Comparative and integrative analysis of RNA structural profiling data: current practices and emerging questions

Abstract

Background: Structure profiling experiments provide single-nucleotide information on RNA structure. Recent advances in chemistry combined with application of high-throughput sequencing have enabled structure profiling at transcriptome scale and in living cells, creating unprecedented opportunities for RNA biology. Propelled by these experimental advances, massive data with ever-increasing diversity and complexity have been generated, which give rise to new challenges in interpreting and analyzing these data.

Results: We review current practices in analysis of structure profiling data with emphasis on comparative and integrative analysis as well as highlight emerging questions. Comparative analysis has revealed structural patterns across transcriptomes and has become an integral component of recent profiling studies. Additionally, profiling data can be integrated into traditional structure prediction algorithms to improve prediction accuracy.

Conclusions: To keep pace with experimental developments, methods to facilitate, enhance and refine such analyses are needed. Parallel advances in analysis methodology will complement profiling technologies and help them reach their full potential.

Graphical abstract

Keywords

RNA structure profiling / high-throughput sequencing / RNA secondary structure prediction / chemical structure probing / SHAPE-Seq

References

[1] Sharp, P. A. (2009) The centrality of RNA. Cell, 136, 577–580

[2] Mortimer, S. A., Kidwell, M. A. and Doudna, J. A. (2014) Insights into RNA structure and function from genome-wide studies. Nat. Rev. Genet., 15, 469–479

[3] He, L. and Hannon, G. J. (2004) MicroRNAs: small RNAs with a big role in gene regulation. Nat. Rev. Genet., 5, 522–531

[4] Mercer, T. R., Dinger, M. E. and Mattick, J. S. (2009) Long non-coding RNAs: insights into functions. Nat. Rev. Genet., 10, 155–159

[5] Strobel, E. J., Watters, K. E., Loughrey, D. and Lucks, J. B. (2016) RNA systems biology: uniting functional discoveries and structural tools to understand global roles of RNAs. Curr. Opin. Biotechnol., 39, 182–191

[6] Al-Hashimi, H. M. (2009) Structural biology: aerial view of the HIV genome. Nature, 460, 696–698

[7] Gutell, R. R., Lee, J. C. and Cannone, J. J. (2002) The accuracy of ribosomal RNA comparative structure models. Curr. Opin. Struct. Biol., 12, 301–310

[8] Hofacker, I. L., Fontana, W., Stadler, P. F., Bonhoeffer, L. S., Tacker, M., and Schuster, P. (1994) Fast folding and comparison of RNA secondary structures. Monatsh. Chem., 125, 167–188

[9] Mathews, D. H., Moss, W. N. and Turner, D. H. (2010) Folding and finding RNA secondary structure. Cold Spring Harb. Perspect. Biol., 2, a003665

[10] Ehresmann, C., Baudin, F., Mougel, M., Romby, P., Ebel, J.-P. and Ehresmann, B. (1987) Probing the structure of RNAs in solution. Nucleic Acids Res., 15, 9109–9128

[11] Weeks, K. M. (2010) Advances in RNA structure analysis by chemical probing. Curr. Opin. Struct. Biol., 20, 295–304

[12] Tijerina, P., Mohr, S. and Russell, R. (2007) DMS footprinting of structured RNAs and RNA-protein complexes. Nat. Protoc., 2, 2608–2623

[13] Brow, D. A. and Noller, H. F. (1983) Protection of ribosomal RNA from kethoxal in polyribosomes: implication of specific sites in ribosome function. J. Mol. Biol., 163, 27–46

[14] Tullius, T. D. and Greenbaum, J. A. (2005) Mapping nucleic acid structure by hydroxyl radical cleavage. Curr. Opin. Chem. Biol., 9, 127–134

[15] Singer, B. (1976) All oxygens in nucleic acids react with carcinogenic ethylating agents. Nature, 264, 333–339

[16] Fritz, J. J., Lewin, A., Hauswirth, W., Agarwal, A., Grant, M. and Shaw, L. (2002) Development of hammerhead ribozymes to modulate endogenous gene expression for functional studies. Methods, 28, 276–285

[17] Lindell, M., Romby, P. and Wagner, E. G. H. (2002) Lead(II) as a probe for investigating RNA structure in vivo. RNA, 8, 534–541

[18] Lindell, M., Brännvall, M., Wagner, E. G. H. and Kirsebom, L. A. (2005) Lead(II) cleavage analysis of RNase P RNA in vivo. RNA, 11, 1348–1354

[19] Knapp, G. (1989) Enzymatic approaches to probing of RNA secondary and tertiary structure. Methods Enzymol., 180, 192–212

[20] Wilkinson, K. A., Merino, E. J. and Weeks, K. M. (2006) Selective 2’-hydroxyl acylation analyzed by primer extension (SHAPE): quantitative RNA structure analysis at single nucleotide resolution. Nat. Protoc., 1, 1610–1616

[21] Zubradt, M., Gupta, P., Persad, S., Lambowitz, A. M., Weissman, J. S. and Rouskin, S. (2017) DMS-MaPseq for genome-wide or targeted RNA structure probing in vivo. Nat. Methods,14, 75–82

[22] Smola, M. J., Rice, G. M., Busan, S., Siegfried, N. A. and Weeks, K. M. (2015) Selective 2′-hydroxyl acylation analyzed by primer extension and mutational profiling (SHAPE-MaP) for direct, versatile and accurate RNA structure analysis. Nat. Protoc., 10, 1643–1669

[23] Watters, K. E., Yu, A. M., Strobel, E. J., Settle, A. H. and Lucks, J. B. (2016) Characterizing RNA structures in vitro and in vivo with selective 2′-hydroxyl acylation analyzed by primer extension sequencing (SHAPE-Seq). Methods, 103, 34–48

[24] Poulsen, L. D., Kielpinski, L. J., Salama, S. R., Krogh, A. and Vinther, J. (2015) SHAPE Selection (SHAPES) enrich for RNA structure signal in SHAPE sequencing-based probing data. RNA, 21, 1042–1052

[25] Hector, R. D., Burlacu, E., Aitken, S., Le Bihan, T., Tuijtel, M., Zaplatina, A., Cook, A. G. and Granneman, S. (2014) Snapshots of pre-rRNA structural flexibility reveal eukaryotic 40S assembly dynamics at nucleotide resolution. Nucleic Acids Res., 42, 12138–12154

[26] Rouskin, S., Zubradt, M., Washietl, S., Kellis, M. and Weissman, J. S. (2014) Genome-wide probing of RNA structure reveals active unfolding of mRNA structures in vivo. Nature, 505, 701–705

[27] Kwok, C. K., Ding, Y., Tang, Y., Assmann, S. M. and Bevilacqua, P. C. (2013) Determination of in vivo RNA structure in low-abundance transcripts. Nat. Commun., 4, 2971

[28] Ding, Y., Tang, Y., Kwok, C. K., Zhang, Y., Bevilacqua, P. C. and Assmann, S. M. (2013) In vivo genome-wide profiling of RNA secondary structure reveals novel regulatory features. Nature, 505, 696–700

[29] Ding, Y., Kwok, C. K., Tang, Y., Bevilacqua, P. C. and Assmann, S. M. (2015) Genome-wide profiling of in vivo RNA structure at single-nucleotide resolution using structure-seq. Nat. Protoc., 10, 1050–1066

[30] Kertesz, M., Wan, Y., Mazor, E., Rinn, J. L., Nutter, R. C., Chang, H. Y. and Segal, E. (2010) Genome-wide measurement of RNA secondary structure in yeast. Nature, 467, 103–107

[31] Underwood, J. G., Uzilov, A. V., Katzman, S., Onodera, C. S., Mainzer, J. E., Mathews, D. H., Lowe, T. M., Salama, S. R.and Haussler, D. (2010) FragSeq: transcriptome-wide RNA structure probing using high-throughput sequencing. Nat. Methods, 7, 995–1001

[32] Lucks, J. B., Mortimer, S. A., Trapnell, C., Luo, S., Aviran, S., Schroth, G. P., Pachter, L., Doudna, J. A. and Arkin, A. P. (2011) Multiplexed RNA structure characterization with selective 2′-hydroxyl acylation analyzed by primer extension sequencing (SHAPE-Seq). Proc. Natl. Acad. Sci. USA, 108, 11063–11068

[33] Loughrey, D., Watters, K. E., Settle, A. H. and Lucks, J. B. (2014) SHAPE-Seq 2.0: systematic optimization and extension of high-throughput chemical probing of RNA secondary structure with next generation sequencing. Nucleic Acids Res, 42, 000

[34] Wan, Y., Qu, K., Ouyang, Z. and Chang, H. Y. (2013) Genome-wide mapping of RNA structure using nuclease digestion and high-throughput sequencing. Nat. Protoc., 8, 849–869

[35] Talkish, J., May, G., Lin, Y., Woolford, J. L. Jr and McManus, C. J. (2014) Mod-seq: high-throughput sequencing for chemical probing of RNA structure. RNA, 20, 713–720

[36] Incarnato, D., Neri, F., Anselmi, F. and Oliviero, S. (2014) Genome-wide profiling of mouse RNA secondary structures reveals key features of the mammalian transcriptome. Genome Biol., 15, 491

[37] Kielpinski, L. J. and Vinther, J. (2014) Massive parallel-sequencing-based hydroxyl radical probing of RNA accessibility. Nucleic Acids Res., 42, e70

[38] Seetin, M. G., Kladwang, W., Bida, J. P. and Das, R. (2014) Massively parallel RNA chemical mapping with a reduced bias MAP-seq protocol. In RNA Folding: Methods and Protocols, 95–117. New York: Humana Press

[39] Siegfried, N. A., Busan, S., Rice, G. M., Nelson, J. A. and Weeks, K. M. (2014) RNA motif discovery by SHAPE and mutational profiling (SHAPE-MaP). Nat. Methods, 11, 959–965

[40] Spitale, R. C., Flynn, R. A., Zhang, Q. C., Crisalli, P., Lee, B., Jung, J.-W., Kuchelmeister, H. Y., Batista, P. J., Torre, E. A., Kool, E. T., (2015) Structural imprints in vivo decode RNA regulatory mechanisms. Nature. 519, 486–490

[41] Kwok, C. K., Sahakyan, A. B. and Balasubramanian, S. (2016) Structural analysis using SHALiPE to reveal RNA G-quadruplex formation in human precursor microRNA. Angew. Chem. Int. Ed. Engl., 55, 8958–8961

[42] Kwok, C. K., Marsico, G., Sahakyan, A. B., Chambers, V. S. and Balasubramanian, S. (2016) rG4-seq reveals widespread formation of G-quadruplex structures in the human transcriptome. Nat. Methods, 13, 841–844

[43] Kwok, C. K., Tang, Y., Assmann, S. M. and Bevilacqua, P. C. (2015) The RNA structurome: transcriptome-wide structure probing with next-generation sequencing. Trends Biochem. Sci., 40, 221–232

[44] Lu, Z. and Chang, H. Y. (2016) Decoding the RNA structurome. Curr. Opin. Struct. Biol., 36, 142–148

[45] Kwok, C. K. (2016) Dawn of the in vivo RNA structurome and interactome. Biochem. Soc. Trans., 44, 1395–1410

