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doi: https://doi.org/10.53941/aim.2024.100006
Zhao, Q., Chen, J., Zhao, Z., Mao, Q., Shi, H., & Fan, X. ML-Based RNA Secondary Structure Prediction Methods: A Survey. AI Medicine. 2024, 1(1), 6. doi: https://doi.org/10.53941/aim.2024.100006
Volume 1, lssue 1, Dec 2024
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Article

ML-Based RNA Secondary Structure Prediction Methods: A Survey

Qi Zhao 1, Jingjing Chen 1, Zheng Zhao 2, Qian Mao 3, Haoxuan Shi 1 and Xiaoya Fan 4,∗

1 School of Medicine and Biological Information Engineering, Northeastern University, Shenyang 110000, China

2 School of Artificial Intelligence, Dalian Maritime University, Dalian 116000, China

3 Department of Food Science and Engineering, College of Light Industry, Liaoning University, Shenyang 110000, China

4 School of Software, Dalian University of Technology, Key Laboratory for Ubiquitous Network and Service Software, Dalian 116000, China

∗ Correspondence: xiaoyafan@dlut.edu.cn

Received: 6 May 2024; Revised: 17 October 2024; Accepted: 22 October 2024; Published: 29 October 2024

 

Abstract: The secondary structure of noncoding RNAs (ncRNA) is significantly related to their functions, emphasizing the importance and value of identifying ncRNA secondary structure. Computational prediction methods have been widely used in this field. However, the performance of existing computational methods has plateaued in recent years despite various advancements. Fortunately, the emergence of machine learning, particularly deep learning, has brought new hope to this field. In this review, we present a comprehensive overview of machine learning-based methods for predicting RNA secondary structures, with a particular emphasis on deep learning approaches. Additionally, we discuss the current challenges and prospects in RNA secondary structure prediction.

Keywords:

RNA secondary structure prediction machine learning; deep learning

References

  1. Wang, D.; Farhana, A. Biochemistry, RNA Structure. In StatPearls; StatPearls Publishing: Treasure Island, FL, USA, 2024.
  2. Zhao, Y.; Wang, J.; Zeng, C.; Xiao, Y. Evaluation of rna secondary structure prediction for both base-pairing and topology. Biophys. Rep. 2018, 4, 123–132. DOI: https://doi.org/10.1007/s41048-018-0058-y
  3. Leontis, N.B.; Westhof, E. Geometric nomenclature and classification of RNA base pairs. RNA 2001, 7, 499–512. DOI: https://doi.org/10.1017/S1355838201002515
  4. Almakarem, A.S.A.; Petrov, A.I.; Stombaugh, J.; Zirbel, C.L.; Leontis, N.B. Comprehensive survey and geometric classification of base triples in RNA structures. Nucleic Acids Res. 2012, 40, 407–1423. DOI: https://doi.org/10.1093/nar/gkr810
  5. Doherty, E.A.; Batey, R.T.; Masquida, B.; Doudna, J.A. A universal mode of helix packing in RNA. Nat. Struct. Biol. 2001, 8, 339–343. DOI: https://doi.org/10.1038/86221
  6. Van Batenburg, F.H.D.; Gultyaev, A.P.; Pleij, C.W.A. PseudoBase: structural information on RNA pseudoknots. Nucleic Acids Res. 2001, 29, 194–195. DOI: https://doi.org/10.1093/nar/29.1.194
  7. Staple, D.W.; Butcher, S.E. Pseudoknots: RNA Structures with Diverse Functions. PLoS Biol. 2005, 3, e213. DOI: https://doi.org/10.1371/journal.pbio.0030213
  8. ENCODE Project Consortium. An Integrated Encyclopedia of DNA Elements in the Human Genome. Nature 2012, 489, 57–74. DOI: https://doi.org/10.1038/nature11247
  9. Kovalchuk, I. Chapter 24-Non-coding RNAs in genome integrity. In Genome Stability, 2nd ed.; Kovalchuk, I., Kovalchuk, O., Eds.; Volume 26 of Translational Epigenetics; Academic Press: Boston, MA, USA 2021; pp. 453–475. DOI: https://doi.org/10.1016/B978-0-323-85679-9.00024-6
  10. Kasprzyk, M.E.; Kazimierska, M.; Sura, W.; Dzikiewicz-Krawczyk, A.; Podralska, M. Chapter 3-Non-coding RNAs: Mechanisms of action. In Navigating Non-Coding RNA; Sztuba-Solinska, J., Ed.; Academic Press: Cambridge, MA, USA, 2023; pp. 89–138. DOI: https://doi.org/10.1016/B978-0-323-90406-3.00010-5
