Small‐Angle Scattering of Neutrons and X‐Rays


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.


Augustus AM, Reardon PN, Heller WT and Spicer LD (2006) Structural basis for the differential regulation of DNA by the methionine repressor MetJ. Journal of Biological Chemistry 281: 34269–34276.

Bergman A, Fritz G and Glatter O (2000) Solving the generalized indirect Fourier transformation (GIFT) by Boltzmann simplex simulated annealing (BSSA). Journal of Applied Crystallography 33: 1212–1216.

Bick MJ, Lamour V, Rajashankar KR, et al. (2009) How to switch off a histidine kinase: crystal structure of Geobacillus stearothermophilus KinB with the inhibitor Sda. Journal of Molecular Biology 386: 163–177.

Cho HS, Schotte F, Dashdorj N, Kyndt J and Anfinrud P (2013) Probing anisotropic structure changes in proteins with picosecond time‐resolved small‐angle X‐ray scattering. The Journal of Physical Chemistry 17 (49): 15825–15832.

Cho HS, Dashdorj N, Schotte F, et al. (2010) Protein structural dynamics in solution unveiled via 100‐ps time‐resolved x‐ray scattering. Proceedings of the National Academy of Sciences USA 107 (16): 7281–7286.

Claridge JK, Headey SJ, Chow JY, et al. (2009) A picornaviral loop‐to‐loop replication complex. Journal of Structural Biology 166: 251–262.

Debye P, Anderson HR and Brumberger H (1957) Scattering by an inhomogeneous solid. 2. The correlation function and its application. Journal of Applied Physics 28: 679–683.

Eliezer D, Jennings PA, Wright PE, et al. (1995) The radius of gyration of an apomyoglobin folding intermediate. Science 270: 487–488.

Graceffa R, Nobrega RP, Barrea RA, et al. (2013) Sub‐millisecond time‐resolved SAXS using a continuous‐flow mixer and X‐ray microbeam. Journal of Synchrotron Radiation 20: 820–825.

Grant TD, Luft JR, Wolfley JR, et al. (2011) Small angle X‐ray scattering as a complementary tool for high‐throughput structural studies. Biopolymers 95 (8): 517–530.

Grishaev A, Tugarinov V, Kay LE, Trewhella J and Bax A (2008) Refined solution structure of the 82‐kDa enzyme malate synthase G from joint NMR and synchrotron SAXS restraints. Journal of Biomolecular NMR 40: 95–106.

Grishaev A, Wu J, Trewhella J and Bax A (2005) Refinement of multidomain protein structures by combination of solution small‐angle X‐ray scattering and NMR data. Journal of the American Chemical Society 127: 16621–16628.

Guinier A (1939) La diffraction des rayons X aux tres petits angles; application a l'etude de phenomenes ultramicroscopiques. Annals of Physics 12: 161–237.

Gupta K, Curtis JE, Krueger S, et al. (2012) Solution conformations of prototype foamy virus integrase and its stable synaptic complex with U5 viral DNA. Structure 20 (11): 1918–1928.

Heidorn DB and Trewhella J (1988) Comparison of the crystal and solution structures of calmodulin and troponin C. Biochemistry 27: 909–915.

Hura G, Menon A, Hammel M, et al. (2009) Robust, high‐throughput solution structural analyses by small angle X‐ray scattering (SAXS). Nature Methods 6: 606–612.

Jacques DA, Guss JM, Svergun DI and Trewhella J (2012) Publication guidelines for structural modelling of small‐angle scattering data from biomolecules in solution. Acta Crystallographica Section D 68: 620–626.

Jacques DA, Streamer M, Rowland SL, et al. (2009) Structure of the sporulation histidine kinase inhibitor Sda from Bacillus subtilis and insights into its solution state. Acta Crystallographica Section D 65: 574–581.

Kline SR (2006) Reduction and analysis of SANS and USANS data using IGOR Pro. Journal of Applied Crystallography 39: 895–900.

Kratky O (1982) Natural high polymers in dissolved and solid stateChapter 11. In: Glatter O and Kratky O, (eds). Small‐Angle X‐ray Scattering, pp 361–386. London: Academic Press.

Krueger J, Zhi G, Stull JT and Trewhella J (1998) Neutron scattering studies reveal further details of the Ca2+/calmodulin‐dependent activation mechanism of myosin light chain kinase. Biochemistry 37: 13997–14004.

Leiting B, Marsilio F and O'Connell JF (1998) Predictable deuteration of recombinant proteinsexpressed in Eschericia coli. Analytical Biochemistry 265: 351–355.

Orthaber D, Bergmann A and Glatter O (2000) SAXS experiments on absolution scale with Kratky systems using water as a secondary standard. Journal of Applied Crystallography 33: 218–235.

Ortore MG, Spinozzi F, Vilasi S, et al. (2011) Time‐resolved small‐angle x‐ray scattering study of the early stage of amyloid formation of an apomyoglobin mutant. Physical Review E statistical, nonlinear and soft matter physics 84: 061904–061913.

Pardon JF, Worcester DL, Wooley JC, et al. (1975) Low‐angle neutron scattering from chromatin subunit particles. Nucleic Acids Research 2: 2163–2176.

Petoukhov MV, Franke D, Shkumatov AV, et al. (2012) New developments in the ATSAS program package for small‐angle scattering data analysis. Journal of Applied Crystallography 45: 342–350.

