DNA supercoiling, localized bending and thermal fluctuations

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    1 pN, within the range of external forces that were applied in this work, and also published for single-molecule experiments that observed DNA compaction or looping induced by cohesion and condensin [10,12,30,57]. Moreover, in cells, DNA can move or slide by itself if considering the elastic energy that DNA contains, such as supercoiling [58–61]. Our DNA-sliding ratchet model (Fig. 5C) does explain how MukBEF can efficiently organize DNA while having only low ATPase activity, and the intrinsic ability to entrap DNA topologically.

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    Tsen and Levene have developed a topological assay that shows a supercoiling-dependent flexibility of adenosine-tract-containing DNA [29]. Moreover, diverse theoretical treatments including Refs. [30–32], predict that curvature and non-uniform bending rigidity are important features that organize DNA tertiary structure by localizing A-tracts at the apex of superhelical domains. Nelson [25], studying the transport of torsional stress in DNA, concluded that “Natural bends resist flexing, forcing the molecule to translate through the fluid and greatly increasing the viscous drag through the surrounding medium”.

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    Local variations in nucleosome positioning and, most importantly, thermal fluctuations at room temperature will cause random deviations from this regular structure; to understand the dynamics of the chromatin chain, it is very important to include these fluctuations into the model. The same issue has been discussed in the DNA field some time ago: while elastic rod models were successful in early theoretical descriptions of DNA supercoiling (e.g., [77–79], for review see Ref. [80]), the computation of real-life structural properties of superhelical DNA is only possible with numerical models that include thermal fluctuations (for a discussion of this point, see also Ref. [81]). Here we will therefore now consider methods that create configurational ensembles which reflect the structure of the chromatin chain at a finite temperature.

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