This Article 
 Bibliographic References 
 Add to: 
Prediction of Consensus RNA Secondary Structures Including Pseudoknots
April-June 2004 (vol. 1 no. 2)
pp. 66-77
Most functional RNA molecules have characteristic structures that are highly conserved in evolution. Many of them contain pseudoknots. Here, we present a method for computing the consensus structures including pseudoknots based on alignments of a few sequences. The algorithm combines thermodynamic and covariation information to assign scores to all possible base pairs, the base pairs are chosen with the help of the maximum weighted matching algorithm. We applied our algorithm to a number of different types of RNA known to contain pseudoknots. All pseudoknots were predicted correctly and more than 85 percent of the base pairs were identified.

[1] T. Akutsu, “Dynamic Programming Algorithms For RNA Secondary Structure with Pseudoknots,” Discrete Applied Math., vol. 104, pp. 45-62, 2000.
[2] M. Antal, E. Boros, F. Solymosy, and T. Kiss, “Analysis of the Structure of Human Telomerase RNA in Vivo,” Nucleic Acids Research, vol. 30, pp. 912-920, 2002.
[3] P. Baldi, S. Brunak, Y. Chauvin, C. Andersen, and H. Nielsen, “Assessing the Accuracy of Prediction Algorithms for Classification: An Overview,” Bioinformatics, vol. 16, pp. 412-424, 2000.
[4] J.W. Brown, “The ribonuclease P Database,” Nucleic Acids Research, vol. 27, no. 1, p. 314, 1999, .
[5] J.W. Brown, J.M. Nolan, E.S. Haas, M.A.T. Rubio, F. Major, and N.R. Pace, “Comparative Analysis of Ribonuclease P RNA Using Gene Sequences from Natural Microbial Populations Reveals Tertiary Structural Elements,” Proc. Nat'l Academy of Sciences, vol. 93, pp. 3001-3006, 1996.
[6] J.J. Cannone, S. Subramanian, M.N. Schnare, J.R. Collett, L.M. D'Souza, Y. Du, B. Feng, N. Lin, L.V. Madabusi, K.M. Mller, N. Pande, Z. Shang, N. Yu, and R.R. Gutell, “The Comparative RNA Web (CRW) Site: An Online Database of Comparative Sequence and Structure Information for Ribosomal, Intron, and other RNAs,” BMC Bioinformatics, vol. 3, p. 2, 2002,
[7] J.L. Chen, M.A. Blasco, and C.W. Greider, “Secondary Structure of Vertebrate Telomerase RNA,” Cell, vol. 100, pp. 503-514, 2000.
[8] J.L. Chen, K.K. Opperman, and C.W. Greider, “A Critical Stem-Loop Structure in the Cr4-Cr5 Domain of Mammalian Telomerase RNA,” Nucleic Acids Research, vol. 30, no. 2, pp. 592-597, 2002.
[9] D.K. Chiu and T. Kolodziejczak, “Inferring Consensus Structure from Nucleic Acid Sequences,” CABIOS, vol. 7, pp. 347-352, 1991.
[10] A. Condon, B. Davy, B. Rastegari, F. Tarrant, and S. Zhao, “Classifying RNA Pseudoknotted Structures,” Theoretical Computer Science, vol. 320, no. 1, pp. 35-50, 2004.
[11] R.M. Dirks and N.A. Pierce, “A Partition Function Algorithm for Nucleic Acid Secondary Structure Including Pseudoknots,” J. Computational Chemistry, vol. 24, pp. 1664-1677, 2003.
[12] K. Doshi, J. Cannone, C. Cobaugh, and R. Gutell, “Evaluation of the Suitability of Free-Energy Minimization Using Nearest-Neighbor Energy Parameters for RNA Secondary Structure Prediction,” BMC Bioinformatics, vol. 5, no. 1, p. 105, 2004.
[13] M.R. Fabian, H. Na, D. Ray, and K.A. White, “3'-Terminal RNA Secondary Structures Are Important for Accumulation of Tomato Bushy Stunt Virus DI Rnas,” Virology, vol. 313, pp. 567-580, 2003.
[14] A.R. Ferre-D'Amare, K. Zhou, and J.A. Doudna, “Crystal Structure of a Hepatitis Delta Virus Ribozyme,” Nature, vol. 395, pp. 567-574, 1998.
