Structure Sorting of Multiple Macromolecular States in Heterogeneous Cryo-EM Samples by 3D Multivariate Statistical Analysis


Heterogeneity of biological samples is usually considered a major obstacle for three-dimensional (3D) structure determination of macromolecular complexes. Heterogeneity may occur at the level of composition or conformational variability of complexes and affects most 3D structure determination methods that rely on signal averaging. Here, an approach is described that allows sorting structural states based on a 3D statistical approach, the 3D sampling and classification (3D-SC) of 3D structures derived from single particles imaged by cryo electron microscopy (cryo-EM). The method is based on jackknifing & bootstrapping of 3D sub-ensembles and 3D multivariate statistical analysis followed by 3D classification. The robustness of the statistical sorting procedure is corroborated using model data from an RNA polymerase structure and experimental data from a ribosome complex. It allows resolving multiple states within heterogeneous complexes that thus become amendable for a structural analysis despite of their highly flexible nature. The method has important implications for high-resolution structural studies and allows describing structure ensembles to provide insights into the dynamics of multi-component macromolecular assemblies.

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Klaholz, B. (2015) Structure Sorting of Multiple Macromolecular States in Heterogeneous Cryo-EM Samples by 3D Multivariate Statistical Analysis. Open Journal of Statistics, 5, 820-836. doi: 10.4236/ojs.2015.57081.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Roblin, P., Potocki-Véronèse, G., Guieysse, D., Guerin, F., Axelos, M.A., Perez, J. and Buleon, A. (2013) SAXS Conformational Tracking of Amylose Synthesized by Amylosucrases. Biomacromolecules, 14, 232-239.
[2] Kikhney, A.G. and Svergun, D.I. (2015) A Practical Guide to Small Angle X-Ray Scattering (SAXS) of Flexible and Intrinsically Disordered Proteins. FEBS Letters, 589, 2570-2577.
[3] Frank, J., Radermacher, M., Penczek, P., Zhu, J., Li, Y., Ladjadj, M. and, Leith, A. (1996) SPIDER and WEB: Processing and Visualization of Images in 3D Electron Microscopy and Related Fields. Journal of Structural Biology, 116, 190-199.
[4] van Heel, M., Harauz, G., Orlova, E.V., Schmidt, R. and, Schatz, M. (1996) A New Generation of the IMAGIC Image Processing System. Journal of Structural Biology, 116, 17-24.
[5] Benzécri, J.P. (1969) Methodologies of Pattern Recognition. Academic Press, New York, 35-74.
[6] van Heel, M. and Frank, J. (1981) Use of Multivariate Statistics in Analyzing the Images of Biological Macromolecules. Ultramicroscopy, 6, 187-194.
[7] van Heel, M. (1984) Multivariate Statistical Classification of Noisy Images (Randomly Oriented Biological Macromolecules). Ultramicroscopy, 13, 165-183.
[8] Borland, L. and van Heel, M. (1990) Classification of Image Data in conjugate Representation Spaces. Journal of the Optical Society of America A, 7, 601-610.
[9] van Heel, M., Portugal, R. and Schatz, M. (2009) An Electronic Text Book: Electron Microscopy in Life Science. 3D-EM Network of Excellence.
[10] Harauz, G. and van Heel, M. (1986) Exact Filters for General Geometry Three Dimensional Reconstruction. Optik, 73, 146-156.
[11] Radermacher, M. (1988) Three-Dimensional Reconstruction of Single Particles from Random and Nonrandom Tilt Series. Journal of Electron Microscopy Technique, 9, 359-394.
[12] Orlov, I.M., Morgan, D.G. and Cheng, R.H. (2006) Efficient Implementation of a Filtered Back-Projection Algorithm Using a Voxel-by-Voxel Approach. Journal of Structural Biology, 154, 287-296.
[13] Orlov, I.M. and Klaholz, B.P. Compensation of Preferable Orientations in 3D Particle Reconstructions Based on Voronoi Diagrams. (in preparation)
[14] Leschziner, A.E. and Nogales, E. (2007) Visualizing Flexibility at Molecular Resolution: Analysis of Heterogeneity in Single-Particle Electron Microscopy Reconstructions. Annual Review of Biophysics and Biomolecular Structure, 36, 43-62.
