Diffusion of knots in nanochannel-confined DNA molecules

Long polymers such as DNA can form knots in confinement. For linear DNA, these knots are destroyed by diffusion of the knot to the chain end. However, the diffusion mechanisms of knots in confined systems, especially the dynamic evolution of untying knots, remain open questions. To address this issue, we used Langevin dynamics simulations to probe the typical mechanisms governing the dynamic evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules of different chain contour lengths in the extended de Gennes regime. Specifically, we investigate the unknotting process by quantifying how the structural properties, such as knot size, knot span, knot radius of gyration, vary with knot position along the chain. The knot untying follows an “opening up process”, wherein the knot continues growing in size and becomes increasingly looser as it moves to the end of DNA molecules. The calculated average size, span and radius of gyration of opened knots increase significantly with chain contour lengths. Additionally, the diffusion process of knots in nanochannel-confined DNA molecules is subdiffusive, albeit without hydrodynamic interactions between DNA and its environment. The unknotting time of knots as a function of chain contour lengths follows a power law, with a scaling exponent around 2.64.