RNA dimerization plays a role in ribosomal frameshifting of the SARS coronavirus

Messenger RNA encoded signals that are involved in programmed -1 ribosomal frameshifting (-1 PRF) are typically two-stemmed hairpin (H)-type pseudoknots (pks). We previously described an unusual three-stemmed pseudoknot from the severe acute respiratory syndrome (SARS) coronavirus (CoV) that stimulated -1 PRF. The conserved existence of a third stem–loop suggested an important hitherto unknown function. Here we present new information describing structure and function of the third stem of the SARS pseudoknot. We uncovered RNA dimerization through a palindromic sequence embedded in the SARS-CoV Stem 3. Further in vitro analysis revealed that SARS-CoV RNA dimers assemble through ‘kissing’ loop–loop interactions. We also show that loop–loop kissing complex formation becomes more efficient at physiological temperature and in the presence of magnesium. When the palindromic sequence was mutated, in vitro RNA dimerization was abolished, and frameshifting was reduced from 15 to 5.7%. Furthermore, the inability to dimerize caused by the silent codon change in Stem 3 of SARS-CoV changed the viral growth kinetics and affected the levels of genomic and subgenomic RNA in infected cells. These results suggest that the homodimeric RNA complex formed by the SARS pseudoknot occurs in the cellular environment and that loop–loop kissing interactions involving Stem 3 modulate -1 PRF and play a role in subgenomic and full-length RNA synthesis.     

A Characteristic Bent Conformation of RNA Pseudoknots Promotes –1 Frameshifting during Translation of Retroviral RNA

The structures of four different RNA pseudoknots that provide one of the signals required for ribosomal frameshifting in mouse mammary tumor virus have been determined by NMR. The RNA pseudoknots have similar sequences and assume similar secondary structures, but show significantly different frameshifting efficiencies. The three-dimensional structures of one frameshifting and one non-frameshifting RNA pseudoknot had been determined previously by our group. Here we determine the structures of two new RNA pseudoknots, and relate the structures of all four pseudoknots to their frameshifting abilities. The two efficient frameshifting pseudoknots adopt characteristic bent conformations with stem 1 bending towards the major groove of stem 2. In contrast, the two poor frameshifting pseudoknots have structures very different from each other and from the efficient frameshifters. One has linear, coaxially stacked stems, the other has stems twisted and bent, but in the opposite direction to the efficient frameshifters. Changes in loop size that favor bending (shorter loops) increase frameshifting efficiency; longer loops that allow linear arrangement of the stems decrease frameshifting. Frameshifting pseudoknots in feline immunodeficiency virus and simian retrovirus have different loop sequences, but the sequences at their stem junctions imply the same bent conformation as in the mouse mammary tumor viral RNA. The requirement for a precise pseudoknot conformation for efficient frameshifting strongly implies that a specific interaction occurs between the viral RNA pseudoknot and the host protein-synthesizing machinery.     

Antisense-induced ribosomal frameshifting

Programmed ribosomal frameshifting provides a mechanism to decode information located in two overlapping reading frames by diverting a proportion of translating ribosomes into a second open reading frame (ORF). The result is the production of two proteins: the product of standard translation from ORF1 and an ORF1–ORF2 fusion protein. Such programmed frameshifting is commonly utilized as a gene expression mechanism in viruses that infect eukaryotic cells and in a subset of cellular genes. RNA secondary structures, consisting of pseudoknots or stem–loops, located downstream of the shift site often act as cis-stimulators of frameshifting. Here, we demonstrate for the first time that antisense oligonucleotides can functionally mimic these RNA structures to induce +1 ribosomal frameshifting when annealed downstream of the frameshift site, UCC UGA. Antisense-induced shifting of the ribosome into the +1 reading frame is highly efficient in both rabbit reticulocyte lysate translation reactions and in cultured mammalian cells. The efficiency of antisense-induced frameshifting at this site is responsive to the sequence context 5′ of the shift site and to polyamine levels.     

