Stepwise unknotting of complex polymer knots under nanochannel confinement

We performed Langevin dynamics simulations to investigate the unknotting dynamics of knotted DNA molecules confined within nanochannels, specifically examining three different torus knot types: 31, 51, and 71 knots, and the 61 twist knot. 51 and 71 knots typically undergo stepwise unknotting, in which knots are partially untied into a simpler knot topology when they first reach the chain end, subsequently requiring multiple rounds of topological simplification before being fully untied. In contrast, as would be expected, simple trefoil knots untie directly as they approach the chain ends, following a one-step process. We further examined the impact of nanochannel size on unknotting dynamics and topological changes across different knot types. For the complex 51 and 71 knots, stepwise unknotting is the prevalent mechanism, and increasing the spatial confinement prolongs the entire stepwise unknotting process. For the 61 knot, the primary mechanism of untying is also sequential, with ∼20% of the knots untying in a single step. In addition, the topological changes induced by both confinement and knot types are found to be correlated with the extended unknotting times; while the topology of the knot (twist vs torus) dictates the possible unknotting pathways, the rate of unknotting is modulated by the channel size.