Intermolecular correlations are necessary to explain diffuse scattering from protein crystals

Abstract

Conformational changes drive protein function, including catalysis, allostery and signaling. X-ray diffuse scattering from protein crystals has frequently been cited as a probe of these correlated motions, with significant potential to advance our understanding of biological dynamics. However, recent work has challenged this prevailing view, suggesting instead that diffuse scattering primarily originates from rigid-body motions and could therefore be applied to improve structure determination. To investigate the nature of the disorder giving rise to diffuse scattering, and thus the potential applications of this signal, a diverse repertoire of disorder models was assessed for its ability to reproduce the diffuse signal reconstructed from three protein crystals. This comparison revealed that multiple models of intramolecular conformational dynamics, including ensemble models inferred from the Bragg data, could not explain the signal. Models of rigid-body or short-range liquid-like motions, in which dynamics are confined to the biological unit, showed modest agreement with the diffuse maps, but were unable to reproduce experimental features indicative of long-range correlations. Extending a model of liquid-like motions to include disorder across neighboring proteins in the crystal significantly improved agreement with all three systems and highlighted the contribution of intermolecular correlations to the observed signal. These findings anticipate a need to account for intermolecular disorder in order to advance the interpretation of diffuse scattering to either extract biological motions or aid structural inference.

Keywords: diffuse scattering; intermolecular correlations.

Figure 1

Reciprocal-space maps from experimental diffuse scattering. The diffuse scattering in diffraction images collected for (a) CypA, (b) AP and (c) WrpA was reconstructed into a reciprocal-space map for each system. These maps take the form of three-dimensional grids that are oversampled by a factor of three relative to the Miller indices along each lattice axis. Left: an example diffraction image from each data set. Right: central slices through reciprocal space are visualized for each unsymmetrized map in the top panels. The lower panels show these slices after symmetrization of Friedel- and Laue-equivalent voxels, followed by subtraction of the average radial intensity profile to highlight anisotropic features. For the symmetrized maps, the color scales do not span the entire range of voxel intensities; this saturates a subset of voxels but improves the overall contrast.

Figure 2

Elastic network models of Gaussian disorder. The highest and lowest magnitude entries in the covariance matrix are overlaid as blue and red cylinders, respectively, on the refined atomic coordinates for (a) CypA, (b) AP and (c) WrpA. The 0kl slices of the predicted diffuse scattering maps are shown on the right, with the overall CC noted in black. The color scales differ from Fig. 1 ▸ to enhance visualization of the features.

Figure 3

Ensemble models inferred from the Bragg data. (a) Multi-conformer modeling of the CypA electron-density map predicts a minor population of alternate conformers (purple) that radiate from the active site. (b) CypA data sets collected at 180 K and below show two loop conformations between residues 79 and 83; the visualized loop conformations are those modeled in the 100 K data set. Above 180 K, the conformation shown in white is not populated. (c) Model of AP assuming that one active site is tungstate-bound (left) while the other is occupied by water molecules that coordinate the active-site metal ions (right). The 0kl plane of the predicted map from each ensemble model is shown on the right, with a different color scale from Fig. 1 ▸ to enhance visual contrast. The overall CC between the experimental map and each predicted map is noted in black.

Figure 4

Comparison of models of rigid-body and liquid-like motions. For the indicated model, parameters that tune the disorder were fitted to maximize overall correlation with the experimental map. The predicted 0kl planes for the best-fit maps are shown, with the experimental 0kl planes displayed in the rightmost column for comparison. The overall CC between the experimental map and each predicted map is noted in black. As with Fig. 1, the color scales span a partial range of the voxel intensities to improve visual contrast.

Figure 5

Speckled features of the experimental maps. The insets highlight the characteristic speckles for the 0kl planes of the (a) CypA and (b) AP maps. In (c)–(f), maps were reconstructed or computed with oversampling by a factor of five along each lattice direction relative to integral Miller indices. Data were binned into 20 resolution shells, and the median profile for the intensity as a function of δq, the distance from reciprocal-lattice sites, is shown for each shell. Intensity profiles were normalized such that the intensity value for voxels that coincided with reciprocal-lattice sites (δq = 0) was unity. For each experimental map, curves with a 1/δq ² (dashed blue) or a 8πγ³/(1 + γ²δq ²)² (dashed red) dependence, as predicted by the phonon and liquid-like motions models, respectively, were fitted to the intensity profile in the lowest resolution shell (red points). For comparison with models whose basis is the molecular transform, intensity profiles for the CypA molecular-transform map are shown in (c).