Torque Spectroscopy of DNA: Base-Pair Stability, Boundary Effects, Backbending, and Breathing Dynamics

Changes in global DNA linking number can be accommodated by localized changes in helical structure. We have used single-molecule torque measurements to investigate sequence-specific strand separation and Z-DNA formation. By controlling the boundary conditions at the edges of sequences of interest, we have confirmed theoretical predictions of distinctive boundary-dependent backbending patterns in torque-twist relationships. Abrupt torque jumps are associated with the formation and collapse of DNA bubbles, permitting direct observations of DNA breathing dynamics.

Figure 1

Static RBT assay for high-resolution torque spectroscopy. (a) A DNA tether is attached between the cover glass surface and a magnetic bead (MB), with torsional constraints at both ends. A rotor bead (RB) is attached site specifically to the side of the DNA molecule. The total twist $\theta$ is controlled by the angular position of the magnets. Transducer twist $\alpha$ is given by $\alpha =\theta -\psi$, where $\psi$ is the angular position of the RB. The torque $\tau$ acting on the DNA can be calculated as $\tau ={\kappa }_{\mathrm{TD}}\alpha$, where ${\kappa }_{\mathrm{TD}}$ is the torsional spring constant of the calibrated transducer segment. A sequence of interest (SOI, red) is inserted in the lower DNA segment. (b) Torque is plotted as a function of imposed twist for a DNA containing a 50 bp long $d(p\mathrm{G}p\mathrm{C})$-repeat SOI (Z50). Data are shown for winding in the ($+$) direction only (see Fig. S1 [16] for overlaid unwinding and rewinding curves). Raw 250 Hz data (gray) were averaged in 0.2 rotation bins (red) and fit to a model for cooperative structural transitions in polymers [8] with fixed boundary conditions (black line, Eq. S7 [16]). The curve shows a transition between two linear elastic regions corresponding to B-DNA and Z-DNA (gray lines). Superhelical density $\sigma =\Delta Lk/L{k}_0$, where $L{k}_0$ is the linking number of the relaxed DNA ($L{k}_0=N_{\mathrm{total}}/10.4$, where $N_{\mathrm{total}}$ is the length of the full DNA construct in base pairs) and $\Delta Lk=\theta$ for our experimental geometry.

Figure 2

Torque-twist signatures of free boundary conditions and the behavior of a 100% AT sequence. (a) Average values for torque and other variables were calculated as a function of imposed twist for a transition with fixed boundary conditions using parameters measured for Z50 (Table S1 [16]). Schematic depictions show representative microstates for portions of the torque-twist curves marked with colored dots. The SOI is outlined as a green rectangle. Domain walls are shown as red and black ovals. (b) Calculations and illustrations for the transition of Z50 under free boundary conditions (blue), shown as in (a). (c) calculations of number of nucleotides, $n$ in the high-energy state, number of domains, $d$, in the high-energy state, number of domain walls, $s$, for Z50 as a function of imposed twist under fixed (green) and free (blue) boundary conditions. (d)–(e) Measured torque-twist plots. For each construct, three independent experiments are shown; dashed and solid lines indicate ($-$) and ($+$) winding directions, respectively. (d) Z50 SOI flanked by atomic spacers (Z50-2SP). (e) 120 bp AAT-repeat SOI flanked by atomic spacers (AAT120-2SP).

Figure 3

The effect of boundary conditions on transitions in GC-repeats. (a) Torque-twist plots for Z50-2SP acquired during unwinding (dashed blue lines) and rewinding (solid blue lines) together with a fit (gray) to a generalized model (equations in the Supplemental Material [16]) which includes a variable boundary penalty $J^{\prime }$ for domain walls at the edges of the SOI. Inset, calculated plots for $J^{\prime }=0$, 0.5, 1, 2, 4 and $J^{\prime }=J=5.6\mathrm{kcal}/\mathrm{mol}$ are in red, yellow, green, light blue, dark blue, and violet, respectively. All other parameters have been kept constant (Table S1, Z50-2SP, Ref. 16). The generalized model reduces to free boundary conditions for $J^{\prime }=0$ and to fixed boundary conditions for $J^{\prime }=J$. (b) Torque-twist plots for Z50-1SP, which contains an atomic spacer on only one side of the SOI, are shown together with a fit to a one-sided model. Inset shows the effect of varying $J^{\prime }$ on the one-sided model, with color-coding as in (a) ranging from $J^{\prime }=0$ to $J^{\prime }=J=6.3\mathrm{kcal}/\mathrm{mol}$ (all other parameters taken from Table S1, Z50-1SP, Ref. 16).

Figure 4

The effect of SOI length on transitions in AAT-repeats. (a) Series of calculated torque-twist plots using the model with free boundary conditions and SOI lengths ranging from $N=20$ to $N=120\mathrm{bp}$ (all other parameters fixed based on AAT120-2SP, Table S1 [16]). (b) Torque-twist plots of three independent AAT120-2SP unwinding (dashed thin lines) and rewinding (solid thin lines) experiments are overlaid with model fits (bold line). (c) Torque-twist plots of three independent AAT50-2SP unwinding (dashed) and rewinding (solid) experiments together with a fit in which $\Delta G_0$, $J$, and $J^{\prime }$ are fixed based on AAT120-2SP (Table S1 [16]). (d) Torque-twist plots of three independent AAT21-2SP unwinding (dashed) and rewinding (solid) experiments. The model displayed (gray bold line) uses the parameters shown in Supplemental Material Table S1 (AAT21-2SP) [16].

Figure 5

“Breathing” dynamics of 21 bp AAT-repeats. (a) Torque response of the AAT21-2SP SOI during linear twist ramps ($10\mathrm{deg}/\mathrm{s}$) in the ($-$)-twisting and ($+$)-twisting directions. The inset contains an expanded view of the transition region, showing reversible hopping. Green lines are used to indicate twist values used for fixed-twist dynamic experiments shown in subsequent panels. (b) Raw data are overlaid with two-state idealizations (black line) used to measure $t_{\mathrm{open}}$ and $t_{\mathrm{closed}}$ as shown. Torque histograms at the right of each panel were generated from the entire 800 s of data collected at each twist condition, and are overlaid with double Gaussian fits. (c) Semi-log plot of mean dwell times $⟨t_{\mathrm{open}}⟩$ and $⟨t_{\mathrm{closed}}⟩$ as a function of total imposed twist (top panel). Probabilities of being in the open state at fixed twists are fit using a two-state model (Eq. S2 [16]). The fit gives a total $\Delta G_0$ of $12\mathrm{kcal}/\mathrm{mol}$; ${\kappa }_0$, $\Delta {\theta }_0$, and $\Delta c_t$ were fixed based on linear fits to the torque-twist curve for this SOI (AAT21-2SP) as described in Table S1 [16].