[15] W. Fontana, D.A. M. Konings, P.F. Stadler, and P. Schuster, “Statistics of RNA Secondary Structures,” Biopolymers, vol. 33, pp. 1389-1404, 1993.
[16] H.N. Gabow, “Implementation of Algorithms for Maximum Matching on Nonbipartite Graphs,” PhD thesis, Stanford Univ., 1973.
[17] O.V. Galzitskaya, “Geometrical Factor and Physical Reasons for Its Influence on the Kinetic and Thermodynamic Properties of RNA-Like Heteropolymers,” Folding and Design, vol. 2, pp. 192-201, 1997.
[18] O.V. Galzitskaya and A.V. Finkelstein, “Computer Simulation of Secondary Structure Folding of Random and “Edited” RNA Chains,” J. Chemical Physics, vol. 105, no. 1, pp. 319-325, 1996.
[19] J. Gorodkin, L.J. Heyer, and G.D. Stormo, “Finding Common Sequences and Structure Motifs in a Set of RNA Molecules,” Proc. ISMB-97, T. Gaasterland, P. Karp, K. Karplus, C. Ouzounis, C. Sander, and A. Valencia, eds., pp. 120-123, 1997.
[20] J. Gorodkin, B. Knudsen, C. Zwieb, and T. Samuelsson, “SRPDB-Signal Recognition Particle Database,” Nucleic Acids Research, vol. 29, no. 1, pp. 169-170, 2001, .
[21] S. Griffiths-Jones, A. Bateman, M. Marshall, A. Khann, and S.R. Eddy, “Rfam: An RNA Family Database,” Nucleic Acids Research, vol. 31, pp. 439-441, 2003, .
[22] A.P. Gultyaev, F.H.D. van Batenburg, and C.W.A. Pleij, “An Approximation of Loop Free Energy Values of RNA H-Pseudoknots,” RNA, vol. 5, pp. 609-617, 1999.
[23] R.R. Gutell, A. Power, G.Z. Hertz, E.J. Putz, and G.D. Stormo, “Identifying Constraints on the Higher-Order Structure of RNA: Continued Development and Application of Comparative Sequence Analysis Methods,” Nucleic Acids Research, vol. 20, pp. 5785-5795, 1992.
[24] J.K. Harris, E.S. Haas, D. Williams, and D.N. Frank, “New Insight into RNAse P RNA Structure from Comparative Analysis of the Archaeal RNA,” RNA, vol. 7, pp. 220-232, 2001.
[25] C. Haslinger, “ Prediction Algorithms for Restricted RNA Pseudoknots,” PhD thesis, Universität Wien, 2001.
[26] C. Haslinger and P.F. Stadler, “RNA Structures with Pseudo-Knots: Graph-Theoretical, Combinatorical, and Statistical Properties,” Bull. Math. Bioliogy, vol. 61, pp. 437-467, 1999.
[27] P.G. Higgs, “RNA secondary structure: physical and computational aspects,” Quarterly Rev. Biophysics, vol. 33, no. 3, pp. 199-253, 2000.
[28] M. Höchsmann, T. Toller, R. Giegerich, and S. Kurtz, “A New Algorithm for Local Similarity of RNA Secondary Structures,” Proc. Computational Systems Bioinformatics Conf., pp. 159-168, 2003.
[29] I.L. Hofacker, S.H.F. Bernhart, and P.F. Stadler, “Alignment of RNA Base Pairing Probability Matrices,” Bioinformatics, vol. 20, pp. 2222-2227, 2004.
[30] I.L. Hofacker, M. Fekete, C. Flamm, M.A. Huynen, S. Rauscher, P.E. Stolorz, and P.F. Stadler, “Automatic Detection of Conserved RNA Structure Elements in Complete RNA Virus Genomes,” Nucleic Acids Research, vol. 26, pp. 3825-3836, 1998.
[31] I.L. Hofacker, M. Fekete, and P.F. Stadler, “Secondary Structure Prediction for Aligned RNA Sequences,” J. Molecular Biology, vol. 319, pp. 1059-1066, 2002.
