Behavior of two knotted DNA molecule under nanochannel confinement

In confined spaces like nanochannels, DNA molecules can form knots. While extant studies have predominantly focused on a single knot, DNA molecules are capable of hosting multiple knots. Herein, we use Langevin dynamics simulations to probe the behaviors of two knotted DNA molecules under nanochannel confinement of different channel sizes. Two distinct knot behaviors were observed: the knots either remained (i) separate or (ii) intertwined to form a prime knot that persisted for a long time duration. The intertwined state is commonly observed in most channel sizes and occurs spontaneously, with an energy preference above the separated state of approximately 0.5 k_BT. Additionally, the study explores the dynamic evolution between the knots, shedding light on the underlying knot passing mechanisms. Specifically, we found that the knot intertwining/passing mechanism is closely related to the knot expansion, where a knot enlarges to allow another knot to move along it. Moreover, we found that knot intertwining/passing is inhibited by small channel size, at which the knot expansion is also restricted.