Modeling RNA Folding

  • Ivo L. Hofacker
  • Peter F. StadlerEmail author
Part of the Topics in Biomedical Engineering International Book Series book series (ITBE)


In recent years it has become evident that functional RNAs in living organisms are not just curious remnants from a primordial RNA world but a ubiquitous phenomenon complementing protein enzyme based activity. Functional RNAs, just like proteins, depend in many cases upon their well-defined and evolutionarily conserved three-dimensional structure. In contrast to protein folds, however, RNA molecules have a biophysically important coarse-grained representation: their secondary structure. At this level of resolution at least, RNA structures can be efficiently predicted given only the sequence information. As a consequence, computational studies of RNA routinely incorporate structural information explicitly. RNA secondary structure prediction has proven useful in diverse fields, ranging from theoretical models of sequence evolution and biopolymer folding, to genome analysis, and even the design of biotechnologically or pharmaceutically useful molecules. Properties such as the existence of neutral networks or shape space covering are emergent properties determined by the complex, highly nonlinear relationship between RNA sequences and their structures.


Hepatitis Delta Virus Neutral Network Functional RNAs Shape Space Covering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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7. References

  1. 1.
    Akutsu, T. 2001. Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots. Discr Appl Math 104:45–62.CrossRefGoogle Scholar
  2. 2.
    Avner P, Heard E. 2001. X-chromosome inactivation: counting, choice, and initiation. Nature Rev Genet 2:59–67.CrossRefGoogle Scholar
  3. 3.
    Babajide A, Farber R, Hofacker IL, Inman J, Lapedes AS, Stadler PF, 2001. Exploring protein sequence space using knowledge-based potentials. J Theor Biol 212:35–46.PubMedCrossRefGoogle Scholar
  4. 4.
    Babajide A, Hofacker IL, Sippl MJ, Stadler PF. 1997. Neutral networks in protein space: a computational study based on knowledge-based potentials of mean force. Folding Des 2:261–269.CrossRefGoogle Scholar
  5. 5.
    Biebricher CK, Gardiner WC. 1997. Molecular evolution of RNA in vitro. Biophys Chem 66:179–192.PubMedCrossRefGoogle Scholar
  6. 6.
    Blackburn E. 1999. Telomerase. In The RNA world, pp. 609–635. Ed. R Gesteland, T Cech, J Atkins. Cold Spring Harbor Laboratory Press, New York.Google Scholar
  7. 7.
    Bosher JM, Labouesse M. 2000. RNA interference: genetic wand and genetic watchdog. Nature Cell Biol 2:E31–E36.PubMedCrossRefGoogle Scholar
  8. 8.
    Brown JW, The ribonuclease P database. 1999. Nucleic Acids Res 27:314–314.PubMedCrossRefGoogle Scholar
  9. 9.
    Bruccoleri RE, Heinrich G. 1988. An improved algorithm for nucleic acid secondary structure display. Comput Appl Biosci 4:167–173.PubMedGoogle Scholar
  10. 10.
    Chetouani F, Monestie P, Thebault P, Gaspin C, Michot B. 1997. ESSA: an integrated and inteactive computer tool for analysing RNA structure. Nucleic Acids Res 25:3514–3522.PubMedCrossRefGoogle Scholar
  11. 11.
    Cogoni C., Macino G. 2000. Post-transcriptional gene silencing across kingdoms. Genes Dev 10:638–643.Google Scholar
  12. 12.
    ten Dam EB, Pleij CW, Bosch L. 1990. RNA pseudoknots: translational frameshifting and readthrough on viral RNAs. Virus Genes 4:121–135.PubMedCrossRefGoogle Scholar
  13. 13.
    ten Dam EB, Pleij K, Draper D. 1992. Structural and functional aspects of RNA pseudoknots. Biochemistry 31:11665–11676.PubMedCrossRefGoogle Scholar
  14. 14.
    ten Dam EB, Verlaan PW, Pleij CW. 1995. Analysis of the role of the pseudoknot component in the SRV-1 gag-pro ribosomal frameshift signal: loop lengths and stability of the stem regions. RNA 1:146–154.PubMedGoogle Scholar
  15. 15.
    Dandekar T, Hentze MW. Finding the hairpin in the haystack: searching for RNA motifs. Trends Genet 11:45–50.Google Scholar
  16. 16.
    Dayton ET, Konings DAM, Powell DM, Shapiro BA, and L B, Maizel JV, Dayton AI. 1992. Extensive sequence-specific information throughout the CAR/RRE the target sequence of the human immunodeficiency virus type 1 Rev protein. J Virol 66:1139–1151.PubMedGoogle Scholar
  17. 17.
    Denduangboripant J, Cronk QCB. 2001. Evolution and alignment of the hypervariable arm 1 of Aeschynanthus (Gesneriaceae) ITS2 nuclear ribosomal DNA. Mol Phylog Evol 20:163–172.CrossRefGoogle Scholar
  18. 18.
