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Chapter G2 - Small-angle scattering

from Part G - X-ray and neutron diffraction

Published online by Cambridge University Press:  05 November 2012

Igor N. Serdyuk ,
Nathan R. Zaccai  and
Joseph Zaccai
Igor N. Serdyuk
Affiliation:
Institute of Protein Research, Moscow
Nathan R. Zaccai
Affiliation:
University of Bristol
Joseph Zaccai
Affiliation:
Institut de Biologie Structurale, Grenoble
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Summary

Theory of small-angle scattering from particles in solution

Small-angle scattering (SAS) is a very useful method in biochemistry, providing information on molecular masses, shapes and interactions in solution (see Comment G2.1).

Dilute solutions of identical particles

In order to have an observable signal in X-ray or neutron SAS a solution of the order of 100 μl containing a few milligrams per millilitre of macromolecule is required – corresponding to about 1015 particles for a 50 kDa protein at 1 mg ml−1 (we note that 1 mg ml−1, the usual unit in biochemistry is in fact equal to 1 g l−1, the unit more conveniently used in equations).

We first consider solution conditions such that the particles do not influence each other, i.e. the position and orientation of each particle is totally independent of that of the others. This is the infinite dilution condition, for which we say there is no interparticle interference. In practice, it is achieved at different, low, concentrations for different macromolecules and solvents. For example, the condition may well be satisfied for a given protein at a few milligrams per millilitre, in a neutral pH buffer, but tRNA molecules, which are highly charged at pH 7 in low-salt buffer, interact with each other even at these concentrations, and it might not be possible to reach the infinite dilution condition without increasing the solvent salt concentration.

Type
Chapter
Information
Methods in Molecular Biophysics
Structure, Dynamics, Function
 , pp. 794 - 837
Publisher: Cambridge University Press
Print publication year: 2007

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References

Svergun, D. I. (1999). Restoring low resolution structure of biological macromolecules from solution scattering using simulated annealing. Biophys. J., 76, 2879–2886.CrossRefGoogle ScholarPubMed
Walther, D., Cohen, F. E., and Doniach, S. (2000). Reconstruction of low-resolution three dimensional density maps from one dimensional small-angle X-ray solution scattering data for biomolecules. J. Appl. Crystallog., 33, 350–363.CrossRefGoogle Scholar
Svergun, D. I. (2000). Advanced solution scattering data analysis methods and their applications. J. Appl. Crystallog., 33, 530–534.CrossRefGoogle Scholar
Svergun, D. I., Malfois, M., Koch, M. H. J., Wigneshweraraj, S. R., and Buck, M. (2000). Low-resolution structure of the sigma54 transcription factor revealed by X-ray solution scattering. J. Biol. Chem., 275, 4210–4214.CrossRefGoogle ScholarPubMed
The program DAMMIN (Svergun, 2000; Svergun et al., 2000), which takes a simulated annealing approach, also allows the input of information about the point symmetry of the particle.
Chacón, P., Moran, F., Díaz, J. F., Pantos, E., and Andreu, J. M. (1998). Low-resolution structures of proteins in solution retrieved from X-ray scattering with a genetic algorithm. Biophys. J., 74, 2760–2775.CrossRefGoogle ScholarPubMed
Goldberg, D. E. (1989). Genetics Algorithms in Search, Optimisation and Machine Learning. San Mateo, CA: Addison-Wesley.Google Scholar
Chacón, P., Díaz, J. F., Morán, F., and Andreu, J. M. (2000). Reconstruction of protein form with X-ray solution scattering and a genetic algorithm. J. Mol. Biol., 299, 1289–1302.CrossRefGoogle Scholar
The genetics approach is implemented in the program DALALGA (Chacón et al., 2000).
Svergun, D. I. (2000). Advanced solution scattering data analysis methods and applications. J. Appl. Crystallogr., 33, 530–534.CrossRefGoogle Scholar
Zaccai, G., and Jacrot, B. (1983). Small angle neutron scattering. Ann. Rev. Biophys. Bioeng., 12, 139–157.CrossRefGoogle ScholarPubMed
Glatter, O., and Kratky, O. (eds.) (1982). Small Angle Scattering. London: Academic Press.Google Scholar

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