Representation theoretic patterns in three dimensional Cryo-Electron Microscopy I: The intrinsic reconstitution algorithm

Annals of Mathematics

Volumn 174, Issue 2, 2011, Pages 1219-1241

  Hadani, Ronny ^a   Singer, Amit ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80051779555     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2011.174.2.11     Document Type: Article

References (13)

1. R. A. Crowther, DeRosier, D. J., and A. Klug, The reconstruction of a three-dimensional structure from projections and its application to electron microscopy, Proc. R. Soc. Lond. A, Math. Phys. Sci. 317 (1970), 319-340.
2. D. A. Doyle, J. M. Cabral, R. A. Pfuetzner, A. Kuo, J. M. Gulbis, S. L. Cohen, B. T. Chait, and R. MacKinnon, The structure of the potassium channel: Molecular basis of K+ conduction and selectivity, Science 280 (1998), 69-77. Available at http://www.ncbi.nlm.nih.gov/pubmed/9525859.
3. A. Goncharov and B. Vainshtein, Determination of the spatial orientation of arbitrarily arranged identical particles of an unknown structure from their projections, Proc. XI Internat. Congr. Elec. Micro., Kyoto I (1986), 459-460.
4. R. Hadani and A. Singer, Representation theoretic patterns in three dimensional cryoelectron macroscopy II - The class averaging problem, accepted for publication in Foundations of Computational Mathematics (FoCM), 2011.
5. R. Henderson, Realizing the potential of electron cryomicroscopy, Q. Rev. Bio-phys. 37 (2004), 3-13, Review. PMID: 17390603 [PubMed - indexed for MED-LINE].
6. S. J. Ludtke, M. L. Baker, D. Chen, J. L. Song, D. T. Chuang, and W. Chiu, De Novo backbone trace of GroEL from single particle electron cryomicroscopy, Structure 16 (2008), 441-448, PMID: 18334219 [PubMed - indexed for MEDLINE].
7. R. MacKinnon, Potassium Channels and the Atomic Basis of Selective Ion Conduction, Nobel Lecture, in Bioscience Reports 24, Springer Science+Business Media, Inc., New York, 2004, PMID: 15628664 [PubMed - indexed for MED-LINE].
8. F. Natterer, The mathematics of computerized tomography, Classics in Applied Mathematics no. 32, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2001.
9. A. Singer and Y. Shkolnisky, Three-dimensional structure determination from common lines in cryo-EM by eigenvectors and semidefinite programming, 2009, submitted.
10. A. Singer, Z. Zhao,, Y. Shkolnisky, and R. Hadani, Viewing angle classification of cryoelectron microscopy images using eigenvectors, SIAM Journal on Imaging Sciences 4 (2011), 723-759.
11. M. E. Taylor, Noncommutative Harmonic Analysis, Math. Surveys and Monogr. 22, Amer. Math. Soc., Providence, RI, 1986.
12. M. Van Heel, Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction, Ultramicroscopy 21 (1987), 111-123, PMID: 12425301 [PubMed - indexed for MEDLINE].
13. X. Zhang, E. Settembre, C. Xu, P. R. Dormitzer, S. C. Harrison, and N. Grigorieff, Near-atomic resolution using electron cryomicroscopy and single-particle reconstruction, Proc. Nat. Acad. Sci. 105 (2008), 1867-1872.