Conformation of Ring Polymers in 2D Constrained Environments

Abstract

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 à ). 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...

Linear and ring polymers in confined geometries

“…In this respect it is necessary to mention polymers with ring topology. As it was shown in a series of the atomic force spectroscopy (AFM) experiments [33,34] biopolymers such as DNA very often present ring topology. Such situation takes place, for example, in the case of Escherichia coli (E.coli) bacteria with a chromosome which is not a linear polymer, but has a ring topology [35].…”

“…Ring topology has an influence on the statistical mechanical properties of polymers, for example, on scaling properties [41,42] and shape [34,43,44] because it restrains the accessible phase space. Looking back into the history of the investigation of the statistical mechanical properties of ring polymers we should mention that an interesting point which was confirmed by numerical studies in [45] is that longer ring polymers are usually knotted with higher frequency and complexity.…”

Density functional theory for inhomogeneous ring polymeric fluids

“…In practical experiments, many kinds of synthetic polymers (e.g., polyethylene and polystyrene) and biopolymers (e.g., DNA, RNA, chromosome, plastid, and actin) can form ringlike structures [1][2][3][4]. By comparison with many kinds of chain fluids, the ringlike polymers show different properties and behavior because they have no free ends.…”

Structure and Dynamics of Dilute Two-Dimensional Ring Polymer Solutions

“…Polymers confined on surfaces have drawn a great deal of attention due to their industrial importance since polymer thin films [1][2][3][4][5][6] were widely used for protective coatings, insulating layers or lubricants. Because the performance of polymer thin films should be determined by the structure and the dynamics of polymers on surfaces, there have been extensive theoretical and experimental studies.…”