DNA is thought to behave as a stiff elastic rod with respect to the ubiquitous mechanical deformations inherent to its biology. Here, we measure the mean and variance of end-to-end length for a series of DNA double helices in solution, using small-angle X-ray scattering interference between gold nanocrystal labels. The data rule out the conventional elastic rod model. Specifically, the variance in end-to-end length follows a quadratic dependence on the number of base pairs rather than the expected linear dependence. Absent applied tension, DNA is at least one order of magnitude softer than measured by single-molecule stretching experiments. Our observations indicate that DNA stretching is cooperative over more than two turns of the DNA double helix, and support the idea of long-range allosteric communication through DNA structure.

We report a novel molecular ruler for measurement of distances and distance distributions with accurate external calibration. Using solution X-ray scattering we determine the scattering interference between two gold nanocrystal probes attached site-specifically to a macromolecule of interest. Fourier transformation of the interference pattern provides a model-independent probability distribution for the distances between the probe centers-of-mass. To test the approach, we measure end-to-end distances for a variety of DNA structures. We demonstrate that measurements with independently prepared samples and using different X-ray sources are highly reproducible, we demonstrate the quantitative accuracy of the first and second moments of the distance distributions, and we demonstrate that the technique recovers complex distribution shapes. Distances measured with the solution scattering-interference ruler match the corresponding crystallographic values, but differ from distances measured previously with alternate ruler techniques. The X-ray scattering interference ruler should be a powerful tool for relating crystal structures to solution structures and for studying molecular fluctuations.

We measured the mean and variance of end-to-end length in short DNA fragments in solution and reported evidence of DNA stretching that is cooperative over more than two turns of the double helix. Becker and Everaers suggest that the structural fluctuations we observed arise from bending motions of the DNA, rather than stretching. We present three experimental tests of this bendingbased explanation. W e recently reported on distance distributions between gold nanocrystals attached to the 3′-hydroxyl groups of short DNA duplexes (1, 2). Our data exhibit two unexpected features: The variance in end-to-end distance grows rapidly with duplex length, and the increase occurs in a nonlinear fashion. We interpret the results to be a manifestation of a soft, correlated stretching motion in DNA. Based on coarse-grained simulations of DNA structural fluctuations, Becker and Everaers (3) offer an alternative explanation: that the observed variances arise from bending motions of the DNA that are amplified through the linker attachments to the nanocrystal particles.As a qualitative interpretation of their simulation results, Becker and Everaers (3) suggest that the axial displacement of the nanocrystal centers from the ends of the DNA duplex acts like a lever arm to amplify bending fluctuations. In (1), we reported values for the bending-induced variance in end-to-end length computed according to the wormlike chain (WLC) model. When these values are increased by the axial amplification factor of Becker and Everaers [a factor of (l + axial 0 ) 2 /l 2 , where axial 0 is the axial offset of the nanocrystals from the duplex ends, fit to be~24 Å], they still only account for a fraction of the observed variance: 1% and 19% respectively for the 10-and 35-base-pair (bp) duplexes.The simulation results of Becker and Everaers (3) appear to be dominated by a different phenomenon: The radial offset of the nanocrystal centers from the helix axis acts as a lever arm to amplify the effect of duplex bending on the internanocrystal distance (Fig. 1A). In our experiments, the nanocrystals were attached to 3′-hydroxyl groups near the edge of the duplex cylinder (fit to be~9 Å off of the axis; D, radial offset).Depending on its direction, a bend in the duplex could either bring the two radially offset nanocrystals closer together or move them farther apart. Thus, the radial-offset phenomenon broadens distributions symmetrically, overcoming one of the objections to a bending-based explanation of our data. This radial-offset amplification is maximal when the two nanocrystals are positioned on the same side of the DNA cylinder and close to zero when the nanocrystals are positioned on opposite sides of the cylinder. Thus, the radially amplified bending model predicts a sinusoidal oscillation in variance with duplex length [proportional to D 2(1 + cosf); see Fig. 1A]. This oscillation matches the helix period of 10 bp, regardless of assumptions about the linkage between the nanocrystals and the DNA.To fit their model to our published variance da...