Petoukhov MV, Billas IM, Takacs M, et al. (2013) Reconstruction of quaternary structure from X‐ray scattering by equilibrium mixtures of biological macromolecules. Biochemistry 52 (39): 6844–6855.

Porod G (1951) X‐ray small angle scattering of close packed colloidal systems. Kolloid Zeitschrift 124: 83–114.

Rowland SL, Burkholder WF, Cunningham KA, et al. (2004) Structure and mechanism of action of Sda, an inhibitor of the histidine kinases that regulate initiation of sporulation in Bacillus subtilis. Molecular Cell 13: 689–701.

Różycki B, Kim YC and Hummer G (2011) SAXS ensemble refinement of ESCRT‐III CHMP3 conformational transitions. Structure 19: 109–116.

Russel D, Lasker K, Webb B, et al. (2012) Putting the pieces together: integrative modeling platform software for structure determination of macromolecular assemblies. PLoS Biology 10: e1001244.

Schneidman‐Duhovny D, Hammel M and Sali A (2011) Macromolecular docking restrained by a small angle X‐ray scattering profile. Journal of Structural Biology 173: 461–471.

Schneidman‐Duhovny D, Hammel M, Tainer JA and Sali A (2013) Accurate SAXS profile computation and its assessment by contrast variation experiments. Biophysical Journal 105: 9629–74.

Shtykova EV, Baratova LA, Fedorova NV, et al. (2013) Structural analysis of influenza A virus matrix protein M1 and its self‐assemblies at low pH. PLoS One 8 (12): e82431.

Spinozzi F, Ferrero C, Ortore MG, et al. (2014) GENFIT: software for the analysis of small‐angle X‐ray and neutron scattering data of macro‐molecules in solution. Journal of Applied Crystallography 47 (3): 1132–1139.

Suau P, Kneale GG, Braddock GW, Baldwin JP and Bradbury EM (1977) A low‐resolution model for the chromatin core particle by neutron scattering. Nucleic Acids Research 4: 3769–3786.

Svergun DI (1992) Determination of the regularization parameter in indirect‐transform methods using perceptual criteria. Journal of Applied Crystallography 25: 495–503.

Toft KN, Vestergaard B, Nielsen S, et al. (2008) High‐throughput small angle X‐ray scattering from proteins in solution using a microfluidic front‐end. Analytical Chemistry 80: 3648–3654.

Trewhella J, Hendrickson WA, Kleywegt GJ, et al. (2013) Report of the wwPDB small‐angle scattering task force: data requirements for biomolecular modeling and the PDB. Structure 21 (6): 875–881.

Tugarinov V, Choy WY, Orekhov VY and Kay LE (2005) Solution NMR‐derived global fold of a monomeric 82‐kDa enzyme. Proceedings of the National Academy of Sciences of the USA 102: 622–627.

Whitten AE, Ca SZ and Trewhella J (2008) MULCh: modules for the analysis of small‐angle neutron contrast variation data from biomolecular assemblies. Journal of Applied Crystallography 41: 222–226.

Whitten AE, Jacques DA, Hammouda B, et al. (2007) The structure of the KinA‐Sda complex suggests an allosteric mechanism of histidine kinase inhibition. Journal of Molecular Biology 368: 407–420.

Zheng W and Tekpinar M (2011) Accurate flexible fitting of high‐resolution protein structures to small‐angle x‐ray scattering data using a coarse‐grained model with implicit hydration shell. Biophysical Journal 101: 2981–2991.

Further Reading

Fitter J, Gutberlet T and Katsaras J (eds) (2006) Neutron Scattering in Biology – Techniques and Applications in the Series: Biological and Medical Physics, Biomedical Engineering. Berlin: Springer.

Glatter O and Kratky O (1982) Small‐Angle X‐ray Scattering. New York: Academic Press(electronic copy available at:

Jacques DA and Trewhella J (2010) Small‐angle scattering for structural biology‐expanding the frontier while avoiding the pitfalls. Protein Science 19: 642–657.

Moore PB (1982) Small‐angle scattering techniques for the study of biological macromolecules and macromolecular aggregates. In: Ehrenstein G and Lecar H, (eds). Methods of Experimental Physics, vol. 20, pp. 337–390, NewYork: Academic Press.

Neylon C (2008) Small angle neutron and X‐ray scattering in structural biology: recent examples from the literature. European Journal of Biophysics 37: 531–541.

Putnam CD, Hammel M, Hura GL and Tainer JA (2007) X‐ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution. Quarterly Reviews of Biophysics 40: 191–285.

Rambo RP and Tainer JA (2010) Bridging the solution divide: comprehensive structural analyses of dynamic RNA, DNA, and protein assemblies by small‐angle X‐ray scattering. Current Opinion in Structural Biology 20: 128–137.

Svergun DI and Koch MH (2003) Small‐angle scattering studies of biological macromolecules in solution. Reports on Progress in Physics 66: 1735–1782.

Svergun DI, Koch MHJ, Timmins PA and May RP (2013) Small Angle X‐Ray and Neutron Scattering from Solutions of Biological Macromolecules. Oxford: Oxford University Press.

Whitten AE and Trewhella J (2009) Small‐angle scattering and neutron contrast variation for studying bio‐molecular complexes. Methods in Molecular Biology 544: 307–323.

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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. [doi: 10.1002/9780470015902.a0003047.pub3]