Enumerating secondary structures and structural moieties for circular RNAs. (English) Zbl 1370.92121
Summary: A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of RNA sequences, with the folded configurations standing as a proxy for the phenotype. Here, we count the secondary structures of circular RNAs of length \(n\) and calculate the asymptotic distributions of different structural moieties, such as stems or hairpin loops, by means of symbolic combinatorics. Circular RNAs differ in essential ways from their linear counterparts. From the mathematical viewpoint, the enumeration of the corresponding secondary structures demands the use of combinatorial techniques additional to those used for linear RNAs. The asymptotic number of secondary structures for circular RNAs grows as \(a^nn^{-5/2}\), with \(a\) depending on particular constraints applied to the secondary structure. As it occurs with linear RNA, the abundance of any structural moiety is normally distributed in the limit \(n\rightarrow\infty\), with a mean and a variance that increase linearly with \(n\).
Software:
PfoldReferences:
| [1] | AbouHaidar, M. G.; Venkataraman, S.; Golshani, A.; Liu, B.; Ahmad, T., Novel coding, translation, and gene expression of a replicating covalently closed circular RNA of 220nt, Proc. Natl. Acad. Sci. USA, 111, 14542-14547 (2014) |
| [2] | Aguirre, J.; Buldú, J. M.; Stich, M.; Manrubia, S. C., Topological structure of the space of phenotypes: the case of RNA neutral networks, PLoS One, 6, e26324 (2011) |
| [3] | Ahnert, S. E.; Johnston, I. G.; Fink, T. M.A.; Doye, J. P.K.; Louis, A. A., Self-assembly, modularity, and physical complexity, Phys. Rev. E, 82, 026117 (2010) |
| [4] | Alberch, P., From genes to phenotype: dynamical systems and evolvability, Genetica, 84, 5-11 (1991) |
| [5] | Arias, C. F.; Catalán, P.; Manrubia, S.; Cuesta, J. A., toyLIFE: a computational framework to study the multi-level organization of the genotype-phenotype map, Sci. Rep., 4, 7549 (2014) |
| [6] | Bergeron, F.; Labelle, G.; Leroux, P., Combinatorial Species and Tree-like Structures (1998), Cambridge University Press · Zbl 0888.05001 |
| [7] | Briones, C.; Stich, M.; Manrubia, S. C., The dawn of the RNA World: toward functional complexity through ligation of random RNA oligomers, RNA, 15, 743-749 (2009) |
| [8] | Chen, S.-J., RNA folding: conformational statistics, folding kinetics, and ion electrostatics, Annu. Rev. Biophys., 37, 197-214 (2008) |
| [9] | Ciliberti, S.; Martin, O. C.; Wagner, A., Innovation and robustness in complex regulatory gene networks, Proc. Natl. Acad. Sci. USA, 104, 13591-13596 (2007) |
| [10] | Diener, T. O.; Raymer, W. B., Potato spindle tuber virus: a plant virus with properties of a free nucleic acid, Science, 158, 378-381 (1967) |
| [11] | Dill, K. A., Theory for the folding and stability of globular proteins, Biochemistry, 24, 1501-1509 (1985) |
| [12] | Fedor, M. J., Tertiary structure stabilization promotes hairpin ribozyme ligation, Biochemistry, 38, 11040-11050 (1999) |
| [13] | Flajolet, P.; Sedgewick, R., Analytic Combinatorics (2009), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1165.05001 |
| [14] | Flores, R.; Serra, P.; Minoia, S.; Serio, F. D.; Navarro, B., Viroids: from genotype to phenotype just relying on RNA sequence and structural motifs, Front. Microbiol., 3, 217 (2012) |
| [15] | Fontana, W.; Konings, D. A.M.; Stadler, P. F.; Schuster, P., Statistics of RNA secondary structures, Biopolymers, 33, 1389-1404 (1993) |
