The Community for Technology Leaders
RSS Icon
Issue No.06 - November/December (2011 vol.8)
pp: 1653-1666
Thomas Fober , Philipps-Universität Marburg, Marburg
Serghei Glinca , Philipps-Universität Marburg, Marburg
Gerhard Klebe , Philipps-Universität Marburg, Marburg
Eyke Hüllermeier , Philipps-Universität Marburg, Marburg
Geometric objects are often represented approximately in terms of a finite set of points in three-dimensional euclidean space. In this paper, we extend this representation to what we call labeled point clouds. A labeled point cloud is a finite set of points, where each point is not only associated with a position in three-dimensional space, but also with a discrete class label that represents a specific property. This type of model is especially suitable for modeling biomolecules such as proteins and protein binding sites, where a label may represent an atom type or a physico-chemical property. Proceeding from this representation, we address the question of how to compare two labeled points clouds in terms of their similarity. Using fuzzy modeling techniques, we develop a suitable similarity measure as well as an efficient evolutionary algorithm to compute it. Moreover, we consider the problem of establishing an alignment of the structures in the sense of a one-to-one correspondence between their basic constituents. From a biological point of view, alignments of this kind are of great interest, since mutually corresponding molecular constituents offer important information about evolution and heredity, and can also serve as a means to explain a degree of similarity. In this paper, we therefore develop a method for computing pairwise or multiple alignments of labeled point clouds. To this end, we proceed from an optimal superposition of the corresponding point clouds and construct an alignment which is as much as possible in agreement with the neighborhood structure established by this superposition. We apply our methods to the structural analysis of protein binding sites.
Structural bioinformatics, protein binding sites, protein structure comparison, similarity, computational geometry, point clouds, graphs, alignment, evolutionary algorithms, fuzzy logic.
Thomas Fober, Serghei Glinca, Gerhard Klebe, Eyke Hüllermeier, "Superposition and Alignment of Labeled Point Clouds", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 6, pp. 1653-1666, November/December 2011, doi:10.1109/TCBB.2011.42
[1] H. Alt, K. Mehlhorn, H. Wagener, and E. Welzl, “Congruence, Similarity, and Symmetries of Geometric Objects,” Discrete and Computational Geometry, vol. 3, pp. 237-256, 1987.
[2] F.R. Bach, “Graph Kernels between Point Clouds,” Proc. Int'l Conf. Machine Learning, pp. 25-32, 2008.
[3] O. Bachar, D. Fischer, R. Nussinov, and H.J. Wolfson, “A Computer Vision Based Technique for 3-D Sequence-Independent Structural Comparison of Proteins,” Protein Eng., vol. 6, no. 3, pp. 279-287, 1993.
[4] T. Bartz-Beielstein, Experimental Research in Evolutionary Computation: The New Experimentalism. Springer, 2006.
[5] H.-G. Beyer and H.-P. Schwefel, “Evolution Strategies: A Comprehensive Introduction,” Natural Computing, vol. 1, no. 1, pp. 3-52, 2002.
[6] M. Böhm, J. Stürzebecher, and G. Klebe, “Three-Dimensional Quantitative Structure-Activity Relationship Analyses Using Comparative Molecular Field Analysis and Comparative Molecular Similarity Indices Analysis to Elucidate Selectivity Differences of Inhibitors Binding to Trypsin, Thrombin, and Factor xa,” J. Medicinal Chemistry, vol. 42, no. 3, pp. 458-477, 1999.
[7] K.M. Borgwardt, “Graph Kernels,” PhD thesis, Ludwig-Maximilians-Universität München, 2007.
[8] K.M. Borgwardt and H.P. Kriegel, “Shortest-Path Kernels on Graphs,” Proc. Int'l Conf. Data Mining, pp. 74-81, 2005.
[9] F. Briganti, S. Mangani, P. Orioli, A. Scozzafava, G. Vernaglione, and C.T. Supuran, “Carbonic Anhydrase Activators: X-Ray Crystallographic and Spectroscopic Investigations for the Interaction of Isozymes I and II with Histamine,” Biochemistry, vol. 36, no. 34, pp. 10384-10392, 1997.
