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

Abstract

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.

Pore translocation of knotted DNA rings

“…These were generated with a Monte Carlo scheme applied to a coarse-grained DNA model and were subsequently refined and relaxed with the oxDNA model. All configurations featured a trefoil or 31 knot, which is by far the dominant topology at the considered DNA length (17,32,46). These initial configurations were primed at the pore entrance at a random point lying on their convex hull.…”

“…Because knots are statistically inevitable in long polymers and biopolymers (13)(14)(15)(16)(17)(18)(19)(20), a relevant question is how such forms of entanglement affect pore translocation (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34).…”

Are There Knots in Chromosomes?

“…Recently, experiments and simulations have extended this analysis to sequences of up to 500,000 base pairs. At these length scales, unconstrained DNA tends to be highly knotted [ 42 , 43 ].…”

Entropic Interactions between Two Knots on a Semiflexible Polymer

“…Interest in knots among natural scientists was revitalized in the 1960s [ 4 , 5 ], when knots were conjectured to appear in polymers and DNA of sufficient length. The subsequent discovery and creation of molecular knots in DNA [ 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ], polymers [ 14 , 15 ] and proteins [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] led to a renaissance of this interdisciplinary field in which computer simulations of prime [ 23 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ] and composite knots [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 ] played a pivotal role.…”

“…Modern coarse-grained models of DNA in the context of knotting became available with the first experimentally determined knotting probabilities for DNA (of up to 10,000 base pairs) based on gel-electrophoresis [ 9 , 10 ]. These models map DNA either onto bead-spring(/-stick) [ 35 , 42 ] or cylinder-type models [ 10 ], which incorporate stiffness and self-avoidance so that experimental knotting probabilities are matched. Screened Coulomb interactions—which depend on salt conditions—are typically subsumed in the form of an effective diameter, which again influences the stiffness of the chain.…”