Pseudoknots: RNA structures with diverse functions

The molecular interactions that stabilize RNA tertiary structure: RNA motifs, patterns, and networks

RNA molecules adopt specific three-dimensional structures critical to their function. Many essential metabolic processes, including protein synthesis and RNA splicing, are carried out by RNA molecules with elaborate tertiary structures (e.g. 3QIQ, right). Indeed, the ribosome and self-splicing introns are complex RNA machines. But even the coding regions in messenger RNAs and viral RNAs are flanked by highly structured untranslated regions, which provide regulatory information necessary for gene expression. RNA tertiary structure is defined as the three-dimensional arrangement of RNA building blocks, which include helical duplexes, triple-stranded structures, and other components that are held together through connections collectively termed RNA tertiary interactions. The structural diversity of these interactions is now a subject of intense investigation, involving the techniques of NMR, X-ray crystallography, chemical genetics, and phylogenetic analysis. At the same time, many investigators are using biophysical techniques to elucidate the driving forces for tertiary structure formation and the mechanisms for its stabilization. RNA tertiary folding is promoted by maximization of base stacking, much like the hydrophobic effect that drives protein folding. RNA folding also requires electrostatic stabilization, both through charge screening and site binding of metals, and it is enhanced by desolvation of the phosphate backbone. In this Account, we provide an overview of the features that specify and stabilize RNA tertiary structure. A major determinant for overall tertiary RNA architecture is local conformation in secondary-structure junctions, which are regions from which two or more duplexes project. At junctions and other structures, such as pseudoknots and kissing loops, adjacent helices stack on one another, and these coaxial stacks play a major role in dictating the overall architectural form of an RNA molecule. In addition to RNA junction topology, a second determinant for RNA tertiary structure is the formation of sequence-specific interactions. Networks of triple helices, tetraloop-receptor interactions, and other sequence-specific contacts establish the framework for the overall tertiary fold. The third determinant of tertiary structure is the formation of stabilizing stacking and backbone interactions, and many are not sequence specific. For example, ribose zippers allow 2'-hydroxyl groups on different RNA strands to form networks of interdigitated hydrogen bonds, serving to seal strands together and thereby stabilize adjacent substructures. These motifs often require monovalent and divalent cations, which can interact diffusely or through chelation to specific RNA functional groups. As we learn more about the components of RNA tertiary structure, we will be able to predict the structures of RNA molecules from their sequences, thereby obtaining key information about biological function. Understanding and predicting RNA structure is particularly important given the recent discovery that although most of our genome is transcribed into RNA molecules, few of them have a known function. The prevalence of RNA viruses and pathogens with RNA genomes makes RNA drug discovery an active area of research. Finally, knowledge of RNA structure will facilitate the engineering of supramolecular RNA structures, which can be used as nanomechanical components for new materials. But all of this promise depends on a better understanding of the RNA parts list, and how the pieces fit together.

Function annotation for pseudoknot using structure similarity

Many raw biological sequence data have been generated by the human genome project and related efforts. The understanding of structural information encoded by biological sequences is important to acquire knowledge of their biochemical functions but remains a fundamental challenge. Recent interest in RNA regulation has resulted in a rapid growth of deposited RNA secondary structures in varied databases. However, a functional classification and characterization of the RNA structure have only been partially addressed. This article aims to introduce a novel interval-based distance metric for structure-based RNA function assignment. The characterization of RNA structures relies on distance vectors learned from a collection of predicted structures. The distance measure considers the intersected, disjoint, and inclusion between intervals. A set of RNA pseudoknotted structures with known function are applied and the function of the query structure is determined by measuring structure similarity. This not only offers sequence distance criteria to measure the similarity of secondary structures but also aids the functional classification of RNA structures with pesudoknots.

IPknot: fast and accurate prediction of RNA secondary structures with pseudoknots using integer programming

MOTIVATION

Pseudoknots found in secondary structures of a number of functional RNAs play various roles in biological processes. Recent methods for predicting RNA secondary structures cover certain classes of pseudoknotted structures, but only a few of them achieve satisfying predictions in terms of both speed and accuracy.

RESULTS

We propose IPknot, a novel computational method for predicting RNA secondary structures with pseudoknots based on maximizing expected accuracy of a predicted structure. IPknot decomposes a pseudoknotted structure into a set of pseudoknot-free substructures and approximates a base-pairing probability distribution that considers pseudoknots, leading to the capability of modeling a wide class of pseudoknots and running quite fast. In addition, we propose a heuristic algorithm for refining base-paring probabilities to improve the prediction accuracy of IPknot. The problem of maximizing expected accuracy is solved by using integer programming with threshold cut. We also extend IPknot so that it can predict the consensus secondary structure with pseudoknots when a multiple sequence alignment is given. IPknot is validated through extensive experiments on various datasets, showing that IPknot achieves better prediction accuracy and faster running time as compared with several competitive prediction methods.

AVAILABILITY

The program of IPknot is available at http://www.ncrna.org/software/ipknot/. IPknot is also available as a web server at http://rna.naist.jp/ipknot/.

CONTACT

satoken@k.u-tokyo.ac.jp; ykato@is.naist.jp

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Conformational capture of the SAM-II riboswitch

Riboswitches are gene regulation elements in mRNA that function by specifically responding to metabolites. Although the metabolite-bound states of riboswitches have proven amenable to structure determination efforts, knowledge of the structural features of riboswitches in their ligand-free forms and their ligand-response mechanisms giving rise to regulatory control is lacking. Here we explore the ligand-induced folding process of the S-adenosylmethionine type II (SAM-II) riboswitch using chemical and biophysical methods, including NMR and fluorescence spectroscopy, and single-molecule fluorescence imaging. The data reveal that the unliganded SAM-II riboswitch is dynamic in nature, in that its stem-loop element becomes engaged in a pseudoknot fold through base-pairing with nucleosides in the 3' overhang containing the Shine-Dalgarno sequence. Although the pseudoknot structure is highly transient in the absence of its ligand, S-adenosylmethionine (SAM), it becomes conformationally restrained upon ligand recognition, through a conformational capture mechanism. These insights provide a molecular understanding of riboswitch dynamics that shed new light on the mechanism of riboswitch-mediated translational regulation.

Structural basis of differential ligand recognition by two classes of bis-(3'-5')-cyclic dimeric guanosine monophosphate-binding riboswitches

The bis-(3'-5')-cyclic dimeric guanosine monophosphate (c-di-GMP) signaling pathway regulates biofilm formation, virulence, and other processes in many bacterial species and is critical for their survival. Two classes of c-di-GMP-binding riboswitches have been discovered that bind this second messenger with high affinity and regulate diverse downstream genes, underscoring the importance of RNA receptors in this pathway. We have solved the structure of a c-di-GMP-II riboswitch, which reveals that the ligand is bound as part of a triplex formed with a pseudoknot. The structure also shows that the guanine bases of c-di-GMP are recognized through noncanonical pairings and that the phosphodiester backbone is not contacted by the RNA. Recognition is quite different from that observed in the c-di-GMP-I riboswitch, demonstrating that at least two independent solutions for RNA second messenger binding have evolved. We exploited these differences to design a c-di-GMP analog that selectively binds the c-di-GMP-II aptamer over the c-di-GMP-I RNA. There are several bacterial species that contain both types of riboswitches, and this approach holds promise as an important tool for targeting one riboswitch, and thus one gene, over another in a selective fashion.

Physics-based de novo prediction of RNA 3D structures

Current experiments on structural determination cannot keep up the pace with the steadily emerging RNA sequences and new functions. This underscores the request for an accurate model for RNA three-dimensional (3D) structural prediction. Although considerable progress has been made in mechanistic studies, accurate prediction for RNA tertiary folding from sequence remains an unsolved problem. The first and most important requirement for the prediction of RNA structure from physical principles is an accurate free energy model. A recently developed three-vector virtual bond-based RNA folding model ("Vfold") has allowed us to compute the chain entropy and predict folding free energies and structures for RNA secondary structures and simple pseudoknots. Here we develop a free energy-based method to predict larger more complex RNA tertiary folds. The approach is based on a multiscaling strategy: from the nucleotide sequence, we predict the two-dimensional (2D) structures (defined by the base pairs and tertiary contacts); based on the 2D structure, we construct a 3D scaffold; with the 3D scaffold as the initial state, we combine AMBER energy minimization and PDB-based fragment search to predict the all-atom structure. A key advantage of the approach is the statistical mechanical calculation for the conformational entropy of RNA structures, including those with cross-linked loops. Benchmark tests show that the model leads to significant improvements in RNA 3D structure prediction.

All-atom knowledge-based potential for RNA structure prediction and assessment

MOTIVATION

Over the recent years, the vision that RNA simply serves as information transfer molecule has dramatically changed. The study of the sequence/structure/function relationships in RNA is becoming more important. As a direct consequence, the total number of experimentally solved RNA structures has dramatically increased and new computer tools for predicting RNA structure from sequence are rapidly emerging. Therefore, new and accurate methods for assessing the accuracy of RNA structure models are clearly needed.

RESULTS

Here, we introduce an all-atom knowledge-based potential for the assessment of RNA three-dimensional (3D) structures. We have benchmarked our new potential, called Ribonucleic Acids Statistical Potential (RASP), with two different decoy datasets composed of near-native RNA structures. In one of the benchmark sets, RASP was able to rank the closest model to the X-ray structure as the best and within the top 10 models for ∼93 and ∼95% of decoys, respectively. The average correlation coefficient between model accuracy, calculated as the root mean square deviation and global distance test-total score (GDT-TS) measures of C3' atoms, and the RASP score was 0.85 and 0.89, respectively. Based on a recently released benchmark dataset that contains hundreds of 3D models for 32 RNA motifs with non-canonical base pairs, RASP scoring function compared favorably to ROSETTA FARFAR force field in the selection of accurate models. Finally, using the self-splicing group I intron and the stem-loop IIIc from hepatitis C virus internal ribosome entry site as test cases, we show that RASP is able to discriminate between known structure-destabilizing mutations and compensatory mutations.

AVAILABILITY

RASP can be readily applied to assess all-atom or coarse-grained RNA structures and thus should be of interest to both developers and end-users of RNA structure prediction methods. The computer software and knowledge-based potentials are freely available at http://melolab.org/supmat.html.

CONTACT

fmelo@bio.puc.cl; mmarti@cipf.es

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Recognition of S-adenosylmethionine by riboswitches

Riboswitches are regulatory elements commonly found in the 5' leader sequences of bacterial mRNAs that bind cellular metabolites to direct expression at either the transcriptional or translational level. The effectors of these RNAs are chemically diverse, including nucleobases and nucleosides, amino acids, cofactors, and second messenger molecules. Over the last few years, a number of structures have revealed the architectural means by which RNA creates binding pockets of high affinity and specificity for these compounds. For most effectors, there is a single class of associated riboswitches. However, eight individual classes of S-adenosylmethionine (SAM) and/or S-adenosylhomocysteine (SAH) responsive riboswitches that control various aspects of sulfur metabolism have been validated, revealing a diverse set of solutions to the recognition of these ubiquitous metabolites. This review focuses upon the structures of RNAs that bind SAM and SAH and how they discriminate between these compounds.

