Observation of coherent delocalized phonon-like modes in DNA under physiological conditions

Underdamped terahertz-frequency delocalized phonon-like modes have long been suggested to play a role in the biological function of DNA. Such phonon modes involve the collective motion of many atoms and are prerequisite to understanding the molecular nature of macroscopic conformational changes and related biochemical phenomena. Initial predictions were based on simple theoretical models of DNA. However, such models do not take into account strong interactions with the surrounding water, which is likely to cause phonon modes to be heavily damped and localized. Here we apply state-of-the-art femtosecond optical Kerr effect spectroscopy, which is currently the only technique capable of taking low-frequency (GHz to THz) vibrational spectra in solution. We are able to demonstrate that phonon modes involving the hydrogen bond network between the strands exist in DNA at physiologically relevant conditions. In addition, the dynamics of the solvating water molecules is slowed down by about a factor of 20 compared with the bulk.

Red segments denote the wavelengths used to plot the melting curves on the right.

Supplementary Note 1 -Water OKE spectra and subtraction procedure
Measured OKE spectra have contributions from the solvent and the solvated nucleic acid. In order to extract the latter, the spectrum of water was directly subtracted from the measured OKE spectra (Supplementary Figure 1, Supplementary Tables 1-4). 1 Water spectra are indistinguishable from the phosphate buffer spectra at the concentration employed in the experiments (0.15 M). To simplify the analysis, the spectra of water were simulated in the subtraction process using a model of the dependence of the water spectra on temperature. This model was created after the measurement and fitting of the OKE spectra of water between 298 and 343 K at intervals of 5 K (Supplementary Figure 2). Each spectrum was fitted using a combination of one Cole-Cole function for the diffusive translational motions of water molecules, two gaussian oscillators for the LA and TA phonon modes and two brownian oscillators for the librational modes 2,3 (Supplementary Table 1). Most of the librational modes of higher frequency (9 -30 THz) can not be seen in the recorded OKE spectra but its contribution was fitted keeping the parameters of the brownian oscillator constant with temperature (ABO = 0.007, ω0/2π = 14.3 THz, and γ/2π = 3.62 THz), since this band is scarcely affected by thermal variations in the temperature range of the experiments. 4 Supplementary Figure 3 shows the influence of temperature on each parameter of the employed equations. Only the change on relaxation time with temperature could not be fitted with a linear equation and an exponential fitting had to be used. Most of the fittings show a good regression coefficient. In order to check its quality, the model was compared with the measured spectra and the standard deviation was calculated (Supplementary Figure 4). The low values of the standard deviations confirm that obtained equations are a good model of the water spectra.

Supplementary Note 2 -Rotational diffusion time estimations
The dimensions of a B-DNA 20-mer are 2.37 nm in diameter and 4.6 nm in length. 5 The two rotational frictional drag coefficients, modelling the molecule as an ellipsoid, are for the major axis and for the minor axis 6,7 where a is the radius of the major axis and b is the radius of the minor axis, and η is the shear viscosity of the medium. Using a = 2.3 nm, b = 1.19 nm, and the following expression 8 approximating the experimental shear viscosity of liquid water, where T is the temperature in Kelvin, to calculate the viscosity, we obtain fM = 4.82 × 10 -29 kg m 2 s -1 and fm = 1.06 × 10 -28 kg m 2 s -1 at 298 K and fM = 1.79 × 10 -29 kg m 2 s -1 and fm = 3.93 × 10 -29 kg m 2 s -1 at 358 K. The orientational diffusion coefficient is then given by 9 where k is Boltzmann constant. Our experiment has been made between 298 and 358 K, so at these temperatures the values of the rotational coefficients are DM = 8.54 × 10 7 Hz and Dm = 3.88 × 10 7 Hz at 298 K and DM = 2.76 × 10 8 Hz and Dm = 1.26 × 10 8 Hz at 358 K.
As OKE is a four-wave mixing technique, the orientational relaxation time constant is given by 9 τ = 1 6D . (5) Thus, the orientational relaxation time constants for our oligomer are τM = 2.00 ns and τm = 4.40 ns at 298 K and τM = 0.60 ns and τm = 1.25 ns at 358 K. Supplementary Figure 5 shows the dependence on temperature of the fitted relaxation frequency of the band associated with the orientational diffusion of our AT oligomer. Also shown are the frequency values predicted by the SED equation obtained from the inverse of the orientational relaxation time ν = τ −1 .

