Topological origins of chromosomal territories

Dorier, Julien; Stasiak, Andrzej

doi:10.1093/nar/gkp702

Cited by 67 publications

(105 citation statements)

References 36 publications

(63 reference statements)

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“…[41][42][43] The investigation of the effects of topological constraints on globular polymers, both in and out of equilibrium, is also expected to be a key to understand chromosomal architecture. 44,45 In the present work we considerably extend and discuss in further detail some of the results presented in Refs. 25,26 Rather than assuming the more global perspective implicit in the Zipf law, here we look at the relative asymptotic frequencies of the simplest knots in globular ring polymers.…”

Section: Introductionsupporting

confidence: 65%

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature T , in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low T on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops (preserving their topology) which compete for the chain length, either in contact or separated by a wall as for translocation through a membrane pore. These findings suggest that in macromolecular environments there may be entropic forces with a purely topological origin, whence portions of polymers holding complex knots should tend to expand at the expense of significantly shrinking other topologically simpler portions. 1

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Section: Introductionsupporting

confidence: 65%

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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“…This makes an obvious analogy with the melt of nonconcatenated rings; indeed, if the rings in the simulated melt are shown in different colors, the image of a political map emerges 20 . This strongly suggests topological properties of chromatin chains as a likely mechanism behind chromosome segregation, similar to segregation of non-concatenated rings in the melt [21][22][23] . Why the topology of the chromatin fibers is restricted is a somewhat open question, but it might be that the DNA ends are attached to the nuclear envelope, or simply that the cell lifetime is not long enough for reptation to develop [24][25][26] .…”

Section: Introductionmentioning

confidence: 85%

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics

Halverson

Lee

Grest

et al. 2011

The Journal of Chemical Physics

306

567

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Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, R 2 g , was found to scale as N 4/5 for an intermediate regime and N 2/3 for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper 1 . Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

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“…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.…”

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confidence: 99%

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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Topological origins of chromosomal territories

Cited by 67 publications

References 36 publications

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics

Conformation of Ring Polymers in 2D Constrained Environments

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