  11. Doudna, J.A.; Cech, T.R. The chemical repertoire of natural ribozymes. Nature 2002, 418, 222–228. DOI: https://doi.org/10.1038/418222a
  12. Higgs, P.G.; Lehman, N. The RNA World: Molecular cooperation at the origins of life. Nat. Rev. Genet. 2015, 16, 7–17. DOI: https://doi.org/10.1038/nrg3841
  13. Mortimer, S.A.; Kidwell, M.A.; Doudna, J.A. Insights into RNA structure and function from genome-wide studies. Nat. Rev. Genet. 2014, 15, 469–479. DOI: https://doi.org/10.1038/nrg3681
  14. Meister, G.; Tuschl, T. Mechanisms of gene silencing by double-stranded RNA. Nature 2004, 431, 343–349. DOI: https://doi.org/10.1038/nature02873
  15. Serganov, A.; Nudler, E. A Decade of Riboswitches. Cell 2013, 152, 17–24. DOI: https://doi.org/10.1016/j.cell.2012.12.024
  16. Wu, L.; Belasco, J.G. Let me count the ways: Mechanisms of gene regulation by miRNAs and siRNAs. Mol. Cell 2008, 29, 1–7. DOI: https://doi.org/10.1016/j.molcel.2007.12.010
  17. Zou, Q.; Li, J.; Hong, Q.; Lin, Z.; Wu, Y.; Shi, H.; Ju, Y. Prediction of MicroRNA-Disease Associations Based on Social Network Analysis Methods. BioMed Res. Int. 2015, 2015, 810514, . DOI: https://doi.org/10.1155/2015/810514
  18. Tinoco, I.; Bustamante, C. How RNA folds. J. Mol. Biol. 1999, 293, 271–281. DOI: https://doi.org/10.1006/jmbi.1999.3001
  19. Georgakopoulos-Soares, I.; Parada, G.E.; Hemberg, M. Secondary structures in RNA synthesis, splicing and translation. Comput. Struct. Biotechnol. J. 2022, 20, 2871–2884. DOI: https://doi.org/10.1016/j.csbj.2022.05.041
  20. Celander, D.W.; Cech, T.R. Visualizing the higher order folding of a catalytic RNA molecule. Science 1991, 251, 401–407. DOI: https://doi.org/10.1126/science.1989074
  21. Stephens, Z.D.; Lee, S.Y.; Faghri, F.; Campbell, R.H.; Zhai, C.; Efron, M.J.; Iyer, R.; Schatz, M.C.; Sinha, S.; Robinson, G.E. Big Data: Astronomical or Genomical? PLoS Biol. 2015, 13, e1002195. DOI: https://doi.org/10.1371/journal.pbio.1002195
  22. Zarrinkar, P.P.; Williamson, J.R. Kinetic intermediates in RNA folding. Science 1994, 265, 918–924. DOI: https://doi.org/10.1126/science.8052848
  23. The statistical mechanics of RNA folding. Physics 2006, 35, 218–229. DOI: https://doi.org/10.1017/CBO9780511755620.003
  24. Zhao, Q.; Zhao, Z.; Fan, X.; Yuan, Z.; Mao, Q.; Yao, Y. Review of machine learning methods for RNA secondary structure prediction. PLoS Comput. Biol. 2021, 17, e1009291. DOI: https://doi.org/10.1371/journal.pcbi.1009291
  25. Condon, A. Problems on RNA Secondary Structure Prediction and Design. In Automata, Languages and Programming; (Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginge, G., Eds.; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 2003; pp. 22–32. DOI: https://doi.org/10.1007/3-540-45061-0_2
  26. Fallmann, J.; Will, S.; Engelhardt, J.; Gruning, B.; Backofen, R.; Stadler, P.F. Recent advances in RNA folding. J. Biotechnol. 2017, 261, 97–104. DOI: https://doi.org/10.1016/j.jbiotec.2017.07.007
  27. Seetin, M.G.; Mathews, D.H. RNA structure prediction: An overview of methods. Methods Mol. Biol. 2012, 905, 99–122. DOI: https://doi.org/10.1007/978-1-61779-949-5_8
  28. Furtig, B.; Richter, C.; Wohnert, J.; Schwalbe, H. NMR spectroscopy of RNA. ChemBioChem 2003, 4, 936–962. DOI: https://doi.org/10.1002/cbic.200300700
  29. Westhof, E. Twenty years of RNA crystallography. RNA 2015, 21, 486–487. DOI: https://doi.org/10.1261/rna.049726.115
  30. Tijerina, P.; Mohr, S.; Russell, R. DMS Footprinting of Structured RNAs and RNA-Protein Complexes. Nat. Protoc. 2007, 2, 2608–2623. DOI: https://doi.org/10.1038/nprot.2007.380
  31. Wilkinson, K.A.; Merino, E.J.; Weeks, K.M. Selective 2’-hydroxyl acylation analyzed by primer extension (SHAPE): Quantitative RNA structure analysis at single nucleotide resolution. Nat. Protoc. 2006, 1, 1610– 1616. DOI: https://doi.org/10.1038/nprot.2006.249
  32. Kertesz, M.; Wan, Y.; Mazor, E.; Rinn, J.L.; Nutter, R.C.; Chang, H.Y.; Segal, E. Genome-wide Measurement of RNA Secondary Structure in Yeast. Nature 2010, 467, 9322. DOI: https://doi.org/10.1038/nature09322
  33. Underwood, J.G.; Uzilov, A.V.; Katzman, S.; Onodera, C.S.; Mainzer, J.E.; Mathews, D.H.; Lowe, T.M.; Salama, S.R.; Haussler, D. FragSeq: transcriptome-wide RNA structure probing using high-throughput sequencing. Nat. Methods 2010, 7, 995–1001. DOI: https://doi.org/10.1038/nmeth.1529
  34. Bevilacqua, P.C.; Ritchey, L.E.; Su, Z.; Assmann, S.M. Genome-Wide Analysis of RNA Secondary Structure. Annu. Rev. Genet. 2016, 50, 235–266. DOI: https://doi.org/10.1146/annurev-genet-120215-035034
  35. Tian, S.; Das, R. RNA structure through multidimensional chemical mapping. Q. Rev. Biophys. 2016, 49, e7. DOI: https://doi.org/10.1017/S0033583516000020
  36. RNAcentral: A comprehensive database of non-coding RNA sequences. Nucleic Acids Res. 2017, 45, D128– D134. DOI: https://doi.org/10.1093/nar/gkw1008
  37. Gutell, R.R.; Lee, J.C.; Cannone, J.J. The accuracy of ribosomal RNA comparative structure models. Curr. Opin. Struct. Biol. 2002, 12, 301–310. DOI: https://doi.org/10.1016/S0959-440X(02)00339-1
  38. Madison, J.T.; Everett, G.A.; Kung, H. Nucleotide sequence of a yeast tyrosine transfer RNA. Science 1966, 153, 531–534. DOI: https://doi.org/10.1126/science.153.3735.531
  39. Gutell, R.R.; Weiser, B.; Woese, C.R.; Noller, H.F. Comparative anatomy of 16-S-like ribosomal RNA. Prog. Nucleic Acid Res. Mol. Biol. 1985, 32, 155–216. DOI: https://doi.org/10.1016/S0079-6603(08)60348-7
  40. Ruan, J.; Stormo, G.D.; Zhang, W. An iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots. Bioinformatics 2004, 20, 58–66. DOI: https://doi.org/10.1093/bioinformatics/btg373
  41. Hofacker, I.L.; Fekete, M.; Flamm, C.; Huynen, M.A.; Rauscher, S.; Stolorz, P.E.; Stadler, P.F. Automatic detection of conserved RNA structure elements in complete RNA virus genomes. Nucleic Acids Res. 1998, 26, 3825–3836. DOI: https://doi.org/10.1093/nar/26.16.3825
  42. Bindewald, E.; Shapiro, B.A. Rna secondary structure prediction from sequence alignments using a network of k-nearest neighbor classifiers. RNA 2006, 12, 342–352. DOI: https://doi.org/10.1261/rna.2164906
  43. Legendre, A.; Angel, E.; Tahi, F. Bi-objective integer programming for RNA secondary structure prediction with pseudoknots. BMC Bioinformatics 2018, 19, 1–15. DOI: https://doi.org/10.1186/s12859-018-2007-7
  44. Han, K.; Kim, H.J. Prediction of common folding structures of homologous RNAs. Nucleic Acids Res. 1993, 21, 1251–1257. DOI: https://doi.org/10.1093/nar/21.5.1251
  45. Tahi, F.; Gouy, M.; Regnier, M. Automatic RNA secondary structure prediction with a comparative approach. Comput. Chem. 2002, 26, 521–530. DOI: https://doi.org/10.1016/S0097-8485(02)00012-8
  46. Nussinov, R.; Jacobson, A.B. Fast algorithm for predicting the secondary structure of single-stranded RNA. Proc. Natl. Acad. Sci. USA 1980, 77, 6309–6313. DOI: https://doi.org/10.1073/pnas.77.11.6309
  47. Engelen, S.; Tahi, F. Tfold: Efficient in silico prediction of non-coding RNA secondary structures. Nucleic Acids Res. 2010, 38, 2453–2466. DOI: https://doi.org/10.1093/nar/gkp1067
  48. Bellaousov, S.; Mathews, D.H. ProbKnot: Fast prediction of RNA secondary structure including pseudoknots. RNA 2010, 16, 1870–1880. DOI: https://doi.org/10.1261/rna.2125310
  49. Burge, S.W.; Daub, J.; Eberhardt, R.; Tate, J.; Barquist, L.; Nawrocki, E.P.; Eddy, S.R.; Gardner, P.P.; Bateman, A. Rfam 11.0: 10 years of RNA families. Nucleic Acids Res. 2013, 41, D226–D232. DOI: https://doi.org/10.1093/nar/gks1005
  50. Xia, T.; SantaLucia, J.; Burkard, M.E.; Kierzek, R.; Schroeder, S.J.; Jiao, X.; Cox, C.; Turner, D.H. Thermody- namic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs. Biochemistry 1998, 37, 14719–14735. DOI: https://doi.org/10.1021/bi9809425
  51. Mathews, D.H.; Sabina, J.; Zuker, M.; Turner, D.H. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol. 1999, 288, 911–940. DOI: https://doi.org/10.1006/jmbi.1999.2700
  52. Andronescu, M.; Condon, A.; Turner, D.H.; Mathews, D.H. The determination of RNA folding nearest neighbor parameters. Methods Mol. Biol. 2014, 1097, 45–70. DOI: https://doi.org/10.1007/978-1-62703-709-9_3
  53. Turner, D.H.; Mathews, D.H. NNDB: The nearest neighbor parameter database for predicting stability of nucleic acid secondary structure. Nucleic Acids Res. 2010, 38, D280–D282. DOI: https://doi.org/10.1093/nar/gkp892
  54. Bon, M.; Micheletti, C.; Orland, H. McGenus: A Monte Carlo algorithm to predict RNA secondary structures with pseudoknots. Nucleic Acids Res. 2013, 41, 1895–1900. DOI: https://doi.org/10.1093/nar/gks1204
  55. Reeder, J.; Giegerich, R. Design, implementation and evaluation of a practical pseudoknot folding algorithm based on thermodynamics. BMC Bioinform. 2004, 5, 104. DOI: https://doi.org/10.1186/1471-2105-5-104
  56. Dirks, R.M.; Pierce, N.A. A partition function algorithm for nucleic acid secondary structure including pseudoknots. J. Comput. Chem. 2003, 24, 1664–1677. DOI: https://doi.org/10.1002/jcc.10296
  57. Rivas, E.; Eddy, S.R. A dynamic programming algorithm for RNA structure prediction including pseudoknots. J. Mol. Biol. 1999, 285, 2053–2068. DOI: https://doi.org/10.1006/jmbi.1998.2436
  58. Sato, K.; Kato, Y. Prediction of RNA secondary structure including pseudoknots for long sequences. Brief. Bioinform. 2021, 23, bbab395. DOI: https://doi.org/10.1093/bib/bbab395
  59. Poolsap, U.; Kato, Y.; Akutsu, T. Prediction of RNA secondary structure with pseudoknots using integer programming. BMC Bioinformatics 2009, 10, 1–11. DOI: https://doi.org/10.1186/1471-2105-10-S1-S38
  60. Jordan, M.I.; Mitchell, T.M. Machine learning: Trends, perspectives, and prospects. Science 2015, 349, 255–260. DOI: https://doi.org/10.1126/science.aaa8415
  61. Lorenz, R.; Bernhart, S.H.; Siederdissen, C.H.Z.; Tafer, H.; Flamm, C.; Stadler, P.F.; Hofacker, I.L. ViennaRNA Package 2.0. Algorithms Mol. Biol. 2011, 6, 26. DOI: https://doi.org/10.1186/1748-7188-6-26
  62. Bellaousov, S.; Reuter, J.S.; Seetin, M.G.; Mathews, D.H. RNAstructure: web servers for RNA secondary structure prediction and analysis. Nucleic Acids Res. 2013, 41, W471–W474. DOI: https://doi.org/10.1093/nar/gkt290
  63. Andronescu, M.; Condon, A.; Hoos, H.H.; Mathews, D.H.; Murphy, K.P. Efficient parameter estimation for RNA secondary structure prediction. Bioinformatics 2007, 23, i19–i28. DOI: https://doi.org/10.1093/bioinformatics/btm223
  64. Washietl, S.; Will, S.; Hendrix, D.A.; Goff, L.A.; Rinn, J.L.; Berger, B.; Kellis, M. Computational analysis of noncoding RNAs. Wiley Interdiscip. Rev. RNA 2012, 3, 759–778. DOI: https://doi.org/10.1002/wrna.1134
  65. Tang, X.; Thomas, S.; Tapia, L.; Giedroc, D.P.; Amato, N.M. Simulating RNA folding kinetics on approximated energy landscapes. J. Mol. Biol. 2008, 381, 1055–1067. DOI: https://doi.org/10.1016/j.jmb.2008.02.007
  66. Rehmsmeier, M.; Steffen, P.; Hochsmann, M.; Giegerich, R. Fast and effective prediction of microRNA/target duplexes. RNA 2004, 10, 1507–1517. DOI: https://doi.org/10.1261/rna.5248604
  67. Zakov, S.; Goldberg, Y.; Elhadad, M.; Ziv-Ukelson, M. Rich parameterization improves RNA structure prediction. J. Comput.Biol. A J. Comput. Mol. Cell Biol. 2011, 18, 1525–1542. DOI: https://doi.org/10.1089/cmb.2011.0184
  68. Akiyama, M.; Sato, K.; Sakakibara, Y. A max-margin training of RNA secondary structure prediction integrated with the thermodynamic model. J. Bioinform. Comput. Biol. 2018, 16, 1840025. DOI: https://doi.org/10.1142/S0219720018400255
  69. Sato, K.; Akiyama, M.; Sakakibara, Y. Rna secondary structure prediction using deep learning with thermody- namic integration. Nat. Commun. 2021, 12, 941. DOI: https://doi.org/10.1038/s41467-021-21194-4
  70. Akakibara, Y.; Brown, M.; Hughey, R.; Mian, I.S.; Sjolander, K.; Underwood, R.C.; Haussler, D. Stochastic context-free grammars for tRNA modeling. Nucleic Acids Res. 1994, 22, 5112–5120. DOI: https://doi.org/10.1093/nar/22.23.5112
  71. Woodson, S.A. Recent insights on RNA folding mechanisms from catalytic RNA. Cell. Mol. Life Sci. 2000, 57, 796–808. DOI: https://doi.org/10.1007/s000180050042
  72. Knudsen, B.; Hein, J. RNA secondary structure prediction using stochastic context-free grammars and evolutionary history. Bioinformatics 1999, 15, 446–454. DOI: https://doi.org/10.1093/bioinformatics/15.6.446
  73. Dowell, R.D.; Eddy, S.R. Evaluation of several lightweight stochastic context-free grammars for RNA secondary structure prediction. BMC Bioinform. 2004, 5, 71. DOI: https://doi.org/10.1186/1471-2105-5-71
  74. Rivas, E.; Lang, R.; Eddy, S.R. A range of complex probabilistic models for RNA secondary structure prediction that includes the nearest-neighbor model and more. RNA 2012, 18, 193–212. DOI: https://doi.org/10.1261/rna.030049.111
  75. Sato, K.; Hamada, M.; Mituyama, T.; Asai, K.; Sakakibara, Y. A non-parametric bayesian approach for predicting RNA secondary structures. J. Bioinform. Comput. Biol. 2010, 8, 727–742. DOI: https://doi.org/10.1142/S0219720010004926
  76. Yonemoto, H.; Asai, K.; Hamada, M. A semi-supervised learning approach for RNA secondary structure prediction. Comput. Biol. Chem. 2015, 57, 72–79. DOI: https://doi.org/10.1016/j.compbiolchem.2015.02.002
  77. Do, C.B.; Woods, D.A.; Batzoglou, S. CONTRAfold: RNA secondary structure prediction without physics- based models. Bioinformatics 2006, 22, e90–e98. DOI: https://doi.org/10.1093/bioinformatics/btl246
  78. Hor, C.-Y.; Yang, C.-B.; Chang, C.-H.; Tseng, C.-T.; Chen, H.-H. A tool preference choice method for RNA secondary structure prediction by SVM with statistical tests. Evol. Bioinform. 2013, 9, EBO–S10580. DOI: https://doi.org/10.4137/EBO.S10580
  79. Zhu, Y.; Xie, Z.; Li, Y.; Zhu, M.; Chen, Y.-P.P. Research on folding diversity in statistical learning methods for RNA secondary structure prediction. Int. J. Biol. Sci. 2018, 14, 872–882. DOI: https://doi.org/10.7150/ijbs.24595
  80. Singh, J.; Hanson, J.; Paliwal, K.; Zhou, Y. RNA secondary structure prediction using an ensemble of two-dimensional deep neural networks and transfer learning. Nat. Commun. 2019, 10, 5407. DOI: https://doi.org/10.1038/s41467-019-13395-9
  81. Haynes, T.; Knisley, D.; Knisley, J. Using a neural network to identify secondary RNA structures quantified by graphical invariants. Commun. Math. Comput. Chem. 2008, 60, 277–290.
  82. Koessler, D.R.; Knisley, D.J.; Knisley, J.; Haynes, T. A predictive model for secondary RNA structure using graph theory and a neural network. BMC Bioinform. 2010, 11, S21. DOI: https://doi.org/10.1186/1471-2105-11-S6-S21
  83. Takefuji, Y.; Chen, L.L.; Lee, K.C.; Huffman, J. Parallel algorithms for finding a near-maximum independent set of a circle graph. IEEE Trans. Neural Netw. 1990, 1, 263–267. DOI: https://doi.org/10.1109/72.80251
  84. Qasim, R.; Kauser, N.; Jilani, T. Secondary Structure Prediction of RNA using Machine Learning Method. Int. J. Comput. Appl. 2010, 10, 15–22. DOI: https://doi.org/10.5120/1486-2003
  85. Liu, Q.; Ye, X.; Zhang, Y. A Hopfield Neural Network Based Algorithm for RNA Secondary Structure Prediction. In Proceedings of the First International Multi-Symposiums on Computer and Computational Sciences (IMSCCS’06), Hangzhou, China, 20–24 June 2006; Volume 1, pp. 10–16. DOI: https://doi.org/10.1109/IMSCCS.2006.9
  86. Apolloni, B.; Lotorto, L.; Morpurgo, A.; Zanaboni, A.M. RNA Secondary Structure Prediction by MFT Neural Networks. Psychol. Forsch. 2003, 2003, 143–148.
  87. Steeg, E.W. Neural Networks, Adaptive Optimization, and RNA Secondary Structure Prediction; American Association for Artificial Intelligence: Palo Alto, CA, USA, 1993; pp. 121–160.
