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. 2010 Apr 22;464(7292):1218-22.
doi: 10.1038/nature08892. Epub 2010 Apr 7.

Super-resolution biomolecular crystallography with low-resolution data

Gunnar F Schröder  1 , Michael Levitt, Axel T Brunger
Affiliations

Super-resolution biomolecular crystallography with low-resolution data

Gunnar F Schröder et al. Nature. .

Abstract

X-ray diffraction plays a pivotal role in the understanding of biological systems by revealing atomic structures of proteins, nucleic acids and their complexes, with much recent interest in very large assemblies like the ribosome. As crystals of such large assemblies often diffract weakly (resolution worse than 4 A), we need methods that work at such low resolution. In macromolecular assemblies, some of the components may be known at high resolution, whereas others are unknown: current refinement methods fail as they require a high-resolution starting structure for the entire complex. Determining the structure of such complexes, which are often of key biological importance, should be possible in principle as the number of independent diffraction intensities at a resolution better than 5 A generally exceeds the number of degrees of freedom. Here we introduce a method that adds specific information from known homologous structures but allows global and local deformations of these homology models. Our approach uses the observation that local protein structure tends to be conserved as sequence and function evolve. Cross-validation with R(free) (the free R-factor) determines the optimum deformation and influence of the homology model. For test cases at 3.5-5 A resolution with known structures at high resolution, our method gives significant improvements over conventional refinement in the model as monitored by coordinate accuracy, the definition of secondary structure and the quality of electron density maps. For re-refinements of a representative set of 19 low-resolution crystal structures from the Protein Data Bank, we find similar improvements. Thus, a structure derived from low-resolution diffraction data can have quality similar to a high-resolution structure. Our method is applicable to the study of weakly diffracting crystals using X-ray micro-diffraction as well as data from new X-ray light sources. Use of homology information is not restricted to X-ray crystallography and cryo-electron microscopy: as optical imaging advances to subnanometre resolution, it can use similar tools.

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Conflict of interest statement

AUTHOR INFORMATION

The authors declare no competing financial interests.

Figures

Figure 1
Figure 1. Results for the penicillopepsin test calculations using the MLHL target function (experimental phase information)
In all panels, black lines refer to DEN refinements, whereas red lines refer to noDEN refinements. (a) Showing how the (γ, wDEN) grid-search determines the values that give the best Rfree value for the synthetic diffraction data set at dmin=4.5 Å. The Rfree value is contoured using values calculated on a 6 × 5 grid (marked by small ‘+’ signs) where the parameter γ was [0.0, 0.2, 0.4, 0.06, 0.8, 1.0] and wDEN was [3, 10, 30, 100, 300]. For each parameter pair we performed an extensive refinement protocol (Online Methods). The contour plot shows clear minima and maxima with the value of Rfree varying from 0.295 to 0.35. (b) Showing the contour map of the all-atom RMSD between the target structure 3app and the DEN-refined structure (repeat with the lowest Rfree value) at each grid point in (a). Again there are clear minima and maxima with the RMSD varying from 1.47 to 1.60 Å. (c) Showing the Rfree value as a function of dmin of the four synthetic diffraction data sets. Thick lines mark the lowest Rfree values obtained from the ten repeats using the optimum parameters; the corresponding thin lines mark the highest Rfree values. For the synthetic data sets at dmin ≥ 4 Å, DEN refinement performs much better than noDEN reaching lower Rfree values. (d) Showing how Zemla’s GDT (<1 Å) score, which measures structural similarity to the target structure 3app, varies as a function of dmin; the dashed line indicates the GDT score of the initial model. At all resolutions, DEN out-performs noDEN and gives GDT values that are more favorable (higher) than those of the initial structure. (e) Showing how the RMSD of all atoms to the 3app target structure varies vs. dmin of the four synthetic diffraction data sets. Once again DEN gives lower RMSD values, especially at low-resolution. The DEN-refined models used in (d), and (e) correspond to the best models among ten repeats as assessed by Rfree (black dots in panel (c)). Black ellipses indicate on the contour maps values corresponding to the structure with lowest Rfree value obtained for dmin=4.5Å.
Figure 2
Figure 2. Re-refinement of nineteen low-resolution PDB structures
(a) Rfree values of PDB structures refined with DEN (blue) and without DEN (noDEN, orange). In every case the DEN refined structure has the lower Rfree value. For each protein, (γ, wDEN) parameter optimization was performed (Online Methods, Supplementary Fig. 4), and the structure with the lowest Rfree value used for analysis. (b) Fraction of residues in the favored region of the Ramachandran plot as determined by Molprobity termed here Ramachandran Score. (c) Significant correlation (correlation coefficient 0.83) is seen between Rfree Improvement and Ramachandran Score Improvement for DEN vs. noDEN.
Figure 3
Figure 3. Electron density map improvement upon DEN refinement for three structures 3dmk, 1ye1, and 1xxi
The 1ye1 (c,d) and 1xxi (e,f) structures are among the cases that benefit most from DEN refinement, whereas the 3dmk (a,b) structure showed only moderate improvement of the Rfree value (Table 2). Nevertheless, in all three cases DEN refinement dramatically improves the electron density maps. The structures refined with DEN (DEN, in blue) and without DEN (noDEN, in orange) are superimposed, and the corresponding phase combined σA-weighted 2Fo-Fc electron density maps are shown in blue and red, respectively. The density maps for 3dmk and 1xxi were B-factor sharpened (Bsharp = −50 Å2) and the contour level was set to 1.5 σ.
Figure 4
Figure 4. DEN provides information for degrees of freedom that are weakly defined by the experimental diffraction data
(a) Showing DEN (green) and noDEN (red) histograms of, RMSDD, the root-mean-square deviation of DEN restraint distances in the target structure (3app) from those in the ten refinement repeats (starting from the 4ape initial model with dmin=4.5Å, the MLHL target function, and DEN optimum parameters (γ,wDEN)=(0,10); see Fig. 1a). The largest RMSDD is much smaller for DEN compared to noDEN. Inset: the RMS Fluctuations of each distance over the ten repeats of noDEN refinement (RMSF) are plotted against RMSDD for DEN (b, green) and noDEN (c, red). Large RMSF values (>1.5 Å) represent the DEN distances that are not well defined by the diffraction data. For DEN, these distances have small RMSDD values (<1.0 Å) whereas for noDEN they have large RMSDD values. Restraint distances are much closer to the distances in the target structure for DEN, which effectively provides information missing from low-resolution experimental data.
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