Predicting X-ray diffuse scattering from translation-libration-screw structural ensembles

Abstract

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier's equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation-libration-screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.

Keywords: TLS; correlated motion; diffuse scattering; structural ensemble; structure refinement.

Figure 1

TLS refinement suggests macromolecular motions linked to function. (a) Top and side view of GroEL. Each color denotes a unique chain. (b) TLS refinement of GroEL subunits reveals a ‘tilting’ motion around the center of the subunit. (c) GpdQ diffraction image showing significant diffuse scattering features. (d) Refinement of GpdQ fails to produce substantial changes in R _work and R _free values between alternate TLS groups. TLS refinement significantly improves the overall R _free (23.1% pre-TLS).

Figure 2

Overview of phenix.tls_as_xyz. The input PDB file (1) is broken down into its constituent TLS groups (2) and TLS ensembles are generated for each group independently (3). These groups are then re-assembled into the complete protein structure on a model-by-model basis (4).

Figure 3

Overview of phenix.diffuse. (a) The general form of Guinier’s equation. The motion to be analyzed is captured in a series of ‘snapshots’ defined by the the multi-model PDB file. (b) The general program flow. Each term in Guinier’s equation is calculated separately from the structural ensembles and then combined to obtain the final map.

Figure 4

Differing TLS groups produce unique diffuse scattering. (a) The GpdQ TLS groups projected onto the structure, along with the calculated diffuse scattering (looking down the L axis; the gray sphere denotes 4 Å resolution). The ‘monomer’ and ‘sub-domain’ maps are shown at equivalent density thresholds, while ‘entire molecule’ map is set at 60% of the density threshold. No correlation is assumed between TLS rigid-body groups. (b) Pearson correlation coefficients between anisotropic maps.

Figure 5

Comparison of simulated GpdQ TLS diffuse scattering maps. (a) Cross-section of simulated TLS diffuse scattering maps. Primary and secondary diffuse intensity shells, separated by a gap, can be observed in each model. As the number of TLS groups increase, the intensity shells grow closer, predominantly owing to an expansion in primary intensity shell size. (b) Pearson correlation values between each set of maps across resolution bins.

Figure 6

Different correlations between TLS groups produce unique diffuse scattering. Parallel (a) and antiparallel (b) TLS motions in GpdQ chains result in measurable differences between diffuse scattering patterns (CC = 0.375). Color bars indicate the directionality of the TLS motions; each color represents a unique molecular position. (c) A map cutaway reveals strong secondary-shell features with a small primary diffuse shell (looking down the L axis; the gray sphere denotes 4 Å resolution). (d) Intensity differences between raw ‘antiparallel’ and ‘parallel’ diffuse maps (green, positive; red, negative) highlights the qualitative changes caused by alternative TLS-group correlations. (e) Correlation values across anisotropic map resolution bins reveal that the highest correlation occurs between the maps at low resolution and decreases as a function of scattering-vector length.

Figure 7

TLS models yield unique radial profiles of diffuse intensity. (a) Mode-filtered GpdQ diffraction image used for radial intensity calculation. The white regions correspond to pixels thrown out owing to detector-panel and beamstop artifacts, as well as Bragg scattering contamination. (b) Radial diffuse intensity profiles for experimental and simulated GpdQ data. Resolution data below 15 Å (roughly corresponding to the primary diffuse shell) were removed for more accurate visual comparison. The ‘sub-domain’ map exceeds the limits of the y axis at lower than 10 Å resolution.

Figure 8

Unit-cell expansion allows reciprocal-space subsampling. (a) The unit cell of the input PDB entry is expanded to create the desired unit-cell sampling, each term in Guinier’s equation is calculated separately and then the second term is subtracted from the first to obtain the diffuse intensity. The ‘pseudo-unit cells’ are then averaged across, producing the final diffuse scattering map. (b) Unit-cell expansion allowing for 3× subsampling of reciprocal space. True/‘pseudo’ Bragg peaks are shown in black/orange and red, respectively. The intensity values of the eight pseudo peaks and one orange peak in the blue box are averaged and the resulting value is assigned to the Bragg index of the orange peak. (c) Pearson correlation coefficients between maps.