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Computational Approaches for Automatic Structural Analysis of Large Biomolecular Complexes
October-December 2008 (vol. 5 no. 4)
pp. 568-582
We present computational solutions to two problemsof macromolecular structure interpretation from reconstructedthree-dimensional electron microscopy (3D-EM) maps of largebio-molecular complexes at intermediate resolution (5A-15A). Thetwo problems addressed are: (a) 3D structural alignment (matching)between identified and segmented 3D maps of structure units(e.g. trimeric configuration of proteins), and (b) the secondarystructure identification of a segmented protein 3D map (i.e.locations of a-helices, b -sheets). For problem (a), we presentan efficient algorithm to correlate spatially (and structurally)two 3D maps of structure units. Besides providing a similarityscore between structure units, the algorithm yields an effectivetechnique for resolution refinement of repeated structure units,by 3D alignment and averaging. For problem (b), we present anefficient algorithm to compute eigenvalues and link eigenvectorsof a Gaussian convoluted structure tensor derived from theprotein 3D Map, thereby identifying and locating secondarystructural motifs of proteins. The efficiency and performanceof our approach is demonstrated on several experimentallyreconstructed 3D maps of virus capsid shells from single-particlecryo-EM, as well as computationally simulated protein structuredensity 3D maps generated from protein model entries in theProtein Data Bank.

[1] M. Woolfson, An Introduction to X-Ray Crystallography. Cambridge Univ. Press, Jan. 1997.
[2] Online Course on Protein Crystallography, , 2008.
[3] A.E. Ferentz and G. Wagner, “NMR Spectroscopy: A Multifaceted Approach to Macromolecular Structure,” Quarterly Rev. Biophysics, vol. 33, pp. 29-65, 2000.
[4] P. Guntert, “Structure Calculation of Biological Macromolecules from NMR Data,” Quarterly Rev. Biophysics, vol. 31, pp. 145-237, 1998.
[5] H. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. Bhat, H. Weissig, I. Shindyalov, and P. Bourne, “The Protein Data Bank,” Nucleic Acids Research, vol. 28, pp. 235-242, 2000.
[6] T.S. Baker, N.H. Olson, and S.D. Fuller, “Adding the Third Dimension to Virus Life Cycles: Three-Dimensional Reconstruction of Icosahedral Viruses from Cryo-Electron Micrographs,” Microbiology and Molecular Biology Rev., vol. 63, no. 4, pp. 862-922, 1999.
[7] M. van Heel, B. Gowen, R. Matadeen, E. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, and A. Patwardhan, “Single-Particle Electron Cryo-Microscopy: Towards Atomic Resolution,” Quarterly Rev. Biophysics, vol. 33, no. 4, pp. 307-369, 2000.
[8] Z.H. Zhou, M.L. Baker, W. Jiang, M. Dougherty, J. Jakana, G. Dong, G. Lu, and W. Chiu, “Electron Cryomicroscopy and Bioinformatics Suggest Protein Fold Models for Rice Dwarf Virus,” Nature Structural Biology, vol. 8, no. 10, pp. 868-873, 2001.
[9] W. Jiang, Z. Li, M.L. Baker, P.E. Prevelige, and W. Chiu, “Coat Protein Fold and Maturation Transition of Bacteriophage P22 Seen at Subnanometer Resolution,” Nature Structural Biology, vol. 10, no. 2, pp. 131-135, 2003.
[10] Z. Zhou, M. Dougherty, J. Jakana, J. He, F. Rixon, and W. Chiu, “Seeing the Herpesvirus Capsid at 8.5 Angstrom,” Science, vol. 288, pp. 877-880, 2000.
[11] R. Matadeen, A. Patwardhan, B.G.E. Orlova, T. Pape, M. Cuff, F. Mueller, and R.B.M. van Heel, “The E. Coli Large Ribosomal Subunit at 7.5 Angstrom Resolution,” Structure, vol. 7, pp. 1575-1583, 1999.
[12] IEEE Trans. Image Processing, special issue on molecular and cellular bioimaging, R.F. Murphy, E. Meijering, and G. Danuser, guest eds., vol. 14, no. 9, 2005.
[13] S. Ludtke, P. Baldwin, and W. Chiu, “EMAN: Semiautomated Software for High-Resolution Single-Particle Reconstructions,” J.Structural Biology, vol. 128, pp. 82-97, 1999.
