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.     

Solution structure of a luteoviral P1-P2 frameshifting mRNA pseudoknot

A hairpin-type messenger RNA pseudoknot from pea enation mosaic virus RNA1 (PEMV-1) regulates the efficiency of programmed -1 ribosomal frameshifting. The solution structure and 15N relaxation rates reveal that the PEMV-1 pseudoknot is a compact-folded structure composed almost entirely of RNA triple helix. A three nucleotide reverse turn in loop 1 positions a protonated cytidine, C(10), in the correct orientation to form an A((n-1)).C(+).G-C(n) major groove base quadruple, like that found in the beet western yellows virus pseudoknot and the hepatitis delta virus ribozyme, despite distinct structural contexts. A novel loop 2-loop 1 A.U Hoogsteen base-pair stacks on the C(10)(+).G(28) base-pair of the A(12).C(10)(+).G(28)-C(13) quadruple and forms a wedge between the pseudoknot stems stabilizing a bent and over-rotated global conformation. Substitution of key nucleotides that stabilize the unique conformation of the PEMV-1 pseudoknot greatly reduces ribosomal frameshifting efficacy.     

A conserved RNA pseudoknot in a putative molecular switch domain of the 3'-untranslated region of coronaviruses is only marginally stable

The 3'-untranslated region (UTR) of the group 2 coronavirus mouse hepatitis virus (MHV) genome contains a predicted bulged stem-loop (designated P0ab), a conserved cis-acting pseudoknot (PK), and a more distal stem-loop (designated P2). Base-pairing to create the pseudoknot-forming stem (P1(pk)) is mutually exclusive with formation of stem P0a at the base of the bulged stem-loop; as a result, the two structures cannot be present simultaneously. Herein, we use thermodynamic methods to evaluate the ability of individual subdomains of the 3' UTR to adopt a pseudoknotted conformation. We find that an RNA capable of forming only the predicted PK (58 nt; 3' nucleotides 241-185) adopts the P2 stem-loop with little evidence for P1(pk) pairing in 0.1 M KCl and the absence of Mg(2+); as Mg(2+) or 1 M KCl is added, a new thermal unfolding transition is induced and assignable to P1(pk) pairing. The P1(pk) helix is only marginally stable, ΔG(25) ≈ 1.2 ± 0.3 kcal/mol (5.0 mM Mg(2+), 100 mM K(+)), and unfolded at 37°C. Similar findings characterize an RNA 5' extended through the P0b helix only (89 nt; 294-185). In contrast, an RNA capable of forming either the P0a helix or the pseudoknot (97 nt; 301-185) forms no P1(pk) helix. Thermal unfolding simulations are fully consistent with these experimental findings. These data reveal that the PK forms weakly and only when the competing double-hairpin structure cannot form; in the UTR RNA, the double hairpin is the predominant conformer under all solution conditions.     

Protein NMR structure determination with automated NOE assignment using the new software CANDID and the torsion angle dynamics algorithm DYANA

Combined automated NOE assignment and structure determination module (CANDID) is a new software for efficient NMR structure determination of proteins by automated assignment of the NOESY spectra. CANDID uses an iterative approach with multiple cycles of NOE cross-peak assignment and protein structure calculation using the fast DYANA torsion angle dynamics algorithm, so that the result from each CANDID cycle consists of exhaustive, possibly ambiguous NOE cross-peak assignments in all available spectra and a three-dimensional protein structure represented by a bundle of conformers. The input for the first CANDID cycle consists of the amino acid sequence, the chemical shift list from the sequence-specific resonance assignment, and listings of the cross-peak positions and volumes in one or several two, three or four-dimensional NOESY spectra. The input for the second and subsequent CANDID cycles contains the three-dimensional protein structure from the previous cycle, in addition to the complete input used for the first cycle. CANDID includes two new elements that make it robust with respect to the presence of artifacts in the input data, i.e. network-anchoring and constraint-combination, which have a key role in de novo protein structure determinations for the successful generation of the correct polypeptide fold by the first CANDID cycle. Network-anchoring makes use of the fact that any network of correct NOE cross-peak assignments forms a self-consistent set; the initial, chemical shift-based assignments for each individual NOE cross-peak are therefore weighted by the extent to which they can be embedded into the network formed by all other NOE cross-peak assignments. Constraint-combination reduces the deleterious impact of artifact NOE upper distance constraints in the input for a protein structure calculation by combining the assignments for two or several peaks into a single upper limit distance constraint, which lowers the probability that the presence of an artifact peak will influence the outcome of the structure calculation. CANDID test calculations were performed with NMR data sets of four proteins for which high-quality structures had previously been solved by interactive protocols, and they yielded comparable results to these reference structure determinations with regard to both the residual constraint violations, and the precision and accuracy of the atomic coordinates. The CANDID approach has further been validated by de novo NMR structure determinations of four additional proteins. The experience gained in these calculations shows that once nearly complete sequence-specific resonance assignments are available, the automated CANDID approach results in greatly enhanced efficiency of the NOESY spectral analysis. The fact that the correct fold is obtained in cycle 1 of a de novo structure calculation is the single most important advance achieved with CANDID, when compared with previously proposed automated NOESY assignment methods that do not use network-anchoring and constraint-combination.     

