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

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 (?(2)free) 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, ?(2)free and RSAS) provide analytical tools for unbiased and accurate macromolecular structural characterizations in solution.

SUBMITTER: Rambo RP

PROVIDER: S-EPMC3714217 | biostudies-literature | 2013 Apr

REPOSITORIES: biostudies-literature

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

Rambo Robert P RP Tainer John A JA

Nature 20130401 7446

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 part ...[more]

PMID: 23619693

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Project description:BackgroundGenome sequencing projects have expanded the gap between the amount of known protein sequences and structures. The limitations of current high resolution structure determination methods make it unlikely that this gap will disappear in the near future. Small angle X-ray scattering (SAXS) is an established low resolution method for routinely determining the structure of proteins in solution. The purpose of this study is to develop a method for the efficient calculation of accurate SAXS curves from coarse-grained protein models. Such a method can for example be used to construct a likelihood function, which is paramount for structure determination based on statistical inference.ResultsWe present a method for the efficient calculation of accurate SAXS curves based on the Debye formula and a set of scattering form factors for dummy atom representations of amino acids. Such a method avoids the computationally costly iteration over all atoms. We estimated the form factors using generated data from a set of high quality protein structures. No ad hoc scaling or correction factors are applied in the calculation of the curves. Two coarse-grained representations of protein structure were investigated; two scattering bodies per amino acid led to significantly better results than a single scattering body.ConclusionWe show that the obtained point estimates allow the calculation of accurate SAXS curves from coarse-grained protein models. The resulting curves are on par with the current state-of-the-art program CRYSOL, which requires full atomic detail. Our method was also comparable to CRYSOL in recognizing native structures among native-like decoys. As a proof-of-concept, we combined the coarse-grained Debye calculation with a previously described probabilistic model of protein structure, TorusDBN. This resulted in a significant improvement in the decoy recognition performance. In conclusion, the presented method shows great promise for use in statistical inference of protein structures from SAXS data.

Dataset Information

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

Publications

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

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