Mathias Möhl

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.

Time and space efficient RNA-RNA interaction prediction via sparse folding

In the past years, a large set of new regulatory ncRNAs have been identified, but the number of experimentally verified targets is considerably low Thus, computational target prediction methods are on high demand Whereas all previous approaches for predicting a general joint structure have a complexity of O(n6) running time and O(n4) space, a more time and space efficient interaction prediction that is able to handle complex joint structures is necessary for genome-wide target prediction problems In this paper we show how to reduce both the time and space complexity of the RNA-RNA interaction prediction problem as described by Alkan et al [1] via dynamic programming sparsification - which allows to discard large portions of DP tables without loosing optimality Applying sparsification techniques reduces the complexity of the original algorithm from O(n6) time and O(n4) space to O(n4ψ(n)) time and O(n2ψ(n)+n3) space for some function ψ(n), which turns out to have small values for the range of n that we encounter in practice Under the assumption that the polymer-zeta property holds for RNA-structures, we demonstrate that ψ(n)=O(n) on average, resulting in a linear time and space complexity improvement over the original algorithm We evaluate our sparsified algorithm for RNA-RNA interaction prediction by total free energy minimization, based on the energy model of Chitsaz et al.[2], on a set of known interactions Our results confirm the significant reduction of time and space requirements in practice.

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 five 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 four of the classes, no efficient alignment algorithms were known. For the fifth, 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.

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.

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 O(n6). 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 (≥ 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. Availability and implementation: SPARSE is freely available at http://www.bioinf.uni-freiburg.de/Software/SPARSE. Contact: backofen@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online.

Fixed Parameter Tractable Alignment of RNA Structures Including Arbitrary Pseudoknots

We present an algorithm for computing the edit distance of two RNA structures with arbitrary kinds of pseudoknots. A main benefit of the algorithm is that, despite the problem is NP-hard, the algorithmic complexity adapts to the complexity of the RNA structures. Due to fixed parameter tractability, we can guarantee polynomial run-time for a parameter which is small in practice. Our algorithm can be considered as a generalization of the algorithm of Jiang et al.[1] to arbitrary pseudoknots. In their absence, it gracefully degrades to the same polynomial algorithm. A prototypical implementation demonstrates the applicability of the method.

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

BackgroundIdentifying 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.ResultsThe 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.ConclusionsExpaRNA-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.

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.

Fast RNA Structure Alignment for Crossing Input Structures

The complexity of pairwise RNA structure alignment depends on the structural restrictions assumed for both the input structures and the computed consensus structure. For arbitrarily crossing input and consensus structures, the problem is NP-hard. For non-crossing consensus structures, Jiang et als algorithm [1] computes the alignment in O (n 2 m 2) time where n and m denote the lengths of the two input sequences. If also the input structures are non-crossing, the problem corresponds to tree editing which can be solved in

A propagator for maximum weight string alignment with arbitrary pairwise dependencies

O(m^2n(1+\log\frac{n}{m}))