Conformations of macromolecules and their complexes from heterogeneous datasets

Philosophical Transactions of the Royal Society B: Biological Sciences

Volumn 369, Issue 1647, 2014, Pages

  Schwander, P ^a   Fung, R ^a   Ourmazd, A ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Cryo electron microscopy; Dimensionality reduction; Macromolecular conformations; Macromolecular structure; Manifold embedding; X ray lasers

Indexed keywords

ALGORITHM; DATA SET; HETEROGENEITY; MOLECULAR ANALYSIS; POLYMERIZATION;

MACROMOLECULE;

ALGORITHM; CHEMISTRY; CONFORMATION; CRYOELECTRON MICROSCOPY; LASER; MACROMOLECULE; PROCEDURES; ULTRASTRUCTURE; X RAY DIFFRACTION;

ALGORITHMS; CRYOELECTRON MICROSCOPY; LASERS; MACROMOLECULAR SUBSTANCES; MOLECULAR CONFORMATION; X-RAY DIFFRACTION;

EID: 84902670109     PISSN: 09628436     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rstb.2013.0567     Document Type: Review

References (42)

1. Yu IM, Zhang W, Holdaway HA, Li L, Kostyuchenko VA, Chipman PR, Kuhn RJ, Rossmann MG, Chen J. 2008 Structure of the immature dengue virus at low pH primes proteolytic maturation. Science 319, 1834-1837. (doi: 10. 1126/science. 1153264).
2. Leschziner AE, Nogales E. 2007 Visualizing flexibility at molecular resolution: analysis of heterogeneity in single-particle electron microscopy reconstructions. Annu. Rev. Biophys. Biomol. Struct. 36, 43-62. (doi: 10. 1146/annurev. biophys. 36. 040306. 132742).
3. Sigworth FJ. 2007 From cryo-EM, multiple protein structures in one shot. Nat. Methods 2007, 20-21. (doi: 10. 1038/nmeth0107-20).
4. Scheres SH, Gao H, Valle M, Herman GT, Eggermont PP, Frank J, Carazo JM. 2007 Disentangling conformational states of macromolecules in 3D-EM through likelihood optimization. Nat. Methods 4, 27-29. (doi: 10. 1038/nmeth992).
5. Schuette JC et al. 2009 GTPase activation of elongation factor EF-Tu by the ribosome during decoding. EMBO J. 28, 755-765. (doi: 10. 1038/emboj. 2009. 26).
6. Westfield GH et al. 2011 Structural flexibility of the Gas a-helical domain in the b2-adrenoceptor Gs complex. Proc. Natl Acad. Sci. USA 108, 16 086-16 091. (doi: 10. 1073/pnas. 1113645108).
7. Frank J. 2002 Single-particle imaging of macromolecules by cryo-electron microscopy. Annu. Rev. Biophys. Biomol. Struct. 31, 303-319. (doi: 10. 1146/annurev. biophys. 31. 082901. 134202).
8. Frank J. 2006 Three-dimensional electron microscopy of macromolecular assemblies. New York, NY: Oxford University Press.
9. Solem JC, Baldwin GC. 1982 Microholography of living organisms. Science 218, 229-235. (doi: 10. 1126/science. 218. 4569. 229).
10. Neutze R, Huldt G, Hajdu J, van der Spoel D. 2004 Potential impact of an X-ray free electron laser on structural biology. Radiat. Phys. Chem. 71, 905-916. (doi: 10. 1016/j. radphyschem. 2004. 04. 121).
11. Gaffney KJ, Chapman HN. 2007 Imaging atomic structure and dynamics with ultrafast X-ray scattering. Science 316, 1444-1448. (doi: 10. 1126/science. 1135923).
12. Chapman HN et al. 2006 Femtosecond diffractive imaging with a soft-X-ray free-electron laser. Nat. Phys. 2, 839-843. (doi: 10. 1038/Nphys461).
13. Seibert MM et al. 2011 Single mimivirus particles intercepted and imaged with an X-ray laser. Nature 470, 78-81. (doi: 10. 1038/nature09748).
14. Schwander P, Fung R, Phillips GN, Ourmazd A. 2010 Mapping the conformations of biological assemblies. New J. Phys. 12, 1-15. (doi: 10. 1088/1367-2630/12/3/035007).
15. Yoon CH et al. 2011 Unsupervised classification of single-particle X-ray diffraction snapshots by spectral clustering. Opt. Express. 19, 16 542-16 549. (doi: 10. 1364/OE. 19. 016542).
16. Fung R, Shneerson V, Saldin DK, Ourmazd A. 2009 Structure from fleeting illumination of faint spinning objects in flight. Nat. Phys. 5, 64-67. (doi: 10. 1038/Nphys1129).
17. Giannakis D, Schwander P, Ourmazd A. 2012 The symmetries of image formation by scattering. I. Theoretical framework. Opt. Express. 20, 12 799-12 826. (doi: 10. 1364/OE. 20. 012799).
