Stretched polygons in a lattice tube

Atapour, Mahshid; Soteros, C E; Whittington, S G

doi:10.1088/1751-8113/42/32/322002

Cited by 19 publications

(49 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We next discuss some results about the likelihood of each type of pattern. There are known "pattern theorems" available for both the fixed-edge and fixed-span models studied here (see [3,4]), as well as for Hamiltonian polygons (see [7]). The theorems focus on proper polygon patterns (see [5] for more precise definitions) which include the proper knot patterns defined here.…”

Section: Theoretical Resultsmentioning

confidence: 99%

Characterising knotting properties of polymers in nanochannels

et al. 2018

View full text Add to dashboard Cite

Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local", based on a standard approach for measuring the "size" of a knot within a knotted polymer chain. The method involves associating knot-types to subarcs of the chain, and then identifying a knotted subarc with minimal arclength; this arclength is then the knot-size. If the resulting knot-size is small relative to the whole length of the chain, then the knot is considered to be localised or "local"; otherwise, it is "non-local". Using this definition, we establish that all but exponentially few sufficiently long self-avoiding polygons (closed chains) in a tubular sublattice of the simple cubic lattice are "non-locally" knotted. This is shown to also hold for the case when the same polygons are subject to an external tensile force, as well as in the extreme case when they are as compact as possible (no empty lattice sites). We also provide numerical evidence for small tube sizes that at equilibrium non-local knotting is more likely than local knotting, regardless of the strength of the stretching or compressing force. The relevance of these results to other models and recent experiments involving DNA knots is also discussed.

show abstract

Section: Theoretical Resultsmentioning

confidence: 99%

Characterising knotting properties of polymers in nanochannels

et al. 2018

View full text Add to dashboard Cite

show abstract

“…To the best of our knowledge there exist only * Electronic address: michelet@sissa.it † Electronic address: orlandini@pd.infn.it a limited number of experimental and numerical studied of the size and shape of DNA molecules in nanoslits [8,18,[31][32][33]. These seminal studies have addressed the interesting issue of whether multiple scaling regimes exist in linear DNA filaments inside slits.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Linear and Circular Model DNA Chains Confined in a Slit: Metric and Topological Properties

2012

View full text Add to dashboard Cite

Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2-4.8 µm range and slits widths spanning continuously the 50-1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is nonmonotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for threedimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.

show abstract

“…This result, and that on the probability of knots, both indicate that the number of conformations of a certain height decreases more rapidly with deviation from the entropically favoured height, as knot complexity increases. The effect of applying a force to ring polymer molecules has also been investigated [10,11]. It is found that the force affects the probability of a non-trivial knot for finite chains, but that this probability still tends to unity in the infinite length limit.…”

mentioning

confidence: 99%