Abstract
In this paper, we study irreducibility in RNA structures. By RNA structure, we mean RNA secondary as well as RNA pseudoknot structures as abstract contact structures. We give an analysis contrasting random and minimum free energy (mfe) configurations and secondary versus pseudoknots structures. In the process, we compute various distributions: the numbers of irreducible substructures and their locations and sizes, parameterized in terms of the maximal number of mutually crossing arcs, k−1, and the minimal size of stacks σ. In particular, we analyze the size of the largest irreducible substructure for random and mfe structures, which is the key factor for the folding time of mfe configurations. We show that the largest irreducible substructure is typically unique and contains almost all nucleotides.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Cameron, N.T., Shapiro, L., 2003. Random walks, trees and extensions of Riordan group techniques. In: Annual Joint Mathematics Meetings, Baltimore, MD, US.
Hofacker, I.L., Fontana, W., Stadler, P.F., Bonhoeffer, L.S., Tavker, M., Schuster, P., 1994. Fast folding and comparison of RNA secondary structures, 125, 167–188. http://www.tbi.univie.ac.at/~ivo/RNA.
Howell, J.A., Smith, T.F., Waterman, M.S., 1980. Computation of generating functions for biological molecules. SIAM J. Appl. Math. 39, 119–133.
Huang, F.W.D., Li, L.Y.M., Reidys, C.M., 2009a. Sequence-structure relations of pseudoknot RNA. BMC Bioinformatics 10(S1), S39.
Huang, F.W.D., Peng, W.W.J., Reidys, C.M., 2009b. Folding 3-noncrossing RNA pseudoknot structures. J. Comput. Biol. (to appear).
Jin, E.Y., Reidys, C.M., 2009. Combinatorial design of pseudoknot RNA. Adv. Appl. Math. 42, 135–151.
Jin, E.Y., Reidys, C.M., 2010. On the decomposition of k-noncrossing RNA structures. Adv. Appl. Math. 44, 53–70.
Jin, E.Y., Qin, J., Reidys, C.M., 2008. Combinatorics of RNA structures with pseudoknots. Bull. Math. Biol. 70(1), 45–67.
Konings, D.A.M., Gutell, R.R., 1995. A comparison of thermodynamic foldings with comparatively derived structures of 16S and 16S-like rRNAs. RNA 1, 559–574.
Loria, A., Pan, T., 1996. Domain structure of the ribozyme from eubacterial ribonuclease P. RNA 2, 551–563.
Ma, G., Reidys, C.M., 2008. Canonical RNA pseudoknot structures. J. Comput. Biol. 15(10), 1257–1273.
Penner, R.C., Waterman, M.S., 1993. Spaces of RNA secondary structures. Adv. Math. 101, 31–49.
Searls, D.B., 1999. Formal Language Theory and Biological Macromolecules, Series in Discr. Math. and Theor. Comput. Sci., vol. 47, pp. 117–140.
Tuerk, C., MacDougal, S., Gold, L., 1992. RNA pseudoknots that inhibit human immunodeficiency virus type 1 reverse transcriptase. Proc. Natl. Acad. Sci. USA 89, 6988–6992.
Waterman, M.S., 1979. Combinatorics of RNA hairpins and cloverleafs. Stud. Appl. Math. 60, 91–96.
Waterman, M.S., 1978. Secondary structure of single-stranded nucleic acids. Adv. Math. I (Suppl.) 1, 167–212.
Waterman, M.S., Schmitt, W.R., 1994. Linear trees and RNA secondary structure. Discrete Appl. Math. 51, 317–323.
Westhof, E., Jaeger, L., 1992. RNA pseudoknots. Curr. Opin. Struct. Biol. 2, 327–333.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jin, E.Y., Reidys, C.M. Irreducibility in RNA Structures. Bull. Math. Biol. 72, 375–399 (2010). https://doi.org/10.1007/s11538-009-9451-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-009-9451-5