    Doudna JA. 2000. Structural genomics of RNA. Nature Struct Biol 7:954–956.PubMedCrossRefGoogle Scholar
  19. 19.
    Du Z, Holland JA, Hansen MR, Giedroc DP, Hoffman DW. 1997. Base-pairings within the RNA pseudoknot associated with the simian retrovirus-1 gag-pro frameshift site. J Mol Biol 270:464–470.PubMedCrossRefGoogle Scholar
  20. 20.
    Eddy SR. 2001. Non-coding RNA genes and the modern RNA world. Nature Genet 2:919–929.CrossRefGoogle Scholar
  21. 21.
    Edmonds J. 1965. Maximum matching and a polyhedron with 0,1-vertices. J Res Natl Bur Stand 69B:125–130.Google Scholar
  22. 22.
    Erdmann VA, Barciszewska MZ, Hochberg A, de Groot N, Barciszewski J. 2001. Regulatory RNAs. Cell Mol Life Sci 58:960–977.PubMedCrossRefGoogle Scholar
  23. 23.
    Erdmann VA, Szymanski M, Hochberg A. de Groot N, Barciszewski J. Collection of mRNA-like non-coding RNAs. Nucleic Acids Res 27:192–195.Google Scholar
  24. 24.
    Felciano RM, Chen RO, Altmann RB. 1997. RNA Secondary strucutre as a reusable interface to biological information resources. Gene 190:GC59–GC70.PubMedCrossRefGoogle Scholar
  25. 25.
    Flamm C, Fontana W, and I H, Schuster P. 2000. RNA folding kinetics at elementary step resolution. RNA 6:325–338.PubMedCrossRefGoogle Scholar
  26. 26.
    Flamm C, Hofacker IL, Stadler PF, Wolfinger MT. 2002. Barrier Trees of Degenerate Landscapes. Z Phys Chem 216:155–173.Google Scholar
  27. 27.
    Fontana W, Stadler PF, Bornberg-Bauer EG, Griesmacher T, Hofacker IL, Tacker M, Tarazona P, Weinberger ED, Schuster P. 1993. RNA folding landscapes and combinatory landscapes. Phys Rev E 47:2083–2099.CrossRefGoogle Scholar
  28. 28.
    Fontana W, Konings DAM, Stadler PF, Schuster P. 1993. Statistics of RNA secondary structures. Biopolymers 33:1389–1404.PubMedCrossRefGoogle Scholar
  29. 29.
    Fontana W, Schuster P. 1998. Continuity in evolution: on the nature of transitions. Science 280:1451–1455.PubMedCrossRefGoogle Scholar
  30. 30.
    Fontana W, Schuster P. 1998. Shaping space: the possible and the attainable in RNA genotype-phenotype mapping. J Theor Biol 194:491–515.PubMedCrossRefGoogle Scholar
  31. 31.
    Franke A, Baker BS. 2000. Dosage compensation rox! Curr Opin Cell Biol 12:351–354.PubMedCrossRefGoogle Scholar
  32. 32.
    Freier SM, Kierzek R, Jaeger JA, Sugimoto N, Caruthers MH, Neilson T, Turner DH. 1986. Improved free-energy parameters for prediction of RNA duplex stability. Proc Natl Acad Sci USA 83:9373–9377.PubMedCrossRefGoogle Scholar
  33. 33.
    Gabow HN. 1973. Implementations of algorithms for maximum matching on nonbipartite graphs. Stanford University, Department of Computer Science.Google Scholar
  34. 34.
    Gautheret D, Major F, Cedergren R. 1990. Pattern searching/alignment with RNA primary and secondary structures: an effective descriptor for tRNA. Comput Appl Biosci 6:325–331.PubMedGoogle Scholar
  35. 35.
    Gavrilets S. 1997. Evolution and speciation on holey adaptive landscapes. Trends Ecol Evol 12:307–312.CrossRefGoogle Scholar
  36. 36.
    Giegerich, R, Reeder, J. 2003. From RNA folding to thermodynamic matching including pseudoknots. Report 2003-03, Universität Bielefeld, Germany.Google Scholar
  37. 37.
    Gorodkin J, Knudsen B, Zwieb C, Samuelsson T. 2001. SRPDB (signal recognition particle database) Nucleic Acids Res 29:169–170.PubMedCrossRefGoogle Scholar
  38. 38.
    Gorodkin J, Heyer LJ, Stormo GD. 1997. Finding common sequences and structure motifs in a set of RNA molecules. In Proceedings of the ISMB97, pp. 120–123. Ed. T Gaasterland, P Karp, K Karplus, Ch Ouzounis, Ch Sander, A Valencia. AAAI Press, Menlo Park, CA.Google Scholar
  39. 39.
    Gorodkin J, Heyer LJ, Stormo GD. 1997. Finding the most significant common sequence and structure motifs in a set of RNA sequences. Nucleic Acids Res 25:3724–3732.PubMedCrossRefGoogle Scholar
  40. 40.
