SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics.

MOTIVATION: RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of [Formula: see text]. Subsequently, numerous faster 'Sankoff-style' approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity ([Formula: see text] quartic time). RESULTS: Breaking this barrier, we introduce the novel Sankoff-style algorithm 'sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)', which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff's original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics.

ExpaRNA-P: simultaneous exact pattern matching and folding of RNAs.

BACKGROUND: Identifying sequence-structure motifs common to two RNAs can speed up the comparison of structural RNAs substantially. The core algorithm of the existent approach ExpaRNA solves this problem for a priori known input structures. However, such structures are rarely known; moreover, predicting them computationally is no rescue, since single sequence structure prediction is highly unreliable. RESULTS: The novel algorithm ExpaRNA-P computes exactly matching sequence-structure motifs in entire Boltzmann-distributed structure ensembles of two RNAs; thereby we match and fold RNAs simultaneously, analogous to the well-known "simultaneous alignment and folding" of RNAs. While this implies much higher flexibility compared to ExpaRNA, ExpaRNA-P has the same very low complexity (quadratic in time and space), which is enabled by its novel structure ensemble-based sparsification. Furthermore, we devise a generalized chaining algorithm to compute compatible subsets of ExpaRNA-P's sequence-structure motifs. Resulting in the very fast RNA alignment approach ExpLoc-P, we utilize the best chain as anchor constraints for the sequence-structure alignment tool LocARNA. ExpLoc-P is benchmarked in several variants and versus state-of-the-art approaches. In particular, we formally introduce and evaluate strict and relaxed variants of the problem; the latter makes the approach sensitive to compensatory mutations. Across a benchmark set of typical non-coding RNAs, ExpLoc-P has similar accuracy to LocARNA but is four times faster (in both variants), while it achieves a speed-up over 30-fold for the longest benchmark sequences (≈400nt). Finally, different ExpLoc-P variants enable tailoring of the method to specific application scenarios. ExpaRNA-P and ExpLoc-P are distributed as part of the LocARNA package. The source code is freely available at http://www.bioinf.uni-freiburg.de/Software/ExpaRNA-P . CONCLUSIONS: ExpaRNA-P's novel ensemble-based sparsification reduces its complexity to quadratic time and space. Thereby, ExpaRNA-P significantly speeds up sequence-structure alignment while maintaining the alignment quality. Different ExpaRNA-P variants support a wide range of applications.

Bellman's GAP--a language and compiler for dynamic programming in sequence analysis.

MOTIVATION: Dynamic programming is ubiquitous in bioinformatics. Developing and implementing non-trivial dynamic programming algorithms is often error prone and tedious. Bellman's GAP is a new programming system, designed to ease the development of bioinformatics tools based on the dynamic programming technique. RESULTS: In Bellman's GAP, dynamic programming algorithms are described in a declarative style by tree grammars, evaluation algebras and products formed thereof. This bypasses the design of explicit dynamic programming recurrences and yields programs that are free of subscript errors, modular and easy to modify. The declarative modules are compiled into C++ code that is competitive to carefully hand-crafted implementations. This article introduces the Bellman's GAP system and its language, GAP-L. It then demonstrates the ease of development and the degree of re-use by creating variants of two common bioinformatics algorithms. Finally, it evaluates Bellman's GAP as an implementation platform of 'real-world' bioinformatics tools. AVAILABILITY: Bellman's GAP is available under GPL license from http://bibiserv.cebitec.uni-bielefeld.de/bellmansgap. This Web site includes a repository of re-usable modules for RNA folding based on thermodynamics.

CARNA--alignment of RNA structure ensembles.

