Super-resolution biomolecular crystallography with low-resolution data

Article metrics

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 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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Results for the penicillopepsin test calculations using the MLHL target function (experimental phase information).
Figure 2: Re-refinement of 19 low-resolution PDB structures.
Figure 3: Electron density map improvement upon DEN refinement for three structures, PDB 3DMK, 1YE1 and 1XXI.
Figure 4: DEN provides information for degrees of freedom that are weakly defined by the experimental diffraction data.

References

  1. 1

    Davies, J. M., Brunger, A. T. & Weis, W. I. Improved structures of full-length p97, an AAA ATPase: implications for mechanisms of nucleotide-dependent conformational change. Structure 16, 715–726 (2008)

  2. 2

    Sanishvili, R. et al. A 7 μm mini-beam improves diffraction data from small or imperfect crystals of macromolecules. Acta Crystallogr. D 64, 425–435 (2008)

  3. 3

    Raines, K. S. et al. Three-dimensional structure determination from a single view. Nature 463, 214–217 (2010)

  4. 4

    Moerner, W. E. New directions in single-molecule imaging and analysis. Proc. Natl Acad. Sci. USA 104, 12596–12602 (2007)

  5. 5

    Pertsinidis, A., Zhang, Y. & Chu, S. Localization, registration and distance measurements between single-molecule fluorescent probes with sub-nanometer precision and accuracy. Nature (submitted)

  6. 6

    Karle, J. & Hauptman, H. A theory of phase determination for the four types of non-centrosymmetric space groups 1P222, 2P22, 3P(1)2, 3P(2)2. Acta Crystallogr. 9, 635–651 (1956)

  7. 7

    Luzzati, V. Traitement statistique des erreurs dans la determination des structures cristallines. Acta Crystallogr. 5, 802–809 (1952)

  8. 8

    Hendrickson, W. A. & Konnert, J. H. A restrained-parameter thermal-factor refinement procedure. Acta Crystallogr. A 36, 344–350 (1980)

  9. 9

    Jack, A. & Levitt, M. Refinement of large structures by simultaneous minimization of energy and R factor. Acta Crystallogr. A 34, 931–935 (1987)

  10. 10

    Diamond, R. On the use of normal modes in the thermal parameter refinement: theory and application to the bovine pancreatic trypsin inhibitor. Acta Crystallogr. A 46, 425–435 (1990)

  11. 11

    Levitt, M., Sander, C. & Stern, P. S. Protein normal-mode dynamics: trypsin inhibitor, crambin, ribonuclease and lysozyme. J. Mol. Biol. 181, 423–447 (1985)

  12. 12

    Delarue, M. & Dumas, P. On the use of low-frequency normal modes to enforce collective movements in refining macromolecular structural models. Proc. Natl Acad. Sci. USA 101, 6957–6962 (2004)

  13. 13

    Tama, F., Miyashita, O. & Brooks, C. L. Normal mode based flexible fitting of high-resolution structure into low-resolution experimental data from cryo-EM. J. Struct. Biol. 147, 315–326 (2004)

  14. 14

    Schröder, G. F., Brunger, A. T. & Levitt, M. Combining efficient conformational sampling with a deformable elastic network model facilitates structure refinement at low resolution. Structure 15, 1630–1641 (2007)

  15. 15

    James, M. N. & Sielecki, A. R. Structure and refinement of penicillopepsin at 1.8 A resolution. J. Mol. Biol. 163, 299–361 (1983)

  16. 16

    Zemla, A. LGA: a method for finding 3D similarities in protein structures. Nucleic Acids Res. 31, 3370–3374 (2003)

  17. 17

    Chen, B. et al. Structure of an unliganded simian immunodeficiency virus gp120 core. Nature 433, 834–841 (2005)

  18. 18

    Zhou, T. et al. Structural definition of a conserved neutralization epitope on HIV-1 gp120. Nature 445, 732–737 (2007)

  19. 19

    Qian, B. et al. High-resolution structure prediction and the crystallographic phase problem. Nature 450, 259–264 (2007)

  20. 20

    Engh, R. & Huber, R. Accurate bond and angle parameters for X-ray protein structure refinement. Acta Crystallogr. A 47, 392–400 (1991)

