Abstract
Using complex roots of unity and the Fast Fourier Transform, we design a new thermodynamics-based algorithm, FFTbor, that computes the Boltzmann probability that secondary structures differ by base pairs from an arbitrary initial structure of a given RNA sequence. The algorithm, which runs in quartic time and quadratic space , is used to determine the correlation between kinetic folding speed and the ruggedness of the energy landscape, and to predict the location of riboswitch expression platform candidates. A web server is available at http://bioinformatics.bc.edu/clotelab/FFTbor/.
Highlights
In [1], we developed a dynamic programming algorithm, RNAbor, pronounced RNA neighbor, which simultaneously computes for each integer k, the Boltzmann probability pk ~Zk Z of the subensemble of structures whose base pair distance to a given initial, or reference, structure SÃ is k. (Here, Z denotes the partition function, defined as the sum of all Boltzmann factors exp({E(S)=RT), over all secondary structures S of a givenRNA sequence, and R denotes the universal gas constant and T absolute temperature
Zk denotes the sum of all Boltzmann factors of all structures S, whose base pair distance to the initial structure SÃ is exactly k.) RNAbor stores the value of the partition functions Zk(i,j) for all 1ƒiƒjƒn and 0ƒkƒn, each of which requires quadratic time to compute
A secondary structure S is a set of base pairs (i,j), where 1ƒiƒizhvjƒn and h§0 represents the minimum number of unpaired nucleotides in a hairpin loop, such that if (i,j) and (x,y) both belong to S, i~xZj~y and ivxvjZivyvj
Summary
In [1], we developed a dynamic programming algorithm, RNAbor, pronounced RNA neighbor, which simultaneously computes for each integer k, the Boltzmann probability pk ~Zk Z of the subensemble of structures whose base pair distance to a given initial, or reference, structure SÃ is k. (Here, Z denotes the partition function, defined as the sum of all Boltzmann factors exp({E(S)=RT), over all secondary structures S of a givenRNA sequence, and R denotes the universal gas constant and T absolute temperature. (Here, Z denotes the partition function, defined as the sum of all Boltzmann factors exp({E(S)=RT), over all secondary structures S of a given. Zk denotes the sum of all Boltzmann factors of all structures S, whose base pair distance to the initial structure SÃ is exactly k.) RNAbor stores the value of the (partial) partition functions Zk(i,j) for all 1ƒiƒjƒn and 0ƒkƒn, each of which requires quadratic time to compute. It follows that RNAbor runs in time O(n5) and space O(n3), which severely limits its applicability to genomic annotation. Given two secondary structures S,T on s , we define the base pair distance dBP between S and T to be the number of base pairs that they have that are not in common, i.e
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