[14] J. Frank, M. Radermacher, P. Penczek, J. Zhu, Y. Li, M. Ladjadj, and A. Leith, “SPIDER and WEB: Processing and Visualization of Images in 3D Electron Microscopy and Related Fields,” J.Structural Biology, vol. 116, pp. 190-199, 1996.
[15] M.V. Heel, G. Harauz, E. Orlova, R. Schmidt, and M. Schatz, “A New Generation of the IMAGIC Image Processing System,” J.Structural Biology, vol. 116, pp. 17-24, 1996.
[16] Z. Yu and C. Bajaj, “Automatic Ultra-Structure Segmentation of Reconstructed Cryo-Em Maps of Icosahedral Viruses,” IEEE Trans. Image Processing, vol. 14, no. 9, pp. 1324-1337, 2005.
[17] M. Baker, Z. Yu, W. Chiu, and C. Bajaj, “Automated Segmentation of Molecular Subunits in Electron Cryomicroscopy Density Maps,” J. Structural Biology, vol. 156, no. 3, pp. 432-441, 2006.
[18] W. Chiu, “What Does Electron Cryomicroscopy Provide that X-Ray Crystallography and NMR Spectroscopy Cannot,” Ann. Rev. Biophysics and Biomolecular Structure, vol. 22, pp. 233-255, 1993.
[19] L. Amos, R. Henderson, and P.N. Unwin, “Three-Dimensional Structure Determination by Electron Microscopy of Two-Dimensional Crystals,” Progress in Biophysics and Molecular Biology, vol. 39, pp. 183-231, 1982.
[20] B. McEwen and M. Marko, “The Emergence of Electron Tomography as an Important Tool for Investigating Cellular Ultrastructure,” J. Histochemistry and Cytochemistry, vol. 49, no. 5, pp. 553-563, 2001.
[21] A. Koster, R. Grimm, D. Typke, R. Hegerl, A. Stoschek, J. Walz, and W. Baumeister, “Perspectives of Molecular and Cellular Electron Tomography,” J. Structural Biology, vol. 120, pp. 276-308, 1997.
[22] P. Penczek, M. Marko, K. Buttle, and J. Frank, “Double-Tilt Electron Tomography,” Ultramicroscopy, vol. 60, pp. 393-410, 1995.
[23] J. Frank, Three-Dimensional Electron Microscope of Macromolecular Assemblies. Academic Press, 1996.
[24] S. Ludtke, D. Chen, J. Song, D. Chuang, and W. Chiu, “Seeing Groel at 6-Angstrom Resolution by Single Particle Electron Cryomicroscopy,” Structure, vol. 12, pp. 1129-1136, 2004.
[25] A. Roseman, “Particle Finding in Electron Micrographs Using a Fast Local Correlation Algorithm,” Ultramicroscopy, vol. 94, pp.225-236, 2003.
[26] Z. Yu and C. Bajaj, “Detecting Circular and Rectangular Particles Based on Geometric Feature Detection in Electron Micrographs,” J. Structural Biology, vol. 145, nos. 1-2, pp. 168-180, 2004.
[27] W. Nicholson and R. Glaeser, “Review: Automatic Particle Detection in Electron Microscopy,” J. Structural Biology, vol. 133, nos. 2-3, pp. 90-101, 2001.
[28] F. Sigworth, “A Maximum-Likelihood Approach to Single-Particle Image Refinement,” J. Structural Biology, vol. 122, pp. 328-339, 1998.
[29] M. Sjors, M. Valle, R. Nuñez, C. Sorzano, R. Marabini, G. Herman, and J. Carazo, “Maximum Likelihood Multi-Reference Refinement for Electron Microscopy Images,” J. Molecular Biology, vol. 348, pp.139-149, 2005.
[30] W. Wriggers and P. Chacon, “Modeling Tricks and Fitting Techniques for Multiresolution Structures,” Structure, vol. 9, pp.779-788, 2001.
[31] J. Fernandez, J.R. Sanjurjo, and J. Carazo, “A Spectral Estimation Approach to Contrast Transfer Function Detection in Electron Microscopy,” Ultramicroscopy, vol. 68, pp. 267-295, 1997.