  21. 21

    Bricogne, G. & Gilmore, C. J. A multisolution method of phase determination by combined maximization of entropy and likelihood. I. Theory, algorithms and strategy. Acta Crystallogr. A 46, 284–297 (1990)

  22. 22

    Pannu, S. N. & Read, R. J. Improved structure refinement through maximum likelihood. Acta Crystallogr. A 52, 659–668 (1996)

  23. 23

    Pannu, N. S., Murshudov, G. N., Dodson, E. J. & Read, R. J. Incorporation of prior phase information strengthens maximum-likelihood structure refinement. Acta Crystallogr. D 54, 1285–1294 (1998)

  24. 24

    Levitt, M. & Lifson, S. Refinement of protein conformations using a macromolecular energy minimization procedure. J. Mol. Biol. 46, 269–279 (1969)

  25. 25

    Rice, L. M. & Brunger, A. T. Torsion angle dynamics: reduced variable conformational sampling enhances crystallographic structure refinement. Proteins 19, 277–290 (1994)

  26. 26

    Levitt, M. Accurate modeling of protein conformation by automatic segment matching. J. Mol. Biol. 226, 507–533 (1992)

  27. 27

    Sali, A. & Blundell, T. L. Comparative protein modelling by satisfaction of spatial restraints. J. Mol. Biol. 234, 779–815 (1993)

  28. 28

    Sussman, J. L., Holbrook, S. R., Church, G. M. & Kim, S. H. A structure-factor least squares refinement procedure for macromolecular structures using constrained and restrained parameters. Acta Crystallogr. A 33, 800–804 (1977)

  29. 29

    Davis, I. W., Murray, L. W., Richardson, J. S. & Richardson, D. C. MOLPROBITY: structure validation and all-atom contact analysis for nucleic acids and their complexes. Nucleic Acids Res 32 (Web Server issue). W615–W619 (2004)

  30. 30

    Gibson, K. D. & Scheraga, H. A. Minimization of polypeptide energy. I. Preliminary structures of bovine pancreatic ribonuclease S-peptide. Proc. Natl Acad. Sci. USA 58, 420–427 (1967)

  31. 31

    Levitt, M. Protein folding by restrained energy minimization and molecular dynamics. J. Mol. Biol. 170, 723–764 (1983)

  32. 32

    Brunger, A. T. et al. Crystallography & NMR system: a new software suite for macromolecular structure determination. Acta Crystallogr. D 54, 905–921 (1998)

  33. 33

    Brunger, A. T. Crystallographic refinement by simulated annealing. Application to a 2.8 A resolution structure of aspartate aminotransferase. J. Mol. Biol. 203, 803–816 (1988)

  34. 34

    Brunger, A. T. Version 1.2 of the Crystallography and NMR system. Nature Protocols 2, 2728–2733 (2007)

  35. 35

    Pearl, L. & Blundell, T. The active site of aspartic proteinases. FEBS Lett. 174, 96–101 (1984)

  36. 36

    Adams, P. D., Pannu, N. S., Read, R. J. & Brunger, A. T. Extending the limits of molecular replacement through combined simulated annealing and maximum-likelihood refinement. Acta Crystallogr. D 55, 181–190 (1999)

  37. 37

    Lipman, D. J. & Pearson, W. R. Rapid and sensitive protein similarity searches. Science 227, 1435–1441 (1985)

  38. 38

    Zhang, Y. & Skolnick, J. TM-align: a protein structure alignment algorithm based on the TM-score. Nucleic Acids Res. 33, 2302–2309 (2005)

  39. 39

    DeLano, W. The Pymol Molecular Graphics System. (DeLano Scientific, 2002)

Download references

Acknowledgements

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.

Author information

Correspondence to Gunnar F. Schröder or Axel T. Brunger.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Tables 1- 4, Supplementary Figures 1-5 with legends and Supplementary References. (PDF 2114 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Schröder, G., Levitt, M. & Brunger, A. Super-resolution biomolecular crystallography with low-resolution data. Nature 464, 1218–1222 (2010) doi:10.1038/nature08892

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.