Supplementary Note 3 -Circular dichroism spectra
The melting temperature of the oligomers studied in the article has been determined by tracking the changes in the conformation of the nucleic acids with temperature using circular dichroism and absorption spectroscopies. CD and absorption spectra of a 100-µM solution of oligomer in a 0.1 cm pathlength quartz cuvette have been recorded at intervals of 5 K between 293 and 358 K in a JASCO J-810 spectropolarimeter with a thermoelectric temperature control system (± 0.1 K). The changes in the spectra with temperature have been plotted and fitted to sigmoid curves. The melting point of the oligomer is taken as the temperature at which the sigmoid curve reaches half of its maximum.

AT 20mer
The change in the degree of ellipticity of the sample at 246 nm shows a melting point for AT 20mer of 330.1 ± 0.6 K (see Supplementary Figure 6). These are the data used in the Figure 1 of the article. The maximum of the absorption band at 260 nm has been used to determine the melting point of the AT 20mer, obtaining a Tm = 331.0 ± 0.4 K

CG 20mer
The absorption and CD spectra for CG 20mer only show significant changes above 343 K (see Supplementary Figure 7), so this oligomer does not melt at the temperatures accessible in the OKE experiments. From the curve drawn with the absorption data, a hypothetical melting point of 382 K can be estimated.

Fit functions
Standard fit functions were used to fit to the data. Diffusional processes are modelled using the Havriliak-Negami function where AHN is the amplitude of the function, α and β are empirical parameters, ω is the angular frequency, and τ is the relaxation time of the diffusional process. This function reduces to the Debye function for α = β = 1, which is commonly used to model the lowest frequency orientational diffusion band. The function reduces to the Cole-Cole function for β = 1, which is often used to model intermediate frequency relaxational processes. In particular, we have shown that the lowest frequency part of the OKE spectrum of liquid water can be modelled using a Cole-Cole function with α = 0.96. Peaks in the spectrum due to underdamped librational and vibrational modes were modelled using the Brownian oscillator function 10 where ABO is the amplitude parameter, ω0 is the undamped oscillator angular frequency, and γ is the damping rate, that has units of angular frequency. The phonon modes observed in water spectra were fitted using the anti-symmetrised Gaussian function where AG is the amplitude parameter, ω0 is the undamped oscillator angular frequency, and γ is the damping rate.

Fitting to anti-symmetrised Gaussian vs. Brownian oscillator functions
Supplementary Figure 8 shows a representative experimental OKE spectrum of the 20 base-pair AT oligomer taken at 298 K. As described in the main text, the high frequency region (0.1-5 THz) contains a number of bands, two of which have been assigned to phonon-like delocalised modes. In previous work, we have studied such bands in liquids and found that they could be modelled well using antisymmetrised Gaussian functions suggesting an inhomogeneous distribution of environments. 3,[11][12][13] Here, we attempted to fit the high-frequency OKE spectrum of the 20 base-pair AT oligomer with either anti-symmetrised Gaussian functions (Supplementary Equation (8)) or Brownian oscillator functions (Supplementary Equation (7)). As can be seen in Supplementary Figure 8, the fit to Brownian oscillator functions is far superior. We judge the goodness of the fit using the χ 2 value, which is estimated at χ 2 = 1.36 for the fit using Brownian oscillator functions and χ 2 = 16.0 for the fit using anti-symmetrised Gaussian functions. Although experiments such as spontaneous Raman scattering and related techniques such as OKE cannot distinguish between homogeneous and inhomogeneous broadening, [14][15][16] the Brownian oscillator function is usually considered proof of a homogeneously broadened line. In the unlikely case that an inhomogeneous distribution gave rise to a Lorentzian (Brownian) lineshape, we can still state that the distribution is narrow with the width much less than the average frequency.

Supplementary note 5 -CG 20mer OKE Spectra
The OKE spectra of the CG 20mer (see Supplementary Figure 9) are analogous to the AT 20mer spectra and also are in accordance with the data obtained with circular dichroism spectroscopy. The only changes with increasing temperature in the OKE spectra correspond to the shifting of the molecular orientational diffusion band to higher frequencies.
The OKE spectra of the CG 20mer also clearly show a band with maximum at 2.7 THz like the band B4 of the AT 20mer OKE spectra ( Figure 1). The behaviour of the band with increasing temperature supports the association of the band with the double strand conformation of the oligomer, since the band only starts changing its shape at the higher temperatures of the experiment.