[15] Rossmann, M.G. and Blow, D.M. (1962) The Detection of Sub-Units within the Crystallographic Asymmetric Unit. Acta Crystallographica, 15, 24-31.
[16] Gao, H., Valle, M., Ehrenberg, M. and Frank, J. (2004) Dynamics of EF-G Interaction with the Ribosome Explored by Classification of a Heterogeneous Cryo-EM Dataset. Journal of Structural Biology, 147, 283-290.
[17] Sigworth, F.J. (1998) A Maximum-Likelihood Approach to Single-Particle Image Refinement. Journal of Structural Biology, 122, 328-339.
[18] Scheres, S.H., Valle, M., Nuez, R., Sorzano, C.O., Marabini, R., Herman, G.T. and Carazo, J.M. (2005) Maximum-Likelihood Multi-Reference Refinement for Electron Microscopy Images. Journal of Structural Biology, 22, 139-149.
[19] Scheres, S.H. (2010) Classification of Structural Heterogeneity by Maximum-Likelihood Methods. Methods in Enzymology, 482, 295-320.
[20] Lyumkis, D., Brilot, A.F., Theobald, D.L. and Grigorieff, N. (2013) Likelihood-Based Classification of Cryo-EM Images Using FREALIGN. Journal of Structural Biology, 183, 377-388.
[21] Amunts, A., Brown, A., Toots, J., Scheres, S.H. and Ramakrishnan, V. (2015) The Structure of the Human Mitochondrial Ribosome. Science, 348, 95-98.
[22] Khatter, H., Myasnikov, A.G., Natchiar, S.K. and Klaholz, B.P. (2015) Structure of the Human 80S Ribosome. Nature, 30, 640-645.
[23] Ohi, M., Li, Y., Cheng, Y. and Walz, T. (2004) Negative Staining and Image Classification—Powerful Tools in Modern Electron Microscopy. Biological Procedures Online, 6, 23-34.
[24] Fu, J., Gao, H. and Frank, J. (2006) Unsupervised Classification of Single Particles by Cluster Tracking in Multi-Dimensional Space. Journal of Structural Biology, 157, 226-239.
[25] Herman, G.T. and Kalinowski, M. (2008) Classification of Heterogeneous Electron Microscopic Projections into Homogeneous Subsets. Ultramicroscopy, 108, 327-338.
[26] Shatsky, M., Hall, R.J., Nogales, E., Malik, J. and Brenner, S.E. (2010) Automated Multi-Model Reconstruction from Single-Particle Electron Microscopy Data. Journal of Structural Biology, 170, 98-108.
[27] Tang, G., Peng, L., Baldwin, P.R., Mann, D.S., Jiang, W., Rees, I. and Ludtke, S.J. (2007) EMAN2: An Extensible Image Processing Suite for Electron Microscopy. Journal of Structural Biology, 157, 38-46.
[28] Elmlund, H., Elmlund, D. and Bengio, S. (2013) PRIME: Probabilistic Initial 3D Model Generation for Single-Particle cryo-Electron Microscopy. Structure, 21, 1299-1306.
[29] Liao, H.Y., Hashem, Y. and Frank, J. (2015) Efficient Estimation of Three-Dimensional Covariance and Its Application in the Analysis of Heterogeneous Samples in Cryo-Electron Microscopy. Structure, 23, 1129-1137.
[30] Wang, Q., Matsui, T., Domitrovic, T., Zheng, Y., Doerschuk, P.C. and Johnson, J.E. (2013) Dynamics in Cryo EM Reconstructions Visualized with Maximum-Likelihood Derived Variance Maps. Journal of Structural Biology, 181, 195-206.
[31] Klaholz, B.P., Myasnikov, A.G. and van Heel, M. (2004) Visualization of Release Factor 3 on the Ribosome during Termination of Protein Synthesis. Nature, 427, 862-865.
