Direct Determination of the Base-Pair Force Constant of DNA from the Acoustic Phonon Dispersion of the Double Helix

Quantifying the molecular elasticity of DNA is fundamental to our understanding of its biological functions. Recently different groups, through experiments on tailored DNA samples and numerical models, have reported a range of stretching force constants (0.3 to $3\mathrm{N}/\mathrm{m}$). However, the most direct, microscopic measurement of DNA stiffness is obtained from the dispersion of its vibrations. A new neutron scattering spectrometer and aligned, wet spun samples have enabled such measurements, which provide the first data of collective excitations of DNA and yield a force constant of $83\mathrm{N}/\mathrm{m}$. Structural and dynamic order persists unchanged to within 15 K of the melting point of the sample, precluding the formation of bubbles. These findings are supported by large scale phonon and molecular dynamics calculations, which reconcile hard and soft force constants.

Figure 1

The scattering intensity $S(Q,E)$ of the aligned DNA samples as measured at 70 K on the cold neutron, chopper spectrometer, IN5 at the ILL, France. In configuration 1 the steep dispersion of the acoustic phonon is visible on the anti-Stokes side of the base pair Bragg peak [right arrow in (a)] together with the optic mode (left arrow). The constant-$Q$ cuts of (a) are plotted in (b). The dispersion of the optic mode is extract from the fits. When DNA fibres are rotated from the parallel to perpendicular with respect to the instrumental scattering plane none of these features is visible (c). In configuration 2 the acoustic phonon scattering is observed on both sides of the elastic line (d)

Figure 2

Comparison of the dispersion curves of IXS (open circles) [15], calculations (filled squares) [18] and INS (dashed parabola) [13] with our fitted dispersion curves obtained in configuration 1 (red pentagons) and 2 (blue diamonds). The dispersion curve as previously reported from INS data is probably a convolution of the optic and acoustic modes measured in this work. The sound speed obtained from the acoustic dispersion curve at the base-pair Bragg peak is $4.3\mathrm{km}/\mathrm{s}$.

Figure 3

Constant-$Q$ cuts of $S(Q,E)$ of configuration 2 at 70 K (a) and 335 K (b). In (b) the quasielastic intensity is subtracted as described in the text. The intensity of the 335 K data are rescaled by the Bose factor for comparison with the 70 K data.

Figure 4

A contour map of the calculated scattering intensity (logarithmic scale) versus energy transfer and Q (labeled in terms of the Brillouin zones of the helix) from phonon calculations [18]. The new INS data corresponds to the acoustic mode centered at (0,0,10) and the lower limit of the optic modes intensity at about 2 meV. The published IXS data [15] corresponds to the sinusoidal arc of intensity extending from (0,0,0) to (0,0,10), with a broad maximum at $\sim 10\mathrm{meV}$ and $Q=(0,0,5)$.