Small-angle-scattering-data treatment by the regularization method

The structure of macromolecules can be studied by small-angle scattering (SAS), but as this is an ill-posed problem, prior knowledge about the sample must be included in the analysis. Regularization methods are used for this purpose, as already implemented in indirect Fourier transformation and bead-modeling-based analysis of SAS data, but not yet in the analysis of SAS data with analytical form factors. To fill this gap, a Bayesian regularization method was implemented, where the prior information was quantified as probability distributions for the model parameters and included via a functional S. The quantity Q = χ2 + αS was then minimized and the value of the regularization parameter α determined by probability maximization. The method was tested on small-angle X-ray scattering data from a sample of nanodiscs and a sample of micelles. The parameters refined with the Bayesian regularization method were closer to the prior values as compared with conventional χ2 minimization. Moreover, the errors on the refined parameters were generally smaller, owing to the inclusion of prior information. The Bayesian method stabilized the refined values of the fitted model upon addition of noise and can thus be used to retrieve information from data with low signal-to-noise ratio without risk of overfitting. Finally, the method provides a measure for the information content in data, N g, which represents the effective number of retrievable parameters, taking into account the imposed prior knowledge as well as the noise level in data.

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A direct indirect method of small-angle scattering data treatment

Journal of Applied Crystallography ◽

10.1107/s0021889892011828 ◽

1993 ◽

Vol 26 (2) ◽

pp. 258-267 ◽

Cited By ~ 82

Author(s):

D. I. Svergun

Keyword(s):

Small Angle ◽

Indirect Method ◽

Small Angle Scattering ◽

Scattering Data ◽

Data Treatment ◽

Angle Scattering

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Propagating errors in small-angle scattering data treatment

Journal of Applied Crystallography ◽

10.1107/s0021889893008337 ◽

1994 ◽

Vol 27 (3) ◽

pp. 241-248 ◽

Cited By ~ 21

Author(s):

D. I. Svergun ◽

J. S. Pedersen

Keyword(s):

Small Angle ◽

Small Angle Scattering ◽

Scattering Data ◽

Data Treatment ◽

Angle Scattering

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2017 publication guidelines for structural modelling of small-angle scattering data from biomolecules in solution: an update

Acta Crystallographica Section D Structural Biology ◽

10.1107/s2059798317011597 ◽

2017 ◽

Vol 73 (9) ◽

pp. 710-728 ◽

Cited By ~ 107

Author(s):

Jill Trewhella ◽

Anthony P. Duff ◽

Dominique Durand ◽

Frank Gabel ◽

J. Mitchell Guss ◽

...

Keyword(s):

Small Angle ◽

Task Force ◽

Data Bank ◽

Small Angle Scattering ◽

Scattering Data ◽

Quality Data ◽

Angle Scattering ◽

Publication Guidelines ◽

Guidelines And Recommendations

In 2012, preliminary guidelines were published addressing sample quality, data acquisition and reduction, presentation of scattering data and validation, and modelling for biomolecular small-angle scattering (SAS) experiments. Biomolecular SAS has since continued to grow and authors have increasingly adopted the preliminary guidelines. In parallel, integrative/hybrid determination of biomolecular structures is a rapidly growing field that is expanding the scope of structural biology. For SAS to contribute maximally to this field, it is essential to ensure open access to the information required for evaluation of the quality of SAS samples and data, as well as the validity of SAS-based structural models. To this end, the preliminary guidelines for data presentation in a publication are reviewed and updated, and the deposition of data and associated models in a public archive is recommended. These guidelines and recommendations have been prepared in consultation with the members of the International Union of Crystallography (IUCr) Small-Angle Scattering and Journals Commissions, the Worldwide Protein Data Bank (wwPDB) Small-Angle Scattering Validation Task Force and additional experts in the field.

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