Empirical comparison of cross-platform normalization methods for gene expression data

Background

The prediction of secondary structure, i.e. the set of canonical base pairs between nucleotides, is a first step in developing an understanding of the function of an RNA sequence. The most accurate computational methods predict conserved structures for a set of homologous RNA sequences. These methods usually suffer from high computational complexity. In this paper, TurboFold, a novel and efficient method for secondary structure prediction for multiple RNA sequences, is presented.

Results

TurboFold takes, as input, a set of homologous RNA sequences and outputs estimates of the base pairing probabilities for each sequence. The base pairing probabilities for a sequence are estimated by combining intrinsic information, derived from the sequence itself via the nearest neighbor thermodynamic model, with extrinsic information, derived from the other sequences in the input set. For a given sequence, the extrinsic information is computed by using pairwise-sequence-alignment-based probabilities for co-incidence with each of the other sequences, along with estimated base pairing probabilities, from the previous iteration, for the other sequences. The extrinsic information is introduced as free energy modifications for base pairing in a partition function computation based on the nearest neighbor thermodynamic model. This process yields updated estimates of base pairing probability. The updated base pairing probabilities in turn are used to recompute extrinsic information, resulting in the overall iterative estimation procedure that defines TurboFold. TurboFold is benchmarked on a number of ncRNA datasets and compared against alternative secondary structure prediction methods. The iterative procedure in TurboFold is shown to improve estimates of base pairing probability with each iteration, though only small gains are obtained beyond three iterations. Secondary structures composed of base pairs with estimated probabilities higher than a significance threshold are shown to be more accurate for TurboFold than for alternative methods that estimate base pairing probabilities. TurboFold-MEA, which uses base pairing probabilities from TurboFold in a maximum expected accuracy algorithm for secondary structure prediction, has accuracy comparable to the best performing secondary structure prediction methods. The computational and memory requirements for TurboFold are modest and, in terms of sequence length and number of sequences, scale much more favorably than joint alignment and folding algorithms.

Conclusions

TurboFold is an iterative probabilistic method for predicting secondary structures for multiple RNA sequences that efficiently and accurately combines the information from the comparative analysis between sequences with the thermodynamic folding model. Unlike most other multi-sequence structure prediction methods, TurboFold does not enforce strict commonality of structures and is therefore useful for predicting structures for homologous sequences that have diverged significantly. TurboFold can be downloaded as part of the RNAstructure package at http://rna.urmc.rochester.edu.     

Automatic detection of conserved RNA structure elements in complete RNA virus genomes.

We propose a new method for detecting conserved RNA secondary structures in a family of related RNA sequences. Our method is based on a combination of thermodynamic structure prediction and phylogenetic comparison. In contrast to purely phylogenetic methods, our algorithm can be used for small data sets of approximately 10 sequences, efficiently exploiting the information contained in the sequence variability. The procedure constructs a prediction only for those parts of sequences that are consistent with a single conserved structure. Our implementation produces reasonable consensus structures without user interference. As an example we have analysed the complete HIV-1 and hepatitis C virus (HCV) genomes as well as the small segment of hantavirus. Our method confirms the known structures in HIV-1 and predicts previously unknown conserved RNA secondary structures in HCV.     

A method for rapid similarity analysis of RNA secondary structures

Background  

Owing to the rapid expansion of RNA structure databases in recent years, efficient methods for structure comparison are in demand for function prediction and evolutionary analysis. Usually, the similarity of RNA secondary structures is evaluated based on tree models and dynamic programming algorithms. We present here a new method for the similarity analysis of RNA secondary structures.     

A comparative method for finding and folding RNA secondary structures within protein-coding regions

Existing computational methods for RNA secondary-structure prediction tacitly assume RNA to only encode functional RNA structures. However, experimental studies have revealed that some RNA sequences, e.g. compact viral genomes, can simultaneously encode functional RNA structures as well as proteins, and evidence is accumulating that this phenomenon may also be found in Eukaryotes. We here present the first comparative method, called RNA-DECODER, which explicitly takes the known protein-coding context of an RNA-sequence alignment into account in order to predict evolutionarily conserved secondary-structure elements, which may span both coding and non-coding regions. RNA-DECODER employs a stochastic context-free grammar together with a set of carefully devised phylogenetic substitution-models, which can disentangle and evaluate the different kinds of overlapping evolutionary constraints which arise. We show that RNA-DECODER's parameters can be automatically trained to successfully fold known secondary structures within the HCV genome. We scan the genomes of HCV and polio virus for conserved secondary-structure elements, and analyze performance as a function of available evolutionary information. On known secondary structures, RNA-DECODER shows a sensitivity similar to the programs MFOLD, PFOLD and RNAALIFOLD. When scanning the entire genomes of HCV and polio virus for structure elements, RNA-DECODER's results indicate a markedly higher specificity than MFOLD, PFOLD and RNAALIFOLD.     

Pfold: RNA secondary structure prediction using stochastic context-free grammars

RNA secondary structures are important in many biological processes and efficient structure prediction can give vital directions for experimental investigations. Many available programs for RNA secondary structure prediction only use a single sequence at a time. This may be sufficient in some applications, but often it is possible to obtain related RNA sequences with conserved secondary structure. These should be included in structural analyses to give improved results. This work presents a practical way of predicting RNA secondary structure that is especially useful when related sequences can be obtained. The method improves a previous algorithm based on an explicit evolutionary model and a probabilistic model of structures. Predictions can be done on a web server at http://www.daimi.au.dk/~compbio/pfold.     

Enhancement of accuracy and efficiency for RNA secondary structure prediction by sequence segmentation and MapReduce

Background

Ribonucleic acid (RNA) molecules play important roles in many biological processes including gene expression and regulation. Their secondary structures are crucial for the RNA functionality, and the prediction of the secondary structures is widely studied. Our previous research shows that cutting long sequences into shorter chunks, predicting secondary structures of the chunks independently using thermodynamic methods, and reconstructing the entire secondary structure from the predicted chunk structures can yield better accuracy than predicting the secondary structure using the RNA sequence as a whole. The chunking, prediction, and reconstruction processes can use different methods and parameters, some of which produce more accurate predictions than others. In this paper, we study the prediction accuracy and efficiency of three different chunking methods using seven popular secondary structure prediction programs that apply to two datasets of RNA with known secondary structures, which include both pseudoknotted and non-pseudoknotted sequences, as well as a family of viral genome RNAs whose structures have not been predicted before. Our modularized MapReduce framework based on Hadoop allows us to study the problem in a parallel and robust environment.

Results

On average, the maximum accuracy retention values are larger than one for our chunking methods and the seven prediction programs over 50 non-pseudoknotted sequences, meaning that the secondary structure predicted using chunking is more similar to the real structure than the secondary structure predicted by using the whole sequence. We observe similar results for the 23 pseudoknotted sequences, except for the NUPACK program using the centered chunking method. The performance analysis for 14 long RNA sequences from the Nodaviridae virus family outlines how the coarse-grained mapping of chunking and predictions in the MapReduce framework exhibits shorter turnaround times for short RNA sequences. However, as the lengths of the RNA sequences increase, the fine-grained mapping can surpass the coarse-grained mapping in performance.

Conclusions

By using our MapReduce framework together with statistical analysis on the accuracy retention results, we observe how the inversion-based chunking methods can outperform predictions using the whole sequence. Our chunk-based approach also enables us to predict secondary structures for very long RNA sequences, which is not feasible with traditional methods alone.

     

Comparison of P-RnaPredict and mfold--algorithms for RNA secondary structure prediction

MOTIVATION: Ribonucleic acid is vital in numerous stages of protein synthesis; it also possesses important functional and structural roles within the cell. The function of an RNA molecule within a particular organic system is principally determined by its structure. The current physical methods available for structure determination are time-consuming and expensive. Hence, computational methods for structure prediction are sought after. The energies involved by the formation of secondary structure elements are significantly greater than those of tertiary elements. Therefore, RNA structure prediction focuses on secondary structure. RESULTS: We present P-RnaPredict, a parallel evolutionary algorithm for RNA secondary structure prediction. The speedup provided by parallelization is investigated with five sequences, and a dramatic improvement in speedup is demonstrated, especially with longer sequences. An evaluation of the performance of P-RnaPredict in terms of prediction accuracy is made through comparison with 10 individual known structures from 3 RNA classes (5S rRNA, Group I intron 16S rRNA and 16S rRNA) and the mfold dynamic programming algorithm. P-RnaPredict is able to predict structures with higher true positive base pair counts and lower false positives than mfold on certain sequences. AVAILABILITY: P-RnaPredict is available for non-commercial usage. Interested parties should contact Kay C. Wiese (wiese@cs.sfu.ca).     

Transient RNA structure features are evolutionarily conserved and can be computationally predicted

Functional RNA structures tend to be conserved during evolution. This finding is, for example, exploited by comparative methods for RNA secondary structure prediction that currently provide the state-of-art in terms of prediction accuracy. We here provide strong evidence that homologous RNA genes not only fold into similar final RNA structures, but that their folding pathways also share common transient structural features that have been evolutionarily conserved. For this, we compile and investigate a non-redundant data set of 32 sequences with known transient and final RNA secondary structures and devise a dedicated computational analysis pipeline.     

Consensus folding of unaligned RNA sequences revisited.

As one of the earliest problems in computational biology, RNA secondary structure prediction (sometimes referred to as "RNA folding") problem has attracted attention again, thanks to the recent discoveries of many novel non-coding RNA molecules. The two common approaches to this problem are de novo prediction of RNA secondary structure based on energy minimization and the consensus folding approach (computing the common secondary structure for a set of unaligned RNA sequences). Consensus folding algorithms work well when the correct seed alignment is part of the input to the problem. However, seed alignment itself is a challenging problem for diverged RNA families. In this paper, we propose a novel framework to predict the common secondary structure for unaligned RNA sequences. By matching putative stacks in RNA sequences, we make use of both primary sequence information and thermodynamic stability for prediction at the same time. We show that our method can predict the correct common RNA secondary structures even when we are given only a limited number of unaligned RNA sequences, and it outperforms current algorithms in sensitivity and accuracy.     

RNA Sampler: a new sampling based algorithm for common RNA secondary structure prediction and structural alignment

MOTIVATION: Non-coding RNA genes and RNA structural regulatory motifs play important roles in gene regulation and other cellular functions. They are often characterized by specific secondary structures that are critical to their functions and are often conserved in phylogenetically or functionally related sequences. Predicting common RNA secondary structures in multiple unaligned sequences remains a challenge in bioinformatics research. Methods and RESULTS: We present a new sampling based algorithm to predict common RNA secondary structures in multiple unaligned sequences. Our algorithm finds the common structure between two sequences by probabilistically sampling aligned stems based on stem conservation calculated from intrasequence base pairing probabilities and intersequence base alignment probabilities. It iteratively updates these probabilities based on sampled structures and subsequently recalculates stem conservation using the updated probabilities. The iterative process terminates upon convergence of the sampled structures. We extend the algorithm to multiple sequences by a consistency-based method, which iteratively incorporates and reinforces consistent structure information from pairwise comparisons into consensus structures. The algorithm has no limitation on predicting pseudoknots. In extensive testing on real sequence data, our algorithm outperformed other leading RNA structure prediction methods in both sensitivity and specificity with a reasonably fast speed. It also generated better structural alignments than other programs in sequences of a wide range of identities, which more accurately represent the RNA secondary structure conservations. AVAILABILITY: The algorithm is implemented in a C program, RNA Sampler, which is available at http://ural.wustl.edu/software.html     

Integrated multi-level quality control for proteomic profiling studies using mass spectrometry

Background

Evolutionary conservation of RNA secondary structure is a typical feature of many functional non-coding RNAs. Since almost all of the available methods used for prediction and annotation of non-coding RNA genes rely on this evolutionary signature, accurate measures for structural conservation are essential.

