Interactions between two knots in nanochannel-confined DNA molecules*

Long polymers such as DNA can form composite knots in the polymer chains. The interaction between two knots in DNA molecules remains an open question: Do the knots stay separated or do they attract one another? We will present experimental data on knot-knot interactions in single DNA molecules under nanochannel confinement. We observed that widely separated knots predominantly undergo independent random walks but, when in close proximity, knots attract each other but only remain in close contact for several seconds. The corresponding free energy landscape shows that the separated knot state is more stable than the intertwined knot state, in which the knots have a separation distance of approximately zero. Our experimental observation contradicts observations of knot-knot interactions under tension in flow, where the knots experience an attraction and then can stay in proximity for a much longer time.