Equilibrium Distribution of Secondary Structures for Large RNA
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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- Bellman R, Kaluba R (1960) On Kth best policies. J.Siam 8: 582–588.Google Scholar
- Garey MR, Johnson DS (1979) Computers and Intractability. A Guide to the Theory of NP-completeness. Freeman, New York.Google Scholar
- McCaskill JS (1990) The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Bio polymers 29: 1105–1119.Google Scholar
- Salser W (1977) Globin mRNA sequences: analysis of base pairing and evolutionary implications. Cold Spring Harbor Symp.Quant.Biol. 42: 985–1002.Google Scholar
- 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.Google Scholar
- Wüthrich, K (1986) NMR of Proteins and Nucleic Acids. Wiley, New York.Google Scholar
- Zuker M, Sankoff D (1984) RNA secondary structures and their prediction. Bull.Math.Biol 46: 591–621.Google Scholar