This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Fast Hinge Detection Algorithms for Flexible Protein Structures
April-June 2010 (vol. 7 no. 2)
pp. 333-341
Tetsuo Shibuya, University of Tokyo, Tokyo
Analysis of conformational changes is one of the keys to the understanding of protein functions and interactions. For the analysis, we often compare two protein structures, taking flexible regions like hinge regions into consideration. The Root Mean Square Deviation (RMSD) is the most popular measure for comparing two protein structures, but it is only for rigid structures without hinge regions. In this paper, we propose a new measure called RMSD considering hinges (RMSDh) and its variant {\rm RMSDh}^{(k)} for comparing two flexible proteins with hinge regions. We also propose novel efficient algorithms for computing them, which can detect the hinge positions at the same time. The RMSDh is suitable for cases where there is one small hinge region in each of the two target structures. The new algorithm for computing the RMSDh runs in linear time, which is the same as the time complexity for computing the RMSD and is faster than any of previous algorithms for hinge detection. The {\rm RMSDh}^{(k)} is designed for comparing structures with more than one hinge region. The {\rm RMSDh}^{(k)} measure considers at most k small hinge region, i.e., the {\rm RMSDh}^{(k)} value should be small if the two structures are similar except for at most k hinge regions. To compute the value, we propose an O(kn^{2})-time and O(n)-space algorithm based on a new dynamic programming technique. With the same computational time and space, we can enumerate the predicted hinge positions. We also test our algorithms against actual flexible protein structures, and show that the hinge positions can be correctly detected by our algorithms.

[1] K.S. Arun, T.S. Huang, and S.D. Blostein, "Least-Squares Fitting of Two 3D Point Sets," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, pp. 698-700, 1987.
[2] 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, pp. 235-242, 2000.
[3] N.S. Boutonnet, M.J. Rooman, and S.J. Wodak, "Automatic Analysis of Protein Conformational Changes by Multiple Linkage Clustering," J. Molecular Biology, vol. 253, pp. 633-647, 1995.
[4] K.L. Damm and H.A. Carlson, "Gaussian-Weighted RMSD Superposition of Proteins: A Structural Comparison for Flexible Proteins and Predicted Protein Structures," Biophysical J., vol. 90, pp. 4558-4573, 2006.
[5] N. Echols, D. Milburn, and M. Gerstein, "MolMovDB: Analysis and Visualization of Conformational Change and Structural Flexibility," Nucleic Acids Research, vol. 31, no. 1, pp. 478-482, 2003.
[6] D.W. Eggert, A. Lorusso, and R.B. Fisher, "Estimating 3-D Rigid Body Transformations: A Comparison of Four Major Algorithms," Machine Vision and Applications, vol. 9, pp. 272-290, 1997.
[7] I. Eidhammer, I. Jonassen, and W.R. Taylor, "Structure Comparison and Structure Patterns," J. Computational Biology, vol. 7, no. 5, pp. 685-716, 2000.
[8] U. Emekil, D. Schneidman-Duhovny, H.J. Wolfson, R. Nussinov, and T. Haliloglu, "HingeProt: Automated Prediction of Hinges in Protein Structures," Proteins, vol. 79, pp. 1219-1227, 2008.
[9] S. Flores, N. Echols, D. Milburn, B. Hespenheide, K. Keating, J. Lu, S. Wells, E.Z. Yu, M. Thorpe, and M. Gerstein, "The Database of Macromolecular Motions: New Features Added at the Decade Mark," Nucleic Acids Research, vol. 34, pp. D296-D301, 2006.
[10] S.C. Flores and M.B. Gerstein, "FlexOracle: Predicting Flexible Hinges by Identification of Stable Domains," BMC Bioinformatics, vol. 8, p. 215, 2007.
[11] S.C. Flores, L.J. Lu, J. Yang, N. Carriero, and M.B. Gerstein, "Hinge Atlas: Relating Protein Sequence to Sites of Structural Flexibility," BMC Bioinformatics, vol. 8, p. 167, 2007.
[12] M. Gerstein and C. Chothia, "Analysis of Protein Loop Closure, Two Types of Hinges Produce One Motion in Lactate Dehydrogenase," J. Molecular Biology, vol. 220, pp. 133-149, 1991.
[13] G.H. Golub and C.F. Van Loan, Matrix Computation, third ed. John Hopkins Univ. Press, 1996.
