that the bond orientational correlation satisfies the scaling properties, and construct an interpolating formula for its universal curve that encompasses the short-and large-distance behaviors. Our analytical findings are confirmed by extensive Langevin dynamics simulations, and are in excellent agreement with recent experimental data obtained from DNA molecules imaged by atomic force microscopy without any fitting parameters.

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“…In particular, the simple analytical interpolation formula for the non-linear force-extension relation of a WLC proposed by Marko and Siggia explains force spectroscopy experiments with DNA (Bustamante et al, 1994;Marko & Siggia, 1995) and has led to a surge of applications in single-molecule experiments. Moreover, the WLC enters theories for polymers in confinement (Odijk, 1983;Semenov, 1986;Morse, 2001), under the application of forces (MacKintosh et al, 1995;Kroy & Frey, 1996;Seifert et al, 1996;Hallatschek et al, 2005), compressive load (Baczynski et al, 2007;Emanuel et al, 2007), under shear (Gittes et al, 1997;Morse, 1998c) or in flow fields (Morse, 1998b;Munk et al, 2006), for their bundles (Heussinger et al, 2007) or rings (Alim & Frey, 2007;Ostermeir et al, 2010). The WLC model has been used to characterize a wide range of other biological macromolecules besides DNA and cytoskeletal polymers, including muscle proteins (Tskhovrebova et al, 1997), RNA (Caliskan et al, 2005) or polysaccharides (Vincent et al, 2007).…”

Section: Fluctuations and Response Of Wormlike Chainsmentioning

confidence: 99%