  88. Singh, J.; Paliwal, K.; Zhang, T.; Singh, J.; Litfin, T.; Zhou, Y. Improved RNA secondary structure and tertiary base-pairing prediction using evolutionary profile, mutational coupling and two-dimensional transfer learning. Bioinformatics 2021, 37, 2589–2600. DOI: https://doi.org/10.1093/bioinformatics/btab165
  89. Fu, L.; Cao, Y.; Wu, J.; Peng, Q.; Nie, Q.; Xie, X. UFold: Fast and accurate RNA secondary structure prediction with deep learning. Nucleic Acids Res. 2022, 50, e14. DOI: https://doi.org/10.1093/nar/gkab1074
  90. Chen, X.; Li, Y.; Umarov, R.; Gao, X.; Song, L. RNA Secondary Structure Prediction By Learning Unrolled Algorithms. arXiv 2020, arXiv:2002.05810.
  91. Calonaci, N.; Jones, A.; Cuturello, F.; Sattler, M.; Bussi, G. Machine learning a model for RNA structure prediction. NAR Genom. Bioinform. 2020, 2, lqaa090. DOI: https://doi.org/10.1093/nargab/lqaa090
  92. Wu, H.; Tang, Y.; Lu, W.; Chen, C.; Huang, H.; Fu, Q. RNA Secondary Structure Prediction Based on Long Short-Term Memory Model. In Intelligent Computing Theories and Application; Huang, D.-S., Bevilacqua, V., Premaratne, P., Gupta, P., Eds.; Lecture Notes in Computer Science; Springer International Publishing: Cham, Switzerland, 2018; pp. 595–599. DOI: https://doi.org/10.1007/978-3-319-95930-6_59
  93. Lu, W.; Tang, Y.; Wu, H.; Huang, H.; Fu, Q.; Qiu, J.; Li, H. Predicting RNA secondary structure via adaptive deep recurrent neural networks with energy-based filter. BMC Bioinform. 2019, 20, 684. DOI: https://doi.org/10.1186/s12859-019-3258-7
  94. Quan, L.; Cai, L.; Chen, Y.; Mei, J.; Sun, X.; Lyu, Q. Developing parallel ant colonies filtered by deep learned constrains for predicting RNA secondary structure with pseudo-knots. Neurocomputing 2020, 384, 104–114. DOI: https://doi.org/10.1016/j.neucom.2019.12.041
  95. Fei, Y.; Zhang, H.; Wang, Y.; Liu, Z.; Liu, Y. LTPConstraint: a transfer learning based end-to-end method for RNA secondary structure prediction. BMC Bioinformatics 2022, 23, 354. DOI: https://doi.org/10.1186/s12859-022-04847-z
  96. Hochreiter, S. Long Short-Term Memory; Neural Computation MIT-Press: Cambridge, MA, USA, 1997. DOI: https://doi.org/10.1162/neco.1997.9.8.1735
  97. Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A. N.; Kaiser, L.; Polosukhin, I. Attention is all you need. In Advances in Neural Information Processing Systems; Curran Associates, Inc.: Red Hook, NY, USA, 2017.
  98. Ronneberger, O.; Fischer, P.; Brox, T. U-Net: Convolutional Networks for Biomedical Image Segmentation. arXiv 2015, arXiv:1505.04597. DOI: https://doi.org/10.1007/978-3-319-24574-4_28
  99. Booy, M.; Ilin, A.; Orponen, P. RNA secondary structure prediction with convolutional neural networks. BMC Bioinformatics 2022, 23, 58. DOI: https://doi.org/10.1186/s12859-021-04540-7
  100. Zhang, H.; Zhang, C.; Li, Z.; Li, C.; Wei, X.; Zhang, B.; Liu, Y. A New Method of RNA Secondary Structure Prediction Based on Convolutional Neural Network and Dynamic Programming. Front. Genet. 2019, 10, 467. DOI: https://doi.org/10.3389/fgene.2019.00467
  101. Wang, L.; Liu, Y.; Zhong, X.; Liu, H.; Lu, C.; Li, C.; Zhang, H. Dmfold: A novel method to predict rna secondary structure with pseudoknots based on deep learning and improved base pair maximization principle. Front. Genet. 2019, 10, 143. DOI: https://doi.org/10.3389/fgene.2019.00143
  102. Willmott, D.; Murrugarra, D.; Ye, Q. Improving RNA secondary structure prediction via state inference with deep recurrent neural networks. Comput. Math. Biophys. 2020, 8, 36–50. DOI: https://doi.org/10.1515/cmb-2020-0002
  103. Chen, C.C.; Chan, Y.M. REDfold: Accurate RNA secondary structure prediction using residual encoder- decoder network. BMC Bioinform. 2023, 24, 122. DOI: https://doi.org/10.1186/s12859-023-05238-8
  104. Andronescu, M.; Bereg, V.; Hoos, H.H.; Condon, A. RNA STRAND: The RNA Secondary Structure and Statistical Analysis Database. BMC Bioinform. 2008, 9, 340. DOI: https://doi.org/10.1186/1471-2105-9-340
