Structural transitions and elasticity from torque measurements on DNA


Knowledge of the elastic properties of DNA is required to understand the structural dynamics of cellular processes such as replication and transcription. Measurements of force and extension on single molecules of DNA1,2,3 have allowed direct determination of the molecule's mechanical properties, provided rigorous tests of theories of polymer elasticity4, revealed unforeseen structural transitions induced by mechanical stresses3,5,6,7, and established an experimental and conceptual framework for mechanical assays of enzymes that act on DNA8. However, a complete description of DNA mechanics must also consider the effects of torque, a quantity that has hitherto not been directly measured in micromanipulation experiments. We have measured torque as a function of twist for stretched DNA—torsional strain in over- or underwound molecules was used to power the rotation of submicrometre beads serving as calibrated loads. Here we report tests of the linearity of DNA's twist elasticity, direct measurements of the torsional modulus (finding a value 40% higher than generally accepted), characterization of torque-induced structural transitions, and the establishment of a framework for future assays of torque and twist generation by DNA-dependent enzymes. We also show that cooperative structural transitions in DNA can be exploited to construct constant-torque wind-up motors and force–torque converters.

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Figure 1: Experimental design.
Figure 2: Analysis of bead rotation. A tether was overwound by 1,200 turns before releasing the 760 nm rotor bead.
Figure 3: Torque calibration and twist elasticity of DNA.
Figure 4: Unwinding during overstretching, and the global force–torque phase diagram of DNA.


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We thank E. Watson and Y. Inclán for technical assistance, E. Nogales for microscope time, and A. Vologodskii, V. Croquette, D. Bensimon, D. Collin, N. Pokala and Y. Chemla for critical readings of the manuscript and/or discussions. Z.B. is an HHMI predoctoral fellow, M.D.S. is supported by a PMMB training grant, and J.G. holds a fellowship from the Hertz Foundation. This work was supported by the NIH and DOE.

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Correspondence to Carlos Bustamante.

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The authors declare that they have no competing financial interests.

Supplementary information

Supplementary Movie 1: Assembly of the experimental system. The molecular construct is stretched between an anti-DIG bead on the micropipette and an anti-fluorescein bead held in buffer flow (right to left). A 520 nm streptavidin-coated bead is held in the optical trap in the lower portion of the screen. The stage is moved to position the biotinylated portion of the molecule near the streptavidin bead, which becomes attached to the DNA and is pulled out of the trap. The lower bead is then placed in the trap to complete the assembly of the system (Fig. 1b). In the final half of the movie, the tension on the molecule is repeatedly increased to ~65 pN. Overstretching occurs in the lower DNA segment but not the upper segment, confirming the existence of a nick below the bead (allowing the DNA to unwind and enter the overstretched state) but not above it. Bead rotation is inhibited by flow. (AVI 2627 kb)

Supplementary Movie 2: 520 nm bead rotation during relaxation of an overwound molecule. A molecule with a 520 nm rotor bead was overwound as in Figure 1b. The movie begins subsequent to release of the rotor. The bead rotates at constant velocity for the first ~35 s, due to constant-torque conversion of P-DNA to B-DNA. Next, the angular velocity decays as torque and twist are removed from the molecule. Constant tension was maintained at 45 pN. (AVI 10402 kb)

Supplementary Movie 3: Constant-torque rotation powered by the P-B transition is shown for a 760 nm rotor bead. Constant tension was maintained at 45 pN. Off-axis alignment of outer beads is due to an eccentric DNA attachment point; DNA is held vertically as judged by the absence of horizontal force. (AVI 6085 kb)

Supplementary Movie 4: Overstretching and rewinding. Overstretching and rewinding is shown for a molecule with a 400 nm rotor bead (see Figure 3a). During the first ~26 s of the movie, the molecule is held at 85 pN and the bead rotation reflects unwinding of the molecule during the B-S transition. The separation of the beads increases at constant tension as the molecule converts to the longer S form. During the last part of the movie, the molecule is relaxed to 15 pN and the bead rotates in the opposite direction as the molecule rewinds. The movie is 2X actual speed. (AVI 12270 kb)

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Bryant, Z., Stone, M., Gore, J. et al. Structural transitions and elasticity from torque measurements on DNA. Nature 424, 338–341 (2003).

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