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Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer's physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain-And consequently its persistence length-Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot⁻knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems-Be they artificial or biologica in origin-And for their technological application.

Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers