Interactions between two knots in nanochannel-confined DNA molecules

Experimental data on the interaction between two knots in deoxyribonucleic acid (DNA) confined in nanochannels produced two particular behaviors of knot pairs along the DNA molecules: (i) widely separated knots experience an attractive interaction but only remain in close proximity for several seconds and (ii) knots tend to remain separated until one of the knots unravels at the chain end. The associated free energy profile of the knot-knot separation distance for an ensemble of DNA knots exhibits a global minimum when knots are separated, indicating that the separated knot state is more stable than the intertwined knot state, with dynamics in the separated knot state that are consistent with independent diffusion. The experimental observations of knot-knot interactions under nanochannel confinement are inconsistent with previous simulation-based and experimental results for stretched polymers under tension wherein the knots attract and then stay close to each other. This inconsistency is postulated to result from a weaker fluctuation-induced attractive force between knots under confinement when compared to the knots under tension, the latter of which experience larger fluctuations in transverse directions.