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.
Highlights
Entanglements in molecular cords like polymers or semi-flexible biopolymers like doublestranded DNA often lead to knotted chain conformations
Long DNA strands self-entangle into knotted conformations, and sequencing knotted DNA with nanopores may be subject to error
The typical extent and likelihood of DNA knots is computed for DNA chains of up to half a million base pairs, and we estimate the abundance of complex and composite knots in relation to DNA length
Summary
Entanglements in molecular cords like polymers or semi-flexible biopolymers like doublestranded DNA (dsDNA) often lead to knotted chain conformations. About 50 years ago, Frisch and Wasserman conjectured [11] that any molecular cord will eventually be knotted as the chain length increases. This conjecture was later proven for certain classes of lattice polygons [12], but does not state how polymer length and polymer properties are related to knotting probability. A ground breaking study (Plesa et al, Nature Nanotechnology in press) has pushed these boundaries even further and estimated knotting probabilities for significantly larger strands in high salt concentrations by analysing translocation events in solidstate nanopores
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