Measuring and modeling diffuse scattering in protein X-ray crystallography

Abstract

X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practices for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation-libration-screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. These results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering.

Keywords: diffuse scattering; liquid-like motions; normal modes; protein dynamics; structural biology.

Fig. 1.

Steps in diffuse data integration. (A) Raw CypA diffraction images are processed (B) to remove Bragg peaks and enable direct comparisons of pixel values to models. (C) Pixels in diffraction images are mapped to reciprocal space and values of diffuse intensity are accumulated on a 3D lattice; each diffraction image produces measurements of diffuse intensity on the surface of an Ewald sphere. (D) The data from individual images are combined and symmetrized to yield a nearly complete dataset (isosurface at a value of 65 photon counts in the total intensity, before subtracting the isotropic component).

Fig. 2.

Agreement of models of protein motions with diffuse and Bragg data. (A and B) Linear correlation coefficients (CCs) between diffuse data and LLM (red bars) or NM models (blue bars) computed by resolution shell for (A) CypA and (B) trypsin. (C and D) Correlations and R factors between Bragg data and NM models computed by resolution shell for (C) CypA and (D) trypsin. Agreement factors for the diffuse and Bragg data were computed using LUNUS (60) and Phenix (67), respectively.

Fig. 3.

Simulated diffraction images for CypA frame 67 obtained using the following: (A) LLM model; (B) integrated 3D diffuse data; (C) elastic network NM model. Lighter colors correspond to stronger intensity. White regions correspond to pixel values where there are missing values in the corresponding 3D lattice (Methods).