[10] H. Bunke and X. Jiang, “Graph Matching and Similarity,” Intelligent Systems and Interfaces, vol. 15, pp. 281-304, Kluwer Academic Publishers, 2000.
[11] H. Bunke, X. Jiang, and A. Kandel, “On the Minimum Common Supergraph of Two Graphs,” Computing, vol. 65, no. 1, pp. 13-25, 2000.
[12] W.J. Christmas, J. Kittler, and M. Petrou, “Structural Matching in Computer Vision Using Probabilistic Relaxation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 749-764, Aug. 1995.
[13] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry. Springer, 2000.
[14] M. Ferraroni, S. Tilli, F. Briganti, W.R. Chegwidden, C.T. Supuran, K.E. Wiebauer, R.E. Tashian, and A. Scozzafava, “Crystal Structure of a Zinc-Activated Variant of Human Carbonic Anhydrase I, CA I Michigan 1: Evidence for a Second Zinc Binding Site Involving Arginine Coordination,” Biochemistry, vol. 41, no. 20, pp. 6237-6244, 2002.
[15] T. Gärtner, Kernels for Structured Data. World Scientific, 2008.
[16] J. Gasteiger and T. Engel, Chemoinformatics. Wiley-VCH, 2003.
[17] M.T. Goodrich, J.S.B. Mitchell, and M.W. Orletsky, “Practical Methods for Approximate Geometric Pattern Matching under Rigid Motions,” Proc. Ann. Symp. Computational Geometry, pp. 103-112, 1994.
[18] M. Hendlich, F. Rippmann, and G. Barnickel, “LIGSITE: Automatic and Efficient Detection of Potential Small Molecule-Binding Sites in Proteins,” J. Molecular Graphics and Modelling, vol. 15, pp. 359-363, 1997.
[19] D.P. Huttenlocher, K. Kedem, and J.M. Kleinberg, “On Dynamic Voronoi Diagrams and the Minimum Hausdorff Distance for Point Sets under Euclidean Motion in the Plane,” Proc. Eighth Ann. Symp. Computational Geometry, pp. 110-119, 1992.
[20] D.P. Huttenlocher, K. Kedem, and M. Sharir, “The Upper Envelope of Voronoi Surfaces and Its Applications,” Discrete and Computational Geometry, vol. 9, no. 1, pp. 267-291, 1993.
[21] W. Kabsch, “A Solution of the Best Rotation to Relate Two Sets of Vectors,” Acta Crystallographica, vol. 32, pp. 922-923, 1976.
[22] G. Karypis CLUTO-Family of Data Clustering Software Tools v 2.1.1., , 2006.
[23] E.P. Klement, R. Mesiar, and E. Pap, Triangular Norms. Kluwer Academic Publishers, 2002.
[24] H.W. Kuhn, “The Hungarian Method for the Assignment Problem,” Naval Research Logistics, vol. 52, no. 1, pp. 7-21, 2005.
[25] Y. Lamdan and H.J. Wolfson, “Geometric Hashing: A General and Efficient Model-Based Recognition Scheme,” Proc. Second Int'l Conf. Computer Vision, pp. 238-249, 1988.
[26] N. Leibowitz, Z.Y. Fligelman, R. Nussinov, and H.J. Wolfson, “Multiple Structural Alignment and Core Detection by Geometric Hashing,” Proc. Int'l Conf. Intelligent Systems for Molecular Biology, pp. 169-177, 1999.
[27] N. Leibowitz, R. Nussinov, and H.J. Wolfson, “MUSTA-A General, Efficient, Automated Method for Multiple Structure Alignment and Detection of Common Motifs: Application to Proteins,” J. Computational Biology, vol. 8, no. 2, pp. 93-121, 2001.
[28] S. Lindskog, “Structure and Mechanism of Carbonic Anhydrase,” Pharmacology and Therapeutics, vol. 74, no. 1, pp. 1-20, 1997.
