Abstract
The full distribution of secondary structures for a given RNA (length N < 500) has been available since 1988 using the partition function based calculation developed by the author (McCaskill 1990). All possible non-knotted secondary structures contribute to binding probabilities of base pairs in the equilibrium ensemble. These may be effectively displayed logarithmically as a matrix of scaled boxes. This scalar calculation is of order AT3 in time and N 2 in the storage of intermediate information. Here we demonstrate that this computation may be extended to sequences of lengths 5000 to 10000, providing the only feasible means of gaining structural information on viral size RNA. The development requires a further reduction in the computational order of the algorithm. A careful segmentation and large exponent vectorization reduces the core storage requirements to order N * V, where V is the vectorization length. This is achieved at the cost of an additional contribution to the time of order (N/V) * S, where S is the time to retrieve an N × N array from mass storage (e.g. disk).
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References
Been MD, Barfod ET, Burke JM, Price JV, Tanner NK, Zaug AJ, Cech TR (1987) Structures involved in Tetrahymena rRNA self-splicing and RNA enzyme activity. Cold Spring Harbor Symp.Quant.Biol. 52: 147–157.
Bellman R, Kaluba R (1960) On Kth best policies. J.Siam 8: 582–588.
Cech TR, Tanner NK, Tinoco I. Jr, Weir BR, Zuker M, Perlman PS (1983) Secondary structure of the Tetrahymena ribosomal RNA intervening sequence: structural homology with fungal mitochondrial intervening sequences. Proc. Natl. Acad. Sci. USA 80: 3903–3907.
Eigen M, McCaskill JS, Schuster P (1988) The Molecular Quasispecies. J. Phys. Chem. 92: 6881–6891.
Turner DH, Sugimoto N, Jaeger JA, Longfellow CE, Freier SM, Kierzek R (1987) Improved parameters for prediction of RNA structure. Cold Spring Harbor Symp.Quant.Biol. 52: 123–133.
Garey MR, Johnson DS (1979) Computers and Intractability. A Guide to the Theory of NP-completeness. Freeman, New York.
Gibbs AJ, McIntyre GA (1970) The diagram, a method for comparing sequences. Eur.J.Biochem. 16: 1–11.
McCaskill JS (1990) The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Bio polymers 29: 1105–1119.
Pleij CWA, Bosch L (1989) RNA pseudoknots: structure, detection and prediction. Methods in Enzymology 180: 289–303.
Salser W (1977) Globin mRNA sequences: analysis of base pairing and evolutionary implications. Cold Spring Harbor Symp.Quant.Biol. 42: 985–1002.
Tinoco I Jr, Uhlenbeck OC, Levine MD (1971) Estimation of secondary structure in ribonucleic acids. Nature 230: 362–367.
Waterman MS (1978) Secondary structure of single-stranded nucleic acids. Studies in Foundations and Combinatorics. Advances in Mathematics Supp. Studies. 1: 167–212, Academic Press.
Waterman MS, Smith TF (1978) RNA secondary stucture: a complete mathematical analysis. Math.Biosci. 42: 257–266.
Wüthrich, K (1986) NMR of Proteins and Nucleic Acids. Wiley, New York.
Zuker M, Sankoff D (1984) RNA secondary structures and their prediction. Bull.Math.Biol 46: 591–621.
Zuker M, Stiegler P (1981) Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucl. Acids Res. 9: 133–148.
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© 1993 Springer-Verlag Berlin Heidelberg
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McCaskill, J.S. (1993). Equilibrium Distribution of Secondary Structures for Large RNA. In: Soumpasis, D.M., Jovin, T.M. (eds) Computation of Biomolecular Structures. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77798-1_3
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DOI: https://doi.org/10.1007/978-3-642-77798-1_3
Publisher Name: Springer, Berlin, Heidelberg
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