Inelastic X-ray scattering studies of phonons in liquid crystalline DNA

Abstract

A high resolution X-ray scattering method is used to measure spectra of the collective density oscillations propagating along the axis of a rod-like supra-molecular system made of a shear-aligned columnar hexagonal liquid crystalline phase of DNA dispersed in water. The dynamic structure factor is extracted from the spectrum using a generalized three effective eigenmode (GTEE) theory. The dynamic structure factor consists of three Lorentzian lines, one central Rayleigh and two symmetrically shifted Brillouin peaks, from which the phonon frequency and damping can be obtained. We investigated two systems: a 40 wt.% calf-thymus Na–DNA of molecular weight 8.4 × 10⁶ Da (13 000 base pairs) in water, and 40 wt.% Na–DNA in 0.085 M MgCl₂. The phonon dispersion relations obtained show an oscillatory behavior as a function of Q (magnitude of the scattering vector) in the range of 2 nm⁻¹ to 30 nm⁻¹, similar to that obtained from lipid bilayers before. The dispersion relation of 40 wt.% DNA rods in pure water, for example, starts with a linear dispersion at low Q with a high-frequency sound speed of about 3100 m s⁻¹, similar to that observed in bulk water, reaching a maximum of ω = 12 meV at Q = 9 nm⁻¹, going down to a valley at Q = 18.7 nm⁻¹, coming up to a secondary (lower) maximum at Q = 25 nm⁻¹ and eventually going down at Q = 30 nm⁻¹. One major distinctive feature of the DNA systems from liquids is that the dispersion relation in the shear aligned DNA extends to a considerably higher Q than that observed in liquids. The extended range of Q includes values corresponding to those in the second Brillouin zone in a crystalline system. This latter feature implies that a DNA rod can be regarded approximately as a one-dimensional crystal, as far as the density oscillations are concerned. In the system with 40 wt.% Na–DNA in 0.085 M MgCl₂, we observe a significantly greater phonon damping compared to the one in water.