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Description
At high salt concentrations and elevated temperatures, the persistence length of DNA decreases, increasing its conformational flexibility. Under such conditions, sufficiently long DNA molecules can accommodate multiple knots along the same contour. Using coarse-grained simulations, we investigate how two knots interact and reorganize under applied tension. We consider pairs of identical knots, 31-31, and knots of different topology, 31-51. We find a clear topology-dependent response. Identical 31-31 knots remain predominantly demixed over the range of tensions investigated. In contrast, 31-51 knot pairs preferentially form a mixed state at low tension and progressively demix as the applied tension increases. This difference correlates with the contour length occupied by the knotted region. For 31-51 pairs, the mixed configuration can occupy a smaller contour length than the combined contour lengths of the two separated knots, providing a conformational advantage for mixing at low tension. Such a reduction is much weaker or absent for 31-31 pairs. Increasing tension suppresses the conformational freedom required to maintain the mixed configuration and favors spatial separation of the knots. These results demonstrate that the organization of multiple knots along a stretched polymer is controlled jointly by knot topology and mechanical tension.