    Green MR. 1991. Biochemical mechanisms of constitutive and regulated pre-mRNA splicing. Annu Rev Cell Biol 7:559–599.PubMedCrossRefGoogle Scholar
  41. 41.
    Griffiths-Jones S, Bateman A, Mhairi M, Khanna A, Eddy SR. 2003. Rfam: an RNA family database. Nucleic Acids Res 31:439–441.PubMedCrossRefGoogle Scholar
  42. 42.
    Grüner W, Giegerich R, Strothmann D, Reidys CM, Weber J, Hofacker IL, Stadler PF, Schuster P. 1996. Analysis of RNA sequence structure maps by exhaustive enumeration. I. Neutral networks. Monatsh Chem 127:355–374.CrossRefGoogle Scholar
  43. 43.
    Grüner W, Giegerich R, Strothmann D, Reidys CM, Weber J, Hofacker IL, Stadler PF, Schuster P. 1996. Analysis of RNA sequence structure maps by exhaustive enumeration. II. Structures of neutral networks and shape space covering. Monatsh Chem 127:375–389.CrossRefGoogle Scholar
  44. 44.
    Gultyaev AP, van Batenburg FHD, Pleij CWA. 1999. An approximation of loop free energy values of RNA H-pseudoknots. RNA 5:609–617.PubMedCrossRefGoogle Scholar
  45. 45.
    Guru T. 2000. A silence that speaks volumes. Nature 404:804–808.CrossRefGoogle Scholar
  46. 46.
    Gutell RR, Cannone JJ, Shang Z, Du Y, Serra MJ. 2000. A story: unpaired adenosine bases in ribosomal RNA. J Mol Biol 304:335–354.PubMedCrossRefGoogle Scholar
  47. 47.
    Gutell RR. 1993. Evolutionary characteristics of RNA: inferring higher-order structure from patterns of sequence variation. Curr Opin Struct Biol 3:313–322.CrossRefGoogle Scholar
  48. 48.
    The Genome Sequencing Consortium. 2001. Gene content of the human genome. Nature 409:860–921.CrossRefGoogle Scholar
  49. 49.
    Hammond SM, Caudy AA, Hannon GJ. 2001. Post-transcriptional gene silencing by double-stranded RNA. Nature Rev Genet 2:110–119.CrossRefGoogle Scholar
  50. 50.
    Han K, Kim HJ. 1993. Prediction of common folding structures of homologous RNAs. Nucleic Acids Res 21:1251–1257.PubMedCrossRefGoogle Scholar
  51. 51.
    Han K, Kim D, Kim HJ. 1999. A vector-based method for drawing RNA secondary structure. Bioinformatics 15:286–297.PubMedCrossRefGoogle Scholar
  52. 52.
    Haslinger C. 2001. Prediction algorithms for restricted RNA pseudoknots. PhD dissertation, University of Vienna, Faculty of Sciences.Google Scholar
  53. 53.
    Höbartner C, Micura R. 2003. Bistable secondary structures of small RNAs and their structural probing by comparative imino proton NMR spectroscopy. J Mol Biol 325:421–431.PubMedCrossRefGoogle Scholar
  54. 54.
    Höchsmann M. 2001. Tree and forrest alignments: an algebraic dynamic programming approach for aligning trees and forests. MSc thesis. University of Bielefeld, Germany.Google Scholar
  55. 55.
    Hofacker IL, Fekete M, Stadler PF. 2002. Secondary structure prediction for aligned RNA sequences. J Mol Biol 319:1059–1066.PubMedCrossRefGoogle Scholar
  56. 56.
    Hofacker IL, Fontana W, Stadler PF, Bonhoeffer S, Tacker M, Schuster P. 1994. Fast folding and comparison of RNA secondary structures. Monatsh Chem 125:167–188.CrossRefGoogle Scholar
  57. 57.
    Hofacker IL, Huynen MA, Stadler PF, Stolorz PE. 1996. Knowledge discovery in RNA sequence families of HIV using scalable computers. In Proceedings of the 2nd international conference on knowledge discovery and data mining, Portland, OR, pp. 20–25. Ed. E Simoudis, J Han, U Fayyad. AAAI Press, Menlo Park, CA.Google Scholar
  58. 58.
    Hofacker IL, and P S, Stadler PF. 1998. Combinatorics of RNA secondary structures. Discr Appl Math 89:177–207.Google Scholar
  59. 59.
    Hofacker IL, Fekete M, Flamm C, Huynen MA, Rauscher S, Stolorz PE, Stadler PF. 1998. Automatic detection of conserved RNA structure elements in complete RNA virus genomes. Nucleic Acids Res 26:3825–3836.PubMedCrossRefGoogle Scholar
  60. 60.
    Hofacker IL, Stadler PF. 1999. Automatic detection of conserved base pairing patterns in RNA virus genomes. Comput Chem 23:401–414.PubMedCrossRefGoogle Scholar
  61. 61.
    Hogeweg P, Hesper B. 1984. Energy directed folding of RNA sequences. Nucleic Acids Res 12:67–74.PubMedCrossRefGoogle Scholar
  62. 62.
    Huez I, Créancier L, Audigier S, Gensac M-C, Prats A-C, Prats H. 1998. Two independent internal ribosome entry sites are involved in translation initiation of vascular endothelial growth factor mRNA. Mol Cell Biol 18:6178–6190.PubMedGoogle Scholar
  63. 63.
    Huynen MA, Stadler PF, Fontana W. 1996. Smoothness within ruggedness: the role of neutrality in adaptation. Proc Natl Acad Sci USA 93:397–401.PubMedCrossRefGoogle Scholar
  64. 64.
    Huynen MA, Perelson AS, Viera WA, Stadler PF. 1996. Base pairing probabilities in a complete HIV-1 RNA. J Comput Biol 3:253–274.PubMedCrossRefGoogle Scholar
  65. 65.
    Huynen MA. 1996. Exploring phenotype space through neutral evolution. J Mol Evol 43:165–169.PubMedGoogle Scholar
  66. 66.
    Isambert H, Siggia ED. 2000. Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme. Proc Natl Acad Sci USA 97:6515–6520.PubMedCrossRefGoogle Scholar
  67. 67.
    Jacobs GH, Rackham O, Stockwell PA, Tate W, and Brown CM. 2002. Transterm: a database of mRNAs and translational control elements. Nucleic Acids Res 30:310–311.PubMedCrossRefGoogle Scholar
  68. 68.
    Jacobson AB, Zuker M. 1993. Structural analysis by energy dot plot of large mRNA. J Mol Biol 233:261–269.PubMedCrossRefGoogle Scholar
  69. 69.
    Jaeger JA, Turner DH, Zuker M. 1989. Improved predictions of secondary structures for RNA. Proc Natl Acad Sci USA 86:7706–7710.PubMedCrossRefGoogle Scholar
  70. 70.
    Juan V, Wilson C. 1999. RNA secondary structure prediction based on free energy and phylogenetic analysis. J Mol Biol 289:935–947.PubMedCrossRefGoogle Scholar
  71. 71.
    Keefe AD, Szostak JW. 2001. Functional proteins from a random-sequence library. Nature 410:715–718.PubMedCrossRefGoogle Scholar
  72. 72.
    Keiler KC, Shapiro L, Williams KP. 2000. tmRNAs that encode proteolysis-inducing tags are found in all known bacterial genomes: A two-piece tmRNA functions in Caulobacter. Proc Natl Acad Sci USA 97:7778–7783.PubMedCrossRefGoogle Scholar
  73. 73.
    Kidd-Ljunggren K, Zuker M, Hofacker IL, Kidd AH. 2000. The hepatitis B virus pregenome: prediction of RNA structure and implications for the emergence of deletions. Intervirology 43:154–164.PubMedCrossRefGoogle Scholar
  74. 74.
    Klein RJ, Misulovin Z, Eddy SR. 2002. Noncoding RNA genes identified in AT-rich hyperthermophiles. Proc Natl Acad Sci USA 99:7542–7547.PubMedCrossRefGoogle Scholar
  75. 75.
    Lagos-Quintana M, Rauhut R, Lendeckel W, Tuschl T. 2001. Identification of novel genes coding for small expressed RNAs. Science 294:853–857.PubMedCrossRefGoogle Scholar
  76. 76.
    Laslett D, Canback B, Andersson S. 2002. BRUCE: a program for the detection of transfermessenger RNA genes in nucleotide sequences. Nucleic Acids Res 30:3449–3453.PubMedCrossRefGoogle Scholar
  77. 77.
    Lau NC, Lim LP, Weinstein EG, Bartel DP. 2001. An abundant class of tiny RNAs with probable regulatory roles in Caenorhabditis elegans. Science 294:858–862.PubMedCrossRefGoogle Scholar
  78. 78.
    Le S-Y, Chen J-H, Currey KM, Maizel JV. 1988. A program for predicting significant RNA secondary structures. CABIOS 4:153–159.PubMedGoogle Scholar
  79. 79.
    Le SY, Zuker M. 1991. Predicting common foldings of homologous RNAs. J Biomol Struct Dyn 8:1027–1044.PubMedGoogle Scholar
  80. 80.
    Lee RC, Ambros V. 2001. An extensive class of small RNAs in Caenorhabditis elegans. Science 294:862–864.PubMedCrossRefGoogle Scholar
  81. 81.
    Lee D, Han K. 2002. Prediction of RNA pseudoknots: comparative study of genetic algorithms. Genome Informatics 13:414–415.Google Scholar
  82. 82.
    Leydold J, Stadler PF. 1998. Minimal cycle basis, outerplanar graphs. Elec J Comb 5:R16 (see Scholar
  83. 83.
