Studies of Phononlike Low-Energy Excitations of Protein Molecules by Inelastic X-Ray Scattering

Molecular dynamics simulations and neutron scattering experiments have shown that many hydrated globular proteins exhibit a universal dynamic transition at $T_D=220\mathrm{K}$, below which the biological activity of a protein sharply diminishes. We studied the phononlike low-energy excitations of two structurally very different proteins, lysozyme and bovine serum albumin, using inelastic x-ray scattering above and below $T_D$. We found that the excitation energies of the high-$Q$ phonons show a marked softening above $T_D$. This suggests that the large amplitude motions of wavelengths corresponding to this specific $Q$ range are intimately correlated with the increase of biological activities of the proteins.

Figure 1

Lysozyme structure factor $S(q)$ calculated from the crystallographic structure (red) and from the MD trajectories (blue). Arrows point at the main peaks in the $S(q)$ spectrum: A $7{\mathrm{nm}}^{-1}$, B $14{\mathrm{nm}}^{-1}$, C $30{\mathrm{nm}}^{-1}$, D $55\mathrm{nm}{-}^1$. Only the MD trajectories can reproduce the experimentally observed shoulder Peak A. Peak B corresponds to typical distances of the protein secondary structure, peak C to some medium range order between residues and peak D to the protein covalent bonds. The meaning of the shoulder peak A is still uncertain.

Figure 2

Model fitting of the measured IXS spectra of BSA. The blue circles, cyan solid line, green dashed line and pink solid line represent, respectively, the measured data, DHO model fitted curve, resolution function and Brillouin component of the DHO model. The arrow signs (red) show the Stokes and the anti-Stokes components of the phononlike excitation energy at this $Q$. The upper panel shows the fitted results at $Q=4.5$, 5.6, $6.7{\mathrm{nm}}^{-1}$ (from left to right) at 220 K. The lower panel shows the fitted results at $Q=24.6$, 27.9, $31.2{\mathrm{nm}}^{-1}$ (from left to right) at $T=170$, 220, 250 K (from up to down). At each temperature, clear $Q$-dependence of the phonon excitation energy is shown in the figure. At a given $Q$ value, the phonon energy decreases substantially when temperature exceeds $T_D$.

Figure 3

(a) Structure factor $S(Q)$ of BSA in a relative scale. We can see two major peaks at $Q\approx 5{\mathrm{nm}}^{-1}$ and $15{\mathrm{nm}}^{-1}$. (b) Dispersion of the intraprotein phononlike energy excitations of BSA as a function of $Q$, below and above the second major peak in the structure factor. The square (blue), triangle (orange) and circle (yellow) symbols indicate the phonon energies at 170, 220 and 250 K. (c) The phonon damping as a fuction of temperature. (d) Fractional area of the Brillouin peak vs $Q$. The factor ($1\mathrm{\text{−}}{f}_g$) in Eq. (2) is found to increase proportionally to $Q^2$, $1\mathrm{\text{−}}{f}_g(Q)=\alpha (T)Q^2$, where $\alpha (T)$ is an increasing function of $T$.

Figure 4

Analogous plots for the LYZ case (see Fig. 3 caption for details). They show similar trends as in the BSA case.