Modern small-angle scattering (SAS) experiments with X-rays or neutrons provide a comprehensive, resolution-limited observation of the thermodynamic state. However, methods for evaluating mass and validating SAS-based models and resolution have been inadequate. Here we define the volume of correlation, Vc, a SAS invariant derived from the scattered intensities that is specific to the structural state of the particle, but independent of concentration and the requirements of a compact, folded particle. We show that Vc defines a ratio, QR, that determines the molecular mass of proteins or RNA ranging from 10 to 1,000 kilodaltons. Furthermore, we propose a statistically robust method for assessing model-data agreements (χ2free) akin to cross-validation. Our approach prevents over-fitting of the SAS data and can be used with a newly defined metric, RSAS, for quantitative evaluation of resolution. Together, these metrics (Vc, QR, χ2free and RSAS) provide analytical tools for unbiased and accurate macromolecular structural characterizations in solution.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Harrison, S. C. Comments on the NIGMS PSI. Structure 15, 1344–1346 (2007)
Hura, G. L. et al. Robust, high-throughput solution structural analyses by small angle X-ray scattering (SAXS). Nature Methods 6, 606–612 (2009)
Rambo, R. P. & Tainer, J. A. Bridging the solution divide: comprehensive structural analyses of dynamic RNA, DNA, and protein assemblies by small-angle X-ray scattering. Curr. Opin. Struct. Biol. 20, 128–137 (2010)
Sosnick, T. R. & Woodson, S. A. New era of molecular structure and dynamics from solution scattering experiments. Biopolymers 95, 503–504 (2011)
Glatter, O. & Kratky, O. Small Angle X-Ray Scattering (Academic, 1982)
Putnam, C. D., Hammel, M., Hura, G. L. & Tainer, J. A. X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution. Q. Rev. Biophys. 40, 191–285 (2007)
Jacques, D. A. & Trewhella, J. Small-angle scattering for structural biology—expanding the frontier while avoiding the pitfalls. Protein Sci. 19, 642–657 (2010)
Bai, Y., Das, R., Millett, I. S., Herschlag, D. & Doniach, S. Probing counterion modulated repulsion and attraction between nucleic acid duplexes in solution. Proc. Natl Acad. Sci. USA 102, 1035–1040 (2005)
Moore, P. Small-angle scattering. Information content and error analysis. J. Appl. Crystallogr. 13, 168–175 (1980)
Rambo, R. P. & Tainer, J. A. Improving small-angle X-ray scattering data for structural analyses of the RNA world. RNA 16, 638–646 (2010)
Nishimura, N. et al. Structural mechanism of abscisic acid binding and signaling by dimeric PYR1. Science 326, 1373–1379 (2009)
Santiago, J. et al. Modulation of drought resistance by the abscisic acid receptor PYL5 through inhibition of clade A PP2Cs. Plant J. 60, 575–588 (2009)
Stoddard, C. D. et al. Free state conformational sampling of the SAM-I riboswitch aptamer domain. Structure 18, 787–797 (2010)
Hammond, J. A., Rambo, R. P. & Kieft, J. S. Multi-domain packing in the aminoacylatable 3′ end of a plant viral RNA. J. Mol. Biol. 399, 450–463 (2010)
Orthaber, D., Bergmann, A. & Glatter, O. SAXS experiments on absolute scale with Kratky systems using water as a secondary standard. J. Appl. Crystallogr. 33, 218–225 (2000)
Mylonas, E. & Svergun, D. I. Accuracy of molecular mass determination of proteins in solution by small-angle X-ray scattering. J. Appl. Crystallogr. 40, s245–s249 (2007)
Fischer, H., de Oliveira Neto, M., Napolitano, H. B., Polikarpov, I. & Craievich, A. F. Determination of the molecular weight of proteins in solution from a single small-angle X-ray scattering measurement on a relative scale. J. Appl. Crystallogr. 43, 101–109 (2010)
