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Langevin dynamics simulations of double-knotted DNA molecules in a nanochannel reveal that the interactions between the two knots differ with the degree of channel confinement. In relatively wide channels, the two knots can intertwine with each other, forming a persistently intertwined knot. Moreover, the two knots can pass through each other in large channels. In contrast, for small channel sizes, the knots tend to remain separated, and their crossing is inhibited. The change in knot–knot interactions as the channel size decreases is rationalized through an analysis of the magnitude of the transverse fluctuations, which must be large enough to allow one knot to swell to accommodate the intertwined state. 

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an “opening up process,” wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.