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. 2018 Sep 6;46(15):7998-8009.
doi: 10.1093/nar/gky599.

The temperature dependence of the helical twist of DNA

Franziska Kriegel  1 , Christian Matek  2 , Tomáš Dršata  3 , Klara Kulenkampff  1 , Sophie Tschirpke  1 , Martin Zacharias  4 , Filip Lankaš  3 , Jan Lipfert  1
Affiliations

The temperature dependence of the helical twist of DNA

Franziska Kriegel et al. Nucleic Acids Res. .

Abstract

DNA is the carrier of all cellular genetic information and increasingly used in nanotechnology. Quantitative understanding and optimization of its functions requires precise experimental characterization and accurate modeling of DNA properties. A defining feature of DNA is its helicity. DNA unwinds with increasing temperature, even for temperatures well below the melting temperature. However, accurate quantitation of DNA unwinding under external forces and a microscopic understanding of the corresponding structural changes are currently lacking. Here we combine single-molecule magnetic tweezers measurements with atomistic molecular dynamics and coarse-grained simulations to obtain a comprehensive view of the temperature dependence of DNA twist. Experimentally, we find that DNA twist changes by ΔTw(T) = (-11.0 ± 1.2)°/(°C·kbp), independent of applied force, in the range of forces where torque-induced melting is negligible. Our atomistic simulations predict ΔTw(T) = (-11.1 ± 0.3)°/(°C·kbp), in quantitative agreement with experiments, and suggest that the untwisting of DNA with temperature is predominantly due to changes in DNA structure for defined backbone substates, while the effects of changes in substate populations are minor. Coarse-grained simulations using the oxDNA framework yield a value of ΔTw(T) = (-6.4 ± 0.2)°/(°C·kbp) in semi-quantitative agreement with experiments.