[46] Kubota, M., Chan, D. and Spitale, R. C. (2015) RNA structure: merging chemistry and genomics for a holistic perspective. BioEssays, 37, 1129–1138

[47] Low, J. T. and Weeks, K. M. (2010) SHAPE-directed RNA secondary structure prediction. Methods, 52, 150–158

[48] Lorenz, R., Luntzer, D., Hofacker, I. L., Stadler, P. F. and Wolfinger, M. T. (2015) SHAPE directed RNA folding. Bioinformatics, 32, 145–147

[49] Merino, E. J., Wilkinson, K. A., Coughlan, J. L. and Weeks, K. M. (2005) RNA structure analysis at single nucleotide resolution by selective 2′-hydroxyl acylation and primer extension (SHAPE). J. Am. Chem. Soc., 127, 4223–4231

[50] Lavery, R. and Pullman, A. (1984) A new theoretical index of biochemical reactivity combining steric and electrostatic factors: an application to yeast tRNA^Phe. Biophys. Chem., 19, 171–181

[51] McGinnis, J. L., Dunkle, J. A., Cate, J. H. and Weeks, K. M. (2012) The mechanisms of RNA SHAPE chemistry. J. Am. Chem. Soc., 134, 6617–6624

[52] Eddy, S. R. (2014) Computational analysis of conserved RNA secondary structure in transcriptomes and genomes. Annu. Rev. Biophys., 43, 433–456

[53] Kutchko, K. M. and Laederach, A. (2016) Transcending the prediction paradigm: novel applications of SHAPE to RNA function and evolution. WIREs RNA, 8, e1374

[54] Aviran, S. and Pachter, L. (2014) Rational experiment design for sequencing-based RNA structure mapping. RNA, 20, 1864–1877

[55] Wan, Y., Qu, K., Zhang, Q. C., Flynn, R. A., Manor, O., Ouyang, Z., Zhang, J., Spitale, R. C., Snyder, M. P., Segal, E., (2014) Landscape and variation of RNA secondary structure across the human transcriptome. Nature, 505, 706–709

[56] Ritz, J., Martin, J. S. and Laederach, A. (2012) Evaluating our ability to predict the structural disruption of RNA by SNPs. BMC Genomics, 13, S6

[57] Watters, K. E., Abbott, T. R. and Lucks, J. B. (2016) Simultaneous characterization of cellular RNA structure and function with in-cell SHAPE-Seq. Nucleic Acids Res., 44, e12

[58] Bai, Y., Tambe, A., Zhou, K. and Doudna, J. A. (2014) RNA-guided assembly of Rev-RRE nuclear export complexes. eLife, 3, e03656

[59] Choudhary, K., Shih, N. P., Deng, F., Ledda, M., Li, B. and Aviran, S. (2016) Metrics for rapid quality control in RNA structure probing experiments. Bioinformatics, 32, 3575–3583

[60] Aviran, S., Lucks, J. B. and Pachter, L. (2011) RNA structure characterization from chemical mapping experiments. In the 49th Annual Allerton Conference on Communication, Control, and Computing, pages 1743–1750

[61] Wan, Y., Kertesz, M., Spitale, R. C., Segal, E. and Chang, H. Y. (2011) Understanding the transcriptome through RNA structure. Nat. Rev. Genet., 12, 641–655

[62] McCaskill, J. S. (1990) The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers, 29, 1105–1119

[63] Ding, Y. and Lawrence, C. E. (2003) A statistical sampling algorithm for RNA secondary structure prediction. Nucleic Acids Res., 31, 7280–7301

[64] Rogers, E. and Heitsch, C. (2016) New insights from cluster analysis methods for RNA secondary structure prediction. Wiley Interdiscip. Rev. RNA, 7, 278–294

[65] Quarrier, S., Martin, J. S., Davis-Neulander, L., Beauregard, A. and Laederach, A. (2010) Evaluation of the information content of RNA structure mapping data for secondary structure prediction. RNA, 16, 1108–1117

[66] Bullard, J. H., Purdom, E., Hansen, K. D. and Dudoit, S. (2010) Evaluation of statistical methods for normalization and differential expression in mRNA-Seq experiments. BMC Bioinformatics, 11, 94

[67] Marioni, J. C., Mason, C. E., Mane, S. M., Stephens, M. and Gilad, Y. (2008) RNA-seq: an assessment of technical reproducibility and comparison with gene expression arrays. Genome Res., 18, 1509–1517

[68] Guo, J. U. and Bartel, D. P. (2016) RNA G-quadruplexes are globally unfolded in eukaryotic cells and depleted in bacteria. Science, 353, aaf5371

[69] Robinson, M. D., McCarthy, D. J. and Smyth, G. K. (2010) edgeR: a Bioconductor package for differential expression analysis of digital gene expression data. Bioinformatics, 26, 139–140

[70] Anders, S., and Huber, W. (2012) Differential expression of RNA-Seq data at the gene level-the DESeq package. Heidelberg: European Molecular Biology Laboratory

[71] Law, C. W., Chen, Y., Shi, W. and Smyth, G. K. (2014) voom: precision weights unlock linear model analysis tools for RNA-seq read counts. Genome Biol., 15, R29

[72] Leamy, K. A., Assmann, S. M., Mathews, D. H. and Bevilacqua, P. C. (2016) Bridging the gap between in vitro and in vivo RNA folding. Q. Rev. Biophys., 49, e10

[73] Hu, X., Wu, Y., Lu, Z. J. and Yip, K. Y. (2015) Analysis of sequencing data for probing RNA secondary structures and protein- RNA binding in studying posttranscriptional regulations. Brief. Bioinform., 17,1032–1043

[74] Cordero, P., Kladwang, W.,VanLang, C.C. and Das,R. (2012) Quantitative dimethyl sulfate mapping for automated RNA secondary structure inference. Biochemistry, 51, 7037–7039

[75] Lee, B., Flynn, R. A., Kadina, A., Guo, J. K., Kool, E. T. and Chang, H. Y. (2016) Comparison of SHAPE reagents for mapping RNA structures inside living cells. RNA, rna.058784.116

[76] Mortazavi, A., Williams, B. A., McCue, K., Schaeffer, L. and Wold, B. (2008) Mapping and quantifying mammalian transcriptomes by RNA-Seq. Nat. Methods, 5, 621–628

[77] Sorefan, K., Pais, H., Hall, A. E., Kozomara, A., Griffiths-Jones, S., Moulton, V. and Dalmay, T. (2012) Reducing ligation bias of small RNAs in libraries for next generation sequencing. Silence, 3, 4

[78] Roberts, A., Trapnell, C., Donaghey, J., Rinn, J. L. and Pachter, L. (2011) Improving RNA-Seq expression estimates by correcting for fragment bias. Genome Biol., 12, R22

[79] Li, B., Tambe, A., Aviran, S. and Pachter, L. (2016) Prober: a general toolkit for analyzing sequencing-based ‘toeprinting’ assays. bioRxiv, 063107

[80] Aviran, S., Trapnell, C., Lucks, J. B., Mortimer, S. A., Luo, S., Schroth, G. P., Doudna, J. A., Arkin, A. P. and Pachter, L. (2011) Modeling and automation of sequencing-based characterization of RNA structure. Proc. Natl. Acad. Sci. USA, 108, 11069–11074

[81] Selega, A., Sirocchi, C., Iosub, I., Granneman, S. and Sanguinetti, G.(2017) Robust statistical modeling improves sensitivity of high-throughput RNA structure probing experiments. Nat. Methods, 14, 83–89

[82] Deigan, K. E., Li, T. W., Mathews, D. H. and Weeks, K. M. (2009) Accurate SHAPE-directed RNA structure determination. Proc. Natl. Acad. Sci. USA, 106, 97–102

[83] Sloma, M. F. and Mathews, D. H. (2015) Improving RNA secondary structure prediction with structure mapping data. Methods Enzymol., 553, 91–114

[84] Trapnell, C., Williams, B. A., Pertea, G., Mortazavi, A., Kwan, G., van Baren, M. J., Salzberg, S. L., Wold, B. J., and Pachter, L. (2010) Transcript assembly and quantification by RNA-Seq reveals unannotated transcripts and isoform switching during cell differentiation. Nat. Biotechnol., 28, 511–515

[85] Li, B. and Dewey, C. N. (2011) RSEM: accurate transcript quantification from RNA-Seq data with or without a reference genome. BMC Bioinformatics, 12, 323

[86] Smola, M. J., Calabrese, J. M. and Weeks, K. M. (2015) Detection of RNA-protein interactions in living cells with SHAPE. Biochemistry, 54, 6867–6875

[87] Smola, M. J., Christy, T. W., Inoue, K., Nicholson, C. O., Friedersdorf, M., Keene, J. D., Lee, D. M., Calabrese, J. M. and Weeks, K. M. (2016) SHAPE reveals transcript-wide interactions, complex structural domains, and protein interactions across the Xist lncRNA in living cells. Proc. Natl. Acad. Sci. USA, 113, 10322–10327

[88] Solem, A. C., Halvorsen, M., Ramos, S. B. and Laederach, A. (2015) The potential of the riboSNitch in personalized medicine. Wiley Interdiscip. Rev. RNA, 6, 517–532

[89] Wan, Y., Qu, K., Ouyang, Z., Kertesz, M., Li, J., Tibshirani, R., Makino, D. L., Nutter, R. C., Segal, E. and Chang, H. Y. (2012) Genome-wide measurement of RNA folding energies. Mol. Cell, 48, 169–181

[90] Righetti, F., Nuss, A. M., Twittenhoff, C., Beele, S., Urban, K., Will, S., Bernhart, S. H., Stadler, P. F., Dersch, P. and Narberhaus, F. (2016) Temperature-responsive in vitro RNA structurome of Yersinia pseudotuberculosis. Proc. Natl. Acad. Sci. USA, 113, 7237–7242

[91] Corley, M., Solem, A., Qu, K., Chang, H. Y.and Laederach, A. (2015) Detecting riboSNitches with RNA folding algorithms: a genome-wide benchmark. Nucleic Acids Res., 43,1859–1868

[92] Abdullah, M. B. (1990) On a robust correlation coefficient. Statistician, 39, 455–460

[93] Goodwin, L. D. and Leech, N. L. (2006) Understanding correlation: factors that affect the size of r. J. Exp. Educ., 74, 249–266

[94] Müller, R. and Büttner, P. (1994) A critical discussion of intraclass correlation coefficients. Stat. Med., 13, 2465–2476

[95] Gastwirth, J. L. (1972) The estimation of the Lorenz curve and Gini index. Rev. Econ. Stat., 54, 306–316

[96] Eddy, S. R. and Durbin, R. (1994) RNA sequence analysis using covariance models. Nucleic Acids Res., 22, 2079–2088

[97] Zhang, J. -H., Chung, T. D. and Oldenburg, K. R. (1999) A simple statistical parameter for use in evaluation and validation of high throughput screening assays. J. Biomol. Screen., 4, 67–73

[98] Pollom, E., Dang, K. K., Potter, E. L., Gorelick, R. J., Burch, C. L., Weeks, K. M. and Swanstrom, R. (2013) Comparison of SIV and HIV-1 genomic RNA structures reveals impact of sequence evolution on conserved and non-conserved structural motifs. PLoS Pathog., 9, e1003294

