Abstract
We propose a new method for clustering 3D protein structures. In our method, the 3D structure of a protein is represented by a linear subspace, which is generated using PCA from the set of synthesized multi-view images of the protein. The similarity of two protein structures is then defined by the canonical angles between the corresponding subspaces. The merit of this approach is that we can avoid the difficulties of protein structure alignments because this similarity measure does not rely on the precise alignment and geometry of each alpha carbon atom. In this approach, we tackle the protein structure clustering problem by considering the set of subspaces corresponding to the various proteins. The clustering of subspaces with the same dimension is equivalent to the clustering of a corresponding set of points on a Grassmann manifold. Therefore, we call our approach the Grassmannian Protein Clustering Method (GPCM). We evaluate the effectiveness of our method through experiments on the clustering of randomly selected proteins from the Protein Data Bank into four classes: alpha, beta, alpha/beta, alpha+beta (with multi-domain protein). The results show that GPCM outperforms the k-means clustering with Gauss Integrals Tuned, which is a state-of-the-art descriptor of protein structure.
Chapter PDF
Similar content being viewed by others
References
Holm, L., Sander, C.: DALI: a network tool for protein structure comparison. Trends Biochem. Sci. 20, 478–480 (1995)
Shindyalov, I., Bourne, P.: Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. Protein Engineering 11, 739–747 (1998)
Orengo, C.A., Taylor, W.R.: SSAP: Sequential structure alignment program for protein structure comparison. Methods in Enzymology 266, 617–635 (1996)
Røgen, P., Bohr, H.G.: A new family of global protein shape descriptors. Mathematical Biosciences 182(2), 167–181 (2003)
Røgen, P.: Evaluating protein structure descriptors and tuning Gauss Integrals based descriptors. Journal of Physics Condensed Matter 17, 1523–1538 (2005)
Suryanto, C.H., Jiang, S., Fukui, K.: Protein structures similarity based on multi-view images generated from 3D molecular visualization. In: International Conf. on Pattern Recognition, ICPR 2012 (to appear 2012)
Chatelin, F.: Eigenvalues of matrices. John Wiley & Sons, Chichester (1993)
Jmol: an open-source Java viewer for chemical structures in 3D, http://www.jmol.org/
Yamaguchi, O., Fukui, K., Maeda, K.: Face recognition using temporal image sequence. In: International Conf. on Face and Gesture Recognition, pp. 318–323 (1998)
Fukui, K., Yamaguchi, O.: Face recognition using multi-viewpoint patterns for robot vision. In: 11th International Symposium of Robotics Research, pp. 192–201 (2003)
Harder, T., Borg, M., Boomsma, W., Røgen, P., Hamelryck, T.: Fast large-scale clustering of protein structures using Gauss Integrals. Journal of Bioinformatics, 510–515 (2012)
Oja, E.: Subspace Methods of Pattern Recognition. Research Studies Press, England (1983)
Begelfor, E., Werman, M.: Affine invariance revisited. In: Proceedings of International Conf. on Computer Vision and Pattern Recognition, pp. 2087–2094 (2006)
Lloyd, S.P.: Least squares quantization in PCM. IEEE Trans. Information Theory 28, 129–137 (1982)
Otsu, N., Kurita, T.: A new scheme for practical flexible and intelligent vision systems. In: Proc. of IAPR Workshop on CV, pp. 431–435 (1988)
Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., et al.: The Protein Data Bank. Nucleic Acids Research 28, 235–242 (2000)
Fukui, K., Stenger, B., Yamaguchi, O.: A Framework for 3D Object Recognition Using the Kernel Constrained Mutual Subspace Method. In: Narayanan, P.J., Nayar, S.K., Shum, H.-Y. (eds.) ACCV 2006. LNCS, vol. 3852, pp. 315–324. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Suryanto, C.H., Saigo, H., Fukui, K. (2012). Protein Clustering on a Grassmann Manifold. In: Shibuya, T., Kashima, H., Sese, J., Ahmad, S. (eds) Pattern Recognition in Bioinformatics. PRIB 2012. Lecture Notes in Computer Science(), vol 7632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34123-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-34123-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34122-9
Online ISBN: 978-3-642-34123-6
eBook Packages: Computer ScienceComputer Science (R0)