Small‐Angle Scattering of Neutrons and X‐Rays

Abstract

The small‐angle scattering of X‐rays or neutrons can be used to study the structures of biological macromolecules in solution. In addition, where the components of biomolecular complexes have different scattering densities, scattering data not only can provide structural information on the whole complex but also on the individual components and their relative dispositions. One can therefore study protein–protein and protein–polynucleotide (DNA or RNA) interactions within functional complexes. Although solution scattering data are inherently of low resolution and limited in information content owing to the random orientations of the scattering molecules, recent applications that incorporate information from complementary methods have facilitated the interpretation of scattering data in terms of detailed structural models. Advances in computational methods and user interfaces have enabled nonspecialists to use the technique to reveal important insights into biomolecular systems. The increasing availability of synchrotron‐based facilities for small‐angle scattering has also advanced studies of time‐dependent changes in protein structure and the development of high‐throughput approaches.

Key Concepts

  • Small‐angle scattering provides information on the shapes of biological macromolecules in solution.
  • Small‐angle solution scattering data complements the higher resolution structural data from crystallography and NMR spectroscopy.
  • Small‐angle scattering improves NMR solution structure determination; either by providing long‐range distance information that complements the predominantly short‐range distance information from nuclear Overhauser effects (NOEs) or by providing translational constraints that complement the orientational information from residual dipolar couplings (RDCs).
  • Solution scattering data complements high‐resolution crystallography by providing insights into the range of conformations that are adopted by the molecules in solution, for example, hinge motions, multiple conformations and conformational flexibility.
  • Synchrotron X‐ray sources enable time‐resolved solution scattering experiments to probe conformational dynamics in proteins, DNA and RNA.
  • Structural characterisation by small‐angle scattering requires highly pure, monodisperse identical particles in solution.
  • Proteins and polynucleotides (DNA or RNA) naturally have different scattering densities for X‐rays and neutrons and can therefore be distinguished in a scattering experiment.
  • Neutron contrast variation experiments on biomolecular complexes can reveal the structures and disposition of components having different neutron scattering densities.
  • Deuterium (2H) substitution for hydrogen (1H) is used to change the neutron scattering density of a protein so that it can be distinguished from nondeuterated protein(s) in neutron scattering experiments that involve protein complexes.
  • Neutron scattering contrast variation experiments involve the systematic variation of the solvent deuteration in order to change the scattering density difference (or contrast) between individual biomolecules or between an individual biomolecule and its solvent.

Keywords: biomolecular interactions; protein–protein complex; protein‐DNA structure; protein‐RNA structure; protein structure; polynucleotide structure; solution scattering; SAXS; SANS; contrast variation

Figure 1. Geometry of the scattering experiment. The scattering vector is the difference between the incident wave vector and scattered wave vector . The scattering of the incident beam is elastic and therefore the amplitudes of and are the same and equal to 2π/λ, where λ is the wavelength of both the incident and scattered beams. The amplitude of is equal to , where 2θ is the scattering angle.
Figure 2. Calculated P(r) profiles for differently shaped scattering particles. In the case of the single‐lobed objects, the P(r) functions for the sphere and prolate ellipsoid show how the asymmetry in P(r) increases as the object becomes more asymmetric. For the two‐lobed objects, the P(r) functions are very sensitive to the relative dispositions of the two identically shaped lobes. The peak at the shorter r values is dominated by distances between atoms within a single lobe, whereas the peak or shoulder at longer r values is dominated by distances between atoms in different lobes.
Figure 3. Average scattering densities for biological molecules as a function of the fraction of D2O in the solvent. The slope on the lines arises from the exchange of labile hydrogens.
Figure 4. (a) X‐ray and neutron scattering data for the KinA–Sda complex in which the Sda is deuterated. Each scattering profile is labelled to indicate that it is either X‐ray data, or in the case of the neutron data, the percentage deuteration of the solvent. The data are in black and the model fits based on the model to the right are red lines. (b) The atomic model of KinA–Sda that was optimised against the scattering data. The colour scheme indicates the fact that KinA (cyan) is a dimer (monomers coloured light and dark) that binds two Sda molecules (orange and yellow). KinA is an auto‐kinase that phosphorylates a histidine, coloured red, on the KinA dimerisation domains.
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Further Reading

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Nadvi, Naveed A, Chow, John YH, and Trewhella, Jill(Feb 2015) Small‐Angle Scattering of Neutrons and X‐Rays. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003047.pub3]