Title | ||
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Computing the partition function and sampling for saturated secondary structures of RNA, with respect to the Turner energy model. |
Abstract | ||
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An RNA secondary structure is saturated if no base pairs can be added without violating the definition of secondary structure. Here we describe a new algorithm, RNAsat, which for a given RNA sequence a, an integral temperature 0 <= T <= 100 in degrees Celsius, and for all integers k, computes the Boltzmann partition function x(k)(T) (a) = Sigma(S is an element of SATk(a))exp(-E(S)/RT), where the sum is over all saturated secondary structures of a which have exactly k base pairs, R is universal gas constant and E(S) denotes the free energy with respect to the Turner nearest neighbor energy model. By dynamic programming, we compute Z(k)(T)simultaneously for all values of k in time O(n(5)) and space O(n(3)). Additionally, RNAsat computes the partition function Q(k)(T)(a) = Sigma S is an element of S-k(a) exp(-E(S)/RT), where the sum is over all secondary structures of a which have k base pairs; the latter computation is performed simultaneously for all values of k in O(n(4)) time and O(n(3)) space. Lastly, using the partition function Z(k)(T) [resp. Q(k)(T)]with stochastic backtracking, RNAsat rigorously samples the collection of saturated secondary structures [resp. secondary structures] having k base pairs; for Q(k)(T) this provides a parameterized form of Sfold sampling (Ding and Lawrence, 2003). Using RNAsat, (i) we compute the ensemble free energy for saturated secondary structures having k base pairs, (ii) show cooperativity of the Turner modelm (iii) demonstrate a temperature-dependent phase transition, (iv) illustrate the predictive advantage of RNAsat for the precursor microRNA cel-mire-72 of C. elegans and for the pseudoknot PKB 00152 of Pseudobase (van Batenburg et al., 2001), (v) illustrate the RNA shapes (Giegerich et al., 2004) of sampled secondary structures [resp. saturated structures]having exactly k base pairs. A web server for RNAsat is under construction of bioinformatics.bc.edu/clotelab/RNAsat/. |
Year | DOI | Venue |
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2007 | 10.1089/cmb.2006.0012 | JOURNAL OF COMPUTATIONAL BIOLOGY |
Keywords | Field | DocType |
secondary structure,RNA,Boltzmann partition function,kinetic trap | k-nearest neighbors algorithm,Integer,Discrete mathematics,Gas constant,Combinatorics,Partition function (statistical mechanics),Translational partition function,Boltzmann constant,Nucleic acid secondary structure,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
14.0 | 2 | 1066-5277 |
Citations | PageRank | References |
7 | 0.54 | 17 |
Authors | ||
2 |
Name | Order | Citations | PageRank |
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Jérôme Waldispühl | 1 | 111 | 16.24 |
Peter Clote | 2 | 400 | 47.41 |