18. Schwander P, Yoon CH, Ourmazd A, Giannakis D. 2012 The symmetries of image formation by scattering. II. Applications. Opt. Express. 20, 12 827-12 849. (doi: 10. 1364/OE. 20. 012827).
19. Bishop CM. 1995 Neural networks for pattern recognition, p. 482. Oxford, UK: Oxford University Press.
20. Svensén JFM. 1998 GTM: Generative topographic mapping. Ph. D. thesis, Aston University.
21. Roweis ST, Saul LK. 2000 Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323-2326. (doi: 10. 1126/science. 290. 5500. 2323).
22. Belkin M, Niyogi P. 2003 Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15, 1373-1396. (doi: 10. 1162/089976603321780317).
23. Donoho DL, Grimes C. 2003 Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Proc. Natl Acad. Sci. USA 100, 5591-5596. (doi: 10. 1073/pnas. 1031596100).
24. Coifman RR, Lafon S. 2006 Geometric harmonics: a novel tool for multiscale out-of-sample extension of empirical functions. Appl. Comput. Harmon Anal. 21, 31-52. (doi: 10. 1016/j. acha. 2005. 07. 005).
25. Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW. 2005 Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc. Natl Acad. Sci. USA 102, 7426-7431. (doi: 10. 1073/pnas. 0500334102).
26. Tenenbaum JB, de Silva V, Langford JC. 2000 A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319-2323. (doi: 10. 1126/science. 290. 5500. 2319).
27. Lin T, Zha HB, Lee SU. 2006 Riemannian manifold learning for nonlinear dimensionality reduction. Lect. Notes Comput. Sci. 3951, 44-55. (doi: 10. 1007/11744023_4).
28. Hu BL. 1973 Scalar waves in the mixmaster universe. I. The Helmholtz equation in a fixed background. Phys. Rev. D 8, 1048-1060. (doi: 10. 1103/PhysRevD. 8. 1048).
29. Hu BL. 1974 Scalar waves in the mixmaster universe. II. Particle creation. Phys. Rev. D 9, 3263-3281. (doi: 10. 1103/PhysRevD. 9. 3263).
30. Loh NT, Elser V. 2009 Reconstruction algorithm for single-particle diffraction imaging experiments. Phys. Rev. E 80, 026705. (doi: 10. 1103/PhysRevE. 80. 026705).
31. Moths B, Ourmazd A. 2011 Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison. Acta Crystallogr. A 67, 481-486. (doi: 10. 1107/S0108767311019611).
32. Coifman RR, Kevrekidis IG, Lafon S, Maggioni M, Nadler B. 2008 Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Multiscale Model. Simul. 7, 842-864. (doi: 10. 1137/070696325).
33. Lin T, Zha H, Lee SU. 2006 Riemannian manifold learning for nonlinear dimensionality reduction. In ECCV Part I, LNCS (eds A Leonardis, H Bischof, A Pinz), pp. 44-55. Berlin, Heidelberg: Springer.
34. Bishop CM. 1999 Learning in graphical models, p. 634. Cambridge, MA: MIT Press.
35. Balasubramanian M, Schwartz EL. 2002 The Isomap algorithm and topological stability. Science 295, 7a. (doi: 10. 1126/science. 295. 5552. 7a).
36. Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW. 2005 Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods. Proc. Natl Acad. Sci. USA 102, 7432-7437. (doi: 10. 1073/pnas. 0500896102).
37. Phillips JC et al. 2005 Scalable molecular dynamics with NAMD. J. Comput. Chem. 26, 1781-1802. (doi: 10. 1002/jcc. 20289).
38. Elmlund D, Davis R, Elmlund H. 2010 Ab Initio structure determination from electron microscopic images of single molecules coexisting in different functional states. Structure 18, 777-786. (doi: 10. 1016/j. str. 2010. 06. 001).
39. Champeney DC. 1973 Fourier transforms and their physical applications, p. 256. New York, NY: Academic Press.
40. Coifman RR, Shkolnisky Y, Sigworth FJ, Singer A. 2008 Graph Laplacian tomography from unknown random projections. IEEE Trans. Image Process. 17, 1891-1899. (doi: 10. 1109/TIP. 2008. 2002305).
41. Elmlund D, Elmlund H. 2009 High-resolution singleparticle orientation refinement based on spectrally self-adapting common lines. J. Struct. Biol. 167, 83-94. (doi: 10. 1016/j. jsb. 2009. 04. 009).
42. Shatsky M, Hall RJ, Nogales E, Malik J, Brenner S. 2010 Automated multi-model reconstruction from single-particle electron microscopy data. J. Struct. Biol. 170, 98-108. (doi: 10. 1016/j. jsb. 2010. 01. 007).