Ribosomal Pausing at a Frameshifter RNA Pseudoknot Is Sensitive to Reading Phase but Shows Little Correlation with Frameshift Efficiency

Here we investigated ribosomal pausing at sites of programmed -1 ribosomal frameshifting, using translational elongation and ribosome heelprint assays. The site of pausing at the frameshift signal of infectious bronchitis virus (IBV) was determined and was consistent with an RNA pseudoknot-induced pause that placed the ribosomal P- and A-sites over the slippery sequence. Similarly, pausing at the simian retrovirus 1 gag/pol signal, which contains a different kind of frameshifter pseudoknot, also placed the ribosome over the slippery sequence, supporting a role for pausing in frameshifting. However, a simple correlation between pausing and frameshifting was lacking. Firstly, a stem-loop structure closely related to the IBV pseudoknot, although unable to stimulate efficient frameshifting, paused ribosomes to a similar extent and at the same place on the mRNA as a parental pseudoknot. Secondly, an identical pausing pattern was induced by two pseudoknots differing only by a single loop 2 nucleotide yet with different functionalities in frameshifting. The final observation arose from an assessment of the impact of reading phase on pausing. Given that ribosomes advance in triplet fashion, we tested whether the reading frame in which ribosomes encounter an RNA structure (the reading phase) would influence pausing. We found that the reading phase did influence pausing but unexpectedly, the mRNA with the pseudoknot in the phase which gave the least pausing was found to promote frameshifting more efficiently than the other variants. Overall, these experiments support the view that pausing alone is insufficient to mediate frameshifting and additional events are required. The phase dependence of pausing may be indicative of an activity in the ribosome that requires an optimal contact with mRNA secondary structures for efficient unwinding.     

Identification of Hepta- and Octo-Uridine stretches as sole signals for programmed +1 and -1 ribosomal frameshifting during translation of SARS-CoV ORF 3a variants

Programmed frameshifting is one of the translational recoding mechanisms that read the genetic code in alternative ways. This process is generally programmed by signals at defined locations in a specific mRNA. In this study, we report the identification of hepta- and octo-uridine stretches as sole signals for programmed +1 and −1 ribosomal frameshifting during translation of severe acute respiratory syndrome coronavirus (SARS-CoV) ORF 3a variants. SARS-CoV ORF 3a encodes a minor structural protein of 274 amino acids. Over the course of cloning and expression of the gene, a mixed population of clones with six, seven, eight and nine T stretches located 14 nt downstream of the initiation codon was found. In vitro and in vivo expression of clones with six, seven and eight Ts, respectively, showed the detection of the full-length 3a protein. Mutagenesis studies led to the identification of the hepta- and octo-uridine stretches as slippery sequences for efficient frameshifting. Interestingly, no stimulatory elements were found in the sequences upstream or downstream of the slippage site. When the hepta- and octo-uridine stretches were used to replace the original slippery sequence of the SARS-CoV ORF 1a and 1b, efficient frameshift events were observed. Furthermore, the efficiencies of frameshifting mediated by the hepta- and octo-uridine stretches were not affected by mutations introduced into a downstream stem–loop structure that totally abolish the frameshift event mediated by the original slippery sequence of ORF 1a and 1b. Taken together, this study identifies the hepta- and octo-uridine stretches that function as sole elements for efficient +1 and −1 ribosomal frameshift events.     

Structural requirements for efficient translational frameshifting in the synthesis of the putative viral RNA-dependent RNA polymerase of potato leafroll virus.

The putative RNA-dependent RNA polymerase of potato leafroll luteovirus (PLRV) is expressed by -1 ribosomal frameshifting in the region where the open reading frames (ORF) of proteins 2a and 2b overlap. The signal responsible for efficient frameshift is composed of the slippery site UUUAAAU followed by a sequence that has the potential to adopt two alternative folding patterns, either a structure involving a pseudoknot, or a simple stem-loop structure. To investigate the structure requirements for efficient frameshifting, mutants in the stem-loop or in the potential pseudoknot regions of a Polish isolate of PLRV (PLRV-P) have been analyzed. Mutations that are located in the second stem (S2) of the potential pseudoknot structure, but are located in unpaired regions of the alternative stem-loop structure, reduce frameshift efficiency. Deletion of the 3' end sequence of the alternative stem-loop structure does not reduce frameshift efficiency. Our results confirm that -1 frameshift in the overlap region depends on the slippery site and on the downstream positioned sequence, and propose that in PLRV-P a pseudoknot is required for efficient frameshifting. These results are in agreement with those recently published for the closely related beet western yellows luteovirus (BWYV).     

Characterization of the frameshift signal of Edr, a mammalian example of programmed -1 ribosomal frameshifting

The ribosomal frameshifting signal of the mouse embryonal carcinoma differentiation regulated (Edr) gene represents the sole documented example of programmed -1 frameshifting in mammalian cellular genes [Shigemoto,K., Brennan,J., Walls,E,. Watson,C.J., Stott,D., Rigby,P.W. and Reith,A.D. (2001), Nucleic Acids Res., 29, 4079-4088]. Here, we have employed site-directed mutagenesis and RNA structure probing to characterize the Edr signal. We began by confirming the functionality and magnitude of the signal and the role of a GGGAAAC motif as the slippery sequence. Subsequently, we derived a model of the Edr stimulatory RNA and assessed its similarity to those stimulatory RNAs found at viral frameshift sites. We found that the structure is an RNA pseudoknot possessing features typical of retroviral frameshifter pseudoknots. From these experiments, we conclude that the Edr signal and by inference, the human orthologue PEG10, do not represent a novel 'cellular class' of programmed -1 ribosomal frameshift signal, but rather are similar to viral examples, albeit with some interesting features. The similarity to viral frameshift signals may complicate the design of antiviral therapies that target the frameshift process.     

Programmed ribosomal frameshifting in SIV is induced by a highly structured RNA stem-loop

Simian immunodeficiency virus (SIV), like its human homologues (HIV-1, HIV-2), requires a -1 translational frameshift event to properly synthesize all of the proteins required for viral replication. The frameshift mechanism is dependent upon a seven-nucleotide slippery sequence and a downstream RNA structure. In SIV, the downstream RNA structure has been proposed to be either a stem-loop or a pseudoknot. Here, we report the functional, structural and thermodynamic characterization of the SIV frameshift site RNA. Translational frameshift assays indicate that a stem-loop structure is sufficient to promote efficient frameshifting in vitro. NMR and thermodynamic studies of SIV RNA constructs of varying length further support the absence of any pseudoknot interaction and indicate the presence of a stable stem-loop structure. We determined the structure of the SIV frameshift-inducing RNA by NMR. The structure reveals a highly ordered 12 nucleotide loop containing a sheared G-A pair, cross-strand adenine stacking, two G-C base-pairs, and a novel CCC triloop turn. The loop structure and its high thermostability preclude pseudoknot formation. Sequence conservation and modeling studies suggest that HIV-2 RNA forms the same structure. We conclude that, like the main sub-groups of HIV-1, SIV and HIV-2 utilize stable stem-loop structures to function as a thermodynamic barrier to translation, thereby inducing ribosomal pausing and frameshifting.     

A sequence required for -1 ribosomal frameshifting located four kilobases downstream of the frameshift site

Programmed ribosomal frameshifting allows one mRNA to encode regulate expression of, multiple open reading frames (ORFs). The polymerase encoded by ORF 2 of Barley yellow dwarf virus (BYDV) is expressed via minus one (-1) frameshifting from the overlapping ORF 1. Previously, this appeared to be mediated by a 116 nt RNA sequence that contains canonical -1 frameshift signals including a shifty heptanucleotide followed by a highly structured region. However, unlike known -1 frameshift signals, the reporter system required the zero frame stop codon and did not require a consensus shifty site for expression of the -1 ORF. In contrast, full-length viral RNA required a functional shifty site for frameshifting in wheat germ extract, while the stop codon was not required. Increasing translation initiation efficiency by addition of a 5' cap on the naturally uncapped viral RNA, decreased the frameshift rate. Unlike any other known RNA, a region four kilobases downstream of the frameshift site was required for frameshifting. This included an essential 55 base tract followed by a 179 base tract that contributed to full frameshifting. The effects of most mutations on frameshifting correlated with the ability of viral RNA to replicate in oat protoplasts, indicating that the wheat germ extract accurately reflected control of BYDV RNA translation in the infected cell. However, the overall frameshift rate appeared to be higher in infected cells, based on immunodetection of viral proteins. These findings show that use of short recoding sequences out of context in reporter constructs may overlook distant signals. Most importantly, the remarkably long-distance interaction reported here suggests the presence of a novel structure that can facilitate ribosomal frameshifting.     

