Interpretation of small-angle scattering using models

Engelman, D. M.; Moore, P. B.

doi:10.1107/97809553602060000701

International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

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International Tables for Crystallography (2006). Vol. F. ch. 19.4, p. 441 | 1 | 2 |

Section 19.4.3.6. Interpretation of small-angle scattering using models

D. M. Engelman^a ^* and P. B. Moore^b

^aDepartment of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520, USA, and ^bDepartments of Chemistry and Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520, USA
Correspondence e-mail: don@paradigm.csb.yale.edu

19.4.3.6. Interpretation of small-angle scattering using models

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There have been many attempts to extract more information from solution-scattering experiments than the radius of gyration and forward scattering, including the distance-measuring strategies discussed below. These attempts are of two kinds: testing models and creating models. Each of these must be cast in the context of the intrinsic information content of a scattering measurement, which can be expressed in terms of the number of independent parameters, n, that can be uniquely extracted from a data set (Moore, 1980). $[n = Q_{\max}d_{\max} / \pi, \eqno(19.4.3.10)]$ where $[Q_{\max}]$ is the largest Q at which statistically significant data are measured and $[d_{\max}]$ is the largest dimension of the particle. A further requirement, normally met in small-angle scattering, is that $[Q_{\min}d_{\max} / \pi \lt 1]$ .

The information content is a subtle factor in the first class of modelling, where models are tested for agreement with scattering data. Excellent programs have been written for generating predicted scattering curves from atomic coordinates and have been used to explore perturbations between crystal structures and solution organization. A fine example is the work on ATCase by Svergun, Barberato et al. (1997); the article also contains references to the programs used.

A more challenging task is to work in the other direction, extracting structural information directly from a scattering curve. Considerable effort has been devoted to work in this area, using approaches based on spherical harmonics, sometimes using sets of spheres to represent structure, and occasionally integrating information from electron microscopy (Svergun, 1994; Svergun, Burkhardt et al., 1997).

References

Moore, P. B. (1980). Small-angle scattering. Information content and error analysis. J. Appl. Cryst. 13, 168–175.Google Scholar

Svergun, D. I. (1994). Solution scattering from biopolymers: advanced contrast-variation data analysis. Acta Cryst. A50, 391–402.Google Scholar

Svergun, D. I., Barberato, C., Koch, M. H., Fetler, L. & Vachette, P. (1997). Large differences are observed between the crystal and solution quaternary structures of allosteric aspartate transcarbamylase in the R state. Proteins, 27, 110–117.Google Scholar

Svergun, D. I., Burkhardt, N., Pedersen, J. S., Koch, M. H., Volkov, V. V., Kozin, M. B., Meerwink, W., Stuhrmann, H. B., Diedrich, G. & Nierhaus, K. H. (1997). Solution scattering structural analysis of the 70S Escherichia coli ribosome by contrast variation. II. A model of the ribosome and its RNA at 3.5 nm resolution. J. Mol. Biol. 271, 602–618.Google Scholar

International Tables for Crystallography (2006). Vol. F. ch. 19.4, p. 441