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Setting New Standards in SAS

SBKB [doi:10.1038/sbkb.2012.150]
Technical Highlight - July 2013
Short description: New approaches for data analysis boost confidence in SAS models.

In SAXS, incident X-rays are scattered by a sample of randomly oriented particles scatters onto a 2-dimensional detector. The observed intensities I(q) produce the SAXS curve (blue, left). Rambo and Tainer show that multiplying I(q) by the scattering vector q, plotted over q, yields the total scattered intensity plot (purple, right), which is the Fourier representation of the SAXS curve and shows convergence to a constant value for both folded and flexible particles. 1

Small-angle scattering (SAS) is an increasingly popular biophysical technique for obtaining thermodynamic and structural information about macromolecules in solution. In a typical experiment, SAS with X-rays (SAXS) or neutrons (SANS) scattered from a highly purified biological sample are analyzed to reveal structural details such as particle size and mass distribution. Importantly, SAS does not rely on the signal-amplifying effects of a crystal lattice and can be performed at very high throughput relative to cryo-electron microscopy, NMR and X-ray crystallography. SAS often serves as a powerful complement to other techniques; for example, a SAS-derived molecular envelope can be used to determine whether a crystallographically-observed conformation also exists in solution.

Unfortunately, the noisy, one-dimensional nature of SAS data makes them highly sensitive to subtle perturbations in experimental conditions and susceptible to over-interpretation—small changes in scattering profiles can considerably impact the sizes and shapes of SAS-derived structural models. Unlike its higher-resolution cousins, SAS lacks widely accepted standards for data assessment, analysis and detection of over-fitting. Further, the SAS technique has limited utility in cases of conformational variability—if the sample is flexible, key parameters like molecular weight often cannot be ascertained.

Now, Rambo and Tainer (Lawrence Berkeley National Laboratory's Advanced Light Source) describe new approaches to address these fundamental SAS limitations. Specifically, they demonstrate that an empirically determined scattering ratio, termed the volume of correlation (Vc), greatly facilitates accurate measurement of particle mass, even in cases of conformational flexibility. The Vc parameter is also used to calculate a new residual, RSAS, describing the extent of agreement between a structural model and experimental data. Tapping principles from information theory, the authors also developed an approach for partitioning datasets to calculate a cross-validated statistical indicator of over-fitting. This metric, χ2free, serves a purpose analogous to the widely adopted Rfree statistic in crystallography. Models that yield minimal RSAS values while constrained by a fixed χ2free limit are unlikely to be over-fitted into noise, and adhering to a χ2free cutoff provides a meaningful, objective definition of SAS resolution limit.

These approaches extend the power of SAS to a wider range of macromolecules than previously possible and will add much-needed rigor to SAS data analysis and interpretation.

Mark A. Breidenbach

References

  1. R.P. Rambo and J.A. Tainer. Accurate assessment of mass, models and resolution by small-angle scattering.
    Nature. 496, 477-481 (2013). doi:10.1038/nature12070

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