Abstract
In this chapter we present the classic dynamic programming algorithms for RNA structure prediction by energy minimization, as well as variations of this approach that allow to compute suboptimal foldings, or even the partition function over all possible secondary structures. The latter are essential in order to deal with the inaccuracy of minimum free energy (MFE) structure prediction, and can be used, for example, to derive reliability measures that assign a confidence value to all or part of a predicted structure. In addition, we discuss recently proposed alternatives to the MFE criterion such as the use of maximum expected accuracy (MEA) or centroid structures. The dynamic programming algorithms implicitly assume that the RNA molecule is in thermodynamic equilibrium. However, especially for long RNAs, this need not be the case. In the last section we therefore discuss approaches for predicting RNA folding kinetics and co-transcriptional folding.
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References
Nussinov R, Piecznik G, Griggs JR, Kleitman DJ (1978) Algorithms for loop matching. SIAM J Appl Math 35(1):68–82
Bompfünewerer AF, Backofen R, Bernhart SH, Hertel J, Hofacker IL, Stadler PF, Will S (2008) Variations on RNA folding and alignment: Lessons from Benasque. J Math Biol 56:119–144
Hofacker IL, Stadler PF (2006) Memory efficient folding algorithms for circular RNA secondary structures. Bioinformatics 22(10):1172–1176
Hofacker IL, Fontana W, Stadler PF, Bonhoeffer S, Tacker M, Schuster P (1994) Fast folding and comparison of RNA secondary structures (the Vienna RNA Package). Monatsh Chem 125(2):167–188
Hofacker IL, Fekete M, Stadler PF (2002) Secondary structure prediction for aligned RNA sequences. J Mol Biol 319:1059–1066
Bernhart SH, Hofacker IL, Will S, Gruber AR, Stadler PF (2008) RNAalifold: improved consensus structure prediction for RNA alignments. BMC Bioinformatics 9:474
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
Mathews DH, Disney MD, Childs JL, Schroeder SJ, Zuker M, Turner DH (2004) Incorporating chemical modification constraints into a dynamic programming algorithm for prediction of RNA secondary structure. Proc Natl Acad Sci USA 101:7287–7292
Doshi K, Cannone J, Cobaugh C, Gutell R (2004) Evaluation of the suitability of free-energy minimization using nearest-neighbor energy parameters for RNA secondary structure prediction. BMC Bioinformatics 5(1):105
McCaskill JS (1990) The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29:1105–1119
Zuker M, Jacobson AB (1995) “Well-determined” regions in RNA secondary structure prediction: analysis of small subunit ribosomal RNA. Nuclic Acids Res 23:2791–2798
Zuker M (1989) On finding all suboptimal foldings of an RNA molecule. Science 244(4900):48–52
Wuchty S, Fontana W, Hofacker IL, Schuster P (1999) Complete suboptimal folding of RNA and the stability of secondary structures. Biopolymers 49(2):145–165
Waterman MS, Byers TH (1985) A dynamic programming algorithm to find all solutions in a neighborhood of the optimum. Math Biosci 77:179–188
Flamm C, Hofacker IL, Stadler PF, Wolfinger MT (2002) Barrier trees of degenerate landscapes. Z Phys Chem 216:155–173
Ding Y, Lawrence CE (2003) A statistical sampling algorithm for RNA secondary structure prediction. Nucleic Acids Res 31:7280– 7301
Mathews DH (2004) Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization. RNA 10(8):1178–1190
Do CB, Woods DA, Batzoglou S (2006) CONTRAfold: RNA secondary structure prediction without physics-based models. Bioinformatics 22(14):e90–e98
Kiryu H, Kin T, Asai K (2007) Robust prediction of consensus secondary structures using averaged base pairing probability matrices. Bioinformatics 23(4):434–441
Flamm C, Hofacker IL (2008) Beyond energy minimization: Approaches to the kinetic folding of RNA. Monatsh f Chemie 139(4):447–457
Isambert H, Siggia ED (2000) Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme. Proc Natl Acad Sci USA 97(12):6515–6520
Flamm C, Fontana W, Hofacker IL, Schuster P (2000) RNA folding kinetics at elementary step resolution. RNA 6:325–338
Wolfinger MT, Andreas Svrcek-Seiler W, Flamm C, Hofacker IL, Stadler PF (2004) Efficient folding dynamics of RNA secondary structures. J Phys A Math Gen 37: 4731–4741
Gruber AR, Lorenz R, Bernhart SH, Neuböck R, Hofacker IL (2008) The Vienna RNA websuite. Nuclic Acids Res 36:W70–W74
Lorenz R, Flamm C, Hofacker IL (2009) 2D projections of RNA folding landscapes. In: Grosse I, Neumann S, Posch S, Schreiber F, Stadler PF, (eds) German conference on bioinformatics 2009, vol 157 of Lecture notes in informatics, pp 11–20, Bonn. Gesellschaft f Informatik
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Hofacker, I.L. (2014). Energy-Directed RNA Structure Prediction. In: Gorodkin, J., Ruzzo, W. (eds) RNA Sequence, Structure, and Function: Computational and Bioinformatic Methods. Methods in Molecular Biology, vol 1097. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-709-9_4
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DOI: https://doi.org/10.1007/978-1-62703-709-9_4
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