The stimulatory RNA of the Visna-Maedi retrovirus ribosomal frameshifting signal is an unusual pseudoknot with an interstem element

The stimulatory RNA of the Visna-Maedi virus (VMV) -1 ribosomal frameshifting signal has not previously been characterized but can be modeled either as a two-stem helix, reminiscent of the HIV-1 frameshift-stimulatory RNA, or as an RNA pseudoknot. The pseudoknot is unusual in that it would include a 7 nucleotide loop (termed here an interstem element [ISE]) between the two stems. In almost all frameshift-promoting pseudoknots, ISEs are absent or comprise a single adenosine residue. Using a combination of RNA structure probing, site directed mutagenesis, NMR, and phylogenetic sequence comparisons, we show here that the VMV stimulatory RNA is indeed a pseudoknot, conforming closely to the modeled structure, and that the ISE is essential for frameshifting. Pseudoknot function was predictably sensitive to changes in the length of the ISE, yet altering its sequence to alternate pyrimidine/purine bases was also detrimental to frameshifting, perhaps through modulation of local tertiary interactions. How the ISE is placed in the context of an appropriate helical junction conformation is not known, but its presence impacts on other elements of the pseudoknot, for example, the necessity for a longer than expected loop 1. This may be required to accommodate an increased flexibility of the pseudoknot brought about by the ISE. In support of this, (1)H NMR analysis at increasing temperatures revealed that stem 2 of the VMV pseudoknot is more labile than stem 1, perhaps as a consequence of its connection to stem 1 solely via flexible single-stranded loops.     

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.     

Thermodynamic characterization of the Saccharomyces cerevisiae telomerase RNA pseudoknot domain in vitro

Recent structural and functional characterization of the pseudoknot in the Saccharomyces cerevisiae telomerase RNA (TLC1) has demonstrated that tertiary structure is present, similar to that previously described for the human and Kluyveromyces lactis telomerase RNAs. In order to biophysically characterize the identified pseudoknot secondary and tertiary structures, UV-monitored thermal denaturation experiments, nuclear magnetic resonance spectroscopy, and native gel electrophoresis were used to investigate various potential conformations in the pseudoknot domain in vitro, in the absence of the telomerase protein. Here, we demonstrate that alternative secondary structures are not mutually exclusive in the S. cerevisiae telomerase RNA, tertiary structure contributes 1.5 kcal mol(-1) to the stability of the pseudoknot (≈ half the stability observed for the human telomerase pseudoknot), and identify additional base pairs in the 3' pseudoknot stem near the helical junction. In addition, sequence conservation in an adjacent overlapping hairpin appears to prevent dimerization and alternative conformations in the context of the entire pseudoknot-containing region. Thus, this work provides a detailed in vitro characterization of the thermodynamic features of the S. cerevisiae TLC1 pseudoknot region for comparison with other telomerase RNA pseudoknots.     

Dynamic behavior of the telomerase RNA hairpin structure and its relationship to dyskeratosis congenita

In this paper, we present the results from a comprehensive study of nanosecond-scale implicit and explicit solvent molecular dynamics simulations of the wild-type telomerase RNA hairpin. The effects of various mutations on telomerase RNA dynamics are also investigated. Overall, we found that the human telomerase hairpin is a very flexible molecule. In particular, periodically the molecule exhibits dramatic structural fluctuations represented by the opening and closing of a non-canonical base-pair region. These structural deviations correspond to significant disruptions of the direct hydrogen bonding network in the helix, widening of the major groove of the hairpin structure, and causing several U and C nucleotides to protrude into the major groove from the helix permitting them to hydrogen bond with, for example, the P3 domain of the telomerase RNA. We suggest that these structural fluctuations expose a nucleation point for pseudoknot formation. We also found that mutations in the pentaloop and non-canonical region stabilize the hairpin. Moreover, our results show that the hairpin with dyskeratosis congenita mutations is more stable and less flexible than the wild-type hairpin due to base stacking in the pentaloop. The results from our molecular dynamics simulations are in agreement with experimental observations. In addition, they suggest a possible mechanism for pseudoknot formation based on the dynamics of the hairpin structure and also may explain the mutational aspects of dyskeratosis congenita.     

Distributed torsion angle grid search in high dimensions: A systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized -turn conformation, an alanine octapeptide restrained to a right-handed helical conformation, and the structured region of the peptide SYPFDV.     

NMR assignment of the N-terminal region of human La free and in complex with RNA

¹H, ¹⁵N and ¹³C chemical shift assignments are presented for the N-terminal region of human La protein, in the apo and 5′-UUUU RNA-bound state. Secondary structure analysis shows conformational changes in the interdomain linker upon complex formation.     

Full 1H NMR assignment of a 24-nucleotide RNA hairpin: Application of the 1H 3D-NOE/2QC experiment

The subject RNA models the binding site for the coat protein of the R17 virus, as well as the ribosome recognition sequence for the R17 replicase gene. With an RNA of this size, overlaps among the sugar protons complicate assignments of the ¹H NMR spectrum. The cross peaks that overlap significantly in 2D-NOE spectra can frequently be resolved by introducing a third, in our approach the double-quantum, frequency axis. In particular the planes in a 3D-NOE/2QC spectrum perpendicular to the 2Q axis are extremely useful, showing a highly informative repeating NOE-2Q pattern. In this experiment substantial J-coupling confers special advantages. This always occurs for geminal pairs (H5/H5 for RNA plus H2/H2 for DNA), as well as for H5/H6, for H3/H4 in sugars with substantial populations of the N-pucker, for H1/H2 for S-puckered sugars, and usually for H2/H3. For the 24-mer RNA hairpin the additional information from the 3D-NOE/2QC spectrum allowed assignment of all of the non-exchangeable protons, eliminating the need for stable-isotope labeling.     

Assignment and modeling of the Rev Response Element RNA bound to a Rev peptide using 13C-heteronuclear NMR

Summary The Rev Response Element (RRE) RNA-Rev protein interaction is important for regulation of gene expression in the human immunodeficiency virus. A model system for this interaction, which includes stem IIB of the RRE RNA and an arginine-rich peptide from the RNA-binding domain of Rev, was studied using multidimensional heteronuclear NMR. Assignment of the RNA when bound to the peptide was obtained from NMR experiments utilizing uniformly and specifically ¹³C-labeled RNA. Isotopic filtering experiments on the specifically labeled RNA enabled unambiguous assignment of unusual nonsequential NOE patterns present in the internal loop of the RRE. A three-dimensional model of the RNA in the complex was obtained using restrained molecular dynamics calculations. The internal loop contains two purine-purine base pairs, which are stacked to form one continuous helix flanked by two A-form regions. The formation of a G-G base pair in the internal loop requires an unusual structure of the phosphate backbone. This structural feature is consistent with mutational data as being important for the binding of Rev to the RRE. The G-G base pair may play an important role in opening the normally narrow major groove of A-form RNA to permit binding of the Rev basic domain.     

RNA helical packing in solution: NMR structure of a 30 kDa GAAA tetraloop-receptor complex

Tertiary interactions are critical for proper RNA folding and ribozyme catalysis. RNA tertiary structure is often condensed through long-range helical packing interactions mediated by loop-receptor motifs. RNA structures displaying helical packing by loop-receptor interactions have been solved by X-ray crystallography, but not by NMR. Here, we report the NMR structure of a 30 kDa GAAA tetraloop-receptor RNA complex. In order to stabilize the complex, we used a modular design in which the RNA was engineered to form a homodimer, with each subunit containing a GAAA tetraloop phased one helical turn apart from its cognate 11-nucleotide receptor domain. The structure determination utilized specific isotopic labeling patterns (2H, 13C and 15N) and refinement against residual dipolar couplings. We observe a unique and highly unusual chemical shift pattern for an adenosine platform interaction that reveals a spectroscopic fingerprint for this motif. The structure of the GAAA tetraloop-receptor interaction is well defined solely from experimental NMR data, shows minor deviations from previously solved crystal structures, and verifies the previously inferred hydrogen bonding patterns within this motif. This work demonstrates the feasibility of using engineered homodimers as modular systems for the determination of RNA tertiary interactions by NMR.