Response to Comment on “Remeasuring the Double Helix”

Abstract

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)<a 2 >; 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...

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“…These data are also represented in Figure 2 where the solid red line (ν jf = 0.18) denotes the calculated results and circles correspond to the experimental values [5,6]. Another set of experimental data [7] in Table 1 for version b* with ν jf = 0.14 at ν p = 0.2 also agrees well with the calculation using Equation (1) and is shown in Figure 2. For example, a DNA molecule in the standard buffer solution plus 200 mM NaCl has a persistence length 50 nm [7], while in the standard buffer solution with 0 mM Nacl the persistence length is A bp = 55.2 nm.…”

“…Nonlinear unwinding and the thermomechanical length L c fluctuation variance Var(L c ) of DNA molecules were found in the experimental studies at "remeasuring the double helix" [5][6][7]. Our model (Figure 1(a)) with the hollow pretwisted nanostrip sensor has those features.…”

“…This follows from the possible combination of thermomechanical statistical influence on the two surfaces as √2 or from a necessary thermomechanical energy 2(k B T) at larger material deformation with larger |ν p |. Our experience with the published experimental data [5][6][7] shows that the first value n bp = √2 is more appropriate for a molecule with ν p ≤ 0.2, ν jf = 0.14 and the second value n bp = 2 for a molecule with ν p = 0.5, ν jf = 0.18 in standard solution with 70 mM Tris-Hl, pH 8.0 and 10 mM ascorbic acid. Equation (7) yields persistence length values at T = 293 K within 49-53 nm for both cases.…”

“…Equation (7) yields persistence length values at T = 293 K within 49-53 nm for both cases. In any case, the experimental value of j sp and A bp should preferably be measured or evaluated at the corresponding conditions because the persistence length depends on them [7,10] as well as on the molecular length [11]. A mean experimental value of the DNA persistence length in different cases and different solutions is equal to A bp = (30 + 80)/2 = 55 nm.…”

“…and from Equation (3) Version a ν jf = 0.18, experimental ae after [5,6]; version b* ν jf = 0.14, experimental b*e after [7].…”