Accurate assessment of mass, models and resolution by small-angle scattering

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Abstract

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.

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Figure 1: Concentration independence and conformational dependence of Vc.
Figure 2: Defining the power-law relationship between Vc, Rg and protein mass.
Figure 3: Power-law relationship between QR and particle mass allows direct mass determination.
Figure 4: Objective, quantitative evaluation of models using the least median χ2, that is, χ2free.

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Acknowledgements

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.

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R.P.R. developed the theory and computational algorithms with input from J.A.T. Both J.A.T. and R.P.R. designed the experiments and wrote the paper.

Corresponding authors

Correspondence to Robert P. Rambo or John A. Tainer.

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The authors declare no competing financial interests.

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This file contains Supplementary Text and Data, Supplementary Figures 1-11, Supplementary Tables 1-2 and Supplementary References. (PDF 2840 kb)

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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

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