  In this study we consider an idealization of a typical optical tweezers
experiment involving a semiflexible double-knotted polymer, with steric
hindrance and persistence length matching those of dsDNA in high salt
concentration, under strong stretching. Using exhaustive Molecular Dynamics
simulations we show that not only does a double-knotted dsDNA filament under
tension possess a free energy minimum when the two knots are intertwined, but
also that the depth of this minimum depends on the relative chirality of the
two knots. We rationalize this dependence of the effective interaction on the
chirality in terms of a competition between chain entropy and bending energy.
