Three-dimensional diffuse x-ray scattering from crystals of Staphylococcal nuclease

Abstract

We have developed methods for obtaining and characterizing three-dimensional maps of the reciprocal-space distribution of diffuse x-ray scattering from protein crystals, and have used the methods to study the nature of disorder in crystals of Staphylococcal nuclease. Experimentally obtained maps are 99.5% complete in the reciprocal-space resolution range of 10 A-2.5 A, show symmetry consistent with the P41 space group of the unit cell, and are highly reproducible. Quantitative comparisons of the data with three-dimensional simulations imply liquid-like motions of the protein [Caspar, D. L. D., Clarage, J., Salunke, D. M. & Clarage, M. (1988) Nature (London) 332, 659-662], with a correlation length of 10 A and a root-mean-square displacement of 0.36 A.

Figure 1

Raw image of a room-temperature, 5-second still exposure (roughly 1.5 Å resolution at the edge). Note the structure in the diffuse scattering observable in the image. The distribution of diffuse features is consistent with the unit–cell space group P4₁. We wished to measure these features in the absence of the Bragg peaks.

Figure 2

Diffraction image shown in Fig. 1 after polarization correction, solid angle normalization, and mode filtering to remove Bragg peaks.

Figure 3

A stereo-pair interpolated isosurface in the three-dimensional map of diffuse x-ray scattering from Staphylococcal nuclease (arbitrary colors). Features in the surface illustrate variations of diffuse intensity in the neighborhood of 3.8 Å resolution, the location of the maximum in the “solvent ring.” Reciprocal axes a*, b*, and c* are shown (Offset) to orient the map. Room-temperature still exposures were recorded every degree to span 96° of crystal rotation, so that the map is missing two 84° opposing wedges. Symmetry averaging completes the map.

Figure 4

A shell image of diffuse features in an experimental map ΔI_d(s). To generate this image, diffuse intensity in a 0.033 Å⁻¹ spherical shell about 3.8 Å is mapped to a Cartesian image in a manner similar to generating Mercator projections of the earth’s surface. The polar angle θ is measured from the c*-axis, and varies from 0 at the top to π at the bottom of the image. The azimuthal angle φ is measured from the a*-axis in a right-handed sense, and varies from −π (Left) to π (Right). Pixel values are displayed on a linear grey scale, with −300 corresponding to black, and 300 corresponding to white (missing data is colored black). A full three-dimensional sequence can be generated by subdividing reciprocal space into spherical shells and generating such an image for each of the shells.

Figure 5

Data and the best-fit liquid-like motions model (γ = 10 Å, σ = 0.36 Å) are compared side by side in 0.033 Å⁻¹ shells between 3.8 Å and 2.5 Å. Display parameters are the same as those in Fig. 4, except that the azimuthal angle φ varies from −π (Left) to only −π/2 (Right) (other portions are related by symmetry).