Heuristic RNA pseudoknot prediction including intramolecular kissing hairpins

Pseudoknots are an essential feature of RNA tertiary structures. Simple H-type pseudoknots have been studied extensively in terms of biological functions, computational prediction, and energy models. Intramolecular kissing hairpins are a more complex and biologically important type of pseudoknot in which two hairpin loops form base pairs. They are hard to predict using free energy minimization due to high computational requirements. Heuristic methods that allow arbitrary pseudoknots strongly depend on the quality of energy parameters, which are not yet available for complex pseudoknots. We present an extension of the heuristic pseudoknot prediction algorithm DotKnot, which covers H-type pseudoknots and intramolecular kissing hairpins. Our framework allows for easy integration of advanced H-type pseudoknot energy models. For a test set of RNA sequences containing kissing hairpins and other types of pseudoknot structures, DotKnot outperforms competing methods from the literature. DotKnot is available as a web server under http://dotknot.csse.uwa.edu.au.

Sparsification of RNA structure prediction including pseudoknots

Background

Although many RNA molecules contain pseudoknots, computational prediction of pseudoknotted RNA structure is still in its infancy due to high running time and space consumption implied by the dynamic programming formulations of the problem.

Results

In this paper, we introduce sparsification to significantly speedup the dynamic programming approaches for pseudoknotted RNA structure prediction, which also lower the space requirements. Although sparsification has been applied to a number of RNA-related structure prediction problems in the past few years, we provide the first application of sparsification to pseudoknotted RNA structure prediction specifically and to handling gapped fragments more generally - which has a much more complex recursive structure than other problems to which sparsification has been applied. We analyse how to sparsify four pseudoknot structure prediction algorithms, among those the most general method available (the Rivas-Eddy algorithm) and the fastest one (Reeder-Giegerich algorithm). In all algorithms the number of "candidate" substructures to be considered is reduced.

Conclusions

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

Engineering cooperative tecto-RNA complexes having programmable stoichiometries

High affinity and specificity RNA-RNA binding interfaces can be constructed by combining pairs of GNRA loop/loop-receptor interaction motifs. These interactions can be fused using flexible four-way junction motifs to create divalent, self-assembling scaffolding units ('tecto-RNA') that have favorable properties for nanomedicine and other applications. We describe the design and directed assembly of tecto-RNA units ranging from closed, cooperatively assembling ring-shaped complexes of programmable stoichiometries (dimers, trimers and tetramers) to open multimeric structures. The novelty of this work is that tuning of the stoichiometries of self-assembled complexes is achieved by precise positioning of the interaction motifs in the monomer units rather than changing their binding specificities. Structure-probing and transmission electron microscopy studies as well as thermodynamic analysis support formation of closed cooperative complexes that are highly resistant to nuclease digestion. The present designs provide two helical arms per RNA monomer for further functionalization aims.

Lifting prediction to alignment of RNA pseudoknots

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

Inverse folding of RNA pseudoknot structures

Background

RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and G-U-base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse folding algorithms, RNAinverse, RNA-SSD as well as INFO-RNA are limited to RNA secondary structures, we present in this paper the inverse folding algorithm Inv which can deal with 3-noncrossing, canonical pseudoknot structures.

Results

In this paper we present the inverse folding algorithm Inv. We give a detailed analysis of Inv, including pseudocodes. We show that Inv allows to design in particular 3-noncrossing nonplanar RNA pseudoknot 3-noncrossing RNA structures-a class which is difficult to construct via dynamic programming routines. Inv is freely available at http://www.combinatorics.cn/cbpc/inv.html.

Conclusions

The algorithm Inv extends inverse folding capabilities to RNA pseudoknot structures. In comparison with RNAinverse it uses new ideas, for instance by considering sets of competing structures. As a result, Inv is not only able to find novel sequences even for RNA secondary structures, it does so in the context of competing structures that potentially exhibit cross-serial interactions.

Quantifying the relationship between sequence and three-dimensional structure conservation in RNA

Background

In recent years, the number of available RNA structures has rapidly grown reflecting the increased interest on RNA biology. Similarly to the studies carried out two decades ago for proteins, which gave the fundamental grounds for developing comparative protein structure prediction methods, we are now able to quantify the relationship between sequence and structure conservation in RNA.

Results

Here we introduce an all-against-all sequence- and three-dimensional (3D) structure-based comparison of a representative set of RNA structures, which have allowed us to quantitatively confirm that: (i) there is a measurable relationship between sequence and structure conservation that weakens for alignments resulting in below 60% sequence identity, (ii) evolution tends to conserve more RNA structure than sequence, and (iii) there is a twilight zone for RNA homology detection.

Discussion

The computational analysis here presented quantitatively describes the relationship between sequence and structure for RNA molecules and defines a twilight zone region for detecting RNA homology. Our work could represent the theoretical basis and limitations for future developments in comparative RNA 3D structure prediction.

Prediction of RNA multiloop and pseudoknot conformations from a lattice-based, coarse-grain tertiary structure model

We present a semiquantitative lattice model of RNA folding, which is able to reproduce complex folded structures such as multiloops and pseudoknots without relying on the frequently employed ad hoc generalization of the Jacobson-Stockmayer loop entropy. We derive the model parameters from the Turner description of simple secondary structural elements and pay particular attention to the unification of mismatch and coaxial stacking parameters as well as of border and nonlocal loop parameters, resulting in a reduced, unified parameter set for simple loops of arbitrary type and size. For elementary structures, the predictive power of the model is comparable to the standard secondary structure approaches, from which its parameters are derived. For complex structures, our approach offers a systematic treatment of generic effects of chain connectivity as well as of excluded volume or attractive interactions between and within all elements of the secondary structure. We reproduce the native structures of tRNA multiloops and of viral frameshift signal pseudoknots.

