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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. 

Abstract Nanofluidic structures have over the last two decades emerged as a powerful platform for detailed analysis of DNA on the kilobase pair length scale. When DNA is confined to a nanochannel, the combination of excluded volume and DNA stiffness leads to the DNA being stretched to near its full contour length. Importantly, this stretching takes place at equilibrium, without any chemical modifications to the DNA. As a result, any DNA can be analyzed, such as DNA extracted from cells or circular DNA, and it is straight-forward to study reactions on the ends of linear DNA. In this comprehensive review, we first give a thorough description of the current understanding of the polymer physics of DNA and how that leads to stretching in nanochannels. We then describe how the versatility of nanofabrication can be used to design devices specifically tailored for the problem at hand, either by controlling the degree of confinement or enabling facile exchange of reagents to measure DNA–protein reaction kinetics. The remainder of the review focuses on two important applications of confining DNA in nanochannels. The first is optical DNA mapping, which provides the genomic sequence of intact DNA molecules in excess of 100 kilobase pairs in size, with kilobase pair resolution, through labeling strategies that are suitable for fluorescence microscopy. In this section, we highlight solutions to the technical aspects of genomic mapping, including the use of enzyme-based labeling and affinity-based labeling to produce the genomic maps, rather than recent applications in human genetics. The second is DNA–protein interactions, and several recent examples of such studies on DNA compaction, filamentous protein complexes, and reactions with DNA ends are presented. Taken together, these two applications demonstrate the power of DNA confinement and nanofluidics in genomics, molecular biology, and biophysics.