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

Phylogenetic and Chemical Probing Information as Soft Constraints in RNA Secondary Structure Prediction

Extrinsic, experimental information can be incorporated into thermodynamics-based RNA folding algorithms in the form of pseudo-energies. Evolutionary conservation of RNA secondary structure elements is detectable in alignments of phylogenetically related sequences and provides evidence for the presence of certain base pairs that can also be converted into pseudo-energy contributions. We show that the centroid base pairs computed from a consensus folding model such as RNAalifold result in a substantial improvement of the prediction accuracy for single sequences. Evidence for specific base pairs turns out to be more informative than a position-wise profile for the conservation of the pairing status. A comparison with chemical probing data, furthermore, strongly suggests that phylogenetic base pairing data are more informative than position-specific data on (un)pairedness as obtained from chemical probing experiments. In this context we demonstrate, in addition, that the conversion of signal from probing data into pseudo-energies is possible using thermodynamic structure predictions as a reference instead of known RNA structures.

Recent trends in RNA informatics: a review of machine learning and deep learning for RNA secondary structure prediction and RNA drug discovery

Computational analysis of RNA sequences constitutes a crucial step in the field of RNA biology. As in other domains of the life sciences, the incorporation of artificial intelligence and machine learning techniques into RNA sequence analysis has gained significant traction in recent years. Historically, thermodynamics-based methods were widely employed for the prediction of RNA secondary structures; however, machine learning-based approaches have demonstrated remarkable advancements in recent years, enabling more accurate predictions. Consequently, the precision of sequence analysis pertaining to RNA secondary structures, such as RNA-protein interactions, has also been enhanced, making a substantial contribution to the field of RNA biology. Additionally, artificial intelligence and machine learning are also introducing technical innovations in the analysis of RNA-small molecule interactions for RNA-targeted drug discovery and in the design of RNA aptamers, where RNA serves as its own ligand. This review will highlight recent trends in the prediction of RNA secondary structure, RNA aptamers and RNA drug discovery using machine learning, deep learning and related technologies, and will also discuss potential future avenues in the field of RNA informatics.

Thirteen dubious ways to detect conserved structural RNAs

Covariation induced by compensatory base substitutions in RNA alignments is a great way to deduce conserved RNA structure, in principle. In practice, success depends on many factors, importantly the quality and depth of the alignment and the choice of covariation statistic. Measuring covariation between pairs of aligned positions is easy. However, using covariation to infer evolutionarily conserved RNA structure is complicated by other extraneous sources of covariation such as that resulting from homologous sequences having evolved from a common ancestor. In order to provide evidence of evolutionarily conserved RNA structure, a method to distinguish covariation due to sources other than RNA structure is necessary. Moreover, there are several sorts of artifactually generated covariation signals that can further confound the analysis. Additionally, some covariation signal is difficult to detect due to incomplete comparative data. Here, we investigate and critically discuss the practice of inferring conserved RNA structure by comparative sequence analysis. We provide new methods on how to approach and decide which of the numerous long non-coding RNAs (lncRNAs) have biologically relevant structures.

Strategies for targeting RNA with small molecule drugs

INTRODUCTION

Historically, therapeutic treatment of disease has been restricted to targeting proteins. Of the approximately 20,000 translated human proteins, approximately 1600 are associated with diseases. Strikingly, less than 15% of disease-associated proteins are predicted or known to be 'druggable.' While the concept and narrative of protein druggability continue to evolve with the development of novel technological and pharmacological advances, most of the human proteome remains undrugged. Recent genomic studies indicate that less than 2% of the human genome encodes for proteins, and while as much as 75% of the genome is transcribed, RNA has largely been ignored as a druggable target for therapeutic interventions.

AREAS COVERED

This review delineates the theory and techniques involved in the development of small molecule inhibitors of RNAs from brute force, high-throughput screening technologies to de novo molecular design using computational machine and deep learning. We will also highlight the potential pitfalls and limitations of targeting RNA with small molecules.

EXPERT OPINION

Although significant advances have recently been made in developing systems to identify small molecule inhibitors of RNAs, many challenges remain. Focusing on RNA structure and ligand binding sites may help bring drugging RNA in line with traditional protein drug targeting.

Antisense oligonucleotide is a promising intervention for liver diseases

As the body's critical metabolic organ, the liver plays an essential role in maintaining proper body homeostasis. However, as people's living standards have improved and the number of unhealthy lifestyles has increased, the liver has become overburdened. These have made liver disease one of the leading causes of death worldwide. Under the influence of adverse factors, liver disease progresses from simple steatosis to hepatitis, to liver fibrosis, and finally to cirrhosis and cancer, followed by increased mortality. Until now, there has been a lack of accepted effective treatments for liver disease. Based on current research, antisense oligonucleotide (ASO), as an alternative intervention for liver diseases, is expected to be an effective treatment due to its high efficiency, low toxicity, low dosage, strong specificity, and additional positive characteristics. In this review, we will first introduce the design, modification, delivery, and the mechanisms of ASO, and then summarize the application of ASO in liver disease treatment, including in non-alcoholic fatty liver disease (NAFLD), hepatitis, liver fibrosis, and liver cancer. Finally, we discuss challenges and perspectives on the transfer of ASO drugs into clinical use. This review provides a current and comprehensive understanding of the integrative and systematic functions of ASO for its use in liver disease.

In vivo single-molecule analysis reveals COOLAIR RNA structural diversity

Cellular RNAs are heterogeneous with respect to their alternative processing and secondary structures, but the functional importance of this complexity is still poorly understood. A set of alternatively processed antisense non-coding transcripts, which are collectively called COOLAIR, are generated at the Arabidopsis floral-repressor locus FLOWERING LOCUS C (FLC)1. Different isoforms of COOLAIR influence FLC transcriptional output in warm and cold conditions2-7. Here, to further investigate the function of COOLAIR, we developed an RNA structure-profiling method to determine the in vivo structure of single RNA molecules rather than the RNA population average. This revealed that individual isoforms of the COOLAIR transcript adopt multiple structures with different conformational dynamics. The major distally polyadenylated COOLAIR isoform in warm conditions adopts three predominant structural conformations, the proportions and conformations of which change after cold exposure. An alternatively spliced, strongly cold-upregulated distal COOLAIR isoform6 shows high structural diversity, in contrast to proximally polyadenylated COOLAIR. A hyper-variable COOLAIR structural element was identified that was complementary to the FLC transcription start site. Mutations altering the structure of this region changed FLC expression and flowering time, consistent with an important regulatory role of the COOLAIR structure in FLC transcription. Our work demonstrates that isoforms of non-coding RNA transcripts adopt multiple distinct and functionally relevant structural conformations, which change in abundance and shape in response to external conditions.

KnotAli: informed energy minimization through the use of evolutionary information

BACKGROUND

Improving the prediction of structures, especially those containing pseudoknots (structures with crossing base pairs) is an ongoing challenge. Homology-based methods utilize structural similarities within a family to predict the structure. However, their prediction is limited to the consensus structure, and by the quality of the alignment. Minimum free energy (MFE) based methods, on the other hand, do not rely on familial information and can predict structures of novel RNA molecules. Their prediction normally suffers from inaccuracies due to their underlying energy parameters.

RESULTS

We present a new method for prediction of RNA pseudoknotted secondary structures that combines the strengths of MFE prediction and alignment-based methods. KnotAli takes a multiple RNA sequence alignment as input and uses covariation and thermodynamic energy minimization to predict possibly pseudoknotted secondary structures for each individual sequence in the alignment. We compared KnotAli's performance to that of three other alignment-based programs, two that can handle pseudoknotted structures and one control, on a large data set of 3034 RNA sequences with varying lengths and levels of sequence conservation from 10 families with pseudoknotted and pseudoknot-free reference structures. We produced sequence alignments for each family using two well-known sequence aligners (MUSCLE and MAFFT).

CONCLUSIONS

We found KnotAli's performance to be superior in 6 of the 10 families for MUSCLE and 7 of the 10 for MAFFT. While both KnotAli and Cacofold use background noise correction strategies, we found KnotAli's predictions to be less dependent on the alignment quality. KnotAli can be found online at the Zenodo image: https://doi.org/10.5281/zenodo.5794719.

Efficient Generation of RNA Secondary Structure Prediction Algorithm Under PAR Framework

Prediction of RNA secondary structure is an important part of bioinformatics genomics research. Mastering RNA secondary structure can help us to better analyze protein synthesis, cell differentiation, metabolism, and genetic processes and thus reveal the genetic laws of organisms. Comparative sequence analysis, support vector machine, centroid method, and other algorithms in RNA secondary structure prediction algorithms often use dynamic programming algorithm to predict RNA secondary structure because of their huge time and space consumption and complex data structure. In this article, the domain of RNA secondary structure prediction algorithm based on dynamic programming (DP-SSP) is analyzed in depth, and the domain features are modeled. According to the generative programming method, the DP-SSP algorithm components are interactively designed. With the support of PAR platform, the DP-SSP algorithm component library is formally realized. Finally, the concrete algorithm is generated through component assembly, which improves the efficiency and reliability of algorithm development.

Review of machine learning methods for RNA secondary structure prediction

Secondary structure plays an important role in determining the function of noncoding RNAs. Hence, identifying RNA secondary structures is of great value to research. Computational prediction is a mainstream approach for predicting RNA secondary structure. Unfortunately, even though new methods have been proposed over the past 40 years, the performance of computational prediction methods has stagnated in the last decade. Recently, with the increasing availability of RNA structure data, new methods based on machine learning (ML) technologies, especially deep learning, have alleviated the issue. In this review, we provide a comprehensive overview of RNA secondary structure prediction methods based on ML technologies and a tabularized summary of the most important methods in this field. The current pending challenges in the field of RNA secondary structure prediction and future trends are also discussed.

Searching for universal model of amyloid signaling motifs using probabilistic context-free grammars

Background

Amyloid signaling motifs are a class of protein motifs which share basic structural and functional features despite the lack of clear sequence homology. They are hard to detect in large sequence databases either with the alignment-based profile methods (due to short length and diversity) or with generic amyloid- and prion-finding tools (due to insufficient discriminative power). We propose to address the challenge with a machine learning grammatical model capable of generalizing over diverse collections of unaligned yet related motifs.

Results

First, we introduce and test improvements to our probabilistic context-free grammar framework for protein sequences that allow for inferring more sophisticated models achieving high sensitivity at low false positive rates. Then, we infer universal grammars for a collection of recently identified bacterial amyloid signaling motifs and demonstrate that the method is capable of generalizing by successfully searching for related motifs in fungi. The results are compared to available alternative methods. Finally, we conduct spectroscopy and staining analyses of selected peptides to verify their structural and functional relationship.

Conclusions

While the profile HMMs remain the method of choice for modeling homologous sets of sequences, PCFGs seem more suitable for building meta-family descriptors and extrapolating beyond the seed sample.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04139-y.

Evolutionary conservation of RNA sequence and structure

An RNA structure prediction from a single‐sequence RNA folding program is not evidence for an RNA whose structure is important for function. Random sequences have plausible and complex predicted structures not easily distinguishable from those of structural RNAs. How to tell when an RNA has a conserved structure is a question that requires looking at the evolutionary signature left by the conserved RNA. This question is important not just for long noncoding RNAs which usually lack an identified function, but also for RNA binding protein motifs which can be single stranded RNAs or structures. Here we review recent advances using sequence and structural analysis to determine when RNA structure is conserved or not. Although covariation measures assess structural RNA conservation, one must distinguish covariation due to RNA structure from covariation due to independent phylogenetic substitutions. We review a statistical test to measure false positives expected under the null hypothesis of phylogenetic covariation alone (specificity). We also review a complementary test that measures power, that is, expected covariation derived from sequence variation alone (sensitivity). Power in the absence of covariation signals the absence of a conserved RNA structure. We analyze artifacts that falsely identify conserved RNA structure such as the misuse of programs that do not assess significance, the use of inappropriate statistics confounded by signals other than covariation, or misalignments that induce spurious covariation. Among artifacts that obscure the signal of a conserved RNA structure, we discuss the inclusion of pseudogenes in alignments which increase power but destroy covariation.

This article is categorized under:

RNA Structure and Dynamics > RNA Structure, Dynamics and Chemistry

RNA Evolution and Genomics > Computational Analyses of RNA

RNA Evolution and Genomics > RNA and Ribonucleoprotein Evolution

Deep Learning Method for RNA Secondary Structure Prediction with Pseudoknots Based on Large-Scale Data

Traditional machine learning methods are widely used in the field of RNA secondary structure prediction and have achieved good results. However, with the emergence of large-scale data, deep learning methods have more advantages than traditional machine learning methods. As the number of network layers increases in deep learning, there will often be problems such as increased parameters and overfitting. We used two deep learning models, GoogLeNet and TCN, to predict RNA secondary results. And from the perspective of the depth and width of the network, improvements are made based on the neural network model, which can effectively improve the computational efficiency while extracting more feature information. We process the existing real RNA data through experiments, use deep learning models to extract useful features from a large amount of RNA sequence data and structure data, and then predict the extracted features to obtain each base’s pairing probability. The characteristics of RNA secondary structure and dynamic programming methods are used to process the base prediction results, and the structure with the largest sum of the probability of each base pairing is obtained, and this structure will be used as the optimal RNA secondary structure. We, respectively, evaluated GoogLeNet and TCN models based on 5sRNA, tRNA data, and tmRNA data, and compared them with other standard prediction algorithms. The sensitivity and specificity of the GoogLeNet model on the 5sRNA and tRNA data sets are about 16% higher than the best prediction results in other algorithms. The sensitivity and specificity of the GoogLeNet model on the tmRNA dataset are about 9% higher than the best prediction results in other algorithms. As deep learning algorithms’ performance is related to the size of the data set, as the scale of RNA data continues to expand, the prediction accuracy of deep learning methods for RNA secondary structure will continue to improve.

RNA secondary structure prediction using deep learning with thermodynamic integration

Accurate predictions of RNA secondary structures can help uncover the roles of functional non-coding RNAs. Although machine learning-based models have achieved high performance in terms of prediction accuracy, overfitting is a common risk for such highly parameterized models. Here we show that overfitting can be minimized when RNA folding scores learnt using a deep neural network are integrated together with Turner’s nearest-neighbor free energy parameters. Training the model with thermodynamic regularization ensures that folding scores and the calculated free energy are as close as possible. In computational experiments designed for newly discovered non-coding RNAs, our algorithm (MXfold2) achieves the most robust and accurate predictions of RNA secondary structures without sacrificing computational efficiency compared to several other algorithms. The results suggest that integrating thermodynamic information could help improve the robustness of deep learning-based predictions of RNA secondary structure.

Accurately predicting the secondary structure of non-coding RNAs can help unravel their function. Here the authors propose a method integrating thermodynamic information and deep learning to improve the robustness of RNA secondary structure prediction compared to several existing algorithms.

Fast and accurate structure probability estimation for simultaneous alignment and folding of RNAs with Markov chains

MOTIVATION

Simultaneous alignment and folding (SA&F) of RNAs is the indispensable gold standard for inferring the structure of non-coding RNAs and their general analysis. The original algorithm, proposed by Sankoff, solves the theoretical problem exactly with a complexity of [Formula: see text] in the full energy model. Over the last two decades, several variants and improvements of the Sankoff algorithm have been proposed to reduce its extreme complexity by proposing simplified energy models or imposing restrictions on the predicted alignments.

RESULTS

Here, we introduce a novel variant of Sankoff's algorithm that reconciles the simplifications of PMcomp, namely moving from the full energy model to a simpler base pair-based model, with the accuracy of the loop-based full energy model. Instead of estimating pseudo-energies from unconditional base pair probabilities, our model calculates energies from conditional base pair probabilities that allow to accurately capture structure probabilities, which obey a conditional dependency. This model gives rise to the fast and highly accurate novel algorithm Pankov (Probabilistic Sankoff-like simultaneous alignment and folding of RNAs inspired by Markov chains).

CONCLUSIONS

Pankov benefits from the speed-up of excluding unreliable base-pairing without compromising the loop-based free energy model of the Sankoff's algorithm. We show that Pankov outperforms its predecessors LocARNA and SPARSE in folding quality and is faster than LocARNA.

RNA structure prediction using positive and negative evolutionary information

Knowing the structure of conserved structural RNAs is important to elucidate their function and mechanism of action. However, predicting a conserved RNA structure remains unreliable, even when using a combination of thermodynamic stability and evolutionary covariation information. Here we present a method to predict a conserved RNA structure that combines the following three features. First, it uses significant covariation due to RNA structure and removes spurious covariation due to phylogeny. Second, it uses negative evolutionary information: basepairs that have variation but no significant covariation are prevented from occurring. Lastly, it uses a battery of probabilistic folding algorithms that incorporate all positive covariation into one structure. The method, named CaCoFold (Cascade variation/covariation Constrained Folding algorithm), predicts a nested structure guided by a maximal subset of positive basepairs, and recursively incorporates all remaining positive basepairs into alternative helices. The alternative helices can be compatible with the nested structure such as pseudoknots, or overlapping such as competing structures, base triplets, or other 3D non-antiparallel interactions. We present evidence that CaCoFold predictions are consistent with structures modeled from crystallography.

The availability of deeper comparative sequence alignments and recent advances in statistical analysis of RNA sequence covariation have made it possible to identify a reliable set of conserved base pairs, as well as a reliable set of non-basepairs (positions that vary without covarying). Predicting an overall consensus secondary structure consistent with a set of individual inferred pairs and non-pairs remains a problem. Current RNA structure prediction algorithms that predict nested secondary structures cannot use the full set of inferred covarying pairs, because covariation analysis also identifies important non-nested pairing interactions such as pseudoknots, base triples, and alternative structures. Moreover, although algorithms for incorporating negative constraints exist, negative information from covariation analysis (inferred non-pairs) has not been systematically exploited. Here I introduce an efficient approximate RNA structure prediction algorithm that incorporates all inferred pairs and excludes all non-pairs. Using this, and an improved visualization tool, I show that the method correctly identifies many non-nested structures in agreement with known crystal structures, and improves many curated consensus secondary structure annotations in RNA sequence alignment databases.

How to benchmark RNA secondary structure prediction accuracy

RNA secondary structure prediction is widely used. As new methods are developed, these are often benchmarked for accuracy against existing methods. This review discusses good practices for performing these benchmarks, including the choice of benchmarking structures, metrics to quantify accuracy, the importance of allowing flexibility for pairs in the accepted structure, and the importance of statistical testing for significance.

Estimating probabilistic context-free grammars for proteins using contact map constraints

Interactions between amino acids that are close in the spatial structure, but not necessarily in the sequence, play important structural and functional roles in proteins. These non-local interactions ought to be taken into account when modeling collections of proteins. Yet the most popular representations of sets of related protein sequences remain the profile Hidden Markov Models. By modeling independently the distributions of the conserved columns from an underlying multiple sequence alignment of the proteins, these models are unable to capture dependencies between the protein residues. Non-local interactions can be represented by using more expressive grammatical models. However, learning such grammars is difficult. In this work, we propose to use information on protein contacts to facilitate the training of probabilistic context-free grammars representing families of protein sequences. We develop the theory behind the introduction of contact constraints in maximum-likelihood and contrastive estimation schemes and implement it in a machine learning framework for protein grammars. The proposed framework is tested on samples of protein motifs in comparison with learning without contact constraints. The evaluation shows high fidelity of grammatical descriptors to protein structures and improved precision in recognizing sequences. Finally, we present an example of using our method in a practical setting and demonstrate its potential beyond the current state of the art by creating a grammatical model of a meta-family of protein motifs. We conclude that the current piece of research is a significant step towards more flexible and accurate modeling of collections of protein sequences. The software package is made available to the community.

A max-margin training of RNA secondary structure prediction integrated with the thermodynamic model

A popular approach for predicting RNA secondary structure is the thermodynamic nearest-neighbor model that finds a thermodynamically most stable secondary structure with minimum free energy (MFE). For further improvement, an alternative approach that is based on machine learning techniques has been developed. The machine learning-based approach can employ a fine-grained model that includes much richer feature representations with the ability to fit the training data. Although a machine learning-based fine-grained model achieved extremely high performance in prediction accuracy, a possibility of the risk of overfitting for such a model has been reported. In this paper, we propose a novel algorithm for RNA secondary structure prediction that integrates the thermodynamic approach and the machine learning-based weighted approach. Our fine-grained model combines the experimentally determined thermodynamic parameters with a large number of scoring parameters for detailed contexts of features that are trained by the structured support vector machine (SSVM) with the [Formula: see text] regularization to avoid overfitting. Our benchmark shows that our algorithm achieves the best prediction accuracy compared with existing methods, and heavy overfitting cannot be observed. The implementation of our algorithm is available at https://github.com/keio-bioinformatics/mxfold .

Research on folding diversity in statistical learning methods for RNA secondary structure prediction

How to improve the prediction accuracy of RNA secondary structure is currently a hot topic. The existing prediction methods for a single sequence do not fully consider the folding diversity which may occur among RNAs with different functions or sources. This paper explores the relationship between folding diversity and prediction accuracy, and puts forward a new method to improve the prediction accuracy of RNA secondary structure. Our research investigates the following: 1. The folding feature based on stochastic context-free grammar is proposed. By using dimension reduction and clustering techniques, some public data sets are analyzed. The results show that there is significant folding diversity among different RNA families. 2. To assign folding rules to RNAs without structural information, a classification method based on production probability is proposed. The experimental results show that the classification method proposed in this paper can effectively classify the RNAs of unknown structure. 3. Based on the existing prediction methods of statistical learning models, an RNA secondary structure prediction framework is proposed, namely "Cluster - Training - Parameter Selection - Prediction". The results show that, with information on folding diversity, prediction accuracy can be significantly improved.

Selecting Fully-Modified XNA Aptamers Using Synthetic Genetics

This unit describes the application of "synthetic genetics," i.e., the replication of xeno nucleic acids (XNAs), artificial analogs of DNA and RNA bearing alternative backbone or sugar congeners, to the directed evolution of synthetic oligonucleotide ligands (XNA aptamers) specific for target proteins or nucleic acid motifs, using a cross-chemistry selective exponential enrichment (X-SELEX) approach. Protocols are described for synthesis of diverse-sequence XNA repertoires (typically 10¹⁴ molecules) using DNA templates, isolation and panning for functional XNA sequences using targets immobilized on solid phase or gel shift induced by target binding in solution, and XNA reverse transcription to allow cDNA amplification or sequencing. The method may be generally applied to select fully-modified XNA aptamers specific for a wide range of target molecules. © 2018 by John Wiley & Sons, Inc.

An improved Four-Russians method and sparsified Four-Russians algorithm for RNA folding

Background

The basic RNA secondary structure prediction problem or single sequence folding problem (SSF) was solved 35 years ago by a now well-known \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^3)$$\end{document}O(n3)-time dynamic programming method. Recently three methodologies—Valiant, Four-Russians, and Sparsification—have been applied to speedup RNA secondary structure prediction. The sparsification method exploits two properties of the input: the number of subsequence Z with the endpoints belonging to the optimal folding set and the maximum number base-pairs L. These sparsity properties satisfy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 \le L \le n / 2$$\end{document}0≤L≤n/2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \le Z \le n^2 / 2$$\end{document}n≤Z≤n2/2, and the method reduces the algorithmic running time to O(LZ). While the Four-Russians method utilizes tabling partial results.

Results

In this paper, we explore three different algorithmic speedups. We first expand the reformulate the single sequence folding Four-Russians \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta \left(\frac{n^3}{\log ^2 n}\right)$$\end{document}Θn3log2n-time algorithm, to utilize an on-demand lookup table. Second, we create a framework that combines the fastest Sparsification and new fastest on-demand Four-Russians methods. This combined method has worst-case running time of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\tilde{L}\tilde{Z})$$\end{document}O(L~Z~), where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{L}}{\log n} \le \tilde{L}\le min\left({L},\frac{n}{\log n}\right)$$\end{document}Llogn≤L~≤minL,nlogn and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{Z}}{\log n}\le \tilde{Z} \le min\left({Z},\frac{n^2}{\log n}\right)$$\end{document}Zlogn≤Z~≤minZ,n2logn. Third we update the Four-Russians formulation to achieve an on-demand \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O( n^2/ \log ^2n )$$\end{document}O(n2/log2n)-time parallel algorithm. This then leads to an asymptotic speedup of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\tilde{L}\tilde{Z_j})$$\end{document}O(L~Zj~) where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{Z_j}}{\log n}\le \tilde{Z_j} \le min\left({Z_j},\frac{n}{\log n}\right)$$\end{document}Zjlogn≤Zj~≤minZj,nlogn and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z_j$$\end{document}Zj the number of subsequence with the endpoint j belonging to the optimal folding set.

Conclusions

The on-demand formulation not only removes all extraneous computation and allows us to incorporate more realistic scoring schemes, but leads us to take advantage of the sparsity properties. Through asymptotic analysis and empirical testing on the base-pair maximization variant and a more biologically informative scoring scheme, we show that this Sparse Four-Russians framework is able to achieve a speedup on every problem instance, that is asymptotically never worse, and empirically better than achieved by the minimum of the two methods alone.

RNA folding with hard and soft constraints

Background

A large class of RNA secondary structure prediction programs uses an elaborate energy model grounded in extensive thermodynamic measurements and exact dynamic programming algorithms. External experimental evidence can be in principle be incorporated by means of hard constraints that restrict the search space or by means of soft constraints that distort the energy model. In particular recent advances in coupling chemical and enzymatic probing with sequencing techniques but also comparative approaches provide an increasing amount of experimental data to be combined with secondary structure prediction.

Results

Responding to the increasing needs for a versatile and user-friendly inclusion of external evidence into diverse flavors of RNA secondary structure prediction tools we implemented a generic layer of constraint handling into the ViennaRNA Package. It makes explicit use of the conceptual separation of the “folding grammar” defining the search space and the actual energy evaluation, which allows constraints to be interleaved in a natural way between recursion steps and evaluation of the standard energy function.

Conclusions

The extension of the ViennaRNA Package provides a generic way to include diverse types of constraints into RNA folding algorithms. The computational overhead incurred is negligible in practice. A wide variety of application scenarios can be accommodated by the new framework, including the incorporation of structure probing data, non-standard base pairs and chemical modifications, as well as structure-dependent ligand binding.

Electronic supplementary material

The online version of this article (doi:10.1186/s13015-016-0070-z) contains supplementary material, which is available to authorized users.

ProbFold: a probabilistic method for integration of probing data in RNA secondary structure prediction

MOTIVATION

Recently, new RNA secondary structure probing techniques have been developed, including Next Generation Sequencing based methods capable of probing transcriptome-wide. These techniques hold great promise for improving structure prediction accuracy. However, each new data type comes with its own signal properties and biases, which may even be experiment specific. There is therefore a growing need for RNA structure prediction methods that can be automatically trained on new data types and readily extended to integrate and fully exploit multiple types of data.

RESULTS

Here, we develop and explore a modular probabilistic approach for integrating probing data in RNA structure prediction. It can be automatically trained given a set of known structures with probing data. The approach is demonstrated on SHAPE datasets, where we evaluate and selectively model specific correlations. The approach often makes superior use of the probing data signal compared to other methods. We illustrate the use of ProbFold on multiple data types using both simulations and a small set of structures with both SHAPE, DMS and CMCT data. Technically, the approach combines stochastic context-free grammars (SCFGs) with probabilistic graphical models. This approach allows rapid adaptation and integration of new probing data types.

AVAILABILITY AND IMPLEMENTATION

ProbFold is implemented in C ++. Models are specified using simple textual formats. Data reformatting is done using separate C ++ programs. Source code, statically compiled binaries for x86 Linux machines, C ++ programs, example datasets and a tutorial is available from http://moma.ki.au.dk/prj/probfold/

CONTACT

: jakob.skou@clin.au.dk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Prediction of Secondary Structures Conserved in Multiple RNA Sequences

RNA structure is conserved by evolution to a greater extent than sequence. Predicting the conserved structure for multiple homologous sequences can be much more accurate than predicting the structure for a single sequence. RNAstructure is a software package that includes the programs Dynalign, Multilign, TurboFold, and PARTS for predicting conserved RNA secondary structure. This chapter provides protocols for using these programs.

Algebraic Dynamic Programming over general data structures

Background

Dynamic programming algorithms provide exact solutions to many problems in computational biology, such as sequence alignment, RNA folding, hidden Markov models (HMMs), and scoring of phylogenetic trees. Structurally analogous algorithms compute optimal solutions, evaluate score distributions, and perform stochastic sampling. This is explained in the theory of Algebraic Dynamic Programming (ADP) by a strict separation of state space traversal (usually represented by a context free grammar), scoring (encoded as an algebra), and choice rule. A key ingredient in this theory is the use of yield parsers that operate on the ordered input data structure, usually strings or ordered trees. The computation of ensemble properties, such as a posteriori probabilities of HMMs or partition functions in RNA folding, requires the combination of two distinct, but intimately related algorithms, known as the inside and the outside recursion. Only the inside recursions are covered by the classical ADP theory.

Results

The ideas of ADP are generalized to a much wider scope of data structures by relaxing the concept of parsing. This allows us to formalize the conceptual complementarity of inside and outside variables in a natural way. We demonstrate that outside recursions are generically derivable from inside decomposition schemes. In addition to rephrasing the well-known algorithms for HMMs, pairwise sequence alignment, and RNA folding we show how the TSP and the shortest Hamiltonian path problem can be implemented efficiently in the extended ADP framework. As a showcase application we investigate the ancient evolution of HOX gene clusters in terms of shortest Hamiltonian paths.

Conclusions

The generalized ADP framework presented here greatly facilitates the development and implementation of dynamic programming algorithms for a wide spectrum of applications.

RNA Thermodynamic Structural Entropy

Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner’99 and Turner’04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http://bioinformatics.bc.edu/clotelab/RNAentropy, including source code and ancillary programs.

Fitness Landscapes of Functional RNAs

The notion of fitness landscapes, a map between genotype and fitness, was proposed more than 80 years ago. For most of this time data was only available for a few alleles, and thus we had only a restricted view of the whole fitness landscape. Recently, advances in genetics and molecular biology allow a more detailed view of them. Here we review experimental and theoretical studies of fitness landscapes of functional RNAs, especially aptamers and ribozymes. We find that RNA structures can be divided into critical structures, connecting structures, neutral structures and forbidden structures. Such characterisation, coupled with theoretical sequence-to-structure predictions, allows us to construct the whole fitness landscape. Fitness landscapes then can be used to study evolution, and in our case the development of the RNA world.

Identifying novel sequence variants of RNA 3D motifs

Predicting RNA 3D structure from sequence is a major challenge in biophysics. An important sub-goal is accurately identifying recurrent 3D motifs from RNA internal and hairpin loop sequences extracted from secondary structure (2D) diagrams. We have developed and validated new probabilistic models for 3D motif sequences based on hybrid Stochastic Context-Free Grammars and Markov Random Fields (SCFG/MRF). The SCFG/MRF models are constructed using atomic-resolution RNA 3D structures. To parameterize each model, we use all instances of each motif found in the RNA 3D Motif Atlas and annotations of pairwise nucleotide interactions generated by the FR3D software. Isostericity relations between non-Watson–Crick basepairs are used in scoring sequence variants. SCFG techniques model nested pairs and insertions, while MRF ideas handle crossing interactions and base triples. We use test sets of randomly-generated sequences to set acceptance and rejection thresholds for each motif group and thus control the false positive rate. Validation was carried out by comparing results for four motif groups to RMDetect. The software developed for sequence scoring (JAR3D) is structured to automatically incorporate new motifs as they accumulate in the RNA 3D Motif Atlas when new structures are solved and is available free for download.

Ambivalent covariance models

BACKGROUND

Evolutionary variations let us define a set of similar nucleic acid sequences as a family if these different molecules execute a common function. Capturing their sequence variation by using e. g. position specific scoring matrices significantly improves sensitivity of detection tools. Members of a functional (non-coding) RNA family are affected by these variations not only on the sequence, but also on the structural level. For example, some transfer-RNAs exhibit a fifth helix in addition to the typical cloverleaf structure. Current covariance models - the unrivaled homology search approach for structured RNA - do not benefit from structural variation within a family, but rather penalize it. This leads to artificial subdivision of families and loss of information in the RFAM database.

RESULTS

We propose an extension to the fundamental architecture of covariance models to allow for several, compatible consensus structures. The resulting models are called ambivalent covariance models. Evaluation on several RFAM families shows that coalescence of structural variation within a family by using ambivalent consensus models is superior to subdividing the family into multiple classical covariance models.

CONCLUSION

A prototype and source code is available at http://bibiserv.cebitec.uni-bielefeld.de/acms.

Product Grammars for Alignment and Folding

We develop a theory of algebraic operations over linear and context-free grammars that makes it possible to combine simple "atomic" grammars operating on single sequences into complex, multi-dimensional grammars. We demonstrate the utility of this framework by constructing the search spaces of complex alignment problems on multiple input sequences explicitly as algebraic expressions of very simple one-dimensional grammars. In particular, we provide a fully worked frameshift-aware, semiglobal DNA-protein alignment algorithm whose grammar is composed of products of small, atomic grammars. The compiler accompanying our theory makes it easy to experiment with the combination of multiple grammars and different operations. Composite grammars can be written out in L(A)T(E)X for documentation and as a guide to implementation of dynamic programming algorithms. An embedding in Haskell as a domain-specific language makes the theory directly accessible to writing and using grammar products without the detour of an external compiler. Software and supplemental files available here: http://www.bioinf. uni-leipzig.de/Software/gramprod/.

Secondary structural entropy in RNA switch (Riboswitch) identification

BACKGROUND

RNA regulatory elements play a significant role in gene regulation. Riboswitches, a widespread group of regulatory RNAs, are vital components of many bacterial genomes. These regulatory elements generally function by forming a ligand-induced alternative fold that controls access to ribosome binding sites or other regulatory sites in RNA. Riboswitch-mediated mechanisms are ubiquitous across bacterial genomes. A typical class of riboswitch has its own unique structural and biological complexity, making de novo riboswitch identification a formidable task. Traditionally, riboswitches have been identified through comparative genomics based on sequence and structural homology. The limitations of structural-homology-based approaches, coupled with the assumption that there is a great diversity of undiscovered riboswitches, suggests the need for alternative methods for riboswitch identification, possibly based on features intrinsic to their structure. As of yet, no such reliable method has been proposed.

RESULTS

We used structural entropy of riboswitch sequences as a measure of their secondary structural dynamics. Entropy values of a diverse set of riboswitches were compared to that of their mutants, their dinucleotide shuffles, and their reverse complement sequences under different stochastic context-free grammar folding models. Significance of our results was evaluated by comparison to other approaches, such as the base-pairing entropy and energy landscapes dynamics. Classifiers based on structural entropy optimized via sequence and structural features were devised as riboswitch identifiers and tested on Bacillus subtilis, Escherichia coli, and Synechococcus elongatus as an exploration of structural entropy based approaches. The unusually long untranslated region of the cotH in Bacillus subtilis, as well as upstream regions of certain genes, such as the sucC genes were associated with significant structural entropy values in genome-wide examinations.

CONCLUSIONS

Various tests show that there is in fact a relationship between higher structural entropy and the potential for the RNA sequence to have alternative structures, within the limitations of our methodology. This relationship, though modest, is consistent across various tests. Understanding the behavior of structural entropy as a fairly new feature for RNA conformational dynamics, however, may require extensive exploratory investigation both across RNA sequences and folding models.

Toward a next-generation atlas of RNA secondary structure

RNA structure plays a crucial role in gene maturation, regulation and function. Determining the form and frequency of RNA folds is essential for a better understanding of how RNA exerts its functions. Low-throughput studies have focused on RNA primary sequences and expression levels, but with an emphasis on relatively small numbers of transcripts. However, with the recent advent of high-throughput technologies, it is realistic to begin analyzing RNA secondary structures on a genome-wide scale. Here, we review genome-wide RNA secondary structure profiles as well as advances in computational structure predictions. We further discuss the novel characteristics of RNA secondary structure across messenger RNAs. Probing RNA secondary structure by high-throughput sequencing will enable us to build atlases of RNA secondary structures, an important step in helping us to understand the versatility of RNA functions in diverse cellular processes.

A semi-supervised learning approach for RNA secondary structure prediction

RNA secondary structure prediction is a key technology in RNA bioinformatics. Most algorithms for RNA secondary structure prediction use probabilistic models, in which the model parameters are trained with reliable RNA secondary structures. Because of the difficulty of determining RNA secondary structures by experimental procedures, such as NMR or X-ray crystal structural analyses, there are still many RNA sequences that could be useful for training whose secondary structures have not been experimentally determined. In this paper, we introduce a novel semi-supervised learning approach for training parameters in a probabilistic model of RNA secondary structures in which we employ not only RNA sequences with annotated secondary structures but also ones with unknown secondary structures. Our model is based on a hybrid of generative (stochastic context-free grammars) and discriminative models (conditional random fields) that has been successfully applied to natural language processing. Computational experiments indicate that the accuracy of secondary structure prediction is improved by incorporating RNA sequences with unknown secondary structures into training. To our knowledge, this is the first study of a semi-supervised learning approach for RNA secondary structure prediction. This technique will be useful when the number of reliable structures is limited.

RNA secondary structure prediction from multi-aligned sequences

It has been well accepted that the RNA secondary structures of most functional non-coding RNAs (ncRNAs) are closely related to their functions and are conserved during evolution. Hence, prediction of conserved secondary structures from evolutionarily related sequences is one important task in RNA bioinformatics; the methods are useful not only to further functional analyses of ncRNAs but also to improve the accuracy of secondary structure predictions and to find novel functional RNAs from the genome. In this review, I focus on common secondary structure prediction from a given aligned RNA sequence, in which one secondary structure whose length is equal to that of the input alignment is predicted. I systematically review and classify existing tools and algorithms for the problem, by utilizing the information employed in the tools and by adopting a unified viewpoint based on maximum expected gain (MEG) estimators. I believe that this classification will allow a deeper understanding of each tool and provide users with useful information for selecting tools for common secondary structure predictions.

Faster algorithms for RNA-folding using the Four-Russians method

BACKGROUND

The secondary structure that maximizes the number of non-crossing matchings between complimentary bases of an RNA sequence of length n can be computed in O(n3) time using Nussinov's dynamic programming algorithm. The Four-Russians method is a technique that reduces the running time for certain dynamic programming algorithms by a multiplicative factor after a preprocessing step where solutions to all smaller subproblems of a fixed size are exhaustively enumerated and solved. Frid and Gusfield designed an O(n3logn) algorithm for RNA folding using the Four-Russians technique. In their algorithm the preprocessing is interleaved with the algorithm computation.

THEORETICAL RESULTS

We simplify the algorithm and the analysis by doing the preprocessing once prior to the algorithm computation. We call this the two-vector method. We also show variants where instead of exhaustive preprocessing, we only solve the subproblems encountered in the main algorithm once and memoize the results. We give a simple proof of correctness and explore the practical advantages over the earlier method.The Nussinov algorithm admits an O(n2) time parallel algorithm. We show a parallel algorithm using the two-vector idea that improves the time bound to O(n2logn).

PRACTICAL RESULTS

We have implemented the parallel algorithm on graphics processing units using the CUDA platform. We discuss the organization of the data structures to exploit coalesced memory access for fast running times. The ideas to organize the data structures also help in improving the running time of the serial algorithms. For sequences of length up to 6000 bases the parallel algorithm takes only about 2.5 seconds and the two-vector serial method takes about 57 seconds on a desktop and 15 seconds on a server. Among the serial algorithms, the two-vector and memoized versions are faster than the Frid-Gusfield algorithm by a factor of 3, and are faster than Nussinov by up to a factor of 20. The source-code for the algorithms is available at http://github.com/ijalabv/FourRussiansRNAFolding.

Asymptotic distribution of motifs in a stochastic context-free grammar model of RNA folding

We analyze the distribution of RNA secondary structures given by the Knudsen-Hein stochastic context-free grammar used in the prediction program Pfold. Our main theorem gives relations between the expected number of these motifs--independent of the grammar probabilities. These relations are a consequence of proving that the distribution of base pairs, of helices, and of different types of loops is asymptotically Gaussian in this model of RNA folding. Proof techniques use singularity analysis of probability generating functions. We also demonstrate that these asymptotic results capture well the expected number of RNA base pairs in native ribosomal structures, and certain other aspects of their predicted secondary structures. In particular, we find that the predicted structures largely satisfy the expected relations, although the native structures do not.

Detecting and comparing non-coding RNAs in the high-throughput era

In recent years there has been a growing interest in the field of non-coding RNA. This surge is a direct consequence of the discovery of a huge number of new non-coding genes and of the finding that many of these transcripts are involved in key cellular functions. In this context, accurately detecting and comparing RNA sequences has become important. Aligning nucleotide sequences is a key requisite when searching for homologous genes. Accurate alignments reveal evolutionary relationships, conserved regions and more generally any biologically relevant pattern. Comparing RNA molecules is, however, a challenging task. The nucleotide alphabet is simpler and therefore less informative than that of amino-acids. Moreover for many non-coding RNAs, evolution is likely to be mostly constrained at the structural level and not at the sequence level. This results in very poor sequence conservation impeding comparison of these molecules. These difficulties define a context where new methods are urgently needed in order to exploit experimental results to their full potential. This review focuses on the comparative genomics of non-coding RNAs in the context of new sequencing technologies and especially dealing with two extremely important and timely research aspects: the development of new methods to align RNAs and the analysis of high-throughput data.

The four ingredients of single-sequence RNA secondary structure prediction. A unifying perspective

Any method for RNA secondary structure prediction is determined by four ingredients. The architecture is the choice of features implemented by the model (such as stacked basepairs, loop length distributions, etc.). The architecture determines the number of parameters in the model. The scoring scheme is the nature of those parameters (whether thermodynamic, probabilistic, or weights). The parameterization stands for the specific values assigned to the parameters. These three ingredients are referred to as "the model." The fourth ingredient is the folding algorithms used to predict plausible secondary structures given the model and the sequence of a structural RNA. Here, I make several unifying observations drawn from looking at more than 40 years of methods for RNA secondary structure prediction in the light of this classification. As a final observation, there seems to be a performance ceiling that affects all methods with complex architectures, a ceiling that impacts all scoring schemes with remarkable similarity. This suggests that modeling RNA secondary structure by using intrinsic sequence-based plausible "foldability" will require the incorporation of other forms of information in order to constrain the folding space and to improve prediction accuracy. This could give an advantage to probabilistic scoring systems since a probabilistic framework is a natural platform to incorporate different sources of information into one single inference problem.

Quantifying variances in comparative RNA secondary structure prediction

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.

Visualizing RNA base-pairing probabilities with RNAbow diagrams

There are many effective ways to represent a minimum free energy RNA secondary structure that make it easy to locate its helices and loops. It is a greater challenge to visualize the thermal average probabilities of all folds in a partition function sum; dot plot representations are often puzzling. Therefore, we introduce the RNAbows visualization tool for RNA base pair probabilities. RNAbows represent base pair probabilities with line thickness and shading, yielding intuitive diagrams. RNAbows aid in disentangling incompatible structures, allow comparisons between clusters of folds, highlight differences between wild-type and mutant folds, and are also rather beautiful.

Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information

MOTIVATION

Many computational methods for RNA secondary structure prediction, and, in particular, for the prediction of a consensus structure of an alignment of RNA sequences, have been developed. Most methods, however, ignore biophysical factors, such as the kinetics of RNA folding; no current implementation considers both evolutionary information and folding kinetics, thus losing information that, when considered, might lead to better predictions.

RESULTS

We present an iterative algorithm, Oxfold, in the framework of stochastic context-free grammars, that emulates the kinetics of RNA folding in a simplified way, in combination with a molecular evolution model. This method improves considerably on existing grammatical models that do not consider folding kinetics. Additionally, the model compares favourably to non-kinetic thermodynamic models.

Computational prediction of RNA secondary structure

The purpose of this section is to detail methods for the computational prediction of RNA secondary structure. This protocol is intended to provide an easy entry into the field of RNA structure prediction for those wishing to utilize it in their research and to suggest 'best practices' for going from sequence to secondary structure depending on the available data.

Information-theoretic uncertainty of SCFG-modeled folding space of the non-coding RNA

RNA secondary structure ensembles define probability distributions for alternative equilibrium secondary structures of an RNA sequence. Shannon's entropy is a measure for the amount of diversity present in any ensemble. In this work, Shannon's entropy of the SCFG ensemble on an RNA sequence is derived and implemented in polynomial time for both structurally ambiguous and unambiguous grammars. Micro RNA sequences generally have low folding entropy, as previously discovered. Surprisingly, signs of significantly high folding entropy were observed in certain ncRNA families. More effective models coupled with targeted randomization tests can lead to a better insight into folding features of these families.

AVAILABILITY

URL http://www.plantbio.uga.edu/~russell/index.php?s=1&n=5&r=0.

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.

Evaluating the effect of disturbed ensemble distributions on SCFG based statistical sampling of RNA secondary structures

BACKGROUND

Over the past years, statistical and Bayesian approaches have become increasingly appreciated to address the long-standing problem of computational RNA structure prediction. Recently, a novel probabilistic method for the prediction of RNA secondary structures from a single sequence has been studied which is based on generating statistically representative and reproducible samples of the entire ensemble of feasible structures for a particular input sequence. This method samples the possible foldings from a distribution implied by a sophisticated (traditional or length-dependent) stochastic context-free grammar (SCFG) that mirrors the standard thermodynamic model applied in modern physics-based prediction algorithms. Specifically, that grammar represents an exact probabilistic counterpart to the energy model underlying the Sfold software, which employs a sampling extension of the partition function (PF) approach to produce statistically representative subsets of the Boltzmann-weighted ensemble. Although both sampling approaches have the same worst-case time and space complexities, it has been indicated that they differ in performance (both with respect to prediction accuracy and quality of generated samples), where neither of these two competing approaches generally outperforms the other.

RESULTS

In this work, we will consider the SCFG based approach in order to perform an analysis on how the quality of generated sample sets and the corresponding prediction accuracy changes when different degrees of disturbances are incorporated into the needed sampling probabilities. This is motivated by the fact that if the results prove to be resistant to large errors on the distinct sampling probabilities (compared to the exact ones), then it will be an indication that these probabilities do not need to be computed exactly, but it may be sufficient and more efficient to approximate them. Thus, it might then be possible to decrease the worst-case time requirements of such an SCFG based sampling method without significant accuracy losses. If, on the other hand, the quality of sampled structures can be observed to strongly react to slight disturbances, there is little hope for improving the complexity by heuristic procedures. We hence provide a reliable test for the hypothesis that a heuristic method could be implemented to improve the time scaling of RNA secondary structure prediction in the worst-case - without sacrificing much of the accuracy of the results.

CONCLUSIONS

Our experiments indicate that absolute errors generally lead to the generation of useless sample sets, whereas relative errors seem to have only small negative impact on both the predictive accuracy and the overall quality of resulting structure samples. Based on these observations, we present some useful ideas for developing a time-reduced sampling method guaranteeing an acceptable predictive accuracy. We also discuss some inherent drawbacks that arise in the context of approximation. The key results of this paper are crucial for the design of an efficient and competitive heuristic prediction method based on the increasingly accepted and attractive statistical sampling approach. This has indeed been indicated by the construction of prototype algorithms.