## 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 Å^{2} 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 Å^{2} 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 *n*^{2}-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 *l _{m}*, and bending persistence length

*l*. It is dominated by longitudinal fluctuations =

_{b}*cn*for very short oligonucleotides, the experiment being insensitive to transverse shear. For intermediate lengths, bending fluctuations take over (

*7*,

*8*). In the Gaussian long-chain limit, the distance variance approaches = [1 − 8/(3π)]2

*l*. Using standard literature values for

_{p}l_{m}n*c*,

*l*, and

_{m}*l*determined in single-molecule experiments (

_{p}*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).

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 ∝ *l*^{2}〈α^{2}〉^{2} in terms of the contour length *l* = *l _{m}n* and the total mean square deflection angle 〈α

^{2}〉 = 2

*l*/

*l*. Including an axial lever arm length

_{p}*axial*

_{0}/2 per label yields σ

*∝ (*

_{b}*l*+

*axial*

_{0})

^{2}〈α

^{2}〉

^{2}∝ (

*l*+

_{m}n*axial*

_{0})

^{2}

*n*

^{2}. Similarly, a radial offset

*D*of the nanoparticle from the helical axis leads to an additional oscillating term ∝

*D*

^{2}(1 + cosθ)〈α

^{2}〉 ∝

*n*, where θ is the total azimuthal angle between the nanoparticles. These corrections cannot be absorbed into an

*n*-independent constant offset.

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 *axial*_{0} = 24 Å, and azimuthal starting angle θ_{0} = 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 (*axial*_{0} = 23 Å, *D* = 12.7 Å, and θ_{0} = 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