MOTIVATION: Comparative modeling of RNA is known to be important for making accurate secondary structure predictions. RNA structure prediction tools such as PPfold or RNAalifold use an aligned set of sequences in predictions. Obtaining a multiple alignment from a set of sequences is quite a challenging problem itself, and the quality of the alignment can affect the quality of a prediction. By implementing RNA secondary structure prediction in a statistical alignment framework, and predicting structures from multiple alignment samples instead of a single fixed alignment, it may be possible to improve predictions. RESULTS: We have extended the program StatAlign to make use of RNA-specific features, which include RNA secondary structure prediction from multiple alignments using either a thermodynamic approach (RNAalifold) or a Stochastic Context-Free Grammars (SCFGs) approach (PPfold). We also provide the user with scores relating to the quality of a secondary structure prediction, such as information entropy values for the combined space of secondary structures and sampled alignments, and a reliability score that predicts the expected number of correctly predicted base pairs. Finally, we have created RNA secondary structure visualization plugins and automated the process of setting up Markov Chain Monte Carlo runs for RNA alignments in StatAlign. AVAILABILITY AND IMPLEMENTATION: The software is available from http://statalign.github.com/statalign/.

BACKGROUND: With the advancement of next-generation sequencing and transcriptomics technologies, regulatory effects involving RNA, in particular RNA structural changes are being detected. These results often rely on RNA secondary structure predictions. However, current approaches to RNA secondary structure modelling produce predictions with a high variance in predictive accuracy, and we have little quantifiable knowledge about the reasons for these variances. RESULTS: In this paper we explore a number of factors which can contribute to poor RNA secondary structure prediction quality. We establish a quantified relationship between alignment quality and loss of accuracy. Furthermore, we define two new measures to quantify uncertainty in alignment-based structure predictions. One of the measures improves on the "reliability score" reported by PPfold, and considers alignment uncertainty as well as base-pair probabilities. The other measure considers the information entropy for SCFGs over a space of input alignments. CONCLUSIONS: Our predictive accuracy improves on the PPfold reliability score. We can successfully characterize many of the underlying reasons for and variances in poor prediction. However, there is still variability unaccounted for, which we therefore suggest comes from the RNA secondary structure predictive model itself.

Comparative methods for RNA secondary structure prediction use evolutionary information from RNA alignments to increase prediction accuracy. The model is often described in terms of stochastic context-free grammars (SCFGs), which generate a probability distribution over secondary structures. It is, however, unclear how this probability distribution changes as a function of the input alignment. As prediction programs typically only return a single secondary structure, better characterisation of the underlying probability space of RNA secondary structures is of great interest. In this work, we show how to efficiently compute the information entropy of the probability distribution over RNA secondary structures produced for RNA alignments by a phylo-SCFG, and implement it for the PPfold model. We also discuss interpretations and applications of this quantity, including how it can clarify reasons for low prediction reliability scores. PPfold and its source code are available from http://birc.au.dk/software/ppfold/.

UNLABELLED: PPfold is a multi-threaded implementation of the Pfold algorithm for RNA secondary structure prediction. Here we present a new version of PPfold, which extends the evolutionary analysis with a flexible probabilistic model for incorporating auxiliary data, such as data from structure probing experiments. Our tests show that the accuracy of single-sequence secondary structure prediction using experimental data in PPfold 3.0 is comparable to RNAstructure. Furthermore, alignment structure prediction quality is improved even further by the addition of experimental data. PPfold 3.0 therefore has the potential of producing more accurate predictions than it was previously possible. AVAILABILITY AND IMPLEMENTATION: PPfold 3.0 is available as a platform-independent Java application and can be downloaded from http://birc.au.dk/software/ppfold.

BACKGROUND: The prediction of the structure of large RNAs remains a particular challenge in bioinformatics, due to the computational complexity and low levels of accuracy of state-of-the-art algorithms. The pfold model couples a stochastic context-free grammar to phylogenetic analysis for a high accuracy in predictions, but the time complexity of the algorithm and underflow errors have prevented its use for long alignments. Here we present PPfold, a multithreaded version of pfold, which is capable of predicting the structure of large RNA alignments accurately on practical timescales. RESULTS: We have distributed both the phylogenetic calculations and the inside-outside algorithm in PPfold, resulting in a significant reduction of runtime on multicore machines. We have addressed the floating-point underflow problems of pfold by implementing an extended-exponent datatype, enabling PPfold to be used for large-scale RNA structure predictions. We have also improved the user interface and portability: alongside standalone executable and Java source code of the program, PPfold is also available as a free plugin to the CLC Workbenches. We have evaluated the accuracy of PPfold using BRaliBase I tests, and demonstrated its practical use by predicting the secondary structure of an alignment of 24 complete HIV-1 genomes in 65 minutes on an 8-core machine and identifying several known structural elements in the prediction. CONCLUSIONS: PPfold is the first parallelized comparative RNA structure prediction algorithm to date. Based on the pfold model, PPfold is capable of fast, high-quality predictions of large RNA secondary structures, such as the genomes of RNA viruses or long genomic transcripts. The techniques used in the parallelization of this algorithm may be of general applicability to other bioinformatics algorithms.

A fundamental imaging problem in microstructural analysis of metals is the reconstruction of local crystallographic orientations from X-ray diffraction measurements. This work develops a fast, accurate, and robust method for the computation of the three-dimensional orientation distribution function for individual grains of the material in consideration. We study two iterative large-scale reconstruction algorithms, the algebraic reconstruction technique (ART) and conjugate gradients for least squares (CGLS), and demonstrate that right preconditioning is necessary in both algorithms to provide satisfactory reconstructions. Our right preconditioner is not a traditional one that accelerates convergence; its purpose is to modify the smoothness properties of the reconstruction. We also show that a new stopping criterion, based on the information available in the residual vector, provides a robust choice of the number of iterations for these preconditioned methods.