Statistics of canonical RNA pseudoknot structures

Journal of Theoretical Biology

Volumn 253, Issue 3, 2008, Pages 570-578

  Huang, Fenix W D ^a   Reidys, Christian M ^a  

^a NANKAI UNIVERSITY   (China)

Author keywords

Central limit theorem; D finite; k Noncrossing RNA structure; Singularity analysis

Indexed keywords

NUCLEOTIDE; RNA;

COMPARATIVE STUDY; GENETIC STRUCTURE; GROWTH RATE; RNA;

ARTICLE; ENERGY; PRIORITY JOURNAL; RNA STRUCTURE; STATISTICS;

ALGORITHMS; ANIMALS; MODELS, GENETIC; MODELS, MOLECULAR; NUCLEIC ACID CONFORMATION; RNA;

EID: 46849100443     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2008.04.002     Document Type: Article

References (28)

1. André D. Solution directed du probleème, résolu par M. Bertrand. C. R. Acad. Sci. Paris 105 (1887) 436-437
2. Batey R.T., Rambo R.P., and Doudna J.A. Tertiary motifs in RNA structure and folding angew. Chem. Int. Ed. 38 (1999) 2326-2343
3. Chamorro, M., Parkin, N., Varmus, H.E., 1992. An RNA pseudoknot and an optimal heptameric shift site are required for highly efficient ribosomal frameshifting on a retroviral messenger RNA. Proc. Natl. Acad. Sci. USA 89 (2), 713-717, 1309954.
4. Chen W.Y.C., Deng E.Y.P., Du R.R.X., Stanley R.P., and Yan C.H. Crossings and nestings of matchings and partitions. Trans. Amer. Math. Soc. 359 4 (2007) 1555-1575
5. Chen, W.Y.C., Qin, J., Reidys, C.M., 2007b. Crossings and nestings of tangled-diagrams. arXiv:0710.4053v2.
6. Flajolet P., and Sedgewick R. Analytic Combinatorics (2007)
7. Flajolet P., Fill J.A., and Kapur N. Singularity analysis, Hadamard products, and tree recurrences. J. Comput. Appl. Math. 174 (2005) 271-313
8. Gessel I.M., and Zeilberger D. Random walk in a Weyl chamber. Proc. Amer. Math. Soc. 115 (1992) 27-31
9. Grabiner D.J., and Magyar P. Random walks in Weyl chambers and the decomposition of tensor powers. Discrete Appl. Math. 2 (1993) 239-260
10. Hofacker I.L., Fontana W., Stadler P.F., Bonhoeffer L.S., Tacker M., and Schuster P. Fast folding and comparison of RNA secondary structures. Monatsh. Chem. 125 (1994) 167-188
11. Hofacker I.L., Schuster P., and Stadler P.F. Combinatorics of RNA secondary structures. Discrete Appl. Math. 88 (1998) 207-237
12. Jin, E.Y., Reidys, C.M., 2007a. Asymptotic enumeration of RNA structures with pseudoknots. Bull. Math. Biol. 70 (4), 951-970.
13. Jin E.Y., and Reidys C.M. Central and local limit theorems for RNA structures. J. Theor. Biol. 250 2008 (2007) 547-559
14. Jin, E.Y., Reidys, C.M., 2007c. RNA-Lego: combinatorial design of pseudoknot RNA. arXiv:0711.1405v2.
15. Jin E.Y., Qin J., and Reidys C.M. Combinatorics of RNA structures with pseudoknots. Bull. Math. Biol. 70 2008 (2007) 45-67 PMID: 17896159
16. Jin, E.Y., Reidys, C.M., Wang, R., 2008. Asymptotic analysis of k-noncrossing matchings, arXiv:0803.0848.
17. Konings D.A.M., and Gutell R.R. A comparison of thermodynamic foldings with comparatively derived structures of 16S and 16S-like rRNAs. RNA 1 (1995) 559-574
18. Loria A., and Pan T. Domain structure of the ribozyme from eubacterial ribonuclease P. RNA 2 (1996) 551-563
19. Mapping RNA Form and Function, 2005. Science 309 (5740), 1441-1632.
20. Rivas E., and Eddy S. A dynamic programming algorithm for RNA structure prediction including pseudoknots. J. Mol. Biol. 285 (1999) 2053-2068
21. Stadler, P.F., 2007. Private communication.
22. Stanley R.P. Differentiably finite power series. Eur. J. Combin. 1 (1980) 175-188
23. Titchmarsh E.C. The Theory of Functions (1939), Oxford University Press, London
24. Tuerk C., MacDougal S., and Gold L. RNA pseudoknots that inhibit human immunodeficiency virus type 1 reverse transcriptase. Proc. Natl. Acad. Sci. USA 89 (1992) 6988-6992
25. Waterman M.S. Secondary structure of single-stranded nucleic acids. Adv. Math. I (Suppl.) 1 (1978) 167-212
26. Waterman M.S. Combinatorics of RNA hairpins and cloverleafs. Stud. Appl. Math. 60 (1979) 91-96
27. Waterman M.S., and Schmitt W.R. Linear trees and RNA secondary structure. Discrete Appl. Math. 51 (1994) 317-323
28. Westhof E., and Jaeger L. RNA pseudoknots. Curr. Opin. Struct. Biol. 2 (1992) 327-333