[32] I.L. Hofacker, W. Fontana, P.F. Stadler, S. Bonhoeffer, M. Tacker, and P. Schuster, “Fast Folding and Comparison of RNA Secondary Structures,” Monatshefte fur Chemie, vol. 125, pp. 167-188, 1994.
[33] I.L. Hofacker, W. Fontana, P.F. Stadler, and P. Schuster, “Vienna RNA Package,” / Free Software, 1994.
[34] I.L. Hofacker and P.F. Stadler, “Automatic Detection of Conserved Base Pairing Patterns in RNA Virus Genomes,” Computer and Chemistry, vol. 23, pp. 401-414, 1999.
[35] Y. Ji, X. Xu, and G.D. Stormo, “A Graph Theoretical Approach for Predicting Common RNA Secondary Structures Motifs Including Pseudoknots in Unaligned Sequences,” Bioinformatics, vol. 20, no. 10, pp. 1591-1602, 2004.
[36] V. Juan and C. Wilson, “RNA Secondary Structure Prediction Based on Free Energy and Phylogenetic Analysis,” J. Molecular Biology, vol. 289, no. 4, pp. 935-947, 1999.
[37] B. Knudsen, J. Wower, C. Zwieb, and J. Gorodkin, “tmRDB (tmRNA database),” Nucleic Acids Research, vol. 29, no. 1, pp. 171-172, 2001, .
[38] D.A.M. Konings and R.R. Gutell, “A Comparison of Thermodynamic Foldings with Comparatively Derived Structures of 16S and 16S-Like rRNAs,” RNA, vol. 1, pp. 559-574, 1995.
[39] M.Y. Kuo, L. Sharmeen, G. Dinter-Gottlieb, and J. Taylor, “Characterization of Self-Cleaving RNA Sequences on the Genome and Antigenome of Human Hepatitis Delta Virus,” J. Virology, no. 62, pp. 4439-4444, 1988.
[40] N. Larsen and C. Zwieb, “SRP-RNA Sequence Alignment and Secondary Structure,” Nucleic Acids Research, vol. 19, no. 2, pp. 209-215, 1991.
[41] S.Y. Le and M. Zuker, “Predicting Common Foldings of Homologous RNAs,” J. Biomolecular Structure & Dynamics, vol. 8, pp. 1027-1044, 1991.
[42] T. Leeper, N. Leulliot, and G. Varani, “The Solution Structure of an Essential Stem-Loop of Human Telomerase RNA,” Nucleic Acids Research, vol. 31, pp. 2614-2621, 2003.
[43] R. Lück, S. Graf, and G. Steger, “ConStruct: A Tool for Thermodynamic Controlled Prediction of Conserved Secondary Structure,” Nucleic Acids Research, vol. 27, pp. 4208-4217, 1999.
[44] R.B. Lyngsø and C.N. S. Pedersen, “RNA Pseudoknot Prediction in Energy Based Models,” J. Computational Biology, vol. 7, nos. 3/4, pp. 409-428, 2000.
[45] D.H. Mathews, J. Sabina, M. Zuker, and D.H. Turner, “Expanded Sequence Dependence of Thermodynamic Parameters Provides Robust Prediction of RNA Secondary Structure,” J. Molecular Biology, vol. 288, pp. 911-940, 1999.
[46] F. Michel, K. Umesono, and H. Ozeki, “Comparative and Functional Anatomy of Group II Catalytic Introns: A Review,” Gene, vol. 82, no. 1, pp. 5-30, 1989.
[47] S.R. Morgan and P.G. Higgs, “Evidence for Kinetic Effects in the Folding of Large RNA Molecules,” J. Chemical Physics, vol. 105, no. 16, pp. 7152-7157, 1996.
[48] R. Nussinov, G. Piecznik, J.R. Griggs, and D.J. Kleitman, “Algorithms for Loop Matching,” SIAM J. Applied Math., vol. 35, no. 1, pp. 68-82, 1978.
[49] O. Perriquet, H. Touzet, and M. Dauchet, “Finding the Common Structure Shared by Two Homologous RNAs,” Bioinformatics, vol. 19, no. 1, pp. 108-116, 2003.
[50] J. Pogany, M.R. Fabian, K.A. White, and P.D. Nagy, “A Replication Silencer Element in a Plus-Strand RNA Virus,” EMBO J., vol. 22, pp. 5602-5611, 2003.
