Influence of chain stiffness on knottedness in single polymers

Virnau, Peter; Rieger, Florian; Reith, Daniel

doi:10.1042/bst20120357

Cited by 22 publications

(23 citation statements)

References 40 publications

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“…This is remarkable as it demonstrates that moderate confinement, two orders of magnitude weaker than that found in capsids, can also induce knot formation, suggesting a knot formation mechanism qualitatively different from what has been proposed in refs. 34 , 35 for capsids, where nematic ordering in strong spherical confinement can form toroidal knots with high probability. We show that the free energy scales for knotting under compression in the long-time limit can be estimated by extending known free energy scales for confined knots in a no-flow equilibrium.…”

Section: Discussionmentioning

confidence: 99%

A nanofluidic knot factory based on compression of single DNA in nanochannels

et al. 2018

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Knots form when polymers self-entangle, a process enhanced by compaction with important implications in biological and artificial systems involving chain confinement. In particular, new experimental tools are needed to assess the impact of multiple variables influencing knotting probability. Here, we introduce a nanofluidic knot factory for efficient knot formation and detection. Knots are produced during hydrodynamic compression of single DNA molecules against barriers in a nanochannel; subsequent extension of the chain enables direct assessment of the number of independently evolving knots. Knotting probability increases with chain compression as well as with waiting time in the compressed state. Using a free energy derived from scaling arguments, we develop a knot-formation model that can quantify the effect of interactions and the breakdown of Poisson statistics at high compression. Our model suggests that highly compressed knotted states are stabilized by a decreased free energy as knotted contour contributes a lower self-exclusion derived free energy.

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Section: Discussionmentioning

confidence: 99%

A nanofluidic knot factory based on compression of single DNA in nanochannels

et al. 2018

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“…The computational model is fully determined in terms of the number of beads N and stiffness parameter g ≥ 0. Knotting probabilities of Kratky-Porod chains with excluded volume interactions depend on g in a non-trivial manner [ 36 ], whereas the knotting of ideal Kratky-Porod chains monotonously decreases with stiffness. Screened electrostatic interactions are absorbed in an effective hard sphere diameter d , which depends on the salt concentration [ 20 ].…”

Section: Methodsmentioning

confidence: 99%

A Monte Carlo Study of Knots in Long Double-Stranded DNA Chains

Rieger

Virnau

2016

PLoS Comput Biol

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We determine knotting probabilities and typical sizes of knots in double-stranded DNA for chains of up to half a million base pairs with computer simulations of a coarse-grained bead-stick model: Single trefoil knots and composite knots which include at least one trefoil as a prime factor are shown to be common in DNA chains exceeding 250,000 base pairs, assuming physiologically relevant salt conditions. The analysis is motivated by the emergence of DNA nanopore sequencing technology, as knots are a potential cause of erroneous nucleotide reads in nanopore sequencing devices and may severely limit read lengths in the foreseeable future. Even though our coarse-grained model is only based on experimental knotting probabilities of short DNA strands, it reproduces the correct persistence length of DNA. This indicates that knots are not only a fine gauge for structural properties, but a promising tool for the design of polymer models.

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“…Currently, there is again a growing interest in the role of knots in single polymers [73,74,75,76] and proteins [77,78,79,80,81,82,83]. This is particularly interesting in the context of DNA packing [84,85] with possible implications for DNA sequencing, especially since DNA can be interpreted as a semiflexible homopolymer [86,87,88]. Here, self-avoidance is a crucial aspect for the formation of knots by geometric hindrance, where thickness can be understood as the diameter of the coarse-grained beads.…”

Section: Phase Behavior Of Isolated Semiflexible Polymersmentioning

confidence: 99%

Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

2016

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Abstract:We review the current state on the thermodynamic behavior and structural phases of self-and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on the internal structure. This may go as far as to stable knot phases. Adding polymers results in aggregation, where structural motifs again depend on the internal structure. We discuss in detail the effect of semiflexibility on the collapse and aggregation transition and provide perspectives for interesting future investigations.

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Influence of chain stiffness on knottedness in single polymers

Cited by 22 publications

References 40 publications

A nanofluidic knot factory based on compression of single DNA in nanochannels

A nanofluidic knot factory based on compression of single DNA in nanochannels

A Monte Carlo Study of Knots in Long Double-Stranded DNA Chains

Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

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