  105. Burley, S.K.; Bhikadiya, C.; Bi, C.; Bittrich, S.; Chen, L.; Crichlow, G.V.; Christie, C.H.; Dalenberg, K.; Costanzo, L.D.; Duarte, J.M.; et al. RCSB Protein Data Bank: Powerful new tools for exploring 3D structures of biological macromolecules for basic and applied research and education in fundamental biology, biomedicine, biotechnology, bioengineering and energy sciences. Nucleic Acids Res. 2020, 49, D437–D451. DOI: https://doi.org/10.1093/nar/gkaa1038
  106. Danaee, P.; Rouches, M.; Wiley, M.; Deng, D.; Huang, L.; Hendrix, D. bprna: large-scale automated annotation and analysis of rna secondary structure. Nucleic Acids Res. 2018, 46, 5381–5394. DOI: https://doi.org/10.1093/nar/gky285
  107. Rnacentral 2021: Secondary structure integration, improved sequence search and new member databases. Nucleic Acids Res. 2021, 49, D212–D220. DOI: https://doi.org/10.1093/nar/gkaa921
  108. Sweeney, B.A.; Hoksza, D.; Nawrocki, E.P.; Ribas, C.E.; Madeira, F.; Cannone, J.J.; Gutell, R.; Maddala, A.; Meade, C.D.; Williams, L.D.; et al. R2DT is a framework for predicting and visualising RNA secondary structure using templates. Nat. Commun. 2021, 12, 3494. DOI: https://doi.org/10.1038/s41467-021-23555-5
  109. Juhling, F.; Morl, M.; Hartmann, R.K.; Sprinzl, M.; Stadler, P.F.; Putz, J. tRNAdb 2009: Compilation of tRNA sequences and tRNA genes. Nucleic Acids Res. 2009, 37, D159–D162. DOI: https://doi.org/10.1093/nar/gkn772
  110. Gutell, R.R. Collection of small subunit (16S-and 16S-like) ribosomal RNA structures. Nucleic Acids Res. 1994, 22(17), 3502–3507. DOI: https://doi.org/10.1093/nar/22.17.3502
  111. Zwieb, C.; Gorodkin, J.; Knudsen, B.; Burks, J.; Wower, J. tmRDB (tmRNA database). Nucleic Acids Res. 2003, 31, 446–447. DOI: https://doi.org/10.1093/nar/gkg019
  112. Richardson, K.E.; Kirkpatrick, C.C.; Znosko, B.M. RNA CoSSMos 2.0: An improved searchable database of secondary structure motifs in RNA three-dimensional structures. Database J. Biol. Databases Curation 2020, 2020, baz153. DOI: https://doi.org/10.1093/database/baz153
  113. Korunes, K.L.; Myers, R.B.; Hardy, R.; Noor, M.A.F. PseudoBase: a genomic visualization and exploration resource for the Drosophila pseudoobscura subgroup. Fly 2021, 15, 38–44. DOI: https://doi.org/10.1080/19336934.2020.1864201
  114. Nagaswamy, U.; Larios-Sanz, M.; Hury, J.; Collins, S.; Zhang, Z.; Zhao, Q.; Fox, G.E. NCIR: A database of non-canonical interactions in known RNA structures. Nucleic Acids Res. 2002, 30, 395–397. DOI: https://doi.org/10.1093/nar/30.1.395
  115. Sloma, M.F.; Mathews, D.H. Exact calculation of loop formation probability identifies folding motifs in RNA secondary structures. RNA 2016, 22, 1808–1818. DOI: https://doi.org/10.1261/rna.053694.115
  116. Tan, Z.; Fu, Y.; Sharma, G.; Mathews, D.H. TurboFold II: RNA structural alignment and secondary structure prediction informed by multiple homologs. Nucleic Acids Res. 2017, 45, 11570–11581. DOI: https://doi.org/10.1093/nar/gkx815
  117. Kalvari, I.; Nawrocki, E.P.; Ontiveros-Palacios, N.; Argasinska, J.; Lamkiewicz, K.; Marz, M.; Griffiths-Jones, S.; Toffano-Nioche, C.; Gautheret, D.; Weinberg, Z.; et al. Rfam 14: Expanded coverage of metagenomic, viral and microrna families. Nucleic Acids Res. 2021, 49, D192–D200. DOI: https://doi.org/10.1093/nar/gkaa1047
  118. Wolfinger, M.T.; Svrcek-Seiler, W.A.; Flamm, C.; Hofacker, I.L.; Stadler, P.F. Efficient computation of RNA folding dynamics. J. Phys. A: Math. Gen. 2004, 37, 4731. DOI: https://doi.org/10.1088/0305-4470/37/17/005
  119. Gruber, A.R.; Findeiß, S.; Washietl, S.; Hofacker, I.L.; Stadler, P.F. RNAz 2.0: Improved noncoding RNA detection. Pac. Symp. Biocomputing. 2010, 2010, 69–79. DOI: https://doi.org/10.1142/9789814295291_0009