Structural and functional studies of retroviral RNA pseudoknots involved in ribosomal frameshifting: nucleotides at the junction of the two stems are important for efficient ribosomal frameshifting.

Ribosomal frameshifting, a translational mechanism used during retroviral replication, involves a directed change in reading frame at a specific site at a defined frequency. Such programmed frameshifting at the mouse mammary tumor virus (MMTV) gag-pro shift site requires two mRNA signals: a heptanucleotide shifty sequence and a pseudoknot structure positioned downstream. Using in vitro translation assays and enzymatic and chemical probes for RNA structure, we have defined features of the pseudoknot that promote efficient frameshifting. Heterologous RNA structures, e.g. a hairpin, a tRNA or a synthetic pseudoknot, substituted downstream of the shifty site fail to promote frameshifting, suggesting that specific features of the MMTV pseudoknot are important for function. Site-directed mutations of the MMTV pseudoknot indicate that the pseudoknot junction, including an unpaired adenine nucleotide between the two stems, provides a specific structural determinant for efficient frameshifting. Pseudoknots derived from other retroviruses (i.e. the feline immunodeficiency virus and the simian retrovirus type 1) also promote frameshifting at the MMTV gag-pro shift site, dependent on the same structure at the junction of the two stems.     

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.     

Possible involvement of coaxially stacked double pseudoknots in the regulation of −1 programmed ribosomal frameshifting in RNA viruses

?1 programmed ribosomal frameshifting (PRF) in viruses is often stimulated by a pseudoknot downstream from the slippery sequence. At the PRF junction of HIV-1, transmissible gastroenteritis virus (TGEV), Barmah Forest virus (BFV), Fort Morgan virus (FMV), and Equine arteritis virus (EAV), we identified potential double pseudoknots in either a tandem mode or embedded mode. In viruses with tandem pseudoknots (5′PK & 3′PK), the slippery sequence is encompassed in the 5′PK. The ribosome needs to unwind the 5′PK to get to the slippery sequence. In HIV-1, the 3′PK and several alternative structures are mutually exclusive. Disruption of the tandem pseudoknots may enable one of the alternative structures to form as the effective frameshift stimulator. In TGEV/BFV/FMV, the 3′PK is a conventional frameshift stimulator. In all cases, the tandem pseudoknots may slow down the ribosome before it reaches the conventional PRF signals. In EAV, a compact pseudoknot is embedded within loop2 of the otherwise conventional frameshift-stimulating pseudoknot. All double pseudoknots have the potential to stack their stems coaxially. We built structural models of the HIV-1 and EAV double pseudoknots to show that both the tandem and embedded modes are feasible and reasonable. We hypothesize that the fundamental reason for the viruses to utilize coaxially stacked double pseudoknots is to increase the overall stability of the frameshift regulating structure, and avoid an ultra-stable single pseudoknot which may become a ribosomal roadblock. Our results significantly expand the repertoire of RNA structures and dynamics that may potentially involve in ?1 PRF regulation.     

Ribosomal pausing during translation of an RNA pseudoknot.

The genomic RNA of the coronavirus infectious bronchitis virus contains an efficient ribosomal frameshift signal which comprises a heptanucleotide slippery sequence followed by an RNA pseudoknot structure. The presence of the pseudoknot is essential for high-efficiency frameshifting, and it has been suggested that its function may be to slow or stall the ribosome in the vicinity of the slippery sequence. To test this possibility, we have studied translational elongation in vitro on mRNAs engineered to contain a well-defined pseudoknot-forming sequence. Insertion of the pseudoknot at a specific location within the influenza virus PB1 mRNA resulted in the production of a new translational intermediate corresponding to the size expected for ribosomal arrest at the pseudoknot. The appearance of this protein was transient, indicating that it was a true paused intermediate rather than a dead-end product, and mutational analysis confirmed that its appearance was dependent on the presence of a pseudoknot structure within the mRNA. These observations raise the possibility that a pause is required for the frameshift process. The extent of pausing at the pseudoknot was compared with that observed at a sequence designed to form a simple stem-loop structure with the same base pairs as the pseudoknot. This structure proved to be a less effective barrier to the elongating ribosome than the pseudoknot and in addition was unable to direct efficient ribosomal frameshifting, as would be expected if pausing plays an important role in frameshifting. However, the stem-loop was still able to induce significant pausing, and so this effect alone may be insufficient to account for the contribution of the pseudoknot to frameshifting.     