[32] J. Weickert, Anisotropic Diffusion in Image Processing. ECMI Series, Teubner, Stuttgart, 1998.
[33] Z. Yu and C. Bajaj, “A Fast and Adaptive Algorithm for Image Contrast Enhancement,” Proc. IEEE Int'l Conf. Image Processing (ICIP '04), pp. 1001-1004, 2004.
[34] D. VanArsdale, “Homogeneous Transformation Matrices for Computer Graphics,” Computers and Graphics, vol. 18, no. 2, pp.177-191, 1994.
[35] M. Morais, K. Choi, J. Koti, P. Chipman, D. Anderson, and M. Rossmann, “Conservation of the Capsid Structure in Tailed DSDNA Phage: The Pseudoatomic Structure of phi29,” Molecular Cell, vol. 18, pp. 149-159, 2005.
[36] Y. Tao, N. Olson, W. Xu, D. Anderson, M. Rossmann, and T. Baker, “Assembly of a Tailed Bacterial Virus and Its Genome Release Studied in Three Dimensions,” Cell, vol. 95, pp. 431-437, 1998.
[37] E. Sifakis and G. Tziritas, “Moving Object Localization Using a Multi-Label Fast Marching Algorithm,” Signal Processing: Image Comm., vol. 16, no. 10, pp. 963-976, 2001.
[38] W. Wriggers, R. Milligan, and J. McCammon, “Situs: A Package for Docking Crystal Structures into Low-Resolution Maps from Electron Microscopy,” J. Structural Biology, vol. 125, pp. 185-195, 1999.
[39] W. Jiang, M. Baker, S. Ludtke, and W. Chiu, “Bridging the Information Gap: Computational Tools for Intermediate Resolution Structure Interpretation,” J. Molecular Biology, vol. 308, pp.1033-1044, 2001.
[40] Y. Kong and J. Ma, “A Structural-Informatics Approach for Mining B-Sheets: Locating Sheets in Intermediate-Resolution Density Maps,” J. Molecular Biology, vol. 332, pp. 399-413, 2003.
[41] J.-J. Fernandez and S. Li, “An Improved Algorithm for Anisotropic Nonlinear Diffusion for Denoising Cryo-Tomograms,” J.Structural Biology, vol. 144, pp. 152-161, 2003.
[42] G. Kühne, J. Weickert, O. Schuster, and S. Richter, “A Tensor-Driven Active Contour Model for Moving Object Segmentation,” Proc. Eighth IEEE Int'l Conf. Image Processing (ICIP '01), pp. 73-76, 2001.
[43] I. Jollife, Principal Component Analysis. Springer-Verlag, 1986.
[44] L. Lam, S. Lee, and C. Suen, “Thinning Methodologies—A Comprehensive Survey,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 9, pp. 869-885, Sept. 1992.
[45] R. Ogniewicz and O. Kubler, “Hierarchic Voronoi Skeletons,” Pattern Recognition, vol. 28, no. 3, pp. 343-359, 1995.
[46] J. Jang and K. Hong, “A Pseudo-Distance Map for the Segmentation-Free Skeletonization of Gray-Scale Images,” Proc. Int'l Conf. Computer Vision (ICCV '01), pp. 18-23, 2001.
[47] Z. Yu and C. Bajaj, “A Segmentation-Free Approach for Skeletonization of Gray-Scale Images via Anisotropic Vector Diffusion,” Proc. Int'l Conf. Computer Vision and Pattern Recognition (CVPR '04), pp. 415-420, 2004.
[48] A. Lopes and K. Brodlie, “Improving the Robustness and Accuracy of the Marching Cube Algorithm for Isosurfacing,” IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 1, pp.16-29, Jan.-Mar. 2003.
[49] W. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics, vol. 21, no. 4, pp. 163-169, 1987.

Index Terms:
Structure Analysis, Alignment, Similarity Measure,Segmentation, Secondary Structure Detection, Skeletonization,Cryo-EM Maps, 3D Reconstruction
Zeyun Yu, Chandrajit Bajaj, "Computational Approaches for Automatic Structural Analysis of Large Biomolecular Complexes," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 5, no. 4, pp. 568-582, Oct.-Dec. 2008, doi:10.1109/TCBB.2007.70226
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