Sedimentation of knotted polymers

Piili, Joonas; Marenduzzo, Davide; Kaski, Kimmo; Linna, Riku

doi:10.1103/physreve.87.012728

Cited by 5 publications

(6 citation statements)

References 51 publications

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“…It is worth noticing that, within the five-crossings family, the 5 1 torus knot moves more slowly than the 5 2 twist knots. This is similar to what was observed in the weak field case (although much less enhanced) but different from what is observed in experiments of sedimentation (15).…”

Section: Dna Knots Form An Electrophoretic Arc Only In Irregular Gelssupporting

confidence: 53%

“…For instance, it is now widely accepted that the physics of the size-dependent migration of linear polymers can be explained by the theory of biased polymer reptation (7)(8)(9)(10)(11)(12). Likewise, the behavior of, for example, nicked, torsionally relaxed, DNA knots in a sparse gel and under a weak field is analogous to that of molecules sedimenting under gravity (13)(14)(15). The terminal velocity can be estimated via a balance between the applied force and the frictional opposing force, which is proportional to the average size of the molecule; as a result, more-complex knots, which are smaller, move faster under the field.…”

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confidence: 99%

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Topological patterns in two-dimensional gel electrophoresis of DNA knots

Michieletto

Marenduzzo

Orlandini

2015

Proc. Natl. Acad. Sci. U.S.A.

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Gel electrophoresis is a powerful experimental method to probe the topology of DNA and other biopolymers. Although there is a large body of experimental work that allows us to accurately separate different topoisomers of a molecule, a full theoretical understanding of these experiments has not yet been achieved. Here we show that the mobility of DNA knots depends crucially and subtly on the physical properties of the gel and, in particular, on the presence of dangling ends. The topological interactions between these and DNA molecules can be described in terms of an "entanglement number" and yield a nonmonotonic mobility at moderate fields. Consequently, in 2D electrophoresis, gel bands display a characteristic arc pattern; this turns into a straight line when the density of dangling ends vanishes. We also provide a novel framework to accurately predict the shape of such arcs as a function of molecule length and topological complexity, which may be used to inform future experiments.DNA knots | topology | gel electrophoresis T opology plays a key role in the biophysics of DNA and is intimately related to its functioning. For instance, transcription of a gene redistributes twist locally to create what is known as supercoiling, whereas catenanes or knots can prevent cell division; hence they need to be quickly and accurately removed by specialized enzymes known as topoisomerases. How can one establish experimentally the topological state of a given DNA molecule? By far the most successful and widely used technique to do so is gel electrophoresis (1, 2). This method exploits the empirical observation that the mobility of a charged DNA molecule under an electric field depends on its size, shape, and topology (2). Gel electrophoresis is so reliable that it can be used, for instance, to map replication origins and stalled replication forks (3), to separate plasmids with different amount of supercoiling (3, 4), and to identify DNA knots (5, 6). The most widely used variant of this technique nowadays is 2D gel electrophoresis, where a DNA molecule is subjected to a sequence of two fields, applied along orthogonal directions (2). The two runs are characterized by different field strengths and sometimes also gel concentrations (4); with suitable choices, the joint responses lead to increased sensitivity.Although gel electrophoresis is used very often, and is extremely well characterized empirically, there is still no comprehensive theory to quantitatively understand, or predict, what results will be observed in a particular experiment. Some aspects are reasonably well established. For instance, it is now widely accepted that the physics of the size-dependent migration of linear polymers can be explained by the theory of biased polymer reptation (7-12). Likewise, the behavior of, for example, nicked, torsionally relaxed, DNA knots in a sparse gel and under a weak field is analogous to that of molecules sedimenting under gravity (13-15). The terminal velocity can be estimated via a balance between the applied force and the fr...

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Section: Dna Knots Form An Electrophoretic Arc Only In Irregular Gelssupporting

confidence: 53%

mentioning

confidence: 99%

Topological patterns in two-dimensional gel electrophoresis of DNA knots

Michieletto

Marenduzzo

Orlandini

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…to the knot complexity. This corresponds to the well-known fact that, for a given loop contour length, more complex knots are on average less extended [Stasiak et al, 1996, Piili et al, 2013 (see also the equilibrium configurations in Fig. 6.6).…”

Section: Competition Between Size and Knottednessmentioning

confidence: 67%

“…In particular, it was found [Stasiak et al, 1996] that the square gyration radius is inversely proportional to the ACN, i.e. (3.29) and that this is related to the faster sedimentation speed [Piili et al, 2013, Weber et al, 2013 and faster electrophoretic migration [Stasiak et al, 1996] of more complex knots. Because of these reasons, the ACN obtained from ideal configurations is a good quantity for identifying the complexity of knots travelling through media and it will be used in Ch.…”

Section: Characterising Polymer Knots With Their Average Crossing Numbermentioning

confidence: 99%

“…For instance, it is now widely accepted that the physics of the size-dependent migration of linear polymers can be explained by the theory of biased polymer reptation [Rubinstein, 1987,Duke, 1989,Viovy and Duke, 1993,Barkema et al, 1994,Viovy, 2000. Likewise, the behaviour of, for example, nicked, torsionally relaxed, DNA knots in a sparse gel and under a weak field is analogous to that of molecules sedimenting under gravity [Weber et al, 2013, Piili et al, 2013. The terminal velocity can be estimated via a balance between the applied force and the frictional opposing force, which is proportional to the average size of the molecule: as a result, more complex knots, which are smaller, move faster under the field.…”

Section: A Linked Network Of Rings At the Percolating Pointmentioning

confidence: 99%

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