It has been shown that minimum free energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble based quantities such as melting temperature and equilibrium concentrations can be more reliably predicted. Even structure prediction by sampling from the ensemble and clustering those structures by Sfold [7] has proven to be more reliable than minimum free energy structure prediction. The main obstacle for ensemble based approaches is the computational complexity of the partition function and base pairing probabilities. For instance, the space complexity of the partition function for RNA-RNA interaction is @math and the time complexity is @math which are prohibitively large [4,12]. Our goal in this paper is to give a fast algorithm, based on sparse folding, to calculate an upper bound on the partition function. Our work is based on the recent algorithm of Hazan and Jaakkola [10]. The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is @math for single RNA and @math for RNA-RNA interaction in practice, in which @math is the running time of sparse folding and @math ( @math ) is a sequence dependent parameter.
Methods to the partition function for interacting RNAs have been proposed in the literature. Instead, methods for comutation of the partition function have been developed, having high both time and space complexity. Most notably, @cite_5 developed an @math --time and @math --space dynamic programming algorithm that computes the partition function of RNA--RNA interaction complexes, thereby providing detailed insights into their thermodynamic properties. @cite_4 has developed a algorithm that produces a Boltzmann weighted ensemble of RNA–-RNA interaction structures for the calculation of (and not the partition function) for any given interval on the target RNAs.
@cite_5 @cite_4
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Recent interests, such as RNA interference and antisense RNA regulation, strongly motivate the problem of predicting whether two nucleic acid strands interact. Motivation: Regulatory non-coding RNAs (ncRNAs) such as microRNAs play an important role in gene regulation. Studies on both prokaryotic and eukaryotic cells show that such ncRNAs usually bind to their target mRNA to regulate the translation of corresponding genes. The specificity of these interactions depends on the stability of intermolecular and intramolecular base pairing. While methods like deep sequencing allow to discover an ever increasing set of ncRNAs, there are no high-throughput methods available to detect their associated targets. Hence, there is an increasing need for precise computational target prediction. In order to predict base-pairing probability of any two bases in interacting nucleic acids, it is necessary to compute the interaction partition function over the whole ensemble. The partition function is a scalar value from which various thermodynamic quantities can be derived. For example, the equilibrium concentration of each complex nucleic acid species and also the melting temperature of interacting nucleic acids can be calculated based on the partition function of the complex. Results: We present a model for analyzing the thermodynamics of two interacting nucleic acid strands considering the most general type of interactions studied in the literature. We also present a corresponding dynamic programming algorithm that computes the partition function over (almost) all physically possible joint secondary structures formed by two interacting nucleic acids in O(n6) time. We verify the predictive power of our algorithm by computing (i) the melting temperature for interacting RNA pairs studied in the literature and (ii) the equilibrium concentration for several variants of the OxyS–fhlA complex. In both experiments, our algorithm shows high accuracy and outperforms competitors. Availability: Software and web server is available at http: compbio.cs.sfu.ca taverna pirna Contact:cenk@cs.sfu.ca; backofen@informatik.uni-freiburg.de Supplementary information:Supplementary data are avaliable at Bioinformatics online. Motivation: It has been proven that the accessibility of the target sites has a critical influence on RNA–RNA binding, in general and the specificity and efficiency of miRNAs and siRNAs, in particular. Recently, O(N6) time and O(N4) space dynamic programming (DP) algorithms have become available that compute the partition function of RNA–RNA interaction complexes, thereby providing detailed insights into their thermodynamic properties. Results: Modifications to the grammars underlying earlier approaches enables the calculation of interaction probabilities for any given interval on the target RNA. The computation of the ‘hybrid probabilities’ is complemented by a stochastic sampling algorithm that produces a Boltzmann weighted ensemble of RNA–RNA interaction structures. The sampling of k structures requires only negligible additional memory resources and runs in O(k·N3). Availability: The algorithms described here are implemented in C as part of the rip package. The source code of rip2 can be downloaded from http: www.combinatorics.cn cbpc rip.html and http: www.bioinf.uni-leipzig.de Software rip.html. Contact: duck@santafe.edu Supplementary information:Supplementary data are available at Bioinformatics online.