[51] J. Reeder and R. Giegerich, “Design, Implementation, and Evaluation of a Practical Pseudoknot Folding Algorithm Based on Thermodynamics,” BMC Bioinformatics, vol. 5, no. 1, p. 104, 2004.
[52] E. Rivas and S.R. Eddy, “A Dynamic Programming Algorithm fFor RNA Structure Prediction Including Pseudoknots,” J. Molecular Biology, vol. 285, pp. 2053-2068, 1999.
[53] E. Rothberg, “Solver for the Maximum Weight Matching problem,” / matching/weightedsolver-1, 1985.
[54] J. Ruan, G.D. Stormo, and W. Zhang, “An Iterated Loop Matching Approach to the Prediction of RNA Secondary Structures with Pseudoknots,” Bioinformatics, vol. 20, pp. 58-66, 2004.
[55] S. Siebert and R. Backofen, “MARNA: A Server for Multiple Alignment of RNAs,” Proc. German Conf. Bioinformatics, H.-W. Mewes, V. Heun, D. Frishman, and S. Kramer, eds., vol. 1, pp. 135-140, 2003.
[56] J.E. Tabaska, R.B. Cary, H.N. Gabow, and G.D. Stormo, “An RNA Folding Method Capable of Identifying Pseudoknots and Base Triples,” Bioinformatics, vol. 14, no. 8, pp. 691-699, 1998.
[57] C.K. Tang and D.E. Draper, “An Unusual mRNA Pseudoknot Structure Is Recognized by a Protein Translation Repressor,” Cell, vol. 57, pp. 531-536, 1989.
[58] E.B. ten Dam, C.W.A. Pleij, and D. Draper, “Structural and Functional Aspects of RNA Pseudoknots,” Biochemistry, vol. 31, pp. 11665-11676, 1992.
[59] J.D. Thompson, D.G. Higgs, and T.J. Gibson, “CLUSTALW: Improving the Sensitivity of Progressive Multiple Sequence Alignment through Sequence Weighting, Position Specific Gap Penalties, and Weight Matrix Choice,” Nucleic Acids Research, vol. 22, pp. 4673-4680, 1994.
[60] F. van Batenburg, A. Gultyaev, C.P.J. Ng, and J. Oliehoek, “Pseudobase: A Database with RNA Pseudoknots,” Nucleic Acids Research, vol. 28, no. 1, pp. 201-204, 2000.
[61] J. Wang, J.M.J.E. Bakkers, J.M.D. Galama, H.J. Bruins Slot, E.V. Pilipenko, V.I. Agol, and W.J. G. Melchers, “Structural Requirements of the Higher Order RNA Kissing Element in the Enteroviral 3'UTR,” Nucleic Acids Research, vol. 27, pp. 485-490, 1999.
[62] G.D. Williams, R.Y. Chang, and D.A. Brian, “A Phylogenetically Conserved Hairpin-Type 3' Untranslated Region Pseudoknot Functions in Coronavirus RNA Replication,” J. Virology, vol. 73, pp. 8349-8355, 1999.
[63] B.T. Wimberly, D.E. Brodersen, W.M. Clemons, R.J. Morgan-Warren, A.P. Carter, C. Vonrhein, T. Hartsch, and V. Ramakrishnan, “Structure of the 30S Ribosomal Subunit,” Nature, vol. 407, pp. 327-339, 2000.
[64] M. Zuker and D. Sankoff, “RNA Secondary Structures and Their Prediction,” Bull. Math. Biology, vol. 46, pp. 591-621, 1984.
[65] C. Zwieb, I. Wower, and J. Wower, “Comparative Sequence Analysis of tmRNA,” Nucleic Acids Research, vol. 27, no. 10, pp. 2063-2071, 1999.

Index Terms:
RNA secondary structure, pseudoknots, covariance.
Christina Witwer, Ivo L. Hofacker, Peter F. Stadler, "Prediction of Consensus RNA Secondary Structures Including Pseudoknots," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 1, no. 2, pp. 66-77, April-June 2004, doi:10.1109/TCBB.2004.22
Usage of this product signifies your acceptance of the Terms of Use.