    Lowe TM, Eddy SR. 1997. tRNAscan-SE: a program for improved detection of transfer RNA genes in genomic sequence. Nucleic Acids Res 25:955–964.PubMedCrossRefGoogle Scholar
  84. 84.
    Lück R, Steger G, Riesner D. 1996. Thermodynamic prediction of conserved secondary structure: application to the RRE element of HIV, the tRNA-like element of CMV, and the mRNA of prion protein. J Mol Biol 258:813–826.PubMedCrossRefGoogle Scholar
  85. 85.
    Lück R, Gräf S, Steger G. 1999. ConStruct: A tool for thermodynamic controlled prediction of conserved secondary structure. Nucleic Acids Res 27:4208–4217.PubMedCrossRefGoogle Scholar
  86. 86.
    Lyngsö RB, Pedersen CNS. 2000. RNA pseudoknot prediction in energy-based models. J Comput Biol 7:409–427.PubMedCrossRefGoogle Scholar
  87. 87.
    Macdonald PM. 1990. Bicoid mRNA localization signal: phylogenetic conservation of function and RNA secondary structure. Development 110:161–171.PubMedGoogle Scholar
  88. 88.
    Macke TJ, Ecker DJ, Gutell RR, Gautheret D, Case DA, Sampath R. 2001. RNAMotif, an RNA secondary structure definition and search algorithm. Nucleic Acids Res 29:4724–4735.PubMedCrossRefGoogle Scholar
  89. 89.
    Maidak BL, Cole JR, Lilburn TG, Parker Jr CT, Saxman PR, Farris RJ, Garrity GM, Olsen GJ, Schmidt TM, Tiedje JM. 2001. The RDP-II (ribosomal database project). Nucleic Acids Res 29:173–174.PubMedCrossRefGoogle Scholar
  90. 90.
    Mandl CW, Holzmann H, Meixner T, Rauscher S, Stadler PF, Allison SL, Heinz FX. 1998. Spontaneous and engineered deletions in the 3′-noncoding region of tick-borne encephalitis virus: construction of highly attenuated mutants of Flavivirus. J Virol 72:2132–2140.PubMedGoogle Scholar
  91. 91.
    Mandl CW, Aberle JH, Aberle SW, Holzmann H, Allison SL, Heinz FX. 1998. In vitrosynthesized infectious RNA as an attenuated live vaccine in a flavivirus model. Nature Med 4:1438–1440.PubMedCrossRefGoogle Scholar
  92. 92.
    Mathews DH, Sabina J, Zuker M, Turner H. 1999. Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J Mol Biol 288:911–940.PubMedCrossRefGoogle Scholar
  93. 93.
    Mattick JS. 1994. Introns: evolution and function. Curr Opin Genet Dev 4:823–831.PubMedCrossRefGoogle Scholar
  94. 94.
    Matzke M, Matzke, AJM, Kooter JM. 2001. RNA: guiding gene silencing. Science 293:1080–1083.PubMedCrossRefGoogle Scholar
  95. 95.
    McCaskill JS. 1990. The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29:1105–1119.PubMedCrossRefGoogle Scholar
  96. 96.
    Meyer C, Giegerich R. 2002. Matching and significance evaluation of combined sequence/structure motifs in RNA. Z Phys Chem 216:193–216.Google Scholar
  97. 97.
    Muller G, Gaspin C, Etienne A, Westhof E. 1993. Automatic display of RNA secondary structures. Comput Appl Biosci 9:551–561.PubMedGoogle Scholar
  98. 98.
    Nussinov R, Piecznik G, Griggs JR, Kleitman DJ. 1978. Algorithms for loop matching. SIAM J Appl Math 35:68–82.CrossRefGoogle Scholar
  99. 99.
    Nussinov R, Jacobson AB. 1980. Fast algorithm for predicting the secondary structure of single-stranded RNA. Proc Natl Acad Sci USA 77:6309–6313.PubMedCrossRefGoogle Scholar
  100. 100.
    Ohno M, Mattaj IW. 1999. Meiosis: MeiRNA hits the spot. Curr Biol 28:R66–R69.CrossRefGoogle Scholar
  101. 101.
    Oleynikov Y, Singer RH. 1998. RNA localization: different zipcodes, same postman? Trends Cell Biol 8:381–383.PubMedCrossRefGoogle Scholar
  102. 102.
    Omer AD, Lowe TM, Russel AG, Ebhardt H, Eddy SR, Dennis P. 2000. Homologs of small nucleolar RNAs in Archaea. Science 288:517–522.PubMedCrossRefGoogle Scholar
  103. 103.
    Van de Peer Y, De Rijk P, Wuyts J, Winkelmans T, De Wachter R. 2000. The European small subunit ribosomal RNA database. Nucleic Acids Res 28:175–176.PubMedCrossRefGoogle Scholar
  104. 104.