Results

We systematically assessed the ability of various measures to detect conserved RNA structures in multiple sequence alignments. We tested three existing and eight novel strategies that are based on metrics of folding energies, metrics of single optimal structure predictions, and metrics of structure ensembles. We find that the folding energy based SCI score used in the RNAz program and a simple base-pair distance metric are by far the most accurate. The use of more complex metrics like for example tree editing does not improve performance. A variant of the SCI performed particularly well on highly conserved alignments and is thus a viable alternative when only little evolutionary information is available. Surprisingly, ensemble based methods that, in principle, could benefit from the additional information contained in sub-optimal structures, perform particularly poorly. As a general trend, we observed that methods that include a consensus structure prediction outperformed equivalent methods that only consider pairwise comparisons.

Conclusion

Structural conservation can be measured accurately with relatively simple and intuitive metrics. They have the potential to form the basis of future RNA gene finders, that face new challenges like finding lineage specific structures or detecting mis-aligned sequences.     

Using Evolutionary Trees in Protein Secondary Structure Prediction and Other Comparative Sequence Analyses

Previously proposed methods for protein secondary structure prediction from multiple sequence alignments do not efficiently extract the evolutionary information that these alignments contain. The predictions of these methods are less accurate than they could be, because of their failure to consider explicitly the phylogenetic tree that relates aligned protein sequences. As an alternative, we present a hidden Markov model approach to secondary structure prediction that more fully uses the evolutionary information contained in protein sequence alignments. A representative example is presented, and three experiments are performed that illustrate how the appropriate representation of evolutionary relatedness can improve inferences. We explain why similar improvement can be expected in other secondary structure prediction methods and indeed any comparative sequence analysis method.     

Natural selection is not required to explain universal compositional patterns in rRNA secondary structure categories

We have encountered an unexpected property of rRNA secondary structures that may generalize to all RNAs. Analysis of 8892 ribosomal RNA sequences and structures from a wide range of species revealed unexpected universal compositional trends. First, different categories of rRNA secondary structure (stems, loops, bulges, and junctions) have distinct, characteristic base compositions. Second, the observed patterns of variation are similar among sequences from large and small rRNA subunits and all domains of life, despite extensive evolutionary divergence. Surprisingly, these differences do not seem to be related to selection for different compositions in different structural categories, but rather relate to the overall composition of the molecule: Randomized RNAs with no evolutionary history show the same structure-dependent compositional biases as rRNAs. These compositional trends may improve the accuracy of RNA secondary structure prediction, because they allow us to compare predicted structures against known compositional preferences. They also suggest caution in interpreting differences in the rate of change of the GC content in different parts of the molecule as evidence of differential selection.     

A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences

MOTIVATION: RNA structure motifs contained in mRNAs have been found to play important roles in regulating gene expression. However, identification of novel RNA regulatory motifs using computational methods has not been widely explored. Effective tools for predicting novel RNA regulatory motifs based on genomic sequences are needed. RESULTS: We present a new method for predicting common RNA secondary structure motifs in a set of functionally or evolutionarily related RNA sequences. This method is based on comparison of stems (palindromic helices) between sequences and is implemented by applying graph-theoretical approaches. It first finds all possible stable stems in each sequence and compares stems pairwise between sequences by some defined features to find stems conserved across any two sequences. Then by applying a maximum clique finding algorithm, it finds all significant stems conserved across at least k sequences. Finally, it assembles in topological order all possible compatible conserved stems shared by at least k sequences and reports a number of the best assembled stem sets as the best candidate common structure motifs. This method does not require prior structural alignment of the sequences and is able to detect pseudoknot structures. We have tested this approach on some RNA sequences with known secondary structures, in which it is capable of detecting the real structures completely or partially correctly and outperforms other existing programs for similar purposes. AVAILABILITY: The algorithm has been implemented in C++ in a program called comRNA, which is available at http://ural.wustl.edu/softwares.html     

Prediction of RNA secondary structure by free energy minimization

RNA secondary structure is often predicted from sequence by free energy minimization. Over the past two years, advances have been made in the estimation of folding free energy change, the mapping of secondary structure and the implementation of computer programs for structure prediction. The trends in computer program development are: efficient use of experimental mapping of structures to constrain structure prediction; use of statistical mechanics to improve the fidelity of structure prediction; inclusion of pseudoknots in secondary structure prediction; and use of two or more homologous sequences to find a common structure.     