| [16] | Greenbury, S. F.; Ahnert, S. E., The organization of biological sequences into constrained and unconstrained parts determines fundamental properties of genotype-phenotype maps, J. R. Soc. Interface, 12, 20150724 (2015) |
| [17] | Hofacker, I. L.; Schuster, P.; Stadler, P. F., Combinatorics of RNA secondary structures, Disc. Appl. Math., 88, 207-237 (1998) · Zbl 0918.05004 |
| [18] | Hofacker, I. L.; Reidys, C. M.; Stadler, P. F., Symmetric circular matchings and RNA folding, Disc. Math., 312, 100-112 (2012) · Zbl 1232.05180 |
| [19] | Howell, J. A.; Smith, T. F.; Waterman, M. S., Computation of generating functions for biological molecules, SIAM J. Appl. Math., 39, 119-133 (1980) · Zbl 0445.92006 |
| [20] | Jeck, W. R.; Sharpless, N. E., Detecting and characterizing circular RNAs, Nat. Biotechnol., 32, 453-461 (2014) |
| [21] | Knudsen, B.; Hein, J. J., Pfold: RNA secondary structure prediction using stochastic context-free grammars, Nucl. Acids Res., 31, 3423-3428 (2003) |
| [22] | Li, H.; Helling, R.; Tang, C.; Wingreen, N., Emergence of preferred structures in a simple model of protein folding, Science, 273, 666-669 (1996) |
| [23] | Manrubia, S. C.; Sanjuán, R., Shape matters: effect of point mutations on RNA secondary structure, Adv. Compl. Syst., 16, 1250052 (2013) · Zbl 07865722 |
| [24] | Memczak, S.; Jens, M.; Elefsinioti, A.; Torti, F.; Krueger, J.; Rybak, A.; Maier, L.; Mackowiak, S. D.; Gregersen, L. H.; Munschauer, M.; Loewer, A.; Ziebold, U.; Landthaler, M.; Kocks, C.; le Noble, F.; Rajewsky, N., Circular RNAs are a large class of animal RNAs with regulatory potency, Nature, 495, 333-342 (2013) |
| [25] | Nebel, M. E., Combinatorial properties of RNA secondary structures, J. Comp. Biol., 9, 541-573 (2002) |
| [26] | Poznanović, S.; Heitsch, C. E., Asymptotic distribution of motifs in a stochastic context-free grammar model of RNA folding, J. Math. Biol., 69, 1743-1772 (2014) · Zbl 1320.92065 |
| [27] | Reidys, C. M., Combinatorial Computational Biology of RNA (2002), Springer: Springer New York · Zbl 1012.05060 |
| [29] | Saldanha, J. A.; Thomas, H. C.; Monjardino, J. P., Cloning and sequencing of rna of hepatitis delta virus isolated from human serum, J. Gen. Virol., 71, 1603-1606 (1990) |
| [30] | Salzman, J., Circular RNA expression: its potential regulation and function, Trends Genet., 32, 309 (2016) |
| [31] | Schuster, P.; Fontana, W.; Stadler, P. F.; Hofacker, I. L., From sequences to shapes and back: a case study in RNA secondary structures, P. R. Soc. B, 255, 279-284 (1994) |
| [32] | Seligmann, H., Swinger RNA self-hybridization and mitochondrial non-canonical swinger transcription, transcription systematically exchanging nucleotides, J. Theor. Biol., 399, 84-91 (2016) |
| [33] | Seligmann, H., Systematically frameshifting by deletion of every 4th or 4th and 5th nucleotides during mitochondrial transcription: RNA self-hybridization regulates delRNA expression, BioSystems, 142-143, 43-51 (2016) |
| [34] | Wagner, G. P.; Zhang, J., The pleiotropic structure of the genotype-phenotype map: the evolvability of complex organisms, Nat. Rev. Genet., 12, 204-213 (2011) |
| [35] | Wagner, A., The Origins of Evolutionary Innovations (2011), Oxford University Press |
| [36] | Waterman, M. S.; Smith, T. F., RNA secondary structure: a complete mathematical analysis, Math. Biosci., 42, 257-266 (1978) · Zbl 0402.92016 |
| [37] | Waterman, M. S., Secondary structure of single-stranded nucleic acids, Adv. Math. Suppl. Stud., 1, 167-212 (1978) · Zbl 0434.05007 |
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