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Issue No.04 - July/August (2011 vol.8)
pp: 867-875
Yosi Shibberu , Rose-Hulman Institute of Technology, Terre Haute
Allen Holder , Rose-Hulman Institute of Technology, Terre Haute
ABSTRACT
A new intrinsic geometry based on a spectral analysis is used to motivate methods for aligning protein folds. The geometry is induced by the fact that a distance matrix can be scaled so that its eigenvalues are positive. We provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach and use it to motivate two alignment algorithms. The first uses eigenvalues alone and dynamic programming to quickly compute a fold alignment. Family identification results are reported for the Skolnick40 and Proteus300 data sets. The second algorithm extends our spectral method by iterating between our intrinsic geometry and the 3D geometry of a fold to make high-quality alignments. Results and comparisons are reported for several difficult fold alignments. The second algorithm's ability to correctly identify fold families in the Skolnick40 and Proteus300 data sets is also established.
INDEX TERMS
Protein structure alignment, structural bioinformatics, contact maps, spectral methods.
CITATION
Yosi Shibberu, Allen Holder, "A Spectral Approach to Protein Structure Alignment", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 4, pp. 867-875, July/August 2011, doi:10.1109/TCBB.2011.24
REFERENCES
[1] R. Andonov, N. Malod-Dognin, and N. Yanev, “Maximum Contact Map Overlap Revisited,” J. Computational Biology, vol. 18, no. 1, pp. 1-15, 2011.
[2] R. Andonov, N. Yanev, and N. Malod-Dognin, “An Efficient Lagrangian Relaxation for the Contact Map Overlap Problem,” Proc. WABI '08: Eighth Int'l Workshop Algorithms in Bioinformatics, pp. 162-173, 2008.
[3] A. Andreeva, D. Howorth, J.-M. Chandonia, S.E. Brenner, T.J.P. Hubbard, C. Chothia, and A.G. Murzin, “Data Growth and Its Impact on the Scop Database: New Developments,” Nucleic Acids Research, vol. 36 (Database issue), pp. D419-D425, Jan. 2008.
[4] H.M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T.N. Bhat, H. Weissig, I.N. Shindyalov, and P.E. Bourne, “The Protein Data Bank,” Nucleic Acids Research, vol. 28, no. 1, pp. 235-242, Jan. 2000.
[5] R. Blankenbecler, M. Ohlsson, C. Peterson, and M. Ringner, “Matching Protein Structures with Fuzzy Alignments,” Proc. Nat'l Academy of Sciences USA, vol. 100, no. 21, pp. 11936-11940, Oct. 2003.
[6] F.J. Burkowski, Structural Bioinformatics an Algorithmic Approach. CRC Press, 2009.
[7] A. Caprara, R. Carr, S. Istrail, G. Lancia, and B. Walenz, “1001 Optimal Pdb Structure Alignments: Integer Programming Methods for Finding the Maximum Contact Map Overlap,” J. Computational Biology, vol. 11, no. 1, pp. 27-52, 2004.
[8] J.-M. Chandonia, G. Hon, N.S. Walker, L. Lo Conte, P. Koehl, M. Levitt, and S.E. Brenner, “The Astral Compendium in 2004,” Nucleic Acids Research, vol. 32 (Database issue), pp. D189-D192, Jan. 2004.
[9] L. Chen, L.-Y. Wu, Y. Wang, S. Zhang, and X.-S. Zhang, “Revealing Divergent Evolution, Identifying Circular Permutations and Detecting Active-Sites by Protein Structure Comparison,” BMC Structural Biology, vol. 6, article no. 18, 2006.
[10] P.J.A. Cock, T. Antao, J.T. Chang, B.A. Chapman, C.J. Cox, A. Dalke, I. Friedberg, T. Hamelryck, F. Kauff, B. Wilczynski, and M.J.L. de Hoon, “Biopython: Freely Available Python Tools for Computational Molecular Biology and Bioinformatics,” Bioinformatics, vol. 25, no. 11, pp. 1422-1423, June 2009.
[11] G.M. Crippen and T.F. Havel, Distance Geometry and Molecular Conformations. Wiley, 1988.
[12] I. Eidhammer, I. Jonassen, and W. Taylor, Protein Bioinformatics: An Algorithmic Approach to Sequence and Structure Analysis. John Wiley and Sons, 2004.
[13] S.G. Galaktionov and G.R. Marshall, “Prediction of Protein Structure in Terms of Intraglobular Contacts: 1D to 2D to 3D,” Fourth Int'l Conf. Computational Biology, Intelligent Systems for Molecular Biology '96, June 1996.
