Illustration of the algorithm employed to determine whether a sticky loop is relevant or not for the topological state of the polymer.

<p>If the sticky loop (dark green segment) is entangled with the knot (panels a and b), its removal determines a change in the chain topology (panel c). On the contrary, if no chain segment pierces the sticky loop (panels d and e), its excision does not modify the topological state of the whole polymer (panel f). In the figure, the sticky beads at the termini are orange, while those along the sequence are blue. In the first panel of both cases (a and d) the knotted region is inscribed in a circle. The two configurations are obtained from simulations of S-DNA with sticky monomers located at the {50, 300} point.