[99] Cowell, F. A. and Victoria-Feser, M.-P. (1996) Robustness properties of inequality measures. Econometrica, 64, 77–101

[100] Liang, R., Kierzek, E., Kierzek, R. and Turner, D. H. (2010) Comparisons between chemical mapping and binding to isoenergetic oligonucleotide microarrays reveal unexpected patterns of binding to the Bacillus subtilis RNase P RNA specificity domain. Biochemistry, 49, 8155–8168

[101] Hawkes, E. J., Hennelly, S. P., Novikova, I. V., Irwin, J. A., Dean, C. and Sanbonmatsu, K. Y. (2016) COOLAIR antisense RNAs form evolutionarily conserved elaborate secondary structures. Cell Reports, 16, 3087–3096

[102] Xue, Z., Hennelly, S., Doyle, B., Gulati, A. A., Novikova, I. V., Sanbonmatsu, K. Y. and Boyer, L. A. (2016) A G-rich motif in the lncRNA braveheart interacts with a zinc-finger transcription factor to specify the cardiovascular lineage. Mol. Cell, 64, 37–50

[103] Rice, G. M., Leonard, C. W. and Weeks, K. M. (2014) RNA secondary structure modeling at consistent high accuracy using differential SHAPE. RNA, 20, 846–854

[104] Wu, Y., Shi, B., Ding, X., Liu, T., Hu, X., Yip, K. Y., Yang, Z. R., Mathews, D. H., and Lu., Z. J. (2015) Improved prediction of RNA secondary structure by integrating the free energy model with restraints derived from experimental probing data. Nucleic acids res., 43, 7247–7259

[105] Choudhary, K., Ruan, L., Deng, F., Shih, N. and Aviran, S. (2016) SEQualyzer: interactive tool for quality control and exploratory analysis of high-throughput RNA structural profiling data. Bioinformatics, btw627

[106] Rother, K., Rother, M., Skiba, P. and Bujnicki, J. M. (2014) Automated modeling of RNA 3D structure. In RNA Sequence, Structure, and Function: Computational and Bioinformatic Methods, 395–415. New York: Humana Press

[107] Tabaska, J. E., Cary, R. B., Gabow, H. N. and Stormo, G. D. (1998) An RNA folding method capable of identifying pseudoknots and base triples. Bioinformatics, 14, 691–699

[108] Rivas, E. and Eddy, S. R. (1999) A dynamic programming algorithm for RNA structure prediction including pseudoknots. J. Mol. Biol., 285, 2053–2068

[109] Lyngsø R. B. and Pedersen, C. N. (2000) RNA pseudoknot prediction in energy-based models. J. Comput. Biol., 7, 409–427

[110] Ruan, J., Stormo, G. D. and Zhang, W. (2004) An iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots. Bioinformatics, 20, 58–66

[111] Reeder, J. and Giegerich, R. (2004) Design, implementation and evaluation of a practical pseudoknot folding algorithm based on thermodynamics. BMC Bioinformatics, 5, 104

[112] Ren, J., Rastegari, B., Condon, A. and Hoos, H. H. (2005) HotKnots: heuristic prediction of RNA secondary structures including pseudoknots. RNA, 11, 1494–1504

[113] Cao, S. and Chen, S. -J. (2006) Predicting RNA pseudoknot folding thermodynamics. Nucleic Acids Res., 34, 2634–2652

[114] Reeder, J., Steffen, P. and Giegerich, R. (2007) pknotsRG: RNA pseudoknot folding including near-optimal structures and sliding windows. Nucleic Acids Res., 35, W320–W324

[115] Sato, K., Kato, Y., Hamada, M., Akutsu, T. and Asai, K. (2011) IPknot: fast and accurate prediction of RNA secondary structures with pseudoknots using integer programming. Bioinformatics, 27, i85–i93

[116] Andronescu, M., Condon, A., Turner, D. H. and Mathews, D. H. (2014) The determination of RNA folding nearest neighbor parameters. In RNA Sequence, Structure, and Function: Computational and Bioinformatic Methods, 45–70. New York: Humana Press

[117] Xia, T., SantaLucia, J. Jr., Burkard, M. E., Kierzek, R., Schroeder, S. J., Jiao, X., Cox, C., and Turner, D. H. (1998) Thermodynamic parameters for an expanded Nearest-Neighbor model for formation of RNA duplexes with Watson-Crick base pairs. Biochemistry,14719–14735

[118] Mathews, D. H., Sabina, J., Zuker, M. and Turner, D. H. (1999) Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol., 288, 911–940

[119] Nussinov, R., Pieczenik, G., Griggs, J. R. and Kleitman, D. J. (1978) Algorithms for loop matchings. SIAM J. Appl. Math., 35, 68–82

[120] Waterman, M. S. and Smith, T. F. (1978) RNA secondary structure: a complete mathematical analysis. Math. Biosci., 42, 257–266

[121] Nussinov, R. and Jacobson, A. B. (1980) Fast algorithm for predicting the secondary structure of single-stranded RNA. Proc. Natl. Acad. Sci. USA, 77, 6309–6313

[122] Zuker, M. and Stiegler, P. (1981) Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res., 9, 133–148

[123] Zuker, M. and Sankoff, D. (1984) RNA secondary structures and their prediction. Bull. Math. Biol., 46, 591–621

[124] Markham, N. R. and Zuker, M. (2008) UNAFold. In Bioinformatics: Structure, Function and Applications, 3–31. New York: Humana Press

[125] Reuter, J. S. and Mathews, D. H. (2010) RNAstructure: software for RNA secondary structure prediction and analysis. BMC Bioinformatics, 11, 129