Predicting loop-helix tertiary structural contacts in RNA pseudoknots

Tertiary interactions between loops and helical stems play critical roles in the biological function of many RNA pseudoknots. However, quantitative predictions for RNA tertiary interactions remain elusive. Here we report a statistical mechanical model for the prediction of noncanonical loop-stem base-pairing interactions in RNA pseudoknots. Central to the model is the evaluation of the conformational entropy for the pseudoknotted folds with defined loop-stem tertiary structural contacts. We develop an RNA virtual bond-based conformational model (Vfold model), which permits a rigorous computation of the conformational entropy for a given fold that contains loop-stem tertiary contacts. With the entropy parameters predicted from the Vfold model and the energy parameters for the tertiary contacts as inserted parameters, we can then predict the RNA folding thermodynamics, from which we can extract the tertiary contact thermodynamic parameters from theory-experimental comparisons. These comparisons reveal a contact enthalpy (DeltaH) of -14 kcal/mol and a contact entropy (DeltaS) of -38 cal/mol/K for a protonated C(+)*(G-C) base triple at pH 7.0, and (DeltaH = -7 kcal/mol, DeltaS = -19 cal/mol/K) for an unprotonated base triple. Tests of the model for a series of pseudoknots show good theory-experiment agreement. Based on the extracted energy parameters for the tertiary structural contacts, the model enables predictions for the structure, stability, and folding pathways for RNA pseudoknots with known or postulated loop-stem tertiary contacts from the nucleotide sequence alone.

DotKnot: pseudoknot prediction using the probability dot plot under a refined energy model

RNA pseudoknots are functional structure elements with key roles in viral and cellular processes. Prediction of a pseudoknotted minimum free energy structure is an NP-complete problem. Practical algorithms for RNA structure prediction including restricted classes of pseudoknots suffer from high runtime and poor accuracy for longer sequences. A heuristic approach is to search for promising pseudoknot candidates in a sequence and verify those. Afterwards, the detected pseudoknots can be further analysed using bioinformatics or laboratory techniques. We present a novel pseudoknot detection method called DotKnot that extracts stem regions from the secondary structure probability dot plot and assembles pseudoknot candidates in a constructive fashion. We evaluate pseudoknot free energies using novel parameters, which have recently become available. We show that the conventional probability dot plot makes a wide class of pseudoknots including those with bulged stems manageable in an explicit fashion. The energy parameters now become the limiting factor in pseudoknot prediction. DotKnot is an efficient method for long sequences, which finds pseudoknots with higher accuracy compared to other known prediction algorithms. DotKnot is accessible as a web server at http://dotknot.csse.uwa.edu.au.

RNA structure prediction

We give an overview of RNA structure predictions in this chapter. We discuss here the main approaches to RNA structure prediction: combinatorial approaches, comparative approaches, and kinetic approaches. The main algorithms and mathematical concepts such as transformational grammars will be briefly introduced.

Improved free energy parameters for RNA pseudoknotted secondary structure prediction

Accurate prediction of RNA pseudoknotted secondary structures from the base sequence is a challenging computational problem. Since prediction algorithms rely on thermodynamic energy models to identify low-energy structures, prediction accuracy relies in large part on the quality of free energy change parameters. In this work, we use our earlier constraint generation and Boltzmann likelihood parameter estimation methods to obtain new energy parameters for two energy models for secondary structures with pseudoknots, namely, the Dirks-Pierce (DP) and the Cao-Chen (CC) models. To train our parameters, and also to test their accuracy, we create a large data set of both pseudoknotted and pseudoknot-free secondary structures. In addition to structural data our training data set also includes thermodynamic data, for which experimentally determined free energy changes are available for sequences and their reference structures. When incorporated into the HotKnots prediction algorithm, our new parameters result in significantly improved secondary structure prediction on our test data set. Specifically, the prediction accuracy when using our new parameters improves from 68% to 79% for the DP model, and from 70% to 77% for the CC model.

Random K-noncrossing RNA structures

In this paper, we introduce a combinatorial framework that provides an interpretation of RNA pseudoknot structures as sampling paths of a Markov process. Our results facilitate a variety of applications ranging from the energy-based sampling of pseudoknot structures as well as the ab initio folding via hidden Markov models. Our main result is an algorithm that generates RNA pseudoknot structures with uniform probability. This algorithm serves as a steppingstone to sequence-specific as well as energy-based transition probabilities. The approach employs a correspondence between pseudoknot structures, parametrized in terms of the maximal number of mutually crossing arcs and certain tableau sequences. The latter can be viewed as lattice paths. The main idea of this paper is to view each such lattice path as a sampling path of a stochastic process and to make use of D-finiteness for the efficient computation of the corresponding transition probabilities.

Slow formation of a pseudoknot structure is rate limiting in the productive co-transcriptional folding of the self-splicing Candida intron

Pseudoknots play critical roles in packing the active structure of various functional RNAs. The importance of the P3-P7 pseudoknot in refolding of group I intron ribozymes has been recently appreciated, while little is known about the pseudoknot function in co-transcriptional folding. Here we used the Candida group I intron as a model to address the question. We show that co-transcriptional folding of the active self-splicing intron is twice as fast as refolding. The P3-P7 pseudoknot folds slowly during co-transcriptional folding at a rate constant similar to the folding of the active ribozyme, and folding of both P3-P7 and P1-P10 pseudoknots are inhibited by antisense oligonucleotides. We conclude that when RNA folding is coupled with transcription, formation of pseudoknot structures dominates the productive folding pathway and serves as a rate-limiting step in producing the self-splicing competent Candida intron.

