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

International Tables for Crystallography (2006). Vol. F. ch. 19.4, p. 438   | 1 | 2 |

Section 19.4.1. Introduction

D. M. Engelmana* and P. B. Mooreb

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

19.4.1. Introduction

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Diffuse scatter results when X-ray and neutron beams pass through gases and liquids. It is caused by local inhomogeneities, which all fluids invariably contain, at least transiently, and information about them can be obtained by analysis of the scatter they cause. This diffuse scatter is rotationally symmetric about the direction defined by the incident beam because, on average, gases and liquids are isotropic, and it does depend on scattering angle, 2θ. The intensity of the diffuse X-ray scatter of water, for example, is small at small 2θ, and it reaches a maximum at equivalent Bragg spacings equal to the reciprocal of the average oxygen–oxygen distance. In addition to a `water ring' at high scattering angles, the diffuse scatter of macromolecular solutions includes a peak at [2\theta = 0], due to the presence of the macromolecules themselves. If ångstrom-wavelength radiation is used, the central macromolecular peak is entirely contained in the region where [\sin(2\theta ) \simeq 2\theta]. This is the region examined in small-angle scattering experiments.

Several properties of macromolecules can be determined by analysing their small-angle solution scattering, among them molecular weight, radius of gyration and maximum linear dimension. Approximate shapes can sometimes be obtained, and if a macromolecule is a complex of different chemical species, information about the distribution of its components may emerge. Hydration and conformational changes are also studied this way.

The molecular properties that can be investigated by small-angle scattering are the same for thermal neutrons and X-rays, but the advantages of neutrons are so great that if the equipment required were not so expensive, not many would do small-angle X-ray scattering (SAXS). They are all manifestations of the differences between the ways in which neutrons and X-ray photons interact with matter. For example, thermal neutrons have very low kinetic energies ([\simeq kT]), and, consequently, the energy they deposit in a sample when they are scattered inelastically is negligible. X-ray photons have large energies, and when they are absorbed or scattered inelastically, damaging amounts of energy are deposited. Thus, samples are `safer' in neutron beams than they are in X-ray beams.

The cross section for X-ray absorption rises so fast with increasing wavelength that it is impractical to do solution-scattering experiments using X-rays with wavelengths much greater than 1.5 Å. The combination of this and the fact that X-ray beams scatter strongly off the edges of optical-track components makes it difficult to build small-angle X-ray spectrometers that measure diffuse scatter at equivalent reciprocal spacings of 0.001 Å−1 or less. The cross section for thermal neutron absorption is small and nearly independent of wavelength over the range 1–10 Å. Furthermore, parasitic neutron scatter is easy to control. Thus, it is comparatively straightforward to build small-angle neutron scattering (SANS) spectrometers that measure diffuse scatter at reciprocal spacings considerably less than 0.001 Å−1.

Even more important to those interested in SANS are the vistas opened up by the huge difference in scattering length that exists between 1H and 2H (henceforth termed H and D), to which we will return below. In brief, the scatter of macromolecular solutions can be significantly altered by replacing some or all of the H atoms with D atoms. This control greatly extends the range of problems that can be addressed by SANS, and the chemical `cost' is minimal. A perdeuterated molecule is almost identical to its protonated counterpart. The X-ray scattering of substances depends on the number of electrons they contain, and when this number is changed, chemical properties change also.

Relative to SAXS, the sole disadvantage of SANS is a phenomenon called incoherent scatter, which is a comparatively minor aspect of X-ray work. Neutrons are scattered primarily by atomic nuclei, and if a nucleus has spin, its scattering length depends on the orientation of its spin relative to that of each neutron with which it interacts. Since nuclear spins are usually unoriented in SANS samples, this spin-orientation dependence leads to a random atom-to-atom variation in scattering length. Coherent scatter, on which all diffraction effects depend, is determined by average scattering-length values. The scatter due to fluctuations about the average is incoherent, and in the low-angle region incoherent scatter manifests itself as a featureless background that is independent of scattering angle. The cross section for incoherent scattering is very large for H atoms, and since both water and biological macromolecules contain large proportions of H atoms, incoherent scatter is often a dominant source of background.

Some useful general references for small-angle scattering in general and neutron scattering in particular are Bacon (1975[link]), Glatter & Kratky (1982[link]) and Guinier (1955[link], 1962[link]).

References

First citation Bacon, G. E. (1975). Neutron diffraction. Oxford University Press.Google Scholar
First citation Glatter, O. & Kratky, O. (1982). Small angle X-ray scattering. London: Academic Press.Google Scholar
First citation Guinier, A. (1955). Small angle scattering of X-rays. New York: John Wiley and Sons. Google Scholar
First citation Guinier, A. (1962). Small angle X-ray scattering. In International tables for X-ray crystallography, Vol. III. Physical and chemical tables, pp. 324–329. Birmingham: Kynoch Press. (Present distributor Kluwer Academic Publishers, Dordrecht).Google Scholar








































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