[126] Lorenz, R., Bernhart, S. H., Höner Zu Siederdissen, C., Tafer, H., Flamm, C., Stadler, P. F. and Hofacker, I. L. (2011) ViennaRNA package 2.0. Algorithms Mol. Biol., 6, 26

[127] Eddy, S. R. (2004) How do RNA folding algorithms work? Nat. Biotechnol., 22, 1457–1458

[128] Mathews, D. H. and Turner, D. H. (2006) Prediction of RNA secondary structure by free energy minimization. Curr. Opin. Struct. Biol., 16, 270–278

[129] Shapiro, B. A., Yingling, Y. G., Kasprzak, W. and Bindewald, E. (2007) Bridging the gap in RNA structure prediction. Curr. Opin. Struct. Biol., 17, 157–165

[130] Bai, Y., Dai, X., Harrison, A., Johnston, C. and Chen, M. (2016) Toward a next-generation atlas of RNA secondary structure. Brief. Bioinform., 17, 63–77

[131] Ge, P. and Zhang, S. (2015) Computational analysis of RNA structures with chemical probing data. Methods, 79-80, 60–66

[132] Doshi, K. J., Cannone, J. J., Cobaugh, C. W. and Gutell, R. R. (2004) Evaluation of the suitability of free-energy minimization using nearest-neighbor energy parameters for RNA secondary structure prediction. BMC Bioinformatics, 5, 105

[133] Zuker, M. (1989) On finding all suboptimal foldings of an RNA molecule. Science, 244, 48–52

[134] Darty, K., Denise, A. and Ponty, Y. (2009) VARNA: interactive drawing and editing of the RNA secondary structure. Bioinformatics, 25, 1974–1975

[135] Deng, F., Ledda, M., Vaziri, S. and Aviran, S. (2016) Data-directed RNA secondary structure prediction using probabilistic modeling. RNA, 22, 1109–1119

[136] McGinnis, J. L., Liu, Q., Lavender, C. A., Devaraj, A., McClory, S. P., Fredrick, K. and Weeks, K. M. (2015) In-cell SHAPE reveals that free 30S ribosome subunits are in the inactive state. Proc. Natl. Acad. Sci. USA, 112, 2425–2430

[137] Mathews, D. H. (2004) Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization. RNA, 10, 1178–1190

[138] Bernhart, S. H., Hofacker, I. L. and Stadler, P. F. (2006) Local RNA base pairing probabilities in large sequences. Bioinformatics, 22, 614–615

[139] Ding, Y., Chan, C. Y. and Lawrence, C. E. (2005) RNA secondary structure prediction by centroids in a Boltzmann weighted ensemble. RNA, 11, 1157–1166

[140] Do, C. B., Woods, D. A. and Batzoglou, S. (2006) CONTRAfold: RNA secondary structure prediction without physics-based models. Bioinformatics, 22, e90–e98

[141] Lu, Z. J., Gloor, J. W. and Mathews, D. H. (2009) Improved RNA secondary structure prediction by maximizing expected pair accuracy. RNA, 15, 1805–1813

[142] Hamada, M., Sato, K. and Asai, K. (2010) Prediction of RNA secondary structure by maximizing pseudo-expected accuracy. BMC Bioinformatics, 11, 586

[143] Cordero, P. and Das, R. (2015) Rich RNA structure landscapes revealed by mutate-and-map analysis. PLoS Comput. Biol., 11, e1004473

[144] Breaker, R. R. (2012) Riboswitches and the RNA world. Cold Spring Harb. Perspect. Biol., 4, a003566

[145] Parsch, J., Braverman, J. M. and Stephan, W. (2000) Comparative sequence analysis and patterns of covariation in RNA secondary structures. Genetics, 154, 909–921

[146] Gardner, P. P. and Giegerich, R. (2004) A comprehensive comparison of comparative RNA structure prediction approaches. BMC Bioinformatics, 5, 140

[147] Cannone, J. J., Subramanian, S., Schnare, M. N., Collett, J. R., D’Souza, L. M., Du, Y., Feng, B., Lin, N., Madabusi, L. V., Müller, K. M., (2002) The comparative RNA web (CRW) site: an online database of comparative sequence and structure information for ribosomal, intron, and other RNAs. BMC Bioinformatics, 3, 2

[148] Rupert, L., Stefan, G. and Gerhard, S. (1999) ConStruct: a tool for thermodynamic controlled prediction of conserved secondary structure. Nucleic Acids Res., 27, 4208–4217

[149] Hofacker, I. L., Fekete, M. and Stadler, P. F. (2002) Secondary structure prediction for aligned RNA sequences. J. Mol. Biol., 319, 1059–1066

[150] Bernhart, S. H., Hofacker, I. L., Will, S., Gruber, A. R. and Stadler, P. F. (2008) RNAalifold: improved consensus structure prediction for RNA alignments. BMC Bioinformatics, 9, 474

[151] Knudsen, B. and Hein, J. (2003) Pfold: RNA secondary structure prediction using stochastic context-free grammars. Nucleic Acids Res., 31, 3423–3428

[152] Sakakibara, Y., Brown, M., Hughey, R., Mian, I. S., Sjölander, K., Underwood, R. C. and Haussler, D. (1994) Stochastic context-free grammars for tRNA modeling. Nucleic Acids Res., 22, 5112–5120

[153] Knudsen, B. and Hein, J. (1999) RNA secondary structure prediction using stochastic context-free grammars and evolutionary history. Bioinformatics, 15, 446–454

[154] Sankoff, D. (1985) Simultaneous solution of the RNA folding, alignment and protosequence problems. SIAM J. Appl. Math., 45, 810–825

