Correlated Dynamics Determining X-Ray Diffuse Scattering from a Crystalline Protein Revealed by Molecular Dynamics Simulation

The dynamical origin of the x-ray diffuse scattering by crystals of a protein, Staphylococcal nuclease, is determined using molecular dynamics simulation. A smooth, nearly isotropic scattering shell at $q=0.28{\AA }^{-1}$ originates from equal contributions from correlations in nearest-neighbor water molecule dynamics and from internal protein motions, the latter consisting of $\alpha$-helix pitch and inter-$\beta$-strand fluctuations. Superposed on the shell are intense, three-dimensional scattering features that originate from a very small number of slowly varying ($>10\mathrm{ns}$) collective motions. The individual three-dimensional features are assigned to specific collective motions in the protein, and some of these explicitly involve potentially functional active-site deformations.

Figure 1

X-ray diffuse scattering intensities calculated using Eq. (1) as a function of the magnitude $q$ of the scattering vector. For clarity, intensities are shown as isotropic averages. $I_{\mathrm{diff}}$ is shown (in arbitrary units on the same scale) from the simulation unit cell, the proteins only, and the solvent only. Also shown is the experimental scattering from Ref. 8, which originates from the complete unit cell, i.e., proteins and solvent.

Figure 2

Decomposition of the protein x-ray diffuse scattering intensity. $I_{\mathrm{diff}}^{\mathrm{protein}}$ is compared with (a) $I_{\mathrm{diff}}$ of the protein without secondary structural elements, (b) $I_{\mathrm{diff}}$ of secondary structural elements, and (c) $I_{\mathrm{diff}}$ of selected, single secondary structural elements. For clarity, $I_{\mathrm{diff}}^{\mathrm{protein}}$ has been scaled in (b) and (c).

Figure 3

(a)–(e) Cross sections through the $q_z=0{\AA }^{-1}$ plane of the simulation-derived three-dimensional protein x-ray diffuse intensities (in arbitrary units on the same scale in each plot) due to the full trajectory (a), due to the PCA modes 1–5 (b) and 6–7000 (c), due to the full trajectory but excluding all intraprotein cross-correlations (d), or excluding only those intraprotein cross-correlations between the C and N termini and the O and R loops (e). (f)–(g) $q_z=0{\AA }^{-1}$ cross sections through the all-atom unit-cell scattering of the simulation (f) and experiment (g) on arbitrary intensity scales. All patterns contain inversion symmetry, consistent with the space-group symmetry. Intense 3D features are labeled in (a) and discussed in the text. (h) The agreement factor $R=⟨|I_{\mathrm{diff}}^{\mathrm{sim}}-I_{\mathrm{diff}}^{\exp }|/I_{\mathrm{diff}}^{\exp }{⟩}_{\mathbf{q}}$ between the experimental and simulated pattern varies logarithmically with the length of the simulation.

Figure 4

Two typical relative displacements between the flexible R and O loops [indicated in (b)] of different protein molecules due to the five lowest-frequency PCA modes. Shown are the structures after equilibration (transparent) and after 10 ns (opaque).