Sparsification of RNA structure prediction including pseudoknots

<p>Abstract</p> <p>Background</p> <p>Although many RNA molecules contain pseudoknots, computational prediction of pseudoknotted RNA structure is still in its infancy due to high running time and space consumption implied by the dynamic programming formulations of the problem.</p> <p>Results</p> <p>In this paper, we introduce sparsification to significantly speedup the dynamic programming approaches for pseudoknotted RNA structure prediction, which also lower the space requirements. Although sparsification has been applied to a number of RNA-related structure prediction problems in the past few years, we provide the first application of sparsification to pseudoknotted RNA structure prediction specifically and to handling gapped fragments more generally - which has a much more complex recursive structure than other problems to which sparsification has been applied. We analyse how to sparsify four pseudoknot structure prediction algorithms, among those the most general method available (the Rivas-Eddy algorithm) and the fastest one (Reeder-Giegerich algorithm). In all algorithms the number of "candidate" substructures to be considered is reduced.</p> <p>Conclusions</p> <p>Our experimental results on the sparsified Reeder-Giegerich algorithm suggest a linear speedup over the unsparsified implementation.</p

Sparsification of RNA Structure Prediction Including Pseudoknots

Background: Although many RNA molecules contain pseudoknots, computational prediction of pseudoknottedRNA structure is still in its infancy due to high running time and space consumption implied by the dynamicprogramming formulations of the problem.Results: In this paper, we introduce sparsification to significantly speedup the dynamic programming approachesfor pseudoknotted RNA structure prediction, which also lower the space requirements. Although sparsification hasbeen applied to a number of RNA-related structure prediction problems in the past few years, we provide the firstapplication of sparsification to pseudoknotted RNA structure prediction specifically and to handling gappedfragments more generally - which has a much more complex recursive structure than other problems to whichsparsification has been applied. We analyse how to sparsify four pseudoknot structure prediction algorithms,among those the most general method available (the Rivas-Eddy algorithm) and the fastest one (Reeder-Giegerichalgorithm). In all algorithms the number of “candidate” substructures to be considered is reduced.Conclusions: Our experimental results on the sparsified Reeder-Giegerich algorithm suggest a linear speedup overthe unsparsified implementation

On the combinatorics of sparsification

Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze the sparsification of a particular decomposition rule, $\Lambda^*$, that splits an interval for RNA secondary and pseudoknot structures of fixed topological genus. Essential for quantifying the sparsification is the size of its so called candidate set. We present a combinatorial framework which allows by means of probabilities of irreducible substructures to obtain the expected size of the set of $\Lambda^*$-candidates. We compute these expectations for arc-based energy models via energy-filtered generating functions (GF) for RNA secondary structures as well as RNA pseudoknot structures. For RNA secondary structures we also consider a simplified loop-energy model. This combinatorial analysis is then compared to the expected number of $\Lambda^*$-candidates obtained from folding mfe-structures. In case of the mfe-folding of RNA secondary structures with a simplified loop energy model our results imply that sparsification provides a reduction of time complexity by a constant factor of 91% (theory) versus a 96% reduction (experiment). For the "full" loop-energy model there is a reduction of 98% (experiment).Comment: 27 pages, 12 figure

Sparsification Enables Predicting Kissing Hairpin Pseudoknot Structures of Long RNAs in Practice

While computational RNA secondary structure prediction is an important tool in RNA research, it is still fundamentally limited to pseudoknot-free structures (or at best very simple pseudoknots) in practice. Here, we make the prediction of complex pseudoknots - including kissing hairpin structures - practically applicable by reducing the originally high space consumption. For this aim, we apply the technique of sparsification and other space-saving modifications to the recurrences of the pseudoknot prediction algorithm by Chen, Condon and Jabbari (CCJ algorithm). Thus, the theoretical space complexity of free energy minimization is reduced to Theta(n^3+Z), in the sequence length n and the number of non-optimally decomposable fragments ("candidates") Z. The sparsified CCJ algorithm, sparseCCJ, is presented in detail. Moreover, we provide and compare three generations of CCJ implementations, which continuously improve the space requirements: the original CCJ implementation, our first modified implementation, and our final sparsified implementation. The two latest implementations implement the established HotKnots DP09 energy model. In our experiments, using 244GB of RAM, the original CCJ implementation failed to handle sequences longer than 195 bases; sparseCCJ handles our pseudoknot data set (up to about length 400 bases) in this space limit. All three CCJ implementations are available at https://github.com/HosnaJabbari/CCJ

An Efficient Algorithm for Upper Bound on the Partition Function of Nucleic Acids

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 $O(n^4)$ and the time complexity is $O(n^6)$ 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 $O(MFE(n)\ell)$ for single RNA and $O(MFE(m, n)\ell)$ for RNA-RNA interaction in practice, in which $MFE$ is the running time of sparse folding and $\ell \leq n$ ($\ell \leq n + m$) is a sequence dependent parameter

A Combinatorial Framework for Designing (Pseudoknotted) RNA Algorithms

We extend an hypergraph representation, introduced by Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming energy minimization, partition function, base-pair probabilities...) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one to conceptually detach the conformation space/energy model -- captured by the hypergraph model -- from the specific application, assuming unambiguity of the decomposition. To ensure the latter property, we propose a new combinatorial methodology based on generating functions. We extend the set of generic applications by proposing an exact algorithm for extracting generalized moments in weighted distribution, generalizing a prior contribution by Miklos and al. Finally, we illustrate our full-fledged programme on three exemplary conformation spaces (secondary structures, Akutsu's simple type pseudoknots and kissing hairpins). This readily gives sets of algorithms that are either novel or have complexity comparable to classic implementations for minimization and Boltzmann ensemble applications of dynamic programming

Computational analysis of noncoding RNAs

Noncoding RNAs have emerged as important key players in the cell. Understanding their surprisingly diverse range of functions is challenging for experimental and computational biology. Here, we review computational methods to analyze noncoding RNAs. The topics covered include basic and advanced techniques to predict RNA structures, annotation of noncoding RNAs in genomic data, mining RNA-seq data for novel transcripts and prediction of transcript structures, computational aspects of microRNAs, and database resources.Austrian Science Fund (Schrodinger Fellowship J2966-B12)German Research Foundation (grant WI 3628/1-1 to SW)National Institutes of Health (U.S.) (NIH award 1RC1CA147187