[32] Penczek, P.A., Frank, J. and Spahn, C.M. (2006) A Method of Focused Classification, Based on the Bootstrap 3D Variance Analysis, and Its Application to EF-G-Dependent Translocation. Journal of Structural Biology, 154, 184-194.
[33] White, H.E., Saibil, H.R., Ignatiou, A. and Orlova, E.V. (2004) Recognition and Separation of Single Particles with Size Variation by Statistical Analysis of Their Images. Journal of Structural Biology, 13, 453-460.
[34] Elad, N., Clare, D.K., Saibil, H.R. and Orlova, E.V. (2008) Detection and Separation of Heterogeneity in Molecular Complexes by Statistical Analysis of Their Two-Dimensional Projections. Journal of Structural Biology, 162, 108-120.
[35] Orlova, E.V. and Saibil, H.R. (2010) Methods for Three-Dimensional Reconstruction of Heterogeneous Assemblies. Methods in Enzymology, 482, 321-341.
[36] De Carlo, S., Carles, C., Riva, M. and Schultz, P. (2003) Cryo-Negative Staining Reveals Conformational Flexibility within Yeast RNA Polymerase I. Journal of Molecular Biology, 329, 891-902.
[37] Cheng, A. and Yeager, M. (2007) Bootstrap Resampling for Voxel-Wise Variance Analysis of Three-Dimensional Density Maps Derived by Image Analysis of Two-Dimensional Crystals. Journal of Structural Biology, 158, 19-32.
[38] Myasnikov, A.G., Marzi, S., Simonetti, A., Giuliodori, A.M., Gualerzi, C.O., Yusupova, G., Yusupov, M. and Klaholz, B.P. (2005) Conformational Transition of Initiation Factor 2 from the GTP- to GDP-Bound State Visualized on the Ribosome. Nature Structural & Molecular Biology, 12, 1145-1149.
[39] Penczek, P.A., Yang, C., Frank, J. and Spahn, C.M. (2006) Estimation of Variance in Single-Particle Reconstruction Using the Bootstrap Technique. Journal of Structural Biology, 154, 168-183.
[40] Zhang, W., Kimmel, M., Spahn, C.M. and Penczek, P.A. (2008) Heterogeneity of Large Macromolecular Complexes Revealed by 3D Cryo-EM Variance Analysis. Structure, 16, 1770-1776.
[41] Quenouille, M.H. (1949) Approximate Tests of Correlation in Time Series. Journal of the Royal Statistical Society: Series B, 11, 68-84.
[42] Efron, B. (1979) Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7, 1-26.
[43] Efron, B. (1981) Nonparametric Estimates of Standard Error: The Jackknife, the Bootstrap and Other Methods. Biometrika, 68, 589-599.
[44] Simon, J.L. (1969) Basic Research Methods in Social Sciences: The Art of Empirical Investigation. Random House, New York.
[45] Simon, J.L. (1997) Resampling: The New Statistics. 2nd Edition, Thompson International, Duxbury.
[46] Good, P. (2005) Introduction to Statistics through Resampling Methods and R/S-PLUS. Wiley, Hoboken.
[47] Simonetti, A., Marzi, S., Myasnikov, A.G., Fabbretti, A., Yusupova, G., Yusupov, M., Gualerzi, C.O. and Klaholz, B.P. (2008) Structure of the 30S Translation Initiation Complex. Nature, 455, 416-420.
[48] Kettenberger, H., Armache, K.J. and Cramer, P. (2004) Complete RNA Polymerase II Elongation Complex Structure and Its Interactions with NTP and TFIIS. Molecular Cell, 16, 955-965.
[49] van Heel, M., Gowen, B., Matadeen, R., Orlova, E.V., Finn, R., Pape, T., Cohen, D., Stark, H., Schmidt, R., Schatz, M. and Patwardhan, A. (2000) Single-Particle Eletroncryo-Microscopy: Towards Atomic Resolution. Quarterly Reviews of Biophysics, 33, 307-369.
[50] Haynor, D.R. and Woods, S.D. (1989) Resampling Estimates of Precision in Emission Tomography. IEEE Transactions on Medical Imaging, 8, 337-343.