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Figures

Figure 1.
Figure 1.
Temperature controlled DNA rotation-extension measurements. (A) Schematic of the temperature controlled magnetic tweezers setup. In MT, DNA is tethered between the surface and magnetic beads in a flow cell. An inverted microscope is used to image the flow cell surface onto a CMOS camera. Monochromatic light illuminates the flow cell from top. Permanent magnets are placed on a translational and rotational motor on top of the flow cell to apply stretching forces and torsional control, respectively. A pump is used for buffer exchange. A heating foil around the objective is used to locally heat the flow cell and controlled using a PID controller. (B) Top: Rotation-extension measurements for 7.9 kbp DNA at 0.3 pN (top left) and 0.7 pN (top right) and different temperatures. The center of the extension vs. turns curve shifts to negative turns with increasing temperature. Bottom: Illustration of the approaches to determining the centers of the rotation curves. Gaussian fits (green lines) to the extension vs. applied turns data at F = 0.3, 0.5 and 0.8 pN. The center of the Gaussian function of each curve is used to determine the center of the curves along the turn axis (bottom left). Linear fits (red) to the plectonemic regime of the rotation-extension curves at positive and negative applied turns. Here the intersection of the linear fits is used to determine the center (bottom right). (C) Changes in the DNA linking number with temperature are determined from the shift of the centers of the rotation curves. Data shown here are for 7.9 kbp DNA at 0.7 pN; symbols and error bars are the mean and standard deviation from seven molecules. ΔTw(T) is determined from the fitted slope. (D) Temperature dependence of the helical twist ΔTw(T) as a function of applied force. Data are for 7.9 kbp DNA (dark blue) and 20.6 kbp DNA (light blue), repectively. Symbols and error bars are the mean and standard error of the mean from at least seven individual molecules for each measured force and DNA length. The change in helical twist does not depend on force, within error, as both data sets are consistent with a force-independent ΔTw(T) (dashed lines; reduced χ2 = 0.04 for the 7.9 kbp DNA with ΔTw(T) = (−10.5 ± 0.6)°/(°C·kbp); reduced χ2 = 0.24 for the 20.6 kbp DNA with ΔTw(T) = (−11.5 ± 1.0)°/(°C·kbp).
Figure 2.
Figure 2.
Determination of DNA twist from atomistic MD simulations. Results from atomic-resolution unrestrained molecular dynamics (MD) simulations of a 33 bp DNA oligomer at different temperatures. (A) Snapshot of the DNA structure from a MD simulation and definition of the right-handed orthonormal frames that were attached to the oligomer ends, mimicking the experimental setup. Base-fixed frames in three pairs close to the ends (marked by red contours) were averaged and then projected onto the helical axis (gray), yielding the end frames R1 and R2. (B) End-to-end twist between R1 and R2 as a function of temperature (red circles). Symbols are the average over the entire trajectory, error bars are estimated by repeating the analysis for the first and the second halves of the trajectories and calculating mean difference between these values and the value for the entire trajectory. The resulting twist temperature slope (red line) for the OL15 Amber force field is (−11.1 ± 0.3)°/(°C·kbp). We decompose the change in twist as a superposition of the change in populations of the BI/BII backbone substates and the conformational change of the individual substates. It is seen that the change in BI/BII substate populations, with substate conformations taken constant (green) contributes only very weakly, whereas the conformational change of the individual substates (blue) almost account for the total observed change. (C) Twist free energy landscapes computed from the Boltzmann inversion (solid lines) and harmonic fits with the same mean and variance (dotted lines). The potentials are overall harmonic, with a slight anharmonicity for undertwisting at low temperatures (to the left of the indicated grey, vertical line). All twist values are plotted relative to the mean twist at 27°C.
Figure 3.
Figure 3.
Coarse-grained oxDNA simulations. Results from coarse-grained oxDNA simulations of a 600 bp double-stranded DNA system in the average-base parametrization at 150 mM monovalent salt. A stretching force F = 0.71 pN was used in all simulations. (A) Extension vs. imposed mean twist angle for 27, 37, 47 and 67°C. Note that for 67°C, denaturation bubble formation occurs in the undertwisted system (angles ≤ 33°), leading to asymmetric curves. (B) Molecular conformations observed in oxDNA simulations at T = 67°C for an angle of 31.6°, showing a denaturation bubble (left), 34.0°, showing an extended double-strand (center) and 37.2°, showing a plectoneme (right). For the 31.6° snapshot, a closeup of the 23-bp denaturation bubble is shown in the inset. (C) Torque response at different temperatures, showing a linear regime close to the equilibrium angle, followed by an overshoot and a post-buckling torque which increases more slowly upon further twisting. The inset shows a zoom of the data with the interpolation in the linear torque-regime and determination of the equilibrium angle corresponding to zero torque. (D) Equilibrium twist angles for the different temperatures determined by linear interpolation of the torque response shown in C to zero torque. The black line indicates a linear fit of temperature dependence, yielding ΔTw(T) = −6.5°/(°C·kbp).
Figure 4.
Figure 4.
Values for the change of DNA twist with temperature ΔTw(T) from measurements and simulations. Dark gray bars indicate values obtained from experiments. Indicated with the light grey background are values that were obtained as part of this work. Blue colors refer to data from all-atom MD simulations. Lighter blue colors represent data generated in this work with the OL15 and bsc0 force fields, respectively. Green represents the value gained by coarse-grained oxDNA simulations within this work.
Figure 5.
Figure 5.
Fraction of broken basepairs as a function of temperature. In the all-atom molecular dynamics calculations with the OL15 (dark blue circles) and bsc0 (light blue circles) force fields, the two basepairs at each end of the oligomer were excluded from the analysis and broken pairs are defined as pairs where at least one hydrogen bond donor-acceptor distance exceeds 4 Å. In oxDNA (green circles) broken pairs are defined as basepairs where the interaction energy is less than 15% of the value for a fully formed pair. Errors (from splitting the trajectory in half) are smaller than symbols for most points.
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