[155] Havgaard, J. H., Lyngsø R. B., Stormo, G. D. and Gorodkin, J. (2005) Pairwise local structural alignment of RNA sequences with sequence similarity less than 40%. Bioinformatics, 21, 1815–1824

[156] Mathews, D. H. and Turner, D. H. (2002) Dynalign: an algorithm for finding the secondary structure common to two RNA sequences. J. Mol. Biol., 317, 191–203

[157] Harmanci, A. O., Sharma, G. and Mathews, D. H. (2007) Efficient pairwise RNA structure prediction using probabilistic alignment constraints in Dynalign. BMC Bioinformatics, 8, 130

[158] Gorodkin, J., Heyer, L. J. and Stormo, G. D. (1997) Finding the most significant common sequence and structure motifs in a set of RNA sequences. Nucleic Acids Res., 25, 3724–3732

[159] Perriquet, O., Touzet, H. and Dauchet, M. (2003) Finding the common structure shared by two homologous RNAs. Bioinformatics, 19, 108–116

[160] Hofacker, I. L., Bernhart, S. H. and Stadler, P. F. (2004) Alignment of RNA base pairing probability matrices. Bioinformatics, 20, 2222–2227

[161] Hochsmann, M., Toller, T., Giegerich, R. and Kurtz, S. (2003) Local similarity in RNA secondary structures. In Proceedings of the IEEE Bioinformatics Conference, 2003, pages 159–168

[162] Siebert, S. and Backofen, R. (2003) MARNA: a server for multiple alignment of RNAs. In Proceedings of the German Conference on Bioinformatics, pages 135–140

[163] Hajdin, C. E., Bellaousov, S., Huggins, W., Leonard, C. W., Mathews, D. H. and Weeks, K. M. (2013) Accurate SHAPE-directed RNA secondary structure modeling, including pseudoknots. Proc. Natl. Acad. Sci. USA, 110, 5498–5503

[164] Tang, Y., Bouvier, E., Kwok, C. K., Ding, Y., Nekrutenko, A., Bevilacqua, P. C. and Assmann, S. M. (2015) StructureFold: genome-wide RNA secondary structure mapping and reconstruction in vivo. Bioinformatics, 31, 2668–2675

[165] Watts, J. M., Dang, K. K., Gorelick, R. J., Leonard, C. W., Bess, J. W.Jr, Swanstrom, R., Burch, C. L. and Weeks, K. M. (2009) Architecture and secondary structure of an entire HIV-1 RNA genome. Nature, 460, 711–716

[166] Montaseri, S., Ganjtabesh, M. and Zare-Mirakabad, F. (2016) Evolutionary algorithm for RNA secondary structure prediction based on simulated SHAPE data. PLoS One, 11, e0166965

[167] Lavender, C. A., Lorenz, R., Zhang, G., Tamayo, R., Hofacker, I. L. and Weeks, K. M. (2015) Model-free RNA sequence and structure alignment informed by SHAPE probing reveals a conserved alternate secondary structure for 16S rRNA. PLoS Comput. Biol., 11, e1004126

[168] Novikova, I. V., Dharap, A., Hennelly, S. P. and Sanbonmatsu, K. Y. (2013) 3S: shotgun secondary structure determination of long non-coding RNAs. Methods, 63, 170–177

[169] Lorenz, R., Wolfinger, M. T., Tanzer, A. and Hofacker, I. L. (2016) Predicting RNA secondary structures from sequence and probing data. Methods, 103, 86–98

[170] Zarringhalam, K., Meyer, M. M., Dotu, I., Chuang, J. H. and Clote, P. (2012) Integrating chemical footprinting data into RNA secondary structure prediction. PLoS One, 7, e45160

[171] Washietl, S., Hofacker, I. L., Stadler, P. F. and Kellis, M. (2012) RNA folding with soft constraints: reconciliation of probing data and thermodynamic secondary structure prediction. Nucleic Acids Res., 40, 4261–4272

[172] Ouyang, Z., Snyder, M. P. and Chang, H. Y. (2013) SeqFold: genome-scale reconstruction of RNA secondary structure integrating high-throughput sequencing data. Genome Res., 23, 377–387

[173] Sükösd, Z., Knudsen, B., Kjems, J. and Pedersen, C. N. (2012) PPfold 3.0: fast RNA secondary structure prediction using phylogeny and auxiliary data. Bioinformatics, 28, 2691–2692

[174] Sahoo, S., Świtnicki, M. P. and Pedersen, J. S. (2016) ProbFold: a probabilistic method for integration of probing data in RNA secondary structure prediction. Bioinformatics, 32, 2626–2635

[175] Kladwang, W., VanLang, C. C., Cordero, P. and Das, R. (2011) A two-dimensional mutate-and-map strategy for non-coding RNA structure. Nat. Chem., 3, 954–962

[176] Sükösd, Z., Swenson, M. S., Kjems, J. and Heitsch, C. E. (2013) Evaluating the accuracy of SHAPE-directed RNA secondary structure predictions. Nucleic Acids Res., 41, 2807–2816

[177] Berkowitz, N. D., Silverman, I. M., Childress, D. M., Kazan, H., Wang, L.-S. and Gregory, B. D. (2016) A comprehensive database of high-throughput sequencing-based RNA secondary structure probing data (Structure Surfer). BMC Bioinformatics, 17, 215

[178] Wu, Y., Qu, R., Huang, Y., Shi, B., Liu, M., Li, Y. and Lu, Z. J. (2016) RNAex: an RNA secondary structure prediction server enhanced by high-throughput structure-probing data. Nucleic Acids Res., 44, W294–W301

[179] Norris, M., Cheema, J., Kwok, C. K., Hartley, M., Morris, R. J., Aviran, S., and Ding, Y. (2016) FoldAtlas: a repository for genome-wide RNA structure probing data. Bioinformatics. DOI: 10.1093/bioinformatics/btw611