    Perochon-Dorisse J, Chetouani F, Aurel S, Iscolo N, Michot B. 1995. RNA-d2: a computer programm for editing and display of RNA secondary structures. Bioinformatics 11:101–109.CrossRefGoogle Scholar
  105. 105.
    Pesole G, Mignone F, Gissi C, Grillo Ga, Licciulli F, Sabino L. 2001. Structural and functional features of eukaryotic mRNA untranslated regions. Gene 276:73–81.PubMedCrossRefGoogle Scholar
  106. 106.
    Pleij CW. 1995. Structure and function of RNA pseudoknots. Genet Eng 17:67–80.Google Scholar
  107. 107.
    Rauscher S, Flamm C, Mandl C, Heinz FX, Stadler PF. 1997. Secondary structure of the 3′-non-coding region of Flavivirus genomes: comparative analysis of base pairing probabilities. RNA 3:779–791 (Santa Fe Institute Preprint 97-02-010).PubMedGoogle Scholar
  108. 108.
    Reidys C, Stadler PF, Schuster P. 1997. Generic properties of combinatory maps: neutral networks of RNA secondary Structure. Bull Math Biol 59:339–397.PubMedCrossRefGoogle Scholar
  109. 109.
    De Rijk P, De Wachter R. 1997. RnaViz, a program for the visualization of RNA secondary structure. Nucleic Acids Res 25:4679–4684.PubMedCrossRefGoogle Scholar
  110. 110.
    Rivas E, Eddy SR. 2000. Secondary structure alone is generally not statistically significant for the detection of noncoding RNAs. Bioinformatics 16:583–605.PubMedCrossRefGoogle Scholar
  111. 111.
    Rivas E, Eddy SR. 2000. The language of RNA: a formal grammar that includes pseudoknots. Bioinformatics 16:334–340.PubMedCrossRefGoogle Scholar
  112. 112.
    Rivas E, Klein RJ, Jones TA, Eddy SR. 2001. Computational identification of noncoding RNAs in E. coli by comparative genomics. Curr Biol 11:1369–1373.PubMedCrossRefGoogle Scholar
  113. 113.
    Rivas E, Eddy SR. 2001. Noncoding RNA gene detection using comparative sequence analysis. BMC Bioinformatics 2(8):19 pages.Google Scholar
  114. 114.
    Rivas E, Eddy SR. 1999. A dynamic programming algorithm for RNA structure prediction including pseudoknots. J Mol Biol 285:2053–2068.PubMedCrossRefGoogle Scholar
  115. 115.
    Rueckert RR. 1996. Picornaviridae: the viruses and their replication. In Virology, 3rd ed., pp. 609–654. Ed. NR Fields, DM Knipe, PM Howley. Lippincott-Raven, Philadelphia.Google Scholar
  116. 116.
    Samarsky DA, Fournier MJ. 1999. A comprehensive database for the small nucleolar RNAs from Saccharomyces cerevisiae. Nucleic Acids Res 27:161–164.PubMedCrossRefGoogle Scholar
  117. 117.
    Sankoff D. 1985. Simultaneous solution of the RNA folding alignment, and proto-sequence problems. SIAM J Appl Math 45:810–825.CrossRefGoogle Scholar
  118. 118.
    SantaLucia Jr. J, Turner DH. 1997. Measuring the thermodynamics of RNA secondary structure formation. Biopolymers 44:309–319.PubMedCrossRefGoogle Scholar
  119. 119.
    Schmitz M, Steger G. 1992. Base-pair probability profiles of RNA secondary structures. Comput Appl Biosci 8:389–399.PubMedGoogle Scholar
  120. 120.
    Schultes EA, Bartel DP. 2000. One sequence, two ribozymes: implications for the emergence of new ribozyme folds. Science 289:448–452.PubMedCrossRefGoogle Scholar
  121. 121.
    Schuster P. 2001. Evolution in silico and in vitro: The RNA model. Biol Chem 382:1301–1314.PubMedCrossRefGoogle Scholar
  122. 122.
    Schuster P, Fontana W, Stadler PF, Hofacker IL. 1994. From sequences to shapes and back: a case study in RNA secondary structures. Proc Roy Soc Lond. B 255:279–284.CrossRefGoogle Scholar
  123. 123.
    Schuster P. 1995. How to search for RNA structures: theoretical concepts in evolutionary biotechnology. J Biotechnol 41:239–257.PubMedCrossRefGoogle Scholar
  124. 124.
    Schuster P, Stadler PF. 1998. Sequence redundancy in biopolymers: a study on RNA and protein structures. In Viral regulatory structures, pp. 163–186. Ed. G. Myers. Santa Fe Institute Studies in the Sciences of Complexity, Vol. 28. Addison-Wesley, Reading MA.Google Scholar
  125. 125.
    Shapiro BS. 1988. An algorithm for comparing multiple RNA secondary structures. CABIOS 4:387–393.PubMedGoogle Scholar
  126. 126.
    Shapiro B, Zhang K. 1990. Comparing multiple RNA secondary structures using tree comparisons. CABIOS 6:309–318.PubMedGoogle Scholar
  127. 127.