[51] Maitra, R. (1998) An Approximate Bootstrap Technique for Variance Estimation in Parametric Images. Medical Image Analysis, 2, 379-382.
[52] Voorhees, R.M., Fernández, I.S., Scheres, S.H. and Hegde, R.S. (2014) Structure of the Mammalian Ribosome-Sec61 Complex to 3.4 Å Resolution. Cell, 157, 1632-1643.
[53] Bai, X.C., Fernandez, I.S., McMullan, G. and Scheres, S.H. (2013) Ribosome Structures to Near-Atomic Resolution from Thirty Thousand Cryo-EM Particles. eLife, 2, e00461.
[54] Scheres, S.H., Gao, H., Valle, M., Herman, G.T., Eggermont, P.P., Frank, J. and Carazo, J.M. (2007) Disentangling Conformational States of Macromolecules in 3D-EM through Likelihood Optimization. Nature Methods, 4, 27-29.
[55] Orlov, I., Rochel, N., Moras, D. and Klaholz, B.P. (2012) Structure of the Full Human RXR/VDR Nuclear Receptor Heterodimer Complex with Its DR3 Target DNA. The EMBO Journal, 31, 291-300.
[56] Papai, G., Tripathi, M.K., Ruhlmann, C., Layer, J.H., Weil, P.A. and Schultz, P. (2010) TFIIA and the Transactivator Rap1 Cooperate to Commit TFIID for Transcription Initiation. Nature, 465, 956-960.
[57] Simonetti, A., Marzi, S., Billas, I.M., Tsai, A., Fabbretti, A., Myasnikov, A.G., Roblin, P., Vaiana, A.C., Hazemann, I., Eiler, D., Steitz, T.A., Puglisi, J.D., Gualerzi, C.O. and Klaholz, B.P. (2013) Involvement of Protein IF2 N Domain in Ribosomal Subunit Joining Revealed from Architecture and Function of the Full-Length Initiation Factor. Proceedings of the National Academy of Sciences of the United States of America, 110, 15656-15661.
[58] Fischer, N., Konevega, A.L., Wintermeyer, W., Rodnina, M.V. and Stark, H. (2010) Ribosome Dynamics and tRNA Movement by Time-Resolved Electron Cryomicroscopy. Nature, 466, 329-333.
[59] Behrmann, E., Loerke, J., Budkevich, T.V., Yamamoto, K., Schmidt, A., Penczek, P.A., Vos, M.R., Bürger, J., Mielke, T., Scheerer, P. and Spahn, C.M. (2015) Structural Snapshots of Actively Translating Human Ribosomes. Cell, 161, 845-857.
[60] DePristo, M.A., de Bakker, P.I.W. and Blundell, T.L. (2004) Heterogeneity and Inaccuracy in Protein Structures Solved by X-Ray Crystallography. Structure, 12, 831-838.
[61] Levin, E.J., Kondrashov, D.A., Wesenberg, G.E. and Phillips Jr., G.N. (2007) Ensemble Refinement of Protein Crystal Structures: Validation and Application. Structure, 15, 1040-1052.
[62] Klaholz, B.P., Pape, T., Zavialov, A.V., Myasnikov, A.G., Vestergaard, B., Orlova, E., Ehrenberg, M. and van Heel, M. (2003) Structure of the Escherichia coli Ribosomal Termination Complex with Release Factor 2. Nature, 421, 90-94.
[63] Marzi, S., Myasnikov, A.G., Serganov, A., Ehresmann, C., Romby, P., Yusupov, M. and Klaholz, B.P. (2007) Structured mRNAs Regulate Translation Initiation by Binding to the Platform of the Ribosome. Cell, 130, 1019-1031.
[64] van Heel, M. (1987) Angular Reconstitution: A Posteriori Assignment of Projection Directions for 3D Reconstruction. Ultramicroscopy, 21, 111-123.
[65] Harauz, G. and Ottensmeyer, F.P. (1984) Direct Three-Dimensional Reconstructions for Macromolecular Complexes from Electron Micrographs. Ultramicroscopy, 12, 309-320.

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