Probing the salt dependence of the torsional stiffness of DNA by multiplexed magnetic torque tweezers

Abstract

The mechanical properties of DNA fundamentally constrain and enable the storage and transmission of genetic information and its use in DNA nanotechnology. Many properties of DNA depend on the ionic environment due to its highly charged backbone. In particular, both theoretical analyses and direct single-molecule experiments have shown its bending stiffness to depend on salt concentration. In contrast, the salt-dependence of the twist stiffness of DNA is much less explored. Here, we employ optimized multiplexed magnetic torque tweezers to study the torsional stiffness of DNA under varying salt conditions as a function of stretching force. At low forces (<3 pN), the effective torsional stiffness is ∼10% smaller for high salt conditions (500 mM NaCl or 10 mM MgCl2) compared to lower salt concentrations (20 mM NaCl and 100 mM NaCl). These differences, however, can be accounted for by taking into account the known salt dependence of the bending stiffness. In addition, the measured high-force (6.5 pN) torsional stiffness values of C = 103 ± 4 nm are identical, within experimental errors, for all tested salt concentration, suggesting that the intrinsic torsional stiffness of DNA does not depend on salt.

Figure 1.

Principle of magnetic torque tweezers. (A) A schematic of mMTT. The molecules are tethered between magnetic beads and a glass coverslip. Permanent magnets, placed above the flow cell, exert magnetic fields, therefore enabling the application of forces and torques to the tethered molecules. The beads’ positions are monitored by video tracking using an inverted microscope and monochromatic illumination. mMTT allow tracking of multiple beads in parallel (bottom left, red frames indicate beads marked for tracking), here 36 M270. (B) In FOMT, the bead's anisotropy axis aligns with the vertical magnetic field, exerted by the cylindrical magnets. The bead's motion is (torsionally) unconstrained and traces out a doughnut-like shape in the (X,Y)-plane. (C) An additional side magnet in the (m)MTT slightly tilts the magnetic field. This leads to (weak) angular trapping of the bead. Its motion in the (X,Y)-plan is confined to an arc-like shape. (D) Simulations of the magnetic fields for FOMT (left) and MTT (right) show that the difference in the magnetic field is small (large, blue arrows). The yellow shaded areas in the magnetic field simulations represent the width of the field of view. (E) The tracked (X,Y)-position of the bead is transferred to polar coordinates. Upon turning the magnets N times, the molecule exerts a restoring torque, causing a shift in the equilibrium position (Θ − Θ₀) of the rotation angle. Data shown are for F = 3.5 pN, going from N = −10 turns to N = +30 turns.

Figure 2.

Averaged extension-rotation and torque-rotation measurements of dsDNA at varying forces. Measurements shown were recorded in TE buffer at pH 7.4 with 100 mM NaCl. (A and D) At low forces (<1 pN; indicated in the legend in panel D) the extension versus turn plot is symmetric about zero turns. When applying a number of turns to the DNA molecule (positive and negative), its extension stays constant, while the molecular torque increases linearly. Beyond the buckling point (post-buckling) the extension decreases linearly with each additional turn, while the molecular torque stays constant. (B and E) For higher forces (>1 pN; indicated in the legend in panel E), no plectoneme formation occurs upon underwinding the molecules. Instead, torque induced melting takes place at −10 pN·nm. For forces >6 pN, no supercoiling occurs at all. Instead a transition from B- to P-DNA occurs upon overwinding at 35 pN·nm. (C) Determination of the buckling points (n_B; black triangles), the post-buckling slopes (black lines) and Lk₀ (only for symmetric extension-rotation curves). (F) A line fit to the linear regime in the torque-rotation data (black line) is used to determine the torsional stiffness (C_eff). The mean of the constant plateau for positive turns (beyond buckling) is used to compute the buckling torque (τ_buck; black horizontal line).

Figure 3.

Averaged extension-rotation and torque-rotation responses of dsDNA for different salt conditions. Averaged extension versus turns data for four different buffers and corresponding averaged torque versus turns data at 0.4 pN (A and D), 0.9 pN (B and E) and 2 pN (C and F). Blue colors indicate measurements at low salt (salt 1 and 2); green colors indicate measurements at high salt (salt 3 and 4; see Table 1 for salt conditions). (G) (Normalized) buckling points as a function of force. We averaged salt 1 and 2 to low salt (blue) and salt 3 and 4 to high salt (green). (H) Post buckling slopes, determined from the averaged extension-rotation data against force. Same color code as in G. (I) Buckling torque derived from the torque versus turn data. Color code as in G. Indicated with a filled, square symbol is the measured transition from B-DNA to P-DNA at 6.5 pN. Co-plotted in panels G–I is the Marko model (dashed lines) for dsDNA with fixed parameters: C (110 nm), A (43 nm for high salt conditions and 48 nm for low salt conditions) and P_lowsalt = 20 nm or P_highsalt = 15 nm.

Figure 4.

The effective twist persistence length of dsDNA for different salt conditions. The effective twist persistence length C_effas a function of force and salt. Data points are the means and standard errors of the mean from 10–45 independent molecules for each salt and force condition. (A) C_eff increases strongly with force, saturating for high forces at ∼100 nm for all salts. See Table 1 for salt conditions. (B) C_eff for all four salt conditions at 0.4 pN and 6.5 pN. Color code as in A. (C) low salt (salt 1 and 2, blue) versus high salt (salt 3 and 4, green) torsional stiffness data (see main text) show a trend to be slightly lower for higher salt concentrations. The MN model is co-plotted (solid line), with fixed values C = 110 nm and A = 48 nm (low salt, blue) and A = 43 nm (high salt, green). (D) The ratio of the low salt C_eff data and the high salt C_eff as a function of force. Two models, the MN model (black line) and the aTWLC model (black squares) are co-plotted with the experimental data (red circles).