The frameshift stimulatory signal of human immunodeficiency virus type 1 group O is a pseudoknot

Human immunodeficiency virus type 1 (HIV-1) requires a programmed -1 ribosomal frameshift to produce Gag-Pol, the precursor of its enzymatic activities. This frameshift occurs at a slippery sequence on the viral messenger RNA and is stimulated by a specific structure, downstream of the shift site. While in group M, the most abundant HIV-1 group, the frameshift stimulatory signal is an extended bulged stem-loop, we show here, using a combination of mutagenesis and probing studies, that it is a pseudoknot in group O. The mutagenesis and probing studies coupled to an in silico analysis show that group O pseudoknot is a hairpin-type pseudoknot with two coaxially stacked stems of eight base-pairs (stem 1 and stem 2), connected by single-stranded loops of 2nt (loop 1) and 20nt (loop 2). Mutations impairing formation of stem 1 or stem 2 of the pseudoknot reduce frameshift efficiency, whereas compensatory changes that allow re-formation of these stems restore the frameshift efficiency to near wild-type level. The difference between the frameshift stimulatory signal of group O and group M supports the hypothesis that these groups originate from a different monkey to human transmission.     

Polyamine sensing during antizyme mRNA programmed frameshifting

A key regulator of cellular polyamine levels from yeasts to mammals is the protein antizyme. The antizyme gene consists of two overlapping reading frames with ORF2 in the +1 frame relative to ORF1. A programmed +1 ribosomal frameshift occurs at the last codon of ORF1 and results in the production of full-length antizyme protein. The efficiency of frameshifting is proportional to the concentration of polyamines, thus creating an autoregulatory circuit for controlling polyamine levels. The mRNA recoding signals for frameshifting include an element 5' and a pseudoknot 3' of the shift site. The present work illustrates that the ORF1 stop codon and the 5' element are critical for polyamine sensing, whereas the 3' pseudoknot acts to stimulate frameshifting in a polyamine independent manner. We also demonstrate that polyamines are required to stimulate stop codon readthrough at the MuLV redefinition site required for normal expression of the GagPol precursor protein.     

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.     

NMR structure of the Aquifex aeolicus tmRNA pseudoknot PK1: new insights into the recoding event of the ribosomal trans-translation

The transfer-messenger RNA (tmRNA) pseudoknot PK1 is essential for bacterial trans-translation, a ribosomal rescue mechanism. We report the solution structure of PK1 from Aquifex aeolicus, which despite an unprecedented small number of nucleotides and thus an unprecented compact size, displays a very high thermal stability. Several unusual structural features account for these properties and indicate that PK1 belongs to the class of ribosomal frameshift pseudoknots. This suggests a similarity between the mechanism of programmed ribosomal frameshifting and trans-translation.     

Structure, stability and function of RNA pseudoknots involved in stimulating ribosomal frameshifting

Programmed -1 ribosomal frameshifting has become the subject of increasing interest over the last several years, due in part to the ubiquitous nature of this translational recoding mechanism in pathogenic animal and plant viruses. All cis-acting frameshift signals encoded in mRNAs are minimally composed of two functional elements: a heptanucleotide "slippery sequence" conforming to the general form X XXY YYZ, followed by an RNA structural element, usually an H-type RNA pseudoknot, positioned an optimal number of nucleotides (5 to 9) downstream. The slippery sequence itself promotes a low level ( approximately 1 %) of frameshifting; however, downstream pseudoknots stimulate this process significantly, in some cases up to 30 to 50 %. Although the precise molecular mechanism of stimulation of frameshifting remains poorly understood, significant advances have been made in our knowledge of the three-dimensional structures, thermodynamics of folding, and functional determinants of stimulatory RNA pseudoknots derived from the study of several well-characterized frameshift signals. These studies are summarized here and provide new insights into the structural requirements and mechanism of programmed -1 ribosomal frameshifting.     

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.