We consider self-avoiding rings of up to 1000 beads and study, by Monte Carlo techniques, how their equilibrium knotting properties depend on the bending rigidity. When the rings are taken from the rigid to fully-flexible limit, their average compactness increases, as expected. However, this progressive compactification is not parallelled by a steady increase of the abundance of knots. In fact the knotting probability, P, has a prominent maximum when the persistence length is a few times larger than the bead size. At similar bending rigidities, the knot length has, instead, a minimum. We show that the observed non-monotonicity of P arises from the competition between two effects. The first one is the entropic cost of introducing a knot. The second one is the gain in bending energy due to the presence of essential crossings. These, in fact, constrain the knotted region and keep it less bent than average. The two competing effects make knots maximally abundant when the persistence length is 5-10 times larger than the bead size. At such intermediate bending rigidities, knots in the chains of 500 and 1000 beads are 40 times more likely than in the fully-flexible limit.

xrRNAs from flaviviruses survive in host cells because of their exceptional dichotomic response to the unfolding action of different enzymes. They can be unwound, and hence copied, by replicases, and yet can resist degradation by exonucleases. How the same stretch of xrRNA can encode such diverse responses is an open question. Here, by using atomistic models and translocation simulations, we uncover an elaborate and directional mechanism for how stress propagates when the two xrRNA ends, and , are driven through a pore. Pulling the end, as done by replicases, elicits a progressive unfolding; pulling the end, as done by exonucleases, triggers a counterintuitive molecular tightening. Thus, in what appears to be a remarkable instance of intra-molecular tensegrity, the very pulling of the end is what boosts resistance to translocation and consequently to degradation. The uncovered mechanistic principle might be co-opted to design molecular meta-materials.

Recent studies have revealed that the DNA cross-inversion mechanism of topoisomerase II (topo II) not only removes DNA supercoils and DNA replication intertwines, but also produces small amounts of DNA knots within the clusters of nucleosomes that conform to eukaryotic chromatin. Here, we examine how transcriptional supercoiling of intracellular DNA affects the occurrence of these knots. We show that although (−) supercoiling does not change the basal DNA knotting probability, (+) supercoiling of DNA generated in front of the transcribing complexes increases DNA knot formation over 25-fold. The increase of topo II-mediated DNA knotting occurs both upon accumulation of (+) supercoiling in topoisomerase-deficient cells and during normal transcriptional supercoiling of DNA in TOP1 TOP2 cells. We also show that the high knotting probability (Pkn ≥ 0.5) of (+) supercoiled DNA reflects a 5-fold volume compaction of the nucleosomal fibers in vivo. Our findings indicate that topo II-mediated DNA knotting could be inherent to transcriptional supercoiling of DNA and other chromatin condensation processes and establish, therefore, a new crucial role of topoisomerase II in resetting the knotting–unknotting homeostasis of DNA during chromatin dynamics.

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.

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