[180] Li, F., Zheng, Q., Vandivier, L. E., Willmann, M. R., Chen, Y. and Gregory, B. D. (2012) Regulatory impact of RNA secondary structure across the Arabidopsis transcriptome. Plant Cell, 24, 4346–4359

[181] Mortimer, S. A., Trapnell, C., Aviran, S., Pachter, L. and Lucks, J. B. (2012) SHAPE-Seq: high-throughput RNA structure analysis. Curr Protoc Chem Biol, 4, 275–297

[182] Incarnato, D., Neri, F., Anselmi, F. and Oliviero, S. (2015) RNA structure framework: automated transcriptome-wide reconstruction of RNA secondary structures from highthroughput structure probing data. Bioinformatics, 32, 459–461

[183] Goecks, J., Nekrutenko, A., Taylor, J. and The Galaxy Team. (2010) Galaxy: a comprehensive approach for supporting accessible, reproducible, and transparent computational research in the life sciences. Genome Biol., 11, R86

[184] König, J., Zarnack, K., Rot, G., Curk, T., Kayikci, M., Zupan, B., Turner, D. J., Luscombe, N. M. and Ule, J. (2010) iCLIP reveals the function of hnRNP particles in splicing at individual nucleotide resolution. Nat. Struct. Mol. Biol., 17, 909–915

[185] Van Nostrand, E. L., Pratt, G. A., Shishkin, A. A., Gelboin-Burkhart, C., Fang, M. Y., Sundararaman, B., Blue, S. M., Nguyen, T. B., Surka, C., Elkins, K., (2016) Robust transcriptome-wide discovery of RNA-binding protein binding sites with enhanced CLIP (eCLIP). Nat. Methods, 13, 508–514

[186] Squires, J. E., Patel, H. R., Nousch, M., Sibbritt, T., Humphreys, D. T., Parker, B. J., Suter, C. M. and Preiss, T. (2012) Widespread occurrence of 5-methylcytosine in human coding and non-coding RNA. Nucleic Acids Res., 40, 5023–5033

[187] Dominissini, D., Moshitch-Moshkovitz, S., Schwartz, S., Salmon-Divon, M., Ungar, L., Osenberg, S., Cesarkas, K., Jacob-Hirsch, J., Amariglio, N., Kupiec, M., (2012) Topology of the human and mouse m⁶A RNA methylomes revealed by m⁶A-seq. Nature, 485, 201–206

[188] Meyer, K. D., Saletore, Y., Zumbo, P., Elemento, O., Mason, C. E. and Jaffrey, S. R. (2012) Comprehensive analysis of mRNA methylation reveals enrichment in 3′ UTRs and near stop codons. Cell, 149, 1635–1646

[189] Edelheit, S., Schwartz, S., Mumbach, M. R., Wurtzel, O. and Sorek, R. (2013) Transcriptome-wide mapping of 5-methylcytidine RNA modifications in bacteria, archaea, and yeast reveals m⁵C within archaeal mRNAs. PLoS Genet., 9, e1003602

[190] Batista, P. J., Molinie, B., Wang, J., Qu, K., Zhang, J., Li, L., Bouley, D. M., Lujan, E., Haddad, B., Daneshvar, K., (2014) m⁶A RNA modification controls cell fate transition in mammalian embryonic stem cells. Cell Stem Cell, 15, 707–719

[191] T. M. Carlile, M. F. Rojas-Duran, B. Zinshteyn, H. Shin, K. M. Bartoli, and W. V. Gilbert . (2014) Pseudouridine profiling reveals regulated mRNA pseudouridylation in yeast and human cells. Nature, 515, 43–146

[192] Incarnato, D., Anselmi, F., Morandi, E., Neri, F., Maldotti, M., Rapelli, S., Parlato, C., Basile, G. and Oliviero, S. (2016) High-throughput single-base resolution mapping of RNA 2′-O-methylated residues. Nucleic Acids Res., doi: 10.1093/nar/gkw810

[193] Kudla, G., Granneman, S., Hahn, D., Beggs, J. D. and Tollervey, D. (2011) Cross-linking, ligation, and sequencing of hybrids reveals RNA-RNA interactions in yeast. Proc. Natl. Acad. Sci. USA, 108, 10010–10015

[194] Ramani, V., Qiu, R. and Shendure, J. (2015) High-throughput determination of RNA structure by proximity ligation. Nat. Biotechnol., 33, 980–984

[195] Sugimoto, Y., Vigilante, A., Darbo, E., Zirra, A., Militti, C., D’Ambrogio, A., Luscombe, N. M. and Ule, J. (2015) hiCLIP reveals the in vivo atlas of mRNA secondary structures recognized by Staufen 1. Nature, 519, 491–494

[196] Sharma, E., Sterne-Weiler, T., O’Hanlon, D. and Blencowe, B. J. (2016) Global mapping of human RNA-RNA interactions. Mol. Cell, 62, 618–626

[197] Lu, Z., Zhang, Q. C., Lee, B., Flynn, R. A., Smith, M. A., Robinson, J. T., Davidovich, C., Gooding, A. R., Goodrich, K. J., Mattick, J. S., (2016) RNA duplex map in living cells reveals higher-order transcriptome structure. Cell, 165, 1267–1279

[198] Aw, J. G. A., Shen, Y., Wilm, A., Sun, M., Lim, X. N., Boon, K.-L., Tapsin, S., Chan, Y.-S., Tan, C.-P., Sim, A. Y., (2016) In vivo mapping of eukaryotic RNA interactomes reveals principles of higher-order organization and regulation. Mol. Cell, 62, 603–617

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg