Thermodynamic stability and statistical significance of potential stem-loop structures situated at the frameshift sites of retroviruses.

RNA stem-loop structures situated just 3' to the frameshift sites of the retroviral gag-pol or gag-pro and pro-pol regions may make important contributions to frame-shifting in retroviruses. In this study, the thermodynamic stability and statistical significance of such secondary structural features relative to others in the sequence have been assessed using a newly developed method that combines calculations of the lowest free energy of formation of RNA secondary structures and the Monte Carlo simulations. Our results show that stem-loop structures situated just 3' to the frameshift sites are both highly stable and statistically significant relative to others in the gag-pol or gag-pro and pro-pol junction domains (both 300 nucleotides upstream and downstream from the possible frameshift sites are included) of Rous sarcoma virus (RSV), human immunodeficiency virus (HIV-1), bovine leukemia virus (BLV), human T-cell leukemia virus type II (HTLV-II), and mouse mammary tumor virus (MMTV). No other more stable, or significant folding regions are predicted in these domains.     

RNA pseudoknots. Stability and loop size requirements.

The effects of ionic conditions, loop size and loop sequence on the formation of pseudoknots by RNA oligonucleotides have been investigated using biochemical and biophysical methods. An oligonucleotide with the sequence 5' GCGAUUUCUGACCGCUUUUUUGUCAG 3' and oligonucleotides with variations in the sequences of the two loop regions, denoted by bold face type, were studied. Each sequence with the potential to form a pseudoknot can also form two stable hairpins. The pseudoknot structure is stabilized relative to the hairpins by addition of Mg2+. Even in the presence of Mg2+, the pseudoknots formed by the sequences investigated are only marginally more stable (1.5 to 2 kcal mol-1 in free energy at 37 degrees C) than either of the constituent hairpins. The pseudoknot structure is the stable conformation in the presence of Mg2+ when the first loop region is at least three nucleotides and the second is at least four nucleotides. Further deletion of nucleotides from the loop regions stabilizes possible hairpin structures relative to the pseudoknot and equilibria among secondary and tertiary structures result.     

Comparative studies of frameshifting and nonframeshifting RNA pseudoknots: a mutational and NMR investigation of pseudoknots derived from the bacteriophage T2 gene 32 mRNA and the retroviral gag-pro frameshift site

Mutational and NMR methods were used to investigate features of sequence, structure, and dynamics that are associated with the ability of a pseudoknot to stimulate a -1 frameshift. In vitro frameshift assays were performed on retroviral gag-pro frameshift-stimulating pseudoknots and their derivatives, a pseudoknot from the gene 32 mRNA of bacteriophage T2 that is not naturally associated with frameshifting, and hybrids of these pseudoknots. Results show that the gag-pro pseudoknot from human endogenous retrovirus-K10 (HERV) stimulates a -1 frameshift with an efficiency similar to that of the closely related retrovirus MMTV. The bacteriophage T2 mRNA pseudoknot was found to be a poor stimulator of frameshifting, supporting a hypothesis that the retroviral pseudoknots have distinctive properties that make them efficient frameshift stimulators. A hybrid, designed by combining features of the bacteriophage and retroviral pseudoknots, was found to stimulate frameshifting while retaining significant structural similarity to the nonframeshifting bacteriophage pseudoknot. Mutational analyses of the retroviral and hybrid pseudoknots were used to evaluate the effects of an unpaired (wedged) adenosine at the junction of the pseudoknot stems, changing the base pairs near the junction of the two stems, and changing the identity of the loop 2 nucleotide nearest the junction of the stems. Pseudoknots both with and without the wedged adenosine can stimulate frameshifting, though the identities of the nucleotides near the stem1/stem2 junction do influence efficiency. NMR data showed that the bacteriophage and hybrid pseudoknots are similar in their local structure at the junction of the stems, indicating that pseudoknots that are similar in this structural feature can differ radically in their ability to stimulate frameshifting. NMR methods were used to compare the internal motions of the bacteriophage T2 pseudoknot and representative frameshifting pseudoknots. The stems of the investigated pseudoknots are similarly well ordered on the time scales to which nitrogen-15 relaxation data are sensitive; however, solvent exchange rates for protons at the junction of the two stems of the nonframeshifting bacteriophage pseudoknot are significantly slower than the analogous protons in the representative frameshifting pseudoknots.     

Characterization of the mechanical unfolding of RNA pseudoknots

The pseudoknot is an important RNA structural element that provides an excellent model system for studying the contributions of tertiary interactions to RNA stability and to folding kinetics. RNA pseudoknots are also of interest because of their key role in the control of ribosomal frameshifting by viral RNAs. Their mechanical properties are directly relevant to their unfolding by ribosomes during translation. We have used optical tweezers to study the kinetics and thermodynamics of mechanical unfolding and refolding of single RNA molecules. Here we describe the unfolding of the frameshifting pseudoknot from infectious bronchitis virus (IBV), three constituent hairpins, and three mutants of the IBV pseudoknot. All four pseudoknots cause −1 programmed ribosomal frameshifting. We have measured the free energies and rates of mechanical unfolding and refolding of the four frameshifting pseudoknots. Our results show that the IBV pseudoknot requires a higher force than its corresponding hairpins to unfold. Furthermore, its rate of unfolding changes little with increasing force, in contrast with the rate of hairpin unfolding. The presence of Mg²⁺ significantly increases the kinetic barriers to unfolding the IBV pseudoknot, but has only a minor effect on the hairpin unfolding. The greater mechanical stability of pseudoknots compared to hairpins, and their kinetic insensitivity to force supports the hypothesis that −1 frameshifting depends on the difficulty of unfolding the mRNA.     

PseudoViewer: automatic visualization of RNA pseudoknots

MOTIVATION: Several algorithms have been developed for drawing RNA secondary structures, however none of these can be used to draw RNA pseudoknot structures. In the sense of graph theory, a drawing of RNA secondary structures is a tree, whereas a drawing of RNA pseudoknots is a graph with inner cycles within a pseudoknot as well as possible outer cycles formed between a pseudoknot and other structural elements. Thus, RNA pseudoknots are more difficult to visualize than RNA secondary structures. Since no automatic method for drawing RNA pseudoknots exists, visualizing RNA pseudoknots relies on significant amount of manual work and does not yield satisfactory results. The task of visualizing RNA pseudoknots by hand becomes more challenging as the size and complexity of the RNA pseudoknots increase. RESULTS: We have developed a new representation and an algorithm for drawing H-type pseudoknots with RNA secondary structures. Compared to existing representations of H-type pseudoknots, the new representation ensures uniform and clear drawings with no edge crossing for any H-type pseudoknots. To the best of our knowledge, this is the first algorithm for automatically drawing RNA pseudoknots with RNA secondary structures. The algorithm has been implemented in a Java program, which can be executed on any computing system. Experimental results demonstrate that the algorithm generates an aesthetically pleasing drawing of all H-type pseudoknots. The results have also shown that the drawing has high readability, enabling the user to quickly and easily recognize the whole RNA structure as well as the pseudoknots themselves.     

Biphasic folding kinetics of RNA pseudoknots and telomerase RNA activity

Using a combined master equation and kinetic cluster approach, we investigate RNA pseudoknot folding and unfolding kinetics. The energetic parameters are computed from a recently developed Vfold model for RNA secondary structure and pseudoknot folding thermodynamics. The folding kinetics theory is based on the complete conformational ensemble, including all the native-like and non-native states. The predicted folding and unfolding pathways, activation barriers, Arrhenius plots, and rate-limiting steps lead to several findings. First, for the PK5 pseudoknot, a misfolded 5' hairpin emerges as a stable kinetic trap in the folding process, and the detrapping from this misfolded state is the rate-limiting step for the overall folding process. The calculated rate constant and activation barrier agree well with the experimental data. Second, as an application of the model, we investigate the kinetic folding pathways for human telomerase RNA (hTR) pseudoknot. The predicted folding and unfolding pathways not only support the proposed role of conformational switch between hairpin and pseudoknot in hTR activity, but also reveal molecular mechanism for the conformational switch. Furthermore, for an experimentally studied hTR mutation, whose hairpin intermediate is destabilized, the model predicts a long-lived transient hairpin structure, and the switch between the transient hairpin intermediate and the native pseudoknot may be responsible for the observed hTR activity. Such finding would help resolve the apparent contradiction between the observed hTR activity and the absence of a stable hairpin.     

PseudoBase: a database with RNA pseudoknots

PseudoBase is a database containing structural, functional and sequence data related to RNA pseudo-knots. It can be reached at http://wwwbio.Leiden Univ.nl/ approximately Batenburg/PKB.html. This page will direct the user to a retrieval page from where a particular pseudoknot can be chosen, or to a submission page which enables the user to add pseudoknot information to the database or to an informative page that elaborates on the various aspects of the database. For each pseudoknot, 12 items are stored, e.g. the nucleotides of the region that contains the pseudoknot, the stem positions of the pseudoknot, the EMBL accession number of the sequence that contains this pseudoknot and the support that can be given regarding the reliability of the pseudoknot. Access is via a small number of steps, using 16 different categories. The development process was done by applying the evolutionary methodology for software development rather than by applying the methodology of the classical waterfall model or the more modern spiral model.     

PseudoBase: structural information on RNA pseudoknots

PseudoBase is a database containing structural, functional and sequence data related to RNA pseudo-knots. It can be reached at http://wwwbio.LeidenUniv.nl/ approximately Batenburg/PKB.html. For each pseudoknot, thirteen items are stored, for example the relevant sequence, the stem positions of the pseudoknot, the EMBL accession number of the sequence and the support that can be given regarding the reliability of the pseudo-knot. Since the last publication, information on sizes of the stems and the loops in the pseudoknots has been added. Also added are alternative entries that produce surveys of where the pseudoknots are, sorted according to stem size or loop size.     

G-ribo motif favors the formation of pseudoknots in ribosomal RNA

Analysis of the pseudoknots existing in the ribosomal RNA showed that four of them are formed with the help of G-ribo, a recently identified RNA recurrent motif. The analysis of these pseudoknots revealed two major aspects in the G-ribo motif structure, which together provide the structural context favoring the formation of two different types of pseudoknots. The first aspect pertains to a particular side-by-side juxtaposition of two double helices that facilitates switches of the polynucleotide chain between different strands. The second aspect deals with the presence of an adenosine at a specific place where it can stabilize a particular arrangement of two quasicoaxial helices required for the pseudoknot formation. Additional analysis shows that the latter aspect is also present in other pseudoknots not related to the G-ribo motif or the ribosome, and thus represents a general structural element favoring the formation of pseudoknots.     

RNA aptamers that bind the nucleocapsid protein contain pseudoknots

We screened two independent RNA libraries consisting of molecules of 50 nucleotides of random sequence, one of which had additional viral psi-sequences to isolate RNA aptamers that bound to the mature form of the nucleocapsid (NC) protein of Human Immunodeficiency Virus Type-1 (HIV-1). Surface Plasmon Resonance measurements and gel shift assays showed that the RNA aptamers bound with high affinity and specificity. We employed RNase footprinting to characterize the RNA structures and to map their protein binding sites. Most of the selected RNA aptamers contained a plausible pseudoknot in addition to the characteristic stem-loop structure. Moreover, the pseudoknots were part of the NC binding sites. We propose that higher order structures such as pseudoknots may constitute binding motifs for nucleic acid binding proteins, especially for NC protein, which is a nucleic acid chaperone.     

Identifying complete RNA structural ensembles including pseudoknots

The close relationship between RNA structure and function underlines the significance of accurately predicting RNA structures from sequence information. Structural topologies such as pseudoknots are of particular interest due to their ubiquity and direct involvement in RNA function, but identifying pseudoknots is a computationally challenging problem and existing heuristic approaches usually perform poorly for RNA sequences of even a few hundred bases. We survey the performance of pseudoknot prediction methods on a data set of full-length RNA sequences representing varied sequence lengths, and biological RNA classes such as RNase P RNA, Group I Intron, tmRNA and tRNA. Pseudoknot prediction methods are compared with minimum free energy and suboptimal secondary structure prediction methods in terms of correct base-pairs, stems and pseudoknots and we find that the ensemble of suboptimal structure predictions succeeds in identifying correct structural elements in RNA that are usually missed in MFE and pseudoknot predictions. We propose a strategy to identify a comprehensive set of non-redundant stems in the suboptimal structure space of a RNA molecule by applying heuristics that reduce the structural redundancy of the predicted suboptimal structures by merging slightly varying stems that are predicted to form in local sequence regions. This reduced-redundancy set of structural elements consistently outperforms more specialized approaches.in data sets. Thus, the suboptimal folding space can be used to represent the structural diversity of an RNA molecule more comprehensively than optimal structure prediction approaches alone.     

Prediction of consensus RNA secondary structures including pseudoknots

Most functional RNA molecules have characteristic structures that are highly conserved in evolution. Many of them contain pseudoknots. Here, we present a method for computing the consensus structures including pseudoknots based on alignments of a few sequences. The algorithm combines thermodynamic and covariation information to assign scores to all possible base pairs, the base pairs are chosen with the help of the maximum weighted matching algorithm. We applied our algorithm to a number of different types of RNA known to contain pseudoknots. All pseudoknots were predicted correctly and more than 85 percent of the base pairs were identified.     

RNA folding: pseudoknots, loops and bulges

The three-dimensional structures adopted by RNA molecules are crucial to their biological functions. The nucleotides of an RNA molecule interact to form characteristic secondary-structure motifs. Tertiary interactions orient these secondary-structure elements with respect to each other to form the functional RNA. Here we describe the basic structural elements with special emphasis on a novel tertiary motif, the pseudoknot.     

On the page number of RNA secondary structures with pseudoknots

Let ${\mathcal {S}}$ denote the set of (possibly noncanonical) base pairs {i, j} of an RNA tertiary structure; i.e. ${\{i, j\} \in \mathcal {S}}$ if there is a hydrogen bond between the ith and jth nucleotide. The page number of ${\mathcal {S}}$ , denoted ${\pi(\mathcal {S})}$ , is the minimum number k such that ${\mathcal {S}}$ can be decomposed into a disjoint union of k secondary structures. Here, we show that computing the page number is NP-complete; we describe an exact computation of page number, using constraint programming, and determine the page number of a collection of RNA tertiary structures, for which the topological genus is known. We describe an approximation algorithm from which it follows that ${\omega(\mathcal {S}) \leq \pi(\mathcal {S}) \leq \omega(\mathcal {S}) \cdot \log n}$ , where the clique number of ${\mathcal {S}, \omega(\mathcal {S})}$ , denotes the maximum number of base pairs that pairwise cross each other.