Investigating site-selection mechanisms of retroviral integration in supercoiled DNA braids

Abstract

We theoretically study the integration of short viral DNA in a DNA braid made up by two entwined double-stranded DNA molecules. We show that the statistics of single integration events substantially differ in the straight and buckled, or plectonemic, phase of the braid and are more likely in the latter. We further discover that integration is most likely close to plectoneme tips, where the larger bending energy helps overcome the associated energy barrier and that successive integration events are spatio-temporally correlated, suggesting a potential mechanistic explanation of clustered integration sites in host genomes. The braid geometry we consider provides a novel experimental set-up to quantify integration in a supercoiled substrate in vitro, and to better understand the role of double-stranded DNA topology during this process.

Keywords: DNA braids; DNA integration; DNA modelling; supercoiling; topology.

Figure 1.

Retroviral integration in DNA braids. (a) Two chains representing two dsDNA molecules (one coloured red and the other blue to ease visualization) are tethered to two impenetrable walls. (b) The top wall is rotated n times to introduce a catenation between the dsDNA strands equal to Ca = n, while a force f is simultaneously applied to stretch the braid. (c) For Ca larger than a critical Ca*(f), the braid buckles and forms plectonemes (see electronic supplementary material, figure S1, for the corresponding phase diagram). (d) A snapshot from BD simulations of the system under investigation. (e,f) Example of an integration event, illustrated by successive snapshots in a BD simulation.

Figure 2.

Effect of integrations on braid dynamics in the buckled state. (a) Kymograph showing the evolution of plectonemes (monitored on the red DNA, see electronic supplementary material) for a simulation with $f=6\frac{\sigma }{k_{B}T}$ and Ca = 36. Yellow regions represent the segments inside plectonemes while black dots their boundaries. During this run four integration events are observed, three in the blue DNA and one in the red one. The red arrow indicates the moment and the position of the integration in the red strand. The numbers (1), (2), (3) and (4) refer to the top snapshots. Between (1) and (2) there is an integration inside a plectoneme, while between (3) and (4) another integration takes place in the braided part of the system. The grey background shows the step-wise increase in length of the red strand, which is initially equal to 250σ (see y axis) and it increases at time t ∼ 80000 τ_LJ when a ring integrates. (b) End-to-end Z distance versus time. Blue and red arrows show the moments of integration in the blue and red strand respectively. At each integration event, we observe a jump in Z.

Figure 3.

Statistics of single integrations. (a) Trajectory of three rings diffusing in the system corresponding to the kymograph in figure 2. The distance between the ring and the braid d_rb is monitored over time: ring₁ integrates, ring₂ gets close to the braid three times without integrating, while ring₃ never gets close to the braid. (b) Plot of the integration probability against the catenation number. The grey background refers to Ca < Ca* (straight braid phase), while the orange one to Ca ≥ Ca* (buckled phase). It is interesting to note that the curve significantly changes its slope in proximity of Ca*. (c) Plot of the average integration time (i.e. the average time to the first successful integration) as a function of Ca. The higher the catenation number, the shorter the time needed to observe the first integration.

Figure 4.

Statistics of multiple integrations. Probability distribution for Δ_fs—the distance along the braid between sites of successive integrations—for three different values of Ca compared to the case in which integrations occur randomly along the polymer, i.e. with a probability P₀(x) = (2(L−x))/L². For the case Ca = 36, we report also the errorbars. We observe a maximum for intermediate values of Δ_fs, suggesting that there is a favoured typical spatial separation between successive integration events. As a convention, if the integration breaks the bond between the beads with ID number id₁ < id₂, we identify the integration site with id₁. Inset: average of the contour distance Δ_fs between successive integrations for the same three values of Ca used in the main figure.

Figure 5.

Bending energy and integration sites. (a) Bending energies per bead for the same run reported in figure 2. Blue and red curves are bending energies E_blue, E_red of the blue and red DNA, respectively. Blue and red arrows indicate the moments of integration events. (b) Histograms of local bending energies per bead in the braided part (blue), plectonemic part (red) and plectonemic tips (green). (c) Integration probabilities in the braided part (blue), plectenemic part (red) and plectonemic tips (green), normalized by the number of beads involved in each of the three motifs, versus Ca. (d) Distribution of Δ_it, the distance between the integration site and the tip of the closest plectoneme, for two values of the catenation number Ca = 31 and Ca = 36. In both cases there is a peak close to zero, indicating that rings prefer to integrate near plectonemic tips. Inset in (a) represents a zoom, while insets in (b,d) report the average values of the quantity plotted in the corresponding panel.