Due to recent algorithmic progress, tools for the gold standard of comparative RNA analysis, namely Sankoff-style simultaneous alignment and folding, are now readily applicable. Such approaches, however, compare RNAs with respect to a simultaneously predicted, single, nested consensus structure. To make multiple alignment of RNAs available in cases, where this limitation of the standard approach is critical, we introduce a web server that provides a complete and convenient interface to the RNA structure alignment tool 'CARNA'. This tool uniquely supports RNAs with multiple conserved structures per RNA and aligns pseudoknots intrinsically; these features are highly desirable for aligning riboswitches, RNAs with conserved folding pathways, or pseudoknots. We represent structural input and output information as base pair probability dot plots; this provides large flexibility in the input, ranging from fixed structures to structure ensembles, and enables immediate visual analysis of the results. In contrast to conventional Sankoff-style approaches, 'CARNA' optimizes all structural similarities in the input simultaneously, for example across an entire RNA structure ensemble. Even compared with already costly Sankoff-style alignment, 'CARNA' solves an intrinsically much harder problem by applying advanced, constraint-based, algorithmic techniques. Although 'CARNA' is specialized to the alignment of RNAs with several conserved structures, its performance on RNAs in general is on par with state-of-the-art general-purpose RNA alignment tools, as we show in a Bralibase 2.1 benchmark. The web server is freely available at http://rna.informatik.uni-freiburg.de/CARNA.

Global or local? Predicting secondary structure and accessibility in mRNAs.

Determining the structural properties of mRNA is key to understanding vital post-transcriptional processes. As experimental data on mRNA structure are scarce, accurate structure prediction is required to characterize RNA regulatory mechanisms. Although various structure prediction approaches are available, it is often unclear which to choose and how to set their parameters. Furthermore, no standard measure to compare predictions of local structure exists. We assessed the performance of different methods using two types of data: transcriptome-wide enzymatic probing information and a large, curated set of cis-regulatory elements. To compare the approaches, we introduced structure accuracy, a measure that is applicable to both global and local methods. Our results showed that local folding was more accurate than the classic global approach. We investigated how the locality parameters, maximum base pair span and window size, influenced the prediction performance. A span of 150 provided a reasonable balance between maximizing the number of accurately predicted base pairs, while minimizing effects of incorrect long-range predictions. We characterized the error at artificial sequence ends, which we reduced by setting the window size sufficiently greater than the maximum span. Our method, LocalFold, diminished all border effects and produced the most robust performance.

Local Exact Pattern Matching for Non-Fixed RNA Structures.

Detecting local common sequence-structure regions of RNAs is a biologically important problem. Detecting such regions allows biologists to identify functionally relevant similarities between the inspected molecules. We developed dynamic programming algorithms for finding common structure-sequence patterns between two RNAs. The RNAs are given by their sequence and a set of potential base pairs with associated probabilities. In contrast to prior work on local pattern matching of RNAs, we support the breaking of arcs. This allows us to add flexibility over matching only fixed structures; potentially matching only a similar subset of specified base pairs. We present an O(n(3)) algorithm for local exact pattern matching between two nested RNAs, and an O(n(3) log n) algorithm for one nested RNA and one bounded-unlimited RNA. In addition, an algorithm for approximate pattern matching is introduced that for two given nested RNAs and a number k, finds the maximal local pattern matching score between the two RNAs with at most k mismatches in O(n(3)k(2)) time. Finally, we present an O(n(3)) algorithm for finding the most similar subforest between two nested RNAs.

Lifting prediction to alignment of RNA pseudoknots.

Prediction and alignment of RNA pseudoknot structures are NP-hard. Nevertheless, several efficient prediction algorithms by dynamic programming have been proposed for restricted classes of pseudoknots. We present a general scheme that yields an efficient alignment algorithm for arbitrary such classes. Moreover, we show that such an alignment algorithm benefits from the class restriction in the same way as the corresponding structure prediction algorithm does. We look at six of these classes in greater detail. The time and space complexity of the alignment algorithm is increased by only a linear factor over the respective prediction algorithm. For five of the classes, no efficient alignment algorithms were known. For the sixth, most general class, we improve the previously best complexity of O(n(5)m(5)) time to O(nm(6)), where n and m denote sequence lengths. Finally, we apply our fastest algorithm with O(nm(4)) time and O(nm(2)) space to comparative de-novo pseudoknot prediction.

Sparsification of RNA structure prediction including pseudoknots.

BACKGROUND: 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. RESULTS: 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. CONCLUSIONS: Our experimental results on the sparsified Reeder-Giegerich algorithm suggest a linear speedup over the unsparsified implementation.