  120. Moulton, V. Tracking down noncoding RNAs. Proc. Natl. Acad. Sci. USA 2005, 102, 2269–2270. DOI: https://doi.org/10.1073/pnas.0500129102
  121. Lu, Z.J.; Mathews, D.H. Efficient siRNA selection using hybridization thermodynamics. Nucleic Acids Res. 2008, 36, 640–647. DOI: https://doi.org/10.1093/nar/gkm920
  122. Tafer, H.; Ameres, S.L.; Obernosterer, G.; Gebeshuber, C.A.; Schroeder, R.; Martinez, J.; Hofacker, I.L. The impact of target site accessibility on the design of effective siRNAs. Nat. Biotechnol. 2008, 26, 578–583. DOI: https://doi.org/10.1038/nbt1404
  123. Sazani, P.; Gemignani, F.; Kang, S.-H.; Maier, M.A.; Manoharan, M.; Persmark, M.; Bortner, D.; Kole, R. Systemically delivered antisense oligomers upregulate gene expression in mouse tissues. Nat. Biotechnol. 2002, 20, 1228–1233. DOI: https://doi.org/10.1038/nbt759
  124. Childs-Disney, J.L.; Wu, M.; Pushechnikov, A.; Aminova, O.; Disney, M.D. A small molecule microarray platform to select RNA internal loop-ligand interactions. ACS Chem. Biol. 2007, 2, 745–754. DOI: https://doi.org/10.1021/cb700174r
  125. Palde, P.B.; Ofori, L.O.; Gareiss, P.C.; Lerea, J.; Miller, B.L. Strategies for Recognition of Stem-loop RNA Structures by Synthetic Ligands: Application to the HIV-1 Frameshift Stimulatory Sequence. J. Med. Chem. 2010, 53, 6018–6027. DOI: https://doi.org/10.1021/jm100231t
  126. Castanotto, D.; Rossi, J.J. The promises and pitfalls of RNA-interference-based therapeutics. Nature 2009, 457, 426–433. DOI: https://doi.org/10.1038/nature07758
  127. Gareiss, P.C.; Sobczak, K.; McNaughton, B.R.; Palde, P.B.; Thornton, C.A.; Miller, B.L. Dynamic Com- binatorial Selection of Molecules Capable of Inhibiting the (CUG) Repeat RNA – MBNL1 Interaction in vitro: Discovery of Lead Compounds Targeting Myotonic Dystrophy (DM1). J. Am. Chem. Soc. 2008, 130, 16254–16261. DOI: https://doi.org/10.1021/ja804398y
  128. Rouillard, J.M.; Zuker, M.; Gulari, E. OligoArray 2.0: design of oligonucleotide probes for DNA microarrays using a thermodynamic approach. Nucleic Acids Res. 2003, 31, 3057–3062. DOI: https://doi.org/10.1093/nar/gkg426
  129. Tavares, R.D.C.A.; Mahadeshwar, G.; Wan, H.; Huston, N.C.; Pyle, A.M. The Global and Local Distribution of RNA Structure throughout the SARS-CoV-2 Genome. J. Virol. 2021, 95, e02190-20. DOI: https://doi.org/10.1128/JVI.02190-20
  130. Vandelli, A.; Monti, M.; Milanetti, E.; Armaos, A.; Rupert, J.; Zacco, E.; Bechara, E.; Ponti, R.D.; Tartaglia, G.G. Structural analysis of SARS-CoV-2 genome and predictions of the human interactome. Nucleic Acids Res. 2020, 48, 11270–11283. DOI: https://doi.org/10.1093/nar/gkaa864
  131. Wang, X.; Gu, R.; Chen, Z.; Li, Y.; Ji, X.; Ke, G.; Wen, H. Uni-Rna: Universal Pre-Trained Models Revolutionize Rna Research. bioRxiv 2023, 2023, 548588. DOI: https://doi.org/10.1101/2023.07.11.548588
  132. Chen, J.; Hu, Z.; Sun, S.; Tan, Q.; Wang, Y.; Yu, Q.; Zong, L.; Hong, L.; Xiao, J.; Shen, T.; et al. Interpretable RNA Foundation Model from Unannotated Data for Highly Accurate RNA Structure and Function Predictions. arXiv 2022, arXiv:2204.00300. DOI: https://doi.org/10.1101/2022.08.06.503062
  133. Akiyama, M.; Sakakibara, Y. Informative rna base embedding for rna structural alignment and clustering by deep representation learning. NAR Genom. Bioinform. 2022, 4, lqac012. DOI: https://doi.org/10.1093/nargab/lqac012
  134. Zhang, J.; Fei, Y.; Sun, L.; ; Zhang, Q.C. Advances and opportunities in RNA structure experimental determination and computational modeling. Nat. Methods 2022, 19, 1193–1207. DOI: https://doi.org/10.1038/s41592-022-01623-y
  135. Lyngsø, R.B.; Pedersen, C.N. RNA pseudoknot prediction in energy-based models. J. Comput. Biol. 2000, 7, 409–427. DOI: https://doi.org/10.1089/106652700750050862
  136. Parisien, M.; Major, F. The MC-Fold and MC-Sym pipeline infers RNA structure from sequence data. Nature 2008, 452, 51–55. DOI: https://doi.org/10.1038/nature06684