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Issue No.06 - November/December (2011 vol.8)
pp: 1604-1619
Xavier Le Faucheur , Georgia Institute of Technology, Atlanta
Eli Hershkovits , Georgia Institute of Technology, Atlanta
Rina Tannenbaum , Georgia Institute of Technology, Atlanta and Technion IIT, Haifa
Allen Tannenbaum , Georgia Institute of Technology, Atlanta and Technion IIT, Haifa
ABSTRACT
The local conformation of RNA molecules is an important factor in determining their catalytic and binding properties. The analysis of such conformations is particularly difficult due to the large number of degrees of freedom, such as the measured torsion angles per residue and the interatomic distances among interacting residues. In this work, we use a nearest-neighbor search method based on the statistical mechanical Potts model to find clusters in the RNA conformational space. The proposed technique is mostly automatic and may be applied to problems, where there is no prior knowledge on the structure of the data space in contrast to many other clustering techniques. Results are reported for both single residue conformations, where the parameter set of the data space includes four to seven torsional angles, and base pair geometries, where the data space is reduced to two dimensions. Moreover, new results are reported for base stacking geometries. For the first two cases, i.e., single residue conformations and base pair geometries, we get a very good match between the results of the proposed clustering method and the known classifications with only few exceptions. For the case of base stacking geometries, we validate our classification with respect to geometrical constraints and describe the content, and the geometry of the new clusters.
INDEX TERMS
RNA conformation, clustering, potts model, statistical mechanics.
CITATION
Xavier Le Faucheur, Eli Hershkovits, Rina Tannenbaum, Allen Tannenbaum, "Nonparametric Clustering for Studying RNA Conformations", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 6, pp. 1604-1619, November/December 2011, doi:10.1109/TCBB.2010.128
REFERENCES
 [1] M. Blatt, S. Wiseman, and E. Domany, “Data Clustering Using a Model Granular Magnet,” Neural Computation, vol. 9, pp. 1805-1842, 1997. [2] T. Cech, “Ribozyme, the First 20 Years,” Biochemical Soc. Trans., vol. 30, pp. 1162-1166, 2001. [3] H.M. Berman, W.K. Olson, D.L. Beveridge, J. Westbrook, A. Gelbin, T. Demeny, S.-H. Hsieh, A.R. Srinivasan, and B. Schneider, “The Nucleic Acid Database: A Comprehensive Relational Database of Three-Dimensional Structures of Nucleic Acids,” Biophysical J., vol. 63, pp. 751-759, 1992. [4] 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. [5] H. Noller, “RNA Structure: Reading the Ribosome,” RNA, vol. 309, pp. 1508-1514, 2005. [6] J. Sponer and F. Lankas, Computational Studies of RNA and DNA. Springer, 2006. [7] P. Moore, “Structural Motifs in RNA,” Ann. Rev. of Biochemistry, vol. 68, pp. 287-300, 1999. [8] E. Hershkovtis, E. Tannenbaum, S. Howerton, A. Sheth, A. Tannenbaum, and L. Williams, “Automated Identification of RNA Conformational Motifs: Theory and Application to the HM LSU 23S rRNA,” Nucleic Acids Research, vol. 1, pp. 6249-6257, 2003. [9] E. Hershkovtis, G. Sapiro, A. Tannenbaum, and L. Williams, “Statistical Analysis of RNA Backbone,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 1, pp. 33-46, Jan.-Mar. 2006. [10] L. Murray, W. Arendall, D. Richardson, and J. Richardson, “RNA Backbone Is Rotameric,” Proc. Nat'l Academy of Sciences USA, vol. 100, pp. 13904-13909, 2003. [11] J. Richardson, B. Schneider, L. Murray, G. Kapral, R. Immormino, J. Headd, D. Richardson, D. Ham, E. Hershkovits, L. Williams, K. Keating, A. Pyle, D. Micallef, J. Westbrook, M. Helen, and H. Berman, “RNA Backbone: Consensus All-Angle Conformers and Modular String Nomenclature,” RNA, vol. 14, pp. 465-481, 2008. [12] C. Duarte and A. Pyle, “Stepping through an RNA Structure: A Novel Approach to Conformational Analysis,” J. Molecular Biology, vol. 284, pp. 1465-1478, 1998. [13] C. Duarte, L. Wadley, and A. Pyle, “RNA Structure Comparison, Motif Search and Discovery Using a Reduced Representation of RNA Conformational Space,” Nucleic Acids Research, vol. 31, pp. 4755-4761, 2003. [14] B. Schneider, Z. Moravek, and H. Berman, “RNA Conformational Classes,” Nucleic Acids Research, vol. 32, pp. 1666-1677, 2004. [15] D. Gautheret, F. Major, and R. Cedergren, “Modeling the Three-Dimensional Structure of RNA Using Discrete Nucleotide Conformational Sets,” J. Molecular Biology, vol. 229, pp. 1049-1064, 1993. [16] N. Leontis and E. Westof, “Analysis of RNA Motifs,” Current Opinion in Structural Biology, vol. 13, pp. 300-308, 2003. [17] N. Leontis and E. Westof, “Geometric Nomenclature and Classification of RNA Base Pairs,” RNA, vol. 7, pp. 499-512, 2001. [18] K. Fukunaga, Introduction to Statistical Pattern Recognition, second ed. Academic Press, 1990. [19] A. Jain and R. Dubes, Algorithms for Clustering Data. Prentice-Hall, 1988. [20] M. Sykes and M. Levitt, “Describing RNA Structure by Libraries of Clustered Nucleotide Doublets,” J. Molecular Biology, vol. 351, pp. 26-38, 2005. [21] F. Lemieux and F. Major, “Automated Extraction and Classification of RNA Tertiary Structure Cyclic Motifs,” Nucleic Acids Research, vol. 34, pp. 2340-2346, 2006. [22] H. Agrawal and E. Domany, “Potts Ferromagnets on Coexpressed Gene Networks: Identifying Maximally Stable Partitions,” Physical Rev. Letters, vol. 90, pp. 158102.1-158102.4, 2003. [23] J. Wang and R. Swendsen, “Cluster Monte Carlo Method,” Physica A, vol. 1, no. 167, pp. 565-579, 1990. [24] P. Florian and G. Domanyiegler, “Kissing Numbers, Sphere Packing and Some Unexpected Proofs,” Notices of the Am. Math. Soc., vol. 51, pp. 873-883, 2004. [25] T. Calinski and J. Harabasz, “A Dendrite Method for Cluster Analysis,” Comm. in Statistics, Simulation and Computation, vol. 3, pp. 1-27, 1974. [26] N. Ban, P. Nissen, J. Hansen, P. Moore, and T. Steitz, “The Complete Atomic Structure of the Large Ribosomal Subunit at $2.4 aa$ Resolution,” Science, vol. 289, pp. 905-919, 2000. [27] M. Sarver, C. Zirbel, J. Stombaugh, A. Mokdad, and N. Leontis, “FR3dD,” J. Math. Biology, vol. 56, pp. 215-252, 2008. [28] D. Cremer and J. Pople, “A General Definition of Ring Puckering Coordinates,” J. the Am. Chemical Soc., vol. 97, pp. 1354-1358, 1975. [29] A. Feffrey, An Introduction to Hydrogen Bonding. Oxford Univ. Press, 1997. [30] S. Lemieux and F. Major, “RNA Canonical and Non-Canonical Base Pairing Types: A Recognition Method and Complete Repertoire,” Nucleic Acids Research, vol. 30, pp. 4250-4263, 2002. [31] D. Klein, P. Moore, and T. Steitz, “The Roles of Ribosomal Proteins in the Structure Assembly, and Evolution of the Large Ribosomal Subunit,” J. Math. Biology, vol. 340, pp. 141-177, 2004. [32] W. Saenger, Principles of Nucleic Acid Structure. Springer-Verlag, 1984. [33] M. Waller, A. Robertazzi, J. Platts, D. Hibbs, and P. Williams, “Hybrid Density Functional Theory for $\pi$ -Stacking Interactions: Application to Benzenes, Pyridines, and DNA Bases,” J. Computational Chemistry, vol. 27, pp. 491-504, 2006. [34] J. Sponer, J. Leszczynski, and P. Hobza, “On the Nature of Nucleic Acid Base Stacking. Nonempirical ab Initio and Empirical Potential Characterization of 10 Stacked Base Pairs. Comparison of Stacked and H-Bonded Base Pairs,” J. Physical Chemistry, vol. 100, pp. 5590-5596, 1996. [35] G. Gupta and V. Sasisekharan, “Theoretical Calculations of Base-Base Interactions in Nucleic Acids: Satcking Interactions in Free Bases,” Nucleic Acid Research, vol. 5, pp. 1639-1653, 1978. [36] C. Bugg, J. Thomas, and M. Sundaralingam, “Stereochemistry of Nucleic Acids and Their Constituents. X. Solid-Slate Base-Slacking Patterns in Nucleic Acid Constituents and Polynucleotides,” Biopolymers, vol. 10, pp. 175-219, 1971. [37] R. Luo, H. Gilson, M. Potter, and M. Gilson, “The Physical Basis of Nucleic Acid Base Stacking in Water,” Biophysical J., vol. 80, pp. 140-148, 2001. [38] R. Friedman and B. Honig, “A Free Energy Anlaysis of Nucleic Acid Base Stacking in Aquaeous Solution,” Biophysical J., vol. 69, pp. 1528-1535, 1995. [39] D. Klein, T. Schmeing, P. Moore, and T. Steitz, “The Kink-Turn: A New RNA Secondary Structure Motif,” European Molecular Biology Organization J., vol. 20, pp. 4214-4221, 2001.