[29] F. Mémoli and G. Sapiro, “Comparing Point Clouds,” Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, pp. 32-40, 2004.
[30] W.R. Pearson and D.J. Lipman, “Improved Tools for Biological Sequence Comparison,” Proc. Nat'l Academy of Sciences USA, vol. 85, no. 8, pp. 2444-2448, 1988.
[31] J. Raymond and P. Willett, “Maximum Common Subgraph Isomorphism Algorithms for the Matching of Chemical Structures,” J. Computer-Aided Molecular Design, vol. 16, no. 7, pp. 521-533, 2002.
[32] S. Schmitt, D. Kuhn, and G. Klebe, “A New Method to Detect Related Function among Proteins Independent of Sequence and Fold Homology,” J. Molecular Biology, vol. 323, no. 2, pp. 387-406, 2002.
[33] M. Shatsky, R. Niussinov, and H.J. Wolfson, “A Method for Simultaneous Alignment of Multiple Protein Structures,” Proteins: Structure, Function, and Bioinformatics, vol. 56, pp. 143-156, 2004.
[34] M. Shatsky, A. Shulman-Peleg, R. Nussinov, and H.J. Wolfson, “The Multiple Common Point Set Problem and Its Application to Molecule Binding Pattern Detection,” J. Computational Biology, vol. 13, no. 2, pp. 407-428, 2006.
[35] P.N. Suganthan, E. Teoh, and D. Mital, “Pattern Recognition by Graph Matching Using the Potts MFT Neural Networks,” Pattern Recognition, vol. 28, no. 7, pp. 997-1009, 1995.
[36] C.T. Supuran and A. Scozzafava, “Carbonic Anhydrases as Targets for Medicinal Chemistry,” Bioorganic and Medicinal Chemistry, vol. 15, no. 13, pp. 4336-4350, 2007.
[37] Y. Wang and N. Ishii, “Method of Similarity Metrics for Structured Representations,” Expert Systems with Applications, vol. 12, pp. 89-100, 1997.
[38] A. Weber, A. Casini, A. Heine, D. Kuhn, C.T. Supuran, A. Scozzafava, and G. Klebe, “Unexpected Nanomolar Inhibition of Carbonic Anhydrase by COX-2-Selective Celecoxib: New Pharmacological Opportunities Due to Related Binding Site Recognition,” J. Medical Chemistry, vol. 47, no. 3, pp. 550-557, 2004.
[39] N. Weskamp, E. Hüllermeier, and G. Klebe, “Merging Chemical and Biological Space: Structural Mapping of Enzyme Binding Pocket Space,” Proteins, vol. 76, no. 2, pp. 317-330, 2009.
[40] N. Weskamp, E. Hüllermeier, D. Kuhn, and G. Klebe, “Multiple Graph Alignment for the Structural Analysis of Protein Active Sites,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 2, pp. 310-320, Apr.-June 2007.
[41] T.J. Wheeler and J.D. Kececioglu, “Multiple Alignment by Aligning Alignments,” Bioinformatics, vol. 23, no. 13, pp. i559-i568, 2007.
[42] H.J. Wolfson and I. Rigoutsos, “Geometric Hashing: An Overview,” IEEE Computational Science and Eng., vol. 4, no. 4, pp. 10-21, Oct.-Dec. 1997.
[43] L. Xu and E. Oja, “Improved Simulated Annealing, Boltzmann Machine, and Attributed Graph Matching,” Proc. EURASIP Workshop Neural Networks, pp. 151-160, 1990.
[44] R.R. Yager, “On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decisionmaking,” IEEE Trans. Systems, Man and Cybernetics, vol. 18, no. 1, pp. 183-190, Jan./Feb. 1988.
[45] L.A. Zadeh, “A Computational Approach to Fuzzy Quantifiers in Natural Languages,” Computing and Math. with Applications, vol. 9, pp. 149-184, 1983.
21 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool