Cryo-electron microscopy (EM) and small angle X-ray scattering (SAXS) are two different data acquisition modalities often used to glean information about the structure of large biomolecular complexes in their native states. A SAXS experiment is generally considered fast and easy but unveils the structure at very low resolution, whereas a cryo-EM experiment needs more extensive preparation and postacquisition computation to yield a three-dimensional (3D) density map at higher resolution. In certain applications, we may need to verify whether the data acquired in the SAXS and cryo-EM experiments correspond to the same structure (e.g., before reconstructing the 3D density map in EM). In this article, a simple and fast method is proposed to verify the compatibility of the SAXS and EM experimental data. The method is based on averaging the two-dimensional correlation of EM images and the Abel transform of the SAXS data. Orientational preferences are known to exist in cryo-EM experiments, and we also consider these effects on our method. The results are verified on simulations of conformational states of large biomolecular complexes.
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References
1.
AfsariB., KimJ.S., and ChirikjianG.S.2015. Cross-validation of data in SAXS and cryo-EM. In Proceedings of IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 1224–1230. Washington, DC.
2.
ArmstrongN., and GouauxE.2000. Mechanisms for activation and antagonism of an AMPA-sensitive glutamate receptor: Crystal structures of the GluR2 ligand binding core. Neuron, 28, 165–181.
3.
BermanH., WestbrookJ., FengZ., et al.2000. The Protein Data Bank. Nucleic Acids Res. 28, 235–242.
4.
BhamreT., ZhangT., and SingerA.2016. Denoising and covariance estimation of single particle cryo-EM images. J. Struct. Biol., 195, 72–81.
5.
BlanchetC.E., and SvergunD.I.2013. Small-angle X-ray scattering on biological macromolecules and nanocomposites in solution. Annu. Rev. Phys. Chem., 64, 37–54.
6.
BracewellR.2003. Fourier Analysis and Imaging. Springer Science & Business Media, New York.
7.
BronP., GiudiceE., RollandJ.-P., et al.2008. Apo-Hsp90 coexists in two open conformational states in solution. Biol. Cell, 100, 413–425.
8.
DavisP.J., and RabinowitzP.1984. Methods of Numerical Integration. Academic Press, New York.
9.
DingledineR., BorgesK., BowieD., et al.1999. The glutamate receptor ion channels. Pharmacol. Rev., 51, 7–61.
10.
DongH., and ChirikjianG.S.2014. A computational model for data acquisition in SAXS. In BDB’14 Proceeding of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics, 695–702, Newport Beach, CA, USA.
11.
DongH., KimJ.S., and ChirikjianG.S.2015. Computational analysis of SAXS data acquisition. J. Comput. Biol., 22, 787–805.
12.
El-TomM.1971. On ignoring the singularity in approximate integration. SIAM J Numer Anal, 8, 412–424.
13.
FeiginL., SvergunD.I., and TaylorG.W.1987. Structure Analysis by Small-Angle X-ray and Neutron Scattering. Springer.
14.
FrankJ.2002. Single-particle imaging of macromolecules by cryo-electron microscopy. Annu. Rev. Biophys. Biomol. Struct, 31, 303–319.
15.
FrankJ.2006. Three-Dimensional Electron Microscopy of Macromolecular Assemblies. Oxford University Press, New York.
16.
GrigorieffN.1998. Three-dimensional structure of bovine NADH: Ubiquinone oxidoreductase (complex I) at 22 A in ice. J. Mol. Biol., 277, 1033–1046.
17.
JiangW., BakerM.L., WuQ., et al.2003. Applications of a bilateral denoising filter in biological electron microscopy. J. Struct. Biol., 144, 114–122.
18.
LamyJ., SizaretP., FrankJ., et al.1982. Architecture of Limulus polyphemus hemocyanin. Biochemistry, 21, 6825–6833.
19.
LiuY., MengX., and LiuZ.2013. Deformed grids for single-particle cryo-electron microscopy of specimens exhibiting a preferred orientation. J. Struct. Biol., 182, 255–258.
20.
MaddenD.R., ArmstrongN., SvergunD., et al.2005. Solution X-ray scattering evidence for agonist- and antagonist-induced modulation of cleft closure in a glutamate receptor ligand-binding domain. J. Biol. Chem., 280, 23637–23642.
21.
MielikäinenT., and RavanttiJ.2005. Sinogram denoising of cryo-electron microscopy images. Lect. Notes Comput. Sci., 3483, 1251–1261.
22.
NattererF.1986. The Mathematics of Computerized Tomography, volume 32. SIAM, Philadelphia.
23.
ParkW., and ChirikjianG.S.2014. An assembly automation approach to alignment of noncircular projections in electron microscopy. IEEE Trans. Autom. Sci. Eng., 11, 668–679.
24.
ParkW., MidgettC.R., MaddenD.R., et al.2011. A stochastic kinematic model of class averaging in single-particle electron microscopy. Int. J. Rob. Res., 30, 730–754.
25.
PenczekP.A.2002. Three-dimensional spectral signal-to-noise ratio for a class of reconstruction algorithms. J. Struct. Biol., 138, 34–46.
26.
PenczekP.A., RadermacherM., and FrankJ.1992. Three-dimensional reconstruction of single particles embedded in ice. Ultramicroscopy, 40, 33–53.
27.
SchatzM., and Van HeelM.1990. Invariant classification of molecular views in electron micrographs. Ultramicroscopy, 32, 255–264.
28.
ScheresS.H., ValleM., NuñezR.N., et al.2005. Maximum-likelihood multi-reference refinement for electron microscopy images. J. Mol. Biol., 348, 139–149.
29.
ShkolniskyY., and SingerA.2012. Viewing direction estimation in cryo-EM using synchronization. SIAM J. Imaging Sci., 5, 1088–1110.
30.
SingerA., ZhaoZ., ShkolniskyY., et al.2011. Viewing angle classification of cryo-electron microscopy images using eigenvectors. SIAM J. Imaging Sci., 4, 723–759.
31.
SvergunD.I., and KochM.H.2003. Small-angle scattering studies of biological macromolecules in solution. Rep. Prog. Phys. 66, 1735.
32.
SvergunD.I., KochM.H., TimminsP.A., et al.2013. Small Angle X-Ray and Neutron Scattering from Solutions of Biological Macromolecules. Oxford University Press, New York.
33.
TischendorfG.W., ZeichhardtH., and StöfflerG.1974. Determination of the location of proteins L14, L17, L18, L19, L22, and L23 on the surface of the 50S ribosomal subunit of Escherichia coli by inmmunoelectron microscopy. Mol. Gen. Genet., 134, 187–208.
34.
Van AntwerpenR.2004. Preferred orientations of LDL in vitreous ice indicate a discoid shape of the lipoprotein particle. Arch. Biochem. Biophys., 1, 122–127.
35.
van HeelM.1984. Multivariate statistical classification of noisy images (randomly oriented biological macromolecules). Ultramicroscopy, 13, 165–184.
36.
van HeelM., and FrankJ.1981. Use of multivariate statistics in analysing the images of biological macromolecules. Ultramicroscopy, 6, 187–194.
37.
Van HeelM., SchatzM., and OrlovaE.1992. Correlation functions revisited. Ultramicroscopy, 46, 307–316.
38.
VestergaardB., SanyalS., RoessleM., et al.2005. The SAXS solution structure of RF1 differs from its crystal structure and is similar to its ribosome bound cryo-EM structure. Mol. Cell, 20, 929–938.
39.
ZhaoZ., and SingerA.2014. Rotationally invariant image representation for viewing direction classification in cryo-EM. J. Struct. Biol., 186, 153–166.