[14] H. Hasegawa and L. Holm, “Advances and Pitfalls of Protein Structural Alignment,” Current Opinion in Structural Biology, vol. 19, no. 3, pp. 341-348, June 2009.
[15] T.F. Havel, I.D. Kuntz, and G.M. Crippen, “The Combinatorial Distance Geometry Method for the Calculation of Molecular Conformation. i. a New Approach to an Old Problem,” J. Theoretical Biology, vol. 104, no. 3, pp. 359-381, Oct. 1983.
[16] L. Holm and C. Sander, “Protein Structure Comparison by Alignment of Distance Matrices,” J. Molecular Biology, vol. 233, no. 1, pp. 123-138, Sept. 1993.
[17] N.C. Jones and P.A. Pevzner, An Introduction to Bioinformatics Algorithms. MIT Press, 2004.
[18] W. Kabsch, “A Discussion of the Solution for the Best Rotation to Relate Two Sets of Vectors,” Acta Crystallographica A, vol. 34, pp. 827-828, 1978.
[19] G. Lancia, R. Carr, B. Walenz, and S. Istrail, “101 Optimal Pdb Structure Alignments: A Branch-and-Cut Algorithm for the Maximum Contact Map Overlap Problem,” Proc. Fifth Ann. Int'l Conf. Computational Biology, pp. 143-202, 2001.
[20] P. Di Lena, P. Fariselli, L. Margara, M. Vassura, and R. Casadio, “Fast Overlapping of Protein Contact Maps by Alignment of Eigenvectors,” Bioinformatics, vol. 26, no. 18, pp. 2250-2258, 2010.
[21] M. Menke, B. Berger, and L. Cowen, “Matt: Local Flexibility Aids Protein Multiple Structure Alignment,” PLoS Computational Biology, vol. 4, no. 1, p. e10, Jan. 2008.
[22] S.B. Needleman and C.D. Wunsch, “A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins,” J. Moleculer Biology, vol. 48, no. 3, pp. 443-453, Mar. 1970.
[23] B. Noble and J.W. Daniel, Applied Linear Algebra. Prentice-Hall, 1977.
[24] M.T. Oakley, D. Barthel, Y. Bykov, J.M. Garibaldi, E.K. Burke, N. Krasnogor, and J.D. Hirst, “Search Strategies in Structural Bioinformatics,” Current Protein and Peptide Science, vol. 9, no. 3, pp. 260-274, June 2008.
[25] A. Poleksic, “Algorithms for Optimal Protein Structure Alignment,” Bioinformatics, vol. 25, no. 21, pp. 2751-2756, Nov. 2009.
[26] S. Saitoh, T. Nakai, and K. Nishikawa, “A Geometrical Constraint Approach for Reproducing the Native Backbone Conformation of a Protein,” Proteins, vol. 15, no. 2, pp. 191-204, Feb. 1993.
[27] Y. Shibberu, A. Holder, and K. Lutz, “Fast Protein Structure Alignment,” Lecture Notes in Computer Science, M. Borodovsky, ed., vol. 6053, pp. 152-165, Springer-Verlag, 2010.
[28] T. Shibuya, “Fast Hinge Detection Algorithms for Flexible Protein Structures,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 7, no. 2, pp. 333-341, Apr.-June 2010.
[29] T. Shibuya, J. Jansson, and K. Sadakane, “Linear-Time Protein 3D Structure Searching with Insertions and Deletions,” Algorithms for Molecular Biology, vol. 5, article no. 7, 2010.
[30] I.N. Shindyalov and P.E. Bourne, “Protein Structure Alignment by Incremental Combinatorial Extension (ce) of the Optimal Path,” Protein Eng., vol. 11, no. 9, pp. 739-747, Sept. 1998.
[31] M. Vendruscolo, E. Kussell, and E. Domany, “Recovery of Protein Structure from Contact Maps,” Folding and Design, vol. 2, no. 5, pp. 295-306, 1997.
[32] Y. Wang, L.-Y. Wu, J.-H. Zhang, Z.-W. Zhan, X.-S. Zhang, and L. Chen, “Evaluating Protein Similarity from Coarse Structures,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 6, no. 4, pp. 583-593, Oct.-Dec. 2009.
[33] W. Xie and N.V. Sahinidis, “A Reduction-Based Exact Algorithm for the Contact Map Overlap Problem,” J. Computational Biology, vol. 14, no. 5, pp. 637-654, June 2007.
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