Evaluation of several lightweight stochastic context-free grammars for RNA secondary structure prediction

Background

RNA secondary structure prediction methods based on probabilistic modeling can be developed using stochastic context-free grammars (SCFGs). Such methods can readily combine different sources of information that can be expressed probabilistically, such as an evolutionary model of comparative RNA sequence analysis and a biophysical model of structure plausibility. However, the number of free parameters in an integrated model for consensus RNA structure prediction can become untenable if the underlying SCFG design is too complex. Thus a key question is, what small, simple SCFG designs perform best for RNA secondary structure prediction?

Results

Nine different small SCFGs were implemented to explore the tradeoffs between model complexity and prediction accuracy. Each model was tested for single sequence structure prediction accuracy on a benchmark set of RNA secondary structures.

Conclusions

Four SCFG designs had prediction accuracies near the performance of current energy minimization programs. One of these designs, introduced by Knudsen and Hein in their PFOLD algorithm, has only 21 free parameters and is significantly simpler than the others.

     

Improving the prediction of RNA secondary structure by detecting and assessing conserved stems

The prediction of RNA secondary structure can be facilitated by incorporating with comparative analysis of homologous sequences. However, most of existing comparative methods are vulnerable to alignment errors and thus are of low accuracy in practical application. Here we improve the prediction of RNA secondary structure by detecting and assessing conserved stems shared by all sequences in the alignment. Our method can be summarized by: 1) we detect possible stems in single RNA sequence using the so-called position matrix with which some possibly paired positions can be uncovered; 2) we detect conserved stems across multiple RNA sequences by multiplying the position matrices; 3) we assess the conserved stems using the Signal-to-Noise; 4) we compute the optimized secondary structure by incorporating the so-called reliable conserved stems with predictions by RNAalifold program. We tested our method on data sets of RNA alignments with known secondary structures. The accuracy, measured as sensitivity and specificity, of our method is greater than predictions by RNAalifold.     

Compact and ordered collapse of randomly generated RNA sequences

As the raw material for evolution, arbitrary RNA sequences represent the baseline for RNA structure formation and a standard to which evolved structures can be compared. Here, we set out to probe, using physical and chemical methods, the structural properties of RNAs having randomly generated oligonucleotide sequences that were of sufficient length and information content to encode complex, functional folds, yet were unbiased by either genealogical or functional constraints. Typically, these unevolved, nonfunctional RNAs had sequence-specific secondary structure configurations and compact magnesium-dependent conformational states comparable to those of evolved RNA isolates. But unlike evolved sequences, arbitrary sequences were prone to having multiple competing conformations. Thus, for RNAs the size of small ribozymes, natural selection seems necessary to achieve uniquely folding sequences, but not to account for the well-ordered secondary structures and overall compactness observed in nature.     

Evolutionary model of protein secondary structure capable of revealing new biological relationships

Ancestral sequence reconstruction has had recent success in decoding the origins and the determinants of complex protein functions. However, phylogenetic analyses of remote homologues must handle extreme amino acid sequence diversity resulting from extended periods of evolutionary change. We exploited the wealth of protein structures to develop an evolutionary model based on protein secondary structure. The approach follows the differences between discrete secondary structure states observed in modern proteins and those hypothesized in their immediate ancestors. We implemented maximum likelihood-based phylogenetic inference to reconstruct ancestral secondary structure. The predictive accuracy from the use of the evolutionary model surpasses that of comparative modeling and sequence-based prediction; the reconstruction extracts information not available from modern structures or the ancestral sequences alone. Based on a phylogenetic analysis of a sequence-diverse protein family, we showed that the model can highlight relationships that are evolutionarily rooted in structure and not evident in amino acid-based analysis.