A Monte Carlo study of knots in long double-stranded DNA chains

Abstract

We develop a coarse-grained model of double-stranded DNA which is solely based on experimentally determined knotting probabilities of short DNA strands. Our analysis is motivated by the emergence of DNA nanopore sequencing technology. The main advantage of nanopore sequencing in comparison to next-generation devices is its capability to sequence rather long DNA strands in a single run, currently up to ≈10,000 base pairs. Unfortunately, long DNA strands easily self-entangle into knotted conformations, and sequencing knotted DNA with nanopores may be subject to error. In our manuscript, 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. Our analysis indicates that DNA knots may be a formidable roadblock for the development of devices which support substantially longer read lengths. We also show that structural properties of DNA, like its resistance to bending, are intimately linked to the molecule's tendency to form knots. We demonstrate how this connection can be utilized to introduce mathematical models of DNA which account for the molecule's overall statistical properties.