    Sousa C, Johansson C, Charon C, Manyani H, Sautter C, Kondorosi A, Crespi M. 2001. Translational and structural requirements of the early nodulin gene enod40, a short-open reading frame-containing RNA, for elicitation of a cell-specific growth response in the alfalfa root cortex. Mol Cell Biol 21:354–366.PubMedCrossRefGoogle Scholar
  128. 128.
    Sprinzl M, Horn C, Brown M, Ioudovitch A, Steinberg S. 1998. Compilation of tRNA sequences and sequences of tRNA genes. Nucleic Acids Res 26:148–153.PubMedCrossRefGoogle Scholar
  129. 129.
    Stocsits R, Hofacker IL, Stadler PF. 1999. Conserved secondary structures in hepatitis B virus RNA. Computer science in biology, pp. 73–79. Proceedings of the GCB’99, Hannover, D. University of Bielefeld, Germany.Google Scholar
  130. 130.
    Stoss O, Stoilov P, Daoud R, Hartmann AM, Olbrich M, Stamm S. 2000. Misregulation of premRNA splicing that causes human diseases: concepts and therapeutic strategies. Gene Therapy Mol Biol 5:9–30.Google Scholar
  131. 131.
    Sung D, Kang H. 1998. Mutational analysis of the RNA pseudoknot involved in efficient ribosomal frameshifting in simian retrovirus-1. Nucleic Acids Res 26:1369–1372.PubMedCrossRefGoogle Scholar
  132. 132.
    Szymanski M, Barciszewska MZ, Barciszewski J, Erdmann VA. 2000. 5S ribosomal RNA database Y2K. Nucleic Acids Res 28:166–167.PubMedCrossRefGoogle Scholar
  133. 133.
    Tabaska JE, Stormo GD. 1997. Automated alignment of RNA sequences to pseudoknotted structures. In Proceedings of the ISMB-97, pp. 311–318. Ed. T Gaasterland, P Karp, K Karplus, Ch Ouzounis, Ch Sander, A Valencia. AAAI Press, Menlo Park, CA.Google Scholar
  134. 134.
    Tabaska JE, Cary RB, Gabow HN, Stormo GD. 1998. An RNA folding method capable of identifying pseudoknots and base triples. Bioinformatics 14:691–699.PubMedCrossRefGoogle Scholar
  135. 135.
    Thompson JD, Higgs DG, Gibson TJ. 1994. CLUSTALW: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position specific gap penalties, and weight matrix choice. Nucleic Acids Res 22:4673–4680.PubMedCrossRefGoogle Scholar
  136. 136.
    Thurner C, Witwer C, Hofacker I, Stadler PF. 2004. Conserved RNA secondary structures in Flaviviridae genomes. J Gen Virol 85:1113–1124.PubMedCrossRefGoogle Scholar
  137. 137.
    Walter AE, Turner DH, Kim J, Lyttle MH, Müller P, Mathews DH, Zuker M. 1994. Co-axial stacking of helixes enhances binding of oligoribonucleotides and improves predicions of RNA folding. Proc Natl Acad Sci USA 91:9218–9222.PubMedCrossRefGoogle Scholar
  138. 138.
    Wang L, Smith D, Bot S, Dellamary L, Bloom A, Bot A. 2002. Noncoding RNA danger motifs bridge innate and adaptive immunity and are potent adjuvants for vaccination. J Clin Invest 110:1175–1184.PubMedCrossRefGoogle Scholar
  139. 139.
    Wang L, Jiang T, Zhang K. 1995. Alignment of trees: an alternative to tree edit. Theor Comput Sci 143:137–148.CrossRefGoogle Scholar
  140. 140.
    Waterman MS. 1978. Secondary structure of single-stranded nucleic acids. In Studies on foundations and combinatorics, pp. 167–212. Advances in mathematics supplementary studies. Academic Press, New York.Google Scholar
  141. 141.
    Waterman MS, Smith TF. 1978. RNA secondary structure: A complete mathematical analysis. Math Biosci 42:257–266.CrossRefGoogle Scholar
  142. 142.
    Waterman MS. 1978. Combinatorics of RNA hairpins and cloverleaves. Stud Appl Math 60:91–96.Google Scholar
  143. 143.
    Waterman MS, Gordon L, Arratia R. 1987. Phase transition in sequence matches and nucleic acid structure. Proc Natl Acad Sci USA 84:1239–1243.PubMedCrossRefGoogle Scholar
  144. 144.
    Waterman MS. 1995. Introduction to computational biology: maps sequences, and genomes. Chapman & Hall, London.Google Scholar
  145. 145.
    Westhof E, Jaeger L. 1992. RNA pseudoknots. Curr Opin Struct Biol 2:327–333.CrossRefGoogle Scholar
  146. 146.
    Williams KP. 2002. The tmRNA Website: invasion by an intron. Nucleic Acids Res 30:179–182.PubMedCrossRefGoogle Scholar
  147. 147.