Rambo, R. P. & Tainer, J. A. Characterizing flexible and intrinsically unstructured biological macromolecules by SAS using the Porod-Debye law. Biopolymers 95, 559–571 (2011)
Berman, H. M. et al. The Protein Data Bank. Nucleic Acids Res. 28, 235–242 (2000)
Wyatt, P. J. Light scattering and the absolute characterization of macromolecules. Anal. Chim. Acta 272, 1–40 (1993)
Svergun, D., Barberato, C. & Koch, M. H. J. CRYSOL – a program to evaluate X-ray solution scattering of biological macromolecules from atomic coordinates. J. Appl. Crystallogr. 28, 768–773 (1995)
Schneidman-Duhovny, D., Hammel, M. & Sali, A. FoXS: a web server for rapid computation and fitting of SAXS profiles. Nucleic Acids Res. 38, W540–W544 (2010)
Brünger, A. T. Free R value: a novel statistical quantity for assessing the accuracy of crystal structures. Nature 355, 472–475 (1992)
Brünger, A. T., Clore, G. M., Gronenborn, A. M., Saffrich, R. & Nilges, M. Assessing the quality of solution nuclear magnetic resonance structures by complete cross-validation. Science 261, 328–331 (1993)
Rousseeuw, P. J. & Leroy, A. M. Robust Regression and Outlier Detection (Wiley, 1987)
Jie, Y., Qi, T., Amores, J. & Sebe, N. Toward Robust Distance Metric Analysis for Similarity Estimation (IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2006)
Karplus, P. A. & Diederichs, K. Linking crystallographic model and data quality. Science 336, 1030–1033 (2012)
Brünger, A. T. et al. Crystallography & NMR system: a new software suite for macromolecular structure determination. Acta Crystallogr. D 54, 905–921 (1998)
de Groot, B. L. et al. Prediction of protein conformational freedom from distance constraints. Proteins 29, 240–251 (1997)
Rambo, R. P. & Doudna, J. A. Assembly of an active group II intron–maturase complex by protein dimerization. Biochemistry 43, 6486–6497 (2004)
Keel, A. Y., Jha, B. K. & Kieft, J. S. Structural architecture of an RNA that competitively inhibits RNase L. RNA 18, 88–89 (2012)
Fulle, S. & Gohlke, H. Analyzing the flexibility of RNA structures by constraint counting. Biophys. J. 94, 4202–4219 (2008)
We thank G. L. Hura, M. Hammel, R. T. Batey, J. Tanamachi and the staff of SIBYLS Beamline 12.3.1 at the Advanced Light Source for discussions and P. Adams for suggestions regarding simulations with CNS. We thank E. Rambo, G. Williams and E. D. Getzoff for manuscript comments. This work is supported in part by funding to foster collaboration with Bruker and the Berkeley Laboratory Directed Research and Development (LDRD) program provided by the Director, Office of Science, US Department of Energy on Novel Technology for Structural Biology. The SIBYLS Beamline 12.3.1 facility and team at the Advanced Light Source is supported by United States Department of Energy program Integrated Diffraction Analysis Technologies (DEAC02-05CH11231) and by National Institutes of Health grant R01GM105404.
The authors declare no competing financial interests.
About this article
Cite this article
Rambo, R., Tainer, J. Accurate assessment of mass, models and resolution by small-angle scattering. Nature 496, 477–481 (2013). https://doi.org/10.1038/nature12070
Inter-α-inhibitor heavy chain-1 has an integrin-like 3D structure mediating immune regulatory activities and matrix stabilization during ovulation
Journal of Biological Chemistry (2020)
Obtaining Tertiary Protein Structures by the ab Initio Interpretation of Small Angle X-ray Scattering Data
Journal of Chemical Theory and Computation (2020)
Improving data quality and expanding BioSAXS experiments to low-molecular-weight and low-concentration protein samples
Acta Crystallographica Section D Structural Biology (2020)
Nucleic Acids Research (2020)
Structural insights into conformational switching in latency-associated peptide between transforming growth factor β-1 bound and unbound states