Random loop model for long polymers

Bohn, Manfred; Heermann, Dieter W.; Driel, Roel van

doi:10.1103/physreve.76.051805

Cited by 98 publications

(119 citation statements)

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“…We have shown that loop structures lead to a strong effective repulsion and for a first time quantitatively analyzed the strength of the resulting interactions. Surely, the formation of multiple loops in the system of chromatin which has been proposed in several models 6,20,45,46 induces even stronger effects and therefore might be responsible for maintaining the segregated state of chromosomes found in several experiments 9 . Indeed, studies of looping polymers have revealed an effect on the abundance of inter-chromosomal contacts 12,13 .…”

Section: Discussionmentioning

confidence: 95%

Topological interactions between ring polymers: Implications for chromatin loops

Bohn

Heermann²

2010

The Journal of Chemical Physics

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Chromatin looping is a major epigenetic regulatory mechanism in higher eukaryotes. Besides its role in transcriptional regulation, chromatin loops have been proposed to play a pivotal role in the segregation of entire chromosomes. The detailed topological and entropic forces between loops still remain elusive. Here, we quantitatively determine the potential of mean force between the centers of mass of two ring polymers, i.e. loops. We find that the transition from a linear to a ring polymer induces a strong increase in the entropic repulsion between these two polymers. On top, topological interactions such as the non-catenation constraint further reduce the number of accessible conformations of close-by ring polymers by about 50%, resulting in an additional effective repulsion. Furthermore, the transition from linear to ring polymers displays changes in the conformational and structural properties of the system. In fact, ring polymers adopt a markedly more ordered and aligned state than linear ones. The forces and accompanying changes in shape and alignment between ring polymers suggest an important regulatory function of such a topology in biopolymers. We conjecture that dynamic loop formation in chromatin might act as a versatile control mechanism regulating and maintaining different local states of compaction and order.

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Section: Discussionmentioning

confidence: 95%

Topological interactions between ring polymers: Implications for chromatin loops

Bohn

Heermann²

2010

The Journal of Chemical Physics

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“…To gain high elasticity, chromatin may change its viscoelastic properties during interphase in such a way that it can rapidly decondense and then consolidate. This could be effected, e.g., by crosslinks that induce the formation of chromatin loops (Bohn et al 2007;Cremer et al 1996;Lieberman-Aiden et al 2009;Münkel and Langowski 1998). In addition to chromatin, then, one might need to invoke contributions by another, stiffer macromolecular network to account for the high elasticity of the nucleus.…”

Section: Discussionmentioning

confidence: 99%

“…There we succeeded in developing a theory for the spatial arrangement of a heterogeneous polymer network in terms of correlations and derived a measure for its "clumpiness" and how this affects macromolecular transport. Simultaneously, this model allowed us to study the effect of loopinduced compartmentalization, a concept that has been discussed for some time (Bohn et al 2007;Cremer et al 1996;Münkel and Langowski 1998), and to compare the simulation results quantitatively with the recent intrachromosomal interaction data measured by Lieberman-Aiden et al (2009). However, the combined effects of chromatin chain mobility, specific chromatin folding, and of crowding by other diffusing macromolecules were not included in our earlier work.…”

Section: Introductionmentioning

confidence: 99%

Chromosome dynamics, molecular crowding, and diffusion in the interphase cell nucleus: a Monte Carlo lattice simulation study

