Integration of small-angle X-ray scattering data into structural modeling of proteins and their assemblies

Abstract

A major challenge in structural biology is to determine the configuration of domains and proteins in multidomain proteins and assemblies, respectively. All available data should be considered to maximize the accuracy and precision of these models. Small-angle X-ray scattering (SAXS) efficiently provides low-resolution experimental data about the shapes of proteins and their assemblies. Thus, we integrated SAXS profiles into our software for modeling proteins and their assemblies by satisfaction of spatial restraints. Specifically, we modeled the quaternary structures of multidomain proteins with structurally defined rigid domains as well as quaternary structures of binary complexes of structurally defined rigid proteins. In addition to SAXS profiles and the component structures, we used stereochemical restraints and an atomic distance-dependent statistical potential. The scoring function is optimized by a biased Monte Carlo protocol, including quasi-Newton and simulated annealing schemes. The final prediction corresponds to the best scoring solution in the largest cluster of many independently calculated solutions. To quantify how well the quaternary structures are determined based on their SAXS profiles, we used a benchmark of 12 simulated examples as well as an experimental SAXS profile of the homotetramer D-xylose isomerase. Optimization of the SAXS-dependent scoring function generally results in accurate models if sufficiently precise approximations for the constituent rigid bodies are available; otherwise, the best scoring models can have significant errors. Thus, SAXS profiles can play a useful role in the structural characterization of proteins and assemblies if they are combined with additional data and used judiciously. Our integration of a SAXS profile into modeling by satisfaction of spatial restraints will facilitate further integration of different kinds of data for structure determination of proteins and their assemblies.

Fig. 1

Flowchart for the modeling protocol. As input, we need a SAXS profile, an initial model, the definition of rigid bodies, and optionally the symmetry. Initialization yields N random configurations, which are subsequently optimized in three stages. For the final analysis, only the 10% of the N models with the best S_SAXS score are retained and clustered.

Fig. 2

Accuracy of the Debye model for calculating SAXS profiles. We compare an experimental profile of lysozyme (black, obtained from http://www.embl-hamburg.de/ExternalInfo/Research/Sax/crysol.html) to the profiles calculated using our methodology (green) and the program CRYSOL (red).

Fig. 3

Modeling Diphteria toxin using a simulated SAXS profile. A: Native monomeric Diphteria toxin (PDB code 1mdtA) has two domains (blue and red). B. We approximated these domains by their structures in the dimeric form (PDB code 2ddtA). C: The sum of S_DOPE and S_overlap of all models optimized with respect to S_DOPE + S_overlap + S_stereo, plotted against their Cα RMSD relative to the crystallographic structure. The yellow and orange circles depict the native structure and the RBNC, respectively. D: The χ² of all models optimized with respect to S_SAXS + S_stereo, plotted against Cα RMSD. The χ² for the native structure and the RBNC are outside the plotted range (χ²=1.21 and χ²=1.57, respectively) E: Overall score S of all models optimized with respect to the complete S, plotted against Cα RMSD. The best-scoring models from the three clusters in Fig. 4 are highlighted in red, blue, and green.

Fig. 4

Clustering of Diphteria toxin models. A: Hierarchical tree of the 10% best-scoring models according to their χ² values. To cluster the models, the tree is cut at a pairwise Cα RMSD of 12.5 Å. B, C, D: Models with the best S within clusters I, II, and III, respectively. E: The I(q) profiles of the best scoring models from cluster I, II, and III compared to the calculated SAXS profiles. The χ² values are 1.4, 1.5, and 1.3, respectively.

Fig. 5

Models of XI and their calculated SAXS profiles compared to the experimental profile. To facilitate visual comparison of the different models, chain A (red) of all models is oriented identically. A: Native XI (χ²=17.7; PDB code 1xib). B: The XI model, based on the native subunit, with the best S_DOPE (χ²=9.6). C: The XI model, based on the native subunit, with the best S_SAXS (χ²=7.5). D: The χ² of the top 10% models (ie, clustered models) plotted against their Cα RMSD with respect to the crystallographic structure. The models with the best S_DOPE and S_SAXS are indicated in red and green, respectively. E: S_DOPE of the top 10% models plotted against their Cα RMSD with respect to the crystallographic structure. F: Combined score S of the top 10% models plotted against their Cα RMSD. G: The XI configuration of subunit comparative models based on 4xim (67% sequence identity); left, best S_DOPE; right, best S_SAXS. H: The XI configuration of subunit comparative models based on 1a0dA (27% sequence identity); left, best S_DOPE; right, best S_SAXS.

Fig. 6

Scoring versus sampling. A: The minimum score S_min (left), the corresponding Cα RMSD (middle), and the minimum Cα RMSD for all models (RMSD_min; right) are plotted as a function of the number of independent optimizations for the benchmark case 1ha0. For comparison, the values for the best scores achieved for local sampling in the vicinity of the RBNC state (RBNC refined) and for local optimization of the native bodies in the vicinity of the native configuration are also shown. B: Dimeric complex 1ibr. C: Three-domain protein 1ko9.