[14] D.S. Hirschberg, "A Linear Space Algorithm for Computing Maximal Common Subsequences," Comm. ACM, vol. 18, pp. 341-343, 1975.
[15] E.S. Huang, E.P. Rock, and S. Subbiah, "Automatic and Accurate Method for Analysis of Proteins That Undergo Hinge-Mediated Domain and Loop Movements," Current Biology, vol. 3, no. 11, pp. 740-748, 1993.
[16] D.J. Jacobs, A.J. Rader, L.A. Kuhn, and M.F. Thorpe, "Protein Flexibility Predictions Using Graph Theory," Proteins: Structure, Function, and Genetics, vol. 44, pp. 150-165, 2001.
[17] W. Kabsch, "A Solution for the Best Rotation to Relate Two Sets of Vectors," Acta Crystallographica, vol. A32, pp. 922-923, 1976.
[18] W. Kabsch, "A Discussion of the Solution for the Best Rotation to Relate Two Sets of Vectors," Acta Crystallographica, vol. A34, pp. 827-828, 1978.
[19] C. Lemmen and T. Lengauer, "Computational Methods for the Structural Alignment of Molecules," J. Computer-Aided Molecular Design, vol. 14, pp. 215-232, 2000.
[20] A. Nigham and D. Hsu, "Protein Conformational Flexibility Analysis with Noisy Data," Proc. Int'l Conf. Research in Computational Molecular Biology (RECOMB), 2007.
[21] M.E. Ochagavia, J. Richeele, and S.J. Wodak, "Advanced Pairwise Structure Alignments of Proteins and Analysis of Conformational Changes," Bioinformatics, vol. 18, no. 4, pp. 637-640, 2002.
[22] A.L. Perryman, J. Lin, and A. McCammon, "HIV-1 Protease Molecular Dynamics of a Wild-Type and of the v82f/i84v Mutant: Possible Contributions to Drug Resistance and a Potential New Target Site for Drugs," Protein Science, vol. 13, pp. 1108-1123, 2004.
[23] G. Qi, R. Lee, and S. Hayward, "A Comprehensive and Non-Redundant Database of Protein Domain Movements," Bioinformatics, vol. 21, no. 12, pp. 2832-2838, 2005.
[24] J.T. Schwartz and M. Sharir, "Identification of Partially Obscured Objects in Two and Three Dimensions by Matching Noisy Characteristic Curves," Int'l J. Robotics Research, vol. 6, pp. 29-44, 1987.
[25] M. Shatsky, R. Nussinov, and H.J. Wolfson, "FlexProt: Alignment of Flexible Protein Structures without a Predefinition of Hinge Regions," J. Computational Biology, vol. 11, no. 1, pp. 83-106, 2004.
[26] T. Shibuya, "Efficient Substructure RMSD Query Algorithms," J. Computational Biology, vol. 14, no. 9, pp. 1201-1207, 2007.
[27] T.B. Thompson, M.G. Thomas, J.C. Escalante-Semerena, and I. Rayment, "Three-Dimensional Structure of Adenosylcobinamide Kinase/Adenosylcobinamide Phosphate Guanylyltransferase from Salmonella Typhimurium Determined to 2.3 $\AA$ Resolution," Biochemistry, vol. 37, no. 21, pp. 7686-7695, 1998.
[28] H.J. Wolfson, M. Shatsky, D. Scheneidman-Duhovny, O. Dror, A. Shulman-Peleg, B. Ma, and R. Nussinov, "From Structure to Function: Methods and Applications," Current Protein and Peptide Science, vol. 6, pp. 171-183, 2005.
[29] W. Wriggers and K. Schulten, "Protein Domain Movements: Detection of Rigid Domains and Visualization of Hinges in Comparisons of Atomic Coordinates," Proteins: Structure, Function, and Genetics, vol. 29, pp. 1-14, 1997.
[30] Y. Ye and A. Godzik, "Flexible Structure Alignment by Chaining Aligned Fragment Pairs Allowing Twists," Bioinformatics, vol. 19, no. Suppl. 2, pp. ii246-ii255, 2003.

Index Terms:
Algorithm, protein hinge detection, protein 3D structure comparison, dynamic programming.
Citation:
Tetsuo Shibuya, "Fast Hinge Detection Algorithms for Flexible Protein Structures," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 7, no. 2, pp. 333-341, April-June 2010, doi:10.1109/TCBB.2008.62
Usage of this product signifies your acceptance of the Terms of Use.