Fritsch

Langowski

2010

Chromosome Res

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Using Monte Carlo simulations, we have investigated the decondensation of chromosomes during interphase and the diffusive transport of spherical probe particles in the chromatin network. The chromatin fibers are modeled as semiflexible polymer chains on a fixed threedimensional grid, taking into account their flexibility and eventual chain crossing by the aid of topoisomerases. The network thus created will obstruct the diffusion of macromolecules. A result of our simulations is that crowding of diffusing molecules leaves the dynamics of the chromosomes and the behavior of other diffusing molecules qualitatively unaffected. Furthermore, the capability of the simulated chromatin network to trap diffusing molecules over long times is lower than that measured in microrheological experiments. Microrheology is a technique that allows to determine the viscoelastic properties of a material by the motion of embedded tracer particles. Long-time trapping requires a stiff network, as only such a network quickly responds to the diffusive fluctuations of tracers C. C. Fritsch · J. Langowski (B) Biophysics of Macromolecules, German Cancer Research Center (Deutsches Krebsforschungszentrum, DKFZ), Im Neuenheimer Feld 580, 69120 Heidelberg, Germany e-mail: joerg.langowski@dkfz-heidelberg.de and prevents them from squeezing through meshes. A high degree of crosslinking amplifies this effect. The presence of a flexible and uncrosslinked polymer simply increases the effective viscosity sensed by tracer particles. The diffusion of tracers in our simulations reveals rather viscous than elastic chromatin networks, suggesting that chromatin alone cannot account for the high elasticity of the cell nucleus.

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“…Dynamic random loop model. This model uses a linear backbone polymer that dynamically folds and builds loops of all length scales (Bohn et al, 2007;Mateos-Langerak et al, 2009). Here, the scaling exponent  becomes 0, as the length N of the polymer exceeds a certain length (2 Mb).…”

Section: Self-avoiding Walk (Saw)mentioning

confidence: 99%

Chromatin folding – from biology to polymer models and back

Tark-Dame

Driel

Heermann

2011

Journal of Cell Science

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Commentary 839 IntroductionHuman cells contain 46 chromatin fibres, i.e. the chromosomes, with a total length of ~5 cm of nucleosomal filaments arranged like beads on a string. Packaging this in an interphase nucleus of typically 5-20 m in diameter requires extensive folding. In the past decades, considerable evidence was accumulated showing that chromatin folding is closely related to genome function. Tightly packed and transcriptionally silent heterochromatin, and more-open transcriptionally active euchromatin represent two classic folding states. In the past decade, we started to see some first principles of chromatin folding. One is that individual chromosomes occupy discrete domains in the interphase nucleus -named chromosome territories -which intermingle only to a limited extent (Cremer and Cremer, 2010). Similarly, different parts of a chromosome also only interact very little (Dietzel et al., 1998;Goetze et al., 2007a;Goetze et al., 2007b). Another organisational principle is based on the finding that mammalian interphase chromosomes are made up of a large number of structural domains, each of which are on averagẽ 1 Mb, that correspond to DNA replication units (Ryba et al., 2010). Furthermore, recent experimental data show that chromatin loops mediated by specific chromatin-chromatin interactions are an important aspect of chromatin organisation, because they bring together distant regulatory elements that control gene expression, such as promoters and enhancers (Carter et al., 2002;Kadauke and Blobel, 2009). Methods that are based on the chromosome conformation capture (3C) technology, which determines two distant genomic sequence elements that are in close proximity in the nucleus (Simonis et al., 2007), have revealed the presence of a large number of intra-chromosomal chromatin-chromatin interactions. The resulting loops vary in length from a few kb to up to tens of Mb and are different in different cell types (Lieberman-Aiden et al., 2009;Simonis et al., 2006). Moreover, it has been shown for many loci that changes in transcriptional activity are tightly correlated with changes in folding (Sproul et al., 2005). Together, these observations show that packaging of the chromatin fibre in the interphase nucleus is closely related to genome function and that loops are a prominent feature of interphase chromatin.The notion that chromatin loops are important for overall genome organisation is also supported from the perspective of polymer models. Recent polymer modelling efforts show that the formation of loops can endow polymers such as chromatin with properties that explain several of its key properties, including chromatin compaction and compartmentalisation. The importance of polymer models is that they aim to explain properties of chromatin on the basis of physical principles and discard those models that do not fulfil this criterion. They make precise predictions that can be tested experimentally and their outcome can be used to further improve the model, thereby increasing our understanding of chro...

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Random loop model for long polymers

Cited by 98 publications

References 25 publications

Topological interactions between ring polymers: Implications for chromatin loops

Topological interactions between ring polymers: Implications for chromatin loops

Chromosome dynamics, molecular crowding, and diffusion in the interphase cell nucleus: a Monte Carlo lattice simulation study

Chromatin folding – from biology to polymer models and back

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