Viral strategies to subvert the mammalian translation machinery

Viruses do not carry their own protein biosynthesis machinery and the translation of viral proteins therefore requires that the virus usurps the machinery of the host cell. To allow optimal translation of viral proteins at the expense of cellular proteins, virus families have evolved a variety of methods to repress the host translation machinery, while allowing effective viral protein synthesis. Many viruses use noncanonical mechanisms that permit translation of their own RNAs under these conditions. Viruses have also developed mechanisms to evade host innate immune responses that would repress translation under conditions of viral infection, in particular PKR activation in response to double-stranded RNA (dsRNA). Importantly, the study of viral translation mechanisms has enormously enhanced our understanding of many aspects of the cellular protein biosynthesis pathway and its components. A number of unusual mechanisms of translation initiation that were first discovered in viruses have since been observed in cellular mRNAs, and it has become apparent that a diverse range of translation mechanisms operates in eukaryotes, allowing subtle regulation of this essential process.

Footprinting analysis of BWYV pseudoknot-ribosome complexes

Many viruses regulate translation of polycistronic mRNA using a -1 ribosomal frameshift induced by an RNA pseudoknot. When the ribosome encounters the pseudoknot barrier that resists unraveling, transient mRNA-tRNA dissociation at the decoding site, results in a shift of the reading frame. The eukaryotic frameshifting pseudoknot from the beet western yellow virus (BWYV) has been well characterized, both structurally and functionally. Here, we show that in order to obtain eukaryotic levels of frameshifting efficiencies using prokaryotic Escherichia coli ribosomes, which depend upon the structural integrity of the BWYV pseudoknot, it is necessary to shorten the mRNA spacer between the slippery sequence and the pseudoknot by 1 or 2 nucleotides (nt). Shortening of the spacer is likely to re-establish tension and/or ribosomal contacts that were otherwise lost with the smaller E. coli ribosomes. Chemical probing experiments for frameshifting and nonframeshifting BWYV constructs were performed to investigate the structural integrity of the pseudoknot confined locally at the mRNA entry site. These data, obtained in the pretranslocation state, show a compact overall pseudoknot structure, with changes in the conformation of nucleotides (i.e., increase in reactivity to chemical probes) that are first "hit" by the ribosomal helicase center. Interestingly, with the 1-nt shortened spacer, this increase of reactivity extends to a downstream nucleotide in the first base pair (bp) of stem 1, consistent with melting of this base pair. Thus, the 3 bp that will unfold upon translocation are different in both constructs with likely consequences on unfolding kinetics.

Evidence for pseudoknot formation of class I preQ1 riboswitch aptamers

All in a knot. The smallest riboswitch forms a pseudoknot in solution. This is demonstrated for preQ(1) class I aptamers by mutational analysis in combination with (1)H NMR-based structure probing. How pseudoknot formation mediates the mRNA response through its expression platform is now open for investigation.

RNA search with decision trees and partial covariance models

The use of partial covariance models to search for RNA family members in genomic sequence databases is explored. The partial models are formed from contiguous subranges of the overall RNA family multiple alignment columns. A binary decision-tree framework is presented for choosing the order to apply the partial models and the score thresholds on which to make the decisions. The decision trees are chosen to minimize computation time subject to the constraint that all of the training sequences are passed to the full covariance model for final evaluation. Computational intelligence methods are suggested to select the decision tree since the tree can be quite complex and there is no obvious method to build the tree in these cases. Experimental results from seven RNA families shows execution times of 0.066-0.268 relative to using the full covariance model alone. Tests on the full sets of known sequences for each family show that at least 95 percent of these sequences are found for two families and 100 percent for five others. Since the full covariance model is run on all sequences accepted by the partial model decision tree, the false alarm rate is at least as low as that of the full model alone.

SARA: a server for function annotation of RNA structures

Recent interest in non-coding RNA transcripts has resulted in a rapid increase of deposited RNA structures in the Protein Data Bank. However, a characterization and functional classification of the RNA structure and function space have only been partially addressed. Here, we introduce the SARA program for pair-wise alignment of RNA structures as a web server for structure-based RNA function assignment. The SARA server relies on the SARA program, which aligns two RNA structures based on a unit-vector root-mean-square approach. The likely accuracy of the SARA alignments is assessed by three different P-values estimating the statistical significance of the sequence, secondary structure and tertiary structure identity scores, respectively. Our benchmarks, which relied on a set of 419 RNA structures with known SCOR structural class, indicate that at a negative logarithm of mean P-value higher or equal than 2.5, SARA can assign the correct or a similar SCOR class to 81.4% and 95.3% of the benchmark set, respectively. The SARA server is freely accessible via the World Wide Web at http://sgu.bioinfo.cipf.es/services/SARA/.

Predicting structures and stabilities for H-type pseudoknots with interhelix loops

RNA pseudoknots play a critical role in RNA-related biology from the assembly of ribosome to the regulation of viral gene expression. A predictive model for pseudoknot structure and stability is essential for understanding and designing RNA structure and function. A previous statistical mechanical theory allows us to treat canonical H-type RNA pseudoknots that contain no intervening loop between the helices (see S. Cao and S.J. Chen [2006] in Nucleic Acids Research, Vol. 34; pp. 2634-2652). Biologically significant RNA pseudoknots often contain interhelix loops. Predicting the structure and stability for such more-general pseudoknots remains an unsolved problem. In the present study, we develop a predictive model for pseudoknots with interhelix loops. The model gives conformational entropy, stability, and the free-energy landscape from RNA sequences. The main features of this new model are the computation of the conformational entropy and folding free-energy base on the complete conformational ensemble and rigorous treatment for the excluded volume effects. Extensive tests for the structural predictions show overall good accuracy with average sensitivity and specificity equal to 0.91 and 0.91, respectively. The theory developed here may be a solid starting point for first-principles modeling of more complex, larger RNAs.

Structural Insights into riboswitch control of the biosynthesis of queuosine, a modified nucleotide found in the anticodon of tRNA

The modified nucleotide queuosine (Q) is almost universally found in the anticodon wobble position of specific tRNAs. In many bacteria, biosynthesis of Q is modulated by a class of regulatory mRNA elements called riboswitches. The preQ(1) riboswitch, found in the 5'UTR of bacterial genes involved in synthesis of the Q precursors preQ(0) and preQ(1), contains the smallest known aptamer domain. We report the solution structure of the preQ(1) riboswitch aptamer domain from Bacillus subtilis bound to preQ(1), which is a unique compact pseudoknot with three loops and two stems that encapsulates preQ(1) at the junction between the two stems. The pseudoknot only forms in the presence of preQ(1), and the 3' A-rich tail of the aptamer domain is an integral part of the pseudoknot. In the absence of preQ(1), the A-rich tail forms part of the antiterminator. These structural studies provide insight into riboswitch transcriptional control of preQ(1) biosynthesis.

Thermodynamics of a model for RNA folding

We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by Vernizzi, Orland, and Zee [Phys. Rev. Lett. 94, 168103 (2005)]. The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be efficiently studied by introducing a NxN Hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topological expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement, and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of 1/N as being a measure of the concentration of Mg2+ in solution.

RNA structure alignment by a unit-vector approach

MOTIVATION

The recent discovery of tiny RNA molecules such as microRNAs and small interfering RNA are transforming the view of RNA as a simple information transfer molecule. Similar to proteins, the native three-dimensional structure of RNA determines its biological activity. Therefore, classifying the current structural space is paramount for functionally annotating RNA molecules. The increasing numbers of RNA structures deposited in the PDB requires more accurate, automatic and benchmarked methods for RNA structure comparison. In this article, we introduce a new algorithm for RNA structure alignment based on a unit-vector approach. The algorithm has been implemented in the SARA program, which results in RNA structure pairwise alignments and their statistical significance.

RESULTS

The SARA program has been implemented to be of general applicability even when no secondary structure can be calculated from the RNA structures. A benchmark against the ARTS program using a set of 1275 non-redundant pairwise structure alignments results in inverted approximately 6% extra alignments with at least 50% structurally superposed nucleotides and base pairs. A first attempt to perform RNA automatic functional annotation based on structure alignments indicates that SARA can correctly assign the deepest SCOR classification to >60% of the query structures.

AVAILABILITY

The SARA program is freely available through a World Wide Web server http://sgu.bioinfo.cipf.es/services/SARA/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Transcriptome-wide analysis of uncapped mRNAs in Arabidopsis reveals regulation of mRNA degradation

The composition of the transcriptome is determined by a balance between mRNA synthesis and degradation. An important route for mRNA degradation produces uncapped mRNAs, and this decay process can be initiated by decapping enzymes, endonucleases, and small RNAs. Although uncapped mRNAs are an important intermediate for mRNA decay, their identity and abundance have never been studied on a large scale until recently. Here, we present an experimental method for transcriptome-wide profiling of uncapped mRNAs that can be used in any eukaryotic system. We applied the method to study the prevalence of uncapped transcripts during the early stages of Arabidopsis thaliana flower development. Uncapped transcripts were identified for the majority of expressed genes, although at different levels. By comparing uncapped RNA levels with steady state overall transcript levels, our study provides evidence for widespread mRNA degradation control in numerous biological processes involving genes of varied molecular functions, implying that uncapped mRNA levels are dynamically regulated. Sequence analyses identified structural features of transcripts and cis-elements that were associated with different levels of uncapping. These transcriptome-wide profiles of uncapped mRNAs will aid in illuminating new regulatory mechanisms of eukaryotic transcriptional networks.

Comparing the three-dimensional structures of Dicistroviridae IGR IRES RNAs with other viral RNA structures

The intergenic region (IGR) internal ribosome entry site (IRES) RNAs do not require any of the canonical translation initiation factors to recruit the ribosome to the viral RNA, they eliminate the need for initiator tRNA, and they begin translation from the A-site. The function of these IRESs depends on a specific three-dimensional folded RNA structure. Thus, a complete understanding of the mechanisms of action of these IRESs requires that we understand their structure in detail. Recently, the structures of both domains of the IGR IRES RNAs were solved by X-ray crystallography, providing the first glimpse into an entire IRES RNA structure. Here, I present an analysis of these structures, emphasizing how the structures explain many aspects of IGR IRES function, discussing how these structures have similarities to motifs found in other viral RNAs, and illustrating how these structures give rise to new mechanistic hypotheses.

RNA folding: conformational statistics, folding kinetics, and ion electrostatics

RNA folding is a remarkably complex problem that involves ion-mediated electrostatic interaction, conformational entropy, base pairing and stacking, and noncanonical interactions. During the past decade, results from a variety of experimental and theoretical studies pointed to (a) the potential ion correlation effect in Mg2+-RNA interactions, (b) the rugged energy landscapes and multistate RNA folding kinetics even for small RNA systems such as hairpins and pseudoknots, (c) the intraloop interactions and sequence-dependent loop free energy, and (d) the strong nonadditivity of chain entropy in RNA pseudoknot and other tertiary folds. Several related issues, which have not been thoroughly resolved, require combined approaches with thermodynamic and kinetic experiments, statistical mechanical modeling, and all-atom computer simulations.

Frameshifting RNA pseudoknots: structure and mechanism

Programmed ribosomal frameshifting (PRF) is one of the multiple translational recoding processes that fundamentally alters triplet decoding of the messenger RNA by the elongating ribosome. The ability of the ribosome to change translational reading frames in the −1 direction (−1 PRF) is employed by many positive strand RNA viruses, including economically important plant viruses and many human pathogens, such as retroviruses, e.g., HIV-1, and coronaviruses, e.g., the causative agent of severe acute respiratory syndrome (SARS), in order to properly express their genomes. −1 PRF is programmed by a bipartite signal embedded in the mRNA and includes a heptanucleotide “slip site” over which the paused ribosome “backs up” by one nucleotide, and a downstream stimulatory element, either an RNA pseudoknot or a very stable RNA stem–loop. These two elements are separated by six to eight nucleotides, a distance that places the 5′ edge of the downstream stimulatory element in direct contact with the mRNA entry channel of the 30S ribosomal subunit. The precise mechanism by which the downstream RNA stimulates −1 PRF by the translocating ribosome remains unclear. This review summarizes the recent structural and biophysical studies of RNA pseudoknots and places this work in the context of our evolving mechanistic understanding of translation elongation. Support for the hypothesis that the downstream stimulatory element provides a kinetic barrier to the ribosome-mediated unfolding is discussed.

Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.

Novel and efficient RNA secondary structure prediction using hierarchical folding

Algorithms for prediction of RNA secondary structure-the set of base pairs that form when an RNA molecule folds-are valuable to biologists who aim to understand RNA structure and function. Improving the accuracy and efficiency of prediction methods is an ongoing challenge, particularly for pseudoknotted secondary structures, in which base pairs overlap. This challenge is biologically important, since pseudoknotted structures play essential roles in functions of many RNA molecules, such as splicing and ribosomal frameshifting. State-of-the-art methods, which are based on free energy minimization, have high run-time complexity (typically Theta(n(5)) or worse), and can handle (minimize over) only limited types of pseudoknotted structures. We propose a new approach for prediction of pseudoknotted structures, motivated by the hypothesis that RNA structures fold hierarchically, with pseudoknot-free (non-overlapping) base pairs forming first, and pseudoknots forming later so as to minimize energy relative to the folded pseudoknot-free structure. Our HFold algorithm uses two-phase energy minimization to predict hierarchically formed secondary structures in O(n(3)) time, matching the complexity of the best algorithms for pseudoknot-free secondary structure prediction via energy minimization. Our algorithm can handle a wide range of biological structures, including kissing hairpins and nested kissing hairpins, which have previously required Theta(n(6)) time.

KnotSeeker: heuristic pseudoknot detection in long RNA sequences

Pseudoknots are folded structures in RNA molecules that perform essential functions as part of cellular transcription machinery and regulatory processes. The prediction of these structures in RNA molecules has important implications in antiviral drug design. It has been shown that the prediction of pseudoknots is an NP-complete problem. Practical structure prediction algorithms based on free energy minimization employ a restricted problem class and dynamic programming. However, these algorithms are computationally very expensive, and their accuracy deteriorates if the input sequence containing the pseudoknot is too long. Heuristic methods can be more efficient, but do not guarantee an optimal solution in regards to the minimum free energy model. We present KnotSeeker, a new heuristic algorithm for the detection of pseudoknots in RNA sequences as a preliminary step for structure prediction. Our method uses a hybrid sequence matching and free energy minimization approach to perform a screening of the primary sequence. We select short sequence fragments as possible candidates that may contain pseudoknots and verify them by using an existing dynamic programming algorithm and a minimum weight independent set calculation. KnotSeeker is significantly more accurate in detecting pseudoknots compared to other common methods as reported in the literature. It is very efficient and therefore a practical tool, especially for long sequences. The algorithm has been implemented in Python and it also uses C/C++ code from several other known techniques. The code is available from http://www.csse.uwa.edu.au/~datta/pseudoknot.

From knotted to nested RNA structures: a variety of computational methods for pseudoknot removal

Pseudoknots are abundant in RNA structures. Many computational analyses require pseudoknot-free structures, which means that some of the base pairs in the knotted structure must be disregarded to obtain a nested structure. There is a surprising diversity of methods to perform this pseudoknot removal task, but these methods are often poorly described and studies can therefore be difficult to reproduce (in part, because different procedures may be intuitively obvious to different investigators). Here we provide a variety of algorithms for pseudoknot removal, some of which can incorporate sequence or alignment information in the removal process. We demonstrate that different methods lead to different results, which might affect structure-based analyses. This work thus provides a starting point for discussion of the extent to which these different methods recapture the underlying biological reality. We provide access to reference implementations through a web interface (at http://www.ibi.vu.nl/programs/k2nwww), and the source code is available in the PyCogent project.

Single-molecule mechanical unfolding and folding of a pseudoknot in human telomerase RNA

RNA unfolding and folding reactions in physiological conditions can be facilitated by mechanical force one molecule at a time. By using force-measuring optical tweezers, we studied the mechanical unfolding and folding of a hairpin-type pseudoknot in human telomerase RNA in a near-physiological solution, and at room temperature. Discrete two-state folding transitions of the pseudoknot are seen at approximately 10 and approximately 5 piconewtons (pN), with ensemble rate constants of approximately 0.1 sec(-1), by stepwise force-drop experiments. Folding studies of the isolated 5'-hairpin construct suggested that the 5'-hairpin within the pseudoknot forms first, followed by formation of the 3'-stem. Stepwise formation of the pseudoknot structure at low forces are in contrast with the one-step unfolding at high forces of approximately 46 pN, at an average rate of approximately 0.05 sec(-1). In the constant-force folding trajectories at approximately 10 pN and approximately 5 pN, transient formation of nonnative structures were observed, which is direct experimental evidence that folding of both the hairpin and pseudoknot takes complex pathways. Possible nonnative structures and folding pathways are discussed.

SimulFold: simultaneously inferring RNA structures including pseudoknots, alignments, and trees using a Bayesian MCMC framework

Computational methods for predicting evolutionarily conserved rather than thermodynamic RNA structures have recently attracted increased interest. These methods are indispensable not only for elucidating the regulatory roles of known RNA transcripts, but also for predicting RNA genes. It has been notoriously difficult to devise them to make the best use of the available data and to predict high-quality RNA structures that may also contain pseudoknots. We introduce a novel theoretical framework for co-estimating an RNA secondary structure including pseudoknots, a multiple sequence alignment, and an evolutionary tree, given several RNA input sequences. We also present an implementation of the framework in a new computer program, called SimulFold, which employs a Bayesian Markov chain Monte Carlo method to sample from the joint posterior distribution of RNA structures, alignments, and trees. We use the new framework to predict RNA structures, and comprehensively evaluate the quality of our predictions by comparing our results to those of several other programs. We also present preliminary data that show SimulFold's potential as an alignment and phylogeny prediction method. SimulFold overcomes many conceptual limitations that current RNA structure prediction methods face, introduces several new theoretical techniques, and generates high-quality predictions of conserved RNA structures that may include pseudoknots. It is thus likely to have a strong impact, both on the field of RNA structure prediction and on a wide range of data analyses.

Accurate multiple sequence-structure alignment of RNA sequences using combinatorial optimization

Background

The discovery of functional non-coding RNA sequences has led to an increasing interest in algorithms related to RNA analysis. Traditional sequence alignment algorithms, however, fail at computing reliable alignments of low-homology RNA sequences. The spatial conformation of RNA sequences largely determines their function, and therefore RNA alignment algorithms have to take structural information into account.

Results

We present a graph-based representation for sequence-structure alignments, which we model as an integer linear program (ILP). We sketch how we compute an optimal or near-optimal solution to the ILP using methods from combinatorial optimization, and present results on a recently published benchmark set for RNA alignments.

Conclusion

The implementation of our algorithm yields better alignments in terms of two published scores than the other programs that we tested: This is especially the case with an increasing number of input sequences. Our program LARA is freely available for academic purposes from .

RNA structure: bioinformatic analysis

The range of functions ascribed to RNA molecules has grown considerably during recent years. Consequently, the analysis and comparison of RNA sequences have become recurrent tasks in molecular biology. Because the biological function of an RNA is expressed more by its folded architecture than by its sequence, original computational tools adapted to the multifaceted RNA functions have to be developed. Such tools, recently published, enable a user to solve classical problems related to RNA research: constructing 'structural' multiple alignments, inferring complete structures and structural motifs from RNA alignments, or searching structural homology in genomic databases.

Parsing nucleic acid pseudoknotted secondary structure: algorithm and applications

Accurate prediction of pseudoknotted nucleic acid secondary structure is an important computational challenge. Prediction algorithms based on dynamic programming aim to find a structure with minimum free energy according to some thermodynamic ("sum of loop energies") model that is implicit in the recurrences of the algorithm. However, a clear definition of what exactly are the loops in pseudoknotted structures, and their associated energies, has been lacking. In this work, we present a complete classification of loops in pseudoknotted nucleic secondary structures, and describe the Rivas and Eddy and other energy models as sum-of-loops energy models. We give a linear time algorithm for parsing a pseudoknotted secondary structure into its component loops. We give two applications of our parsing algorithm. The first is a linear time algorithm to calculate the free energy of a pseudoknotted secondary structure. This is useful for heuristic prediction algorithms, which are widely used since (pseudoknotted) RNA secondary structure prediction is NP-hard. The second application is a linear time algorithm to test the generality of the dynamic programming algorithm of Akutsu for secondary structure prediction. Together with previous work, we use this algorithm to compare the generality of state-of-the-art algorithms on real biological structures.

Flipping off the riboswitch: RNA structures that control gene expression

Riboswitches are metabolite-sensing RNA structures that have been discovered in regulatory regions of messenger RNA (mRNA). They have the remarkable ability to shut off the transcription or translation of their own mRNAs in response to binding a specific metabolite. In other words, riboswitches regulate their own genes using RNA instead of protein. Three new crystal structures reveal how S-adenosylmethionine and thiamine pyrophosphate riboswitches accomplish this task.

Predicting RNA pseudoknot folding thermodynamics

Based on the experimentally determined atomic coordinates for RNA helices and the self-avoiding walks of the P (phosphate) and C₄ (carbon) atoms in the diamond lattice for the polynucleotide loop conformations, we derive a set of conformational entropy parameters for RNA pseudoknots. Based on the entropy parameters, we develop a folding thermodynamics model that enables us to compute the sequence-specific RNA pseudoknot folding free energy landscape and thermodynamics. The model is validated through extensive experimental tests both for the native structures and for the folding thermodynamics. The model predicts strong sequence-dependent helix-loop competitions in the pseudoknot stability and the resultant conformational switches between different hairpin and pseudoknot structures. For instance, for the pseudoknot domain of human telomerase RNA, a native-like and a misfolded hairpin intermediates are found to coexist on the (equilibrium) folding pathways, and the interplay between the stabilities of these intermediates causes the conformational switch that may underlie a human telomerase disease.