Interactions between two knots in a stretched DNA molecule

Knots in DNA serve as a model system with which to study the physics of polymer entanglement, and are known to affect the function of genomic sequencing devices. We use microfluidic devices to stretch viral genomic DNA molecules in an elongational electric field, and observe the molecules using fluorescence microscopy. Previously, we have reported the effects that knots have on the relaxation and elasticity of single molecules, as well as the mechanisms by which knots translate along molecules and untie. Here, we discuss molecules that have two knots, and the interactions between the knots. It has been predicted computationally that in a doubly-knotted molecule an attraction exists between the knots, with a minimum in the free energy occurring when the two knots are intertwined. We see long range attraction of knots towards each other from opposite ends of the molecule over tens of seconds, in contrast to the end-migrating behavior of single knots. At short distances, pairs of knots fluctuate in and out of visual contact, remaining in proximity for tens of seconds to minutes. The distribution of intraknot distances can be used to measure free energy landscapes for the knot-knot interactions, which are qualitatively and quantitatively similar to previous computational studies.