    Wilson DS, Szostak JW. 1999. In vitro selection of fuctional nucleic acids. Annu Rev Biochem 68:611–647.PubMedCrossRefGoogle Scholar
  148. 148.
    Witwer C, Rauscher S, Hofacker IL, Stadler PF. 2001. Conserved RNA secondary structures in Picornaviridae genomes. Nucleic Acids Res 29:5079–5089.PubMedCrossRefGoogle Scholar
  149. 149.
    Wuchty S, Fontana W, Hofacker IL, Schuster P. 1999. Complete Suboptimal folding of RNA and the stability of secondary structures. Biopolymers 49:145–165.PubMedCrossRefGoogle Scholar
  150. 150.
    Wuyts J, De Rijk P, Van de Peer Y, Winkelmans T, De Wachter R. 2001. The European large subunit ribosomal RNA database. Nucleic Acids Res 29:175–177.PubMedCrossRefGoogle Scholar
  151. 151.
    Ying H, Zaks TZ, Wang R-F, Irvine KR, Kammula US, Marincola FM, Leitner WW, Restifo NP. 1999. Cancer therapy using a self-replicating RNA vaccine. Nature Med 5:823–827.PubMedCrossRefGoogle Scholar
  152. 152.
    van Zon A, Mossink MH, Schoester M, Scheffer GL, Scheper RJ, Sonneveld P, Wiemer EA. 2001. Multiple human vault RNAs: expression and association with the vault complex. J Biol Chem 276:37715–37721.PubMedCrossRefGoogle Scholar
  153. 153.
    Zuker M, Stiegler P. 1981. Optimal computer folding of larger RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res 9:133–148.PubMedCrossRefGoogle Scholar
  154. 154.
    Zuker M, Sankoff D. 1984. RNA secondary structures and their prediction. Bull Math Biol 46:591–621.Google Scholar
  155. 155.
    Zuker M. 1989. On finding all suboptimal foldings of an RNA molecule. Science 244:48–52.PubMedCrossRefGoogle Scholar
  156. 156.
    Zuker M, Somorjai RL. 1989. The alignment of protein structures in three dimensions. Bull Math Biol 51:55–78.PubMedGoogle Scholar
  157. 157.
    Zuker M. 1989. The use of dynamic programming algorithms in RNA secondary structure prediction. In Mathematical methods for DNA sequences, pp. 159–184. Ed. MS Waterman. CRC Press, Boca Raton, FL.Google Scholar
  158. 158.
    Zuker M, Jaeger JA, Turner DH. 1991. A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by phylogenetic comparison. Nucleic Acids Res 19:2707–2714.PubMedCrossRefGoogle Scholar
  159. 159.
    Zuker M. 1991. Suboptimal sequence alignment in molecular biology. J Mol Biol 221:403–420.PubMedCrossRefGoogle Scholar
  160. 160.
    Zwieb C, Wower J. 2000. tmRDB (tmRNA database). Nucleic Acids Res 28:169–170.PubMedCrossRefGoogle Scholar
  161. 161.
    Zwieb C. 1996. The uRNA database. Nucleic Acids Res 24:76–79.PubMedCrossRefGoogle Scholar
  162. 162.
    d’Aubenton Carafa Y, Brody E, Thermes C. 1990. Prediction of rho-independent Escherichia coli transcription terminators: a statistical analysis of their RNA stem-loop structures. J Mol Biol 216:835–858.PubMedCrossRefGoogle Scholar
  163. 163.
    Gräf S, Strothmann D, Kurtz S, Steger G. 2001. HyPaLib: a database of RNAs and RNA structural elements defined by hybrid patterns. Nucleic Acids Res 29:196–198.PubMedCrossRefGoogle Scholar
  164. 164.
    Chen S, Lesnik EA, Hall TA, Sampath R, Griffey RH, Ecker DJ, Blyn LB. 2002. A bioinformatics based approach to discover small RNA genes in the Escherichia coli genome. BioSystems 65:157–177.PubMedCrossRefGoogle Scholar
  165. 165.
    Fogel GB, Porto VW, Weekes DG, Fogel DB, Griffey RH, McNeil JA, Lesnik E, Ecker DJ, Sampath R. 2002. Discovery of RNA structural elements using evolutionary computation. Nucleic Acids Res 30:5310–5317.PubMedCrossRefGoogle Scholar
  166. 166.
    Carter RJ, Dubchak I, Holbrook SR. 2001. A computational approach ot indentify genes for functional RNAs in genomic sequences. Nucleic Acids Res 29:3928–3938.PubMedGoogle Scholar

Copyright information

© Springer Inc. 2006

Authors and Affiliations

  1. 1.Institute for Theoretical Chemistry and Structural BiologyUniversity of ViennaVienna
  2. 2.Bioinformatics, Department of Computer ScienceUniversity of LeipzigLeipzigGermany

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