Technical Comments

Comment on “Remeasuring the Double Helix”

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Science  31 Jul 2009:
Vol. 325, Issue 5940, pp. 538
DOI: 10.1126/science.1168786

Abstract

Mathew-Fenn et al. (Reports, 17 October 2008, p. 446) reported unexpected distance fluctuations in short end-labeled DNA constructs and interpreted them as evidence for cooperative DNA stretching modes. We show that when accounting for a subtle linker leverage effect, their data can be understood within standard noncooperative DNA elasticity.

Mathew-Fenn et al. (1) presented a novel measurement of the conformational fluctuations of short DNA oligonucleotides in solution. Their technique (2) yields the thermal distribution of distances between two gold nanoparticles grafted to the ends of the oligonucleotides. The authors reported an increase in variance of these distributions by 42.5 Å2 over the range from n = 10 base pairs (bp) to n = 35 bp and contrasted the finding with a theoretical expectation of no more than a 10 Å2 increase in end-to-end distance variance for an ideal elastic rod model of DNA. They interpreted this as revealing an as-yet-unobserved feature of DNA and suggested a cooperative stretching mechanism to explain the magnitude and apparent n2-dependence of observed variances. Here, we report on Monte Carlo simulations of their molecular constructs using the rigid base-pair model of DNA (3), with elastic and structural parameters derived (4) from structural database analysis (5) and all-atom simulation (6). Our results show that the reported data can be understood in the framework of standard linear and noncooperative DNA elasticity, when properly accounting for the geometry of the molecular linkers between DNA and nanoparticles.

The distance fluctuations measured in (1) are due to a superposition of various modes originating from DNA, DNA-nanoparticle linkers, and other experimental factors. The DNA contribution to the variance depends on its compressional variance per base pair c, helical rise per base pair lm, and bending persistence length lb. It is dominated by longitudinal fluctuations Embedded Image = cn for very short oligonucleotides, the experiment being insensitive to transverse shear. For intermediate lengths, bending fluctuations Embedded Image take over (7, 8). In the Gaussian long-chain limit, the distance variance approaches Embedded Image = [1 − 8/(3π)]2lplmn. Using standard literature values for c, lm, and lp determined in single-molecule experiments (9, 10), these scaling regimes are reproduced (11) by our microscopically parameterized simulations (Fig. 1A). Clearly, standard DNA elasticity alone does not account for the data reported in (1). As emphasized by Mathew-Fenn et al., adding an n-independent correction to include isotropic linker fluctuations and other experimental noise sources is insufficient to reproduce the observed increase in variance (Fig. 1A, inset).

Fig. 1

Distance variance from experiment (black) and from Monte Carlo simulations of different model DNA constructs. (A) DNA only. The rigid base-pair model with bending, twisting, stretching, and shearing fluctuations (blue) exhibits the well-known scaling regimes corresponding to the standard values for DNA stiffness and geometry c ≅ 0.13 Å2/bp (9, 10), lm = 3.3 Å/bp, and lp = 50 nm. As reported in (1), adding an n-independent offset does not allow fitting of the data (green, inset). (B) Constructs including linker geometry, compared with the DNA-only curve. The rigid base-pair model combined with static linkers (orange) of the reported geometry (1) accounts for the magnitude of the observed variances without fitting and reproduces the standard large-scale behavior. When fitting linker geometry, the data are quantitatively reproduced (red, inset). Both curves in (B) are shifted by an n-independent offset. Experimental data points for end-labeled constructs were taken from table S2 in (1). For all simulations, a hybrid elastic parameter set, combined from crystal database analysis and simulation studies, was used (5, 6, 11).

However, the authors disregarded lever-arm effects in the conversion of DNA bending fluctuations into nanoparticle distance variations (Fig. 2). In the absence of leverage, the DNA bending contribution scales as Embedded Imagel2〈α22 in terms of the contour length l = lmn and the total mean square deflection angle 〈α2〉 = 2l/lp. Including an axial lever arm length axial0/2 per label yields σb ∝ (l + axial0)2〈α22 ∝ (lmn + axial0)2n2. Similarly, a radial offset D of the nanoparticle from the helical axis leads to an additional oscillating term ∝ D2(1 + cosθ)〈α2〉 ∝ n, where θ is the total azimuthal angle between the nanoparticles. These corrections cannot be absorbed into an n-independent constant offset.

Fig. 2

Geometry of a 15-bp oligonucleotide, as in (1), approximately to scale. DNA length is about 45 Å; DNA and particle radii are 10 Å and 7 Å, respectively. Each lever arm between DNA end and particle center has a total length of 15 Å. In our calculations, the linker geometry is taken fixed with respect to the terminal base pairs, as shown. (A) Equilibrium conformation of the construct. (B) Thermal conformation snapshot. The small change in DNA end-to-end distance coincides with a large change in nanoparticle distance. Solid and dashed arrows indicate equilibrium and snapshot distances, respectively; bricks represent base pairs; DNA sugar-phosphate backbones and molecular linkers are not shown.

To test these ideas, we included the linkers in the simulation. Using rigid linkers with a geometry as reported in (1) (radial offset D = 9 Å, total axial offset axial0 = 24 Å, and azimuthal starting angle θ0 = 1.34π) yields variances that coincide acceptably with the data (Fig. 1B); about 90% of the total variance increase is reproduced. We also carried out a simultaneous three-parameter least-squares fit of the same model to the mean distance (fig. S1) and distance variance data. This resulted in a somewhat different prediction for the mean linker geometry (axial0 = 23 Å, D = 12.7 Å, and θ0 = 0.91π) and quantitatively fits the data (Fig. 1B, inset). As a result of the radial offset, both the nonfitted and the fitted variance curves exhibit helical oscillations. The results shown in Fig. 1 were obtained using rigid linkers but remain valid when including three-dimensional isotropic linker fluctuations, because these just add a global constant to the variances. In contrast, anisotropic linker fluctuations can modify the apparent oscillations, complicating the fitting of linker geometry (fig. S1). More experimental data are needed for a full characterization of the linkers.

In summary, the data presented in (1) are consistent with standard, noncooperative, linear DNA elasticity using “canonical” microscopic (11) and mesoscopic (9, 10) elastic and structural parameters. Combined with an analysis as outlined above, experiments on short regular oligonucleotides should allow for a full calibration of linker geometry and elasticity. The x-ray molecular ruler (2) would then provide sufficient resolution to study perturbations of DNA, for example, by partial denaturation or protein binding.

Supporting Online Material

www.sciencemag.org/cgi/content/full/325/5940/538-b/DC1

Materials and Methods

Fig. S1

Table S1

References

References

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