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 Å), 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 complex1. 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 Å 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 Rfree (the free R-factor) determines the optimum deformation and influence of the homology model. For test cases at 3.5–5 Å 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-diffraction2 as well as data from new X-ray light sources3. Use of homology information is not restricted to X-ray crystallography and cryo-electron microscopy: as optical imaging advances to subnanometre resolution4,5, it can use similar tools.
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We thank P. D. Adams, S. C. Harrison and T. D. Fenn for discussions. We also thank the National Science Foundation for computing resources (CNS-0619926), the National Institutes of Health for both Roadmap Grant PN2 (EY016525) and grant GM63718 to M.L., and the Deutsche Forschungsgemeinschaft (DFG) for support for G.F.S.
Author Contributions G.F.S. developed the computational algorithms, and G.F.S. and A.T.B. designed the computational experiments and performed all calculations and analysis. All authors wrote the paper.
The authors declare no competing financial interests.
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Schröder, G., Levitt, M. & Brunger, A. Super-resolution biomolecular crystallography with low-resolution data. Nature 464, 1218–1222 (2010). https://doi.org/10.1038/nature08892
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