Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking

Abstract

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.

Figure 1.

(A) Initial configurations of the supercoiled double-stranded DNA rings for the three considered topologies, 0₁, 5₁ and 5₂. The latter two are left-handed, i.e. the topological sign of their projected crossings is negative, as indicated. The 5₁ and 5₂ snapshots have been edited to highlight the over- and underpasses, see Supplementary Figure S1 for the unedited versions. The mesoscopic structural representation of the oxDNA model is illustrated in the inset, which shows a magnified portion of one of the rings. The twist was uniformly adjusted for each of the three cases to yield the same level of negative supercoiling (-5%). (B–D) Identification of the knotted and the plectonemically-wound regions for a typical 5₁-knotted supercoiled conformation, shown in the foreground. (B) The knotted region (green) is the shortest portion that, after suitable bridging of the termini, has the same (5₁) topology of the entire ring. (C) The plectonemically-wound region (blue) is found by using the contact map to identify extended superhelical regions ending in a short apical loop and that are free of cis or trans entanglement, as in the case of panel (D).

Figure 2.

(A) Typical snapshots of supercoiled DNA rings for the three considered topologies. The conformers are grouped by the number of plectonemes (in italics), which increases from left to right, and are shown in colours of different saturation for visual clarity. (B) Normalised histogram of the number of plectonemes observed for each topology.

Figure 3.

Probability distributions of the plectonemes’ length, l_plc and gyration radius, R_g, for supercoiled rings with (A) unknotted and (B) 5₁ topologies. The conditional probabilities for 1 to 3 plectonemes are shown with coloured histograms, see legend, while the normalised combined distribution is shown in grey. (C) Normalised joint probability distribution of R_g and knot length, l_k. (D) Marginal probability distribution of l_k.

Figure 4.

(A) Typical temporal traces of the length of the knotted region, l_k and the gyration radius, R_g, from a trajectory of supercoiled 5₁-knotted ring. The background is coloured according to the instantaneous number of plectonemes, see legend. (B) Semi-log plot of the autocorrelation functions, based on data from all trajectories, of R_g, l_plc and l_k of supercoiled 5₁-knotted rings (B) and of R_g, l_plc for unknotted ones (C).

Figure 5.

Kymographs showing the typical time evolution along the ring contour of knotted and plectonemically-wound regions, see legend for colour code. The three kymographs are for: (A) supercoiled 5₁-knotted rings, (B) torsionally-relaxed 5₁-knotted rings and (C) supercoiled unknotted rings. The boundaries of the knotted and the main plectonemically-wound regions of case (A) are noticeable stabler than for case (B) and (C) due to the persistent interlocking of multiple strands. This is illustrated in the snapshots above panel (A), where the same region at the knot-superhelix boundary (bp 1000–bp 1200, highlighted in red in the insets) remains entangled with other ring portions throughout the trajectory. The midpoint of this region is marked with a red bead in the insets and with a dotted red line in panel A.