Crystal structure of a hairpin ribozyme-inhibitor complex with implications for catalysis

Local RNA structural changes induced by crystallization are revealed by SHAPE

We present a simple approach to locate sites that undergo conformational changes upon crystallization by comparative structural mapping of the same RNA in three different environments. As a proof of principle, we probed the readily crystallized P4-P6DeltaC209 domain from the Tetrahymena thermophila group I intron in a native solution, in a solution mimicking the crystallization drop, and in crystals. We chose the selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE) chemistry, which monitors the flexibility and the conformation of each nucleotide. First, SHAPE successfully revealed the structural changes that occur during the crystallization process. Specifically, 64% of the nucleotides implicated in packing contacts and present in the portion of the molecule analyzed were identified. Second, reactivity differences for some of these nucleotides were already observed in the crystallization solution, suggesting that the crystallization buffer locked down a particular structure that was favorable to crystal formation. Third, the probing of a known structure extends our understanding of the structural basis for the SHAPE reaction by suggesting that reactivity is enhanced by a C2'-endo sugar pucker. Furthermore, by identifying local conformational changes of the RNA that take place during crystallization, SHAPE could be combined with the in vitro selection of stable mutants to rationalize the design of RNA candidates for crystallization.

Insight into the functional versatility of RNA through model-making with applications to data fitting

The RNA World hypothesis posits that life emerged from self-replicating RNA molecules. For any single biopolymer to be the basis for life, it must both store information and perform diverse functions. It is well known that RNA can store information. Advances in recent years have revealed that RNA can exhibit remarkable functional versatility as well. In an effort to judge the functional versatility of RNA and thereby the plausibility that RNA was at one point the basis for life, a statistical chemical approach is adopted. Essential biological functions are reduced to simple molecular models in a minimalist, biopolymer-independent fashion. The models dictate requisite states, populations of states, and physical and chemical changes occurring between the states. Next, equations are derived from the models, which lead to complex phenomenological constants such as observed and functional constants that are defined in terms of familiar elementary chemical descriptors: intrinsic rate constants, microscopic ligand equilibrium constants, secondary structure stability, and ligand concentration. Using these equations, simulations of functional behavior are performed. These functional models provide practical frameworks for fitting and organizing real data on functional RNAs such as ribozymes and riboswitches. At the same time, the models allow the suitability of RNA as a basis for life to be judged. We conclude that RNA, while inferior to extant proteins in most, but not all, functional respects, may be more versatile than proteins, performing a wider range of elementary biological functions at a tolerable level. Inspection of the functional models and various RNA structures uncovers several surprising ways in which the nucleobases can conspire to afford chemical catalysis and evolvability. These models support the plausibility that RNA, or a closely related informational biopolymer, could serve as the basis for a fairly simple form of life.

8-Azaguanine reporter of purine ionization states in structured RNAs

The fluorescent nucleotide analogue 8-azaguanosine-5'-triphosphate (8azaGTP) is prepared easily by in vitro enzymatic synthesis methods. 8azaGTP is an efficient substrate for T7 RNA polymerase and is incorporated specifically opposite cytosine in the transcription template, as expected for a nucleobase analogue with the same Watson-Crick hydrogen bonding face as guanine. 8-Azaguanine (8azaG) in oligonucleotides also is recognized as guanine during ribonuclease T1 digestion. Moreover, replacement of guanine by 8azaG does not alter the melting temperature of base-paired RNAs significantly, evidence that 8azaG does not disrupt stacking and hydrogen bonding interactions. 8azaGTP displays a high fluorescent quantum yield when the N1 position is deprotonated at high pH, but fluorescence intensity decreases significantly when N1 is protonated at neutral pH. Fluorescence is quenched 10-fold to 100-fold when 8azaG is incorporated into base-paired RNA and remains pH-dependent, although apparent pKa values determined from the pH dependence of fluorescence intensity shift in the basic direction. Thus, 8azaG is a guanine analogue that does not perturb RNA structure and displays pH-dependent fluorescence that can be used to probe the ionization states of nucleobases in structured RNAs. A key application will be in determining the ionization state of active site nucleobases that have been implicated in the catalytic mechanisms of RNA enzymes.

Structural methods for studying IRES function

Internal ribosome entry sites (IRESs) substitute RNA sequences for some or all of the canonical translation initiation protein factors. Therefore, an important component of understanding IRES function is a description of the three-dimensional structure of the IRES RNA underlying this mechanism. This includes determining the degree to which the RNA folds, the global RNA architecture, and higher resolution information when warranted. Knowledge of the RNA structural features guides ongoing mechanistic and functional studies. In this chapter, we present a roadmap to structurally characterize a folded RNA, beginning from initial studies to define the overall architecture and leading to high-resolution structural studies. The experimental strategy presented here is not unique to IRES RNAs but is adaptable to virtually any RNA of interest, although characterization of RNA-protein interactions requires additional methods. Because IRES RNAs have a specific function, we present specific ways in which the data are interpreted to gain insight into that function. We provide protocols for key experiments that are particularly useful for studying IRES RNA structure and that provide a framework onto which additional approaches are integrated. The protocols we present are solution hydroxyl radical probing, RNase T1 probing, native gel electrophoresis, sedimentation velocity analytical ultracentrifugation, and strategies to engineer RNA for crystallization and to obtain initial crystals.

Structural investigation of the GlmS ribozyme bound to Its catalytic cofactor

The GlmS riboswitch is located in the 5'-untranslated region of the gene encoding glucosamine-6-phosphate (GlcN6P) synthetase. The GlmS riboswitch is a ribozyme with activity triggered by binding of the metabolite GlcN6P. Presented here is the structure of the GlmS ribozyme (2.5 A resolution) with GlcN6P bound in the active site. The GlmS ribozyme adopts a compact double pseudoknot tertiary structure, with two closely packed helical stacks. Recognition of GlcN6P is achieved through coordination of the phosphate moiety by two hydrated magnesium ions as well as specific nucleobase contacts to the GlcN6P sugar ring. Comparison of this activator bound and the previously published apoenzyme complex supports a model in which GlcN6P does not induce a conformational change in the RNA, as is typical of other riboswitches, but instead functions as a catalytic cofactor for the reaction. This demonstrates that RNA, like protein enzymes, can employ the chemical diversity of small molecules to promote catalytic activity.

Calculation of pKas in RNA: on the structural origins and functional roles of protonated nucleotides

pK(a) calculations based on the Poisson-Boltzmann equation have been widely used to study proteins and, more recently, DNA. However, much less attention has been paid to the calculation of pK(a) shifts in RNA. There is accumulating evidence that protonated nucleotides can stabilize RNA structure and participate in enzyme catalysis within ribozymes. Here, we calculate the pK(a) shifts of nucleotides in RNA structures using numerical solutions to the Poisson-Boltzmann equation. We find that significant shifts are predicted for several nucleotides in two catalytic RNAs, the hairpin ribozyme and the hepatitis delta virus ribozyme, and that the shifts are likely to be related to their functions. We explore how different structural environments shift the pK(a)s of nucleotides from their solution values. RNA structures appear to use two basic strategies to shift pK(a)s: (a) the formation of compact structural motifs with structurally-conserved, electrostatic interactions; and (b) the arrangement of the phosphodiester backbone to focus negative electrostatic potential in specific regions.

DNA aptamer-mediated regulation of the hairpin ribozyme by human alpha-thrombin

The combination of specific ligand-binding aptamers with hairpin ribozyme catalysis generates molecules that can be controlled by external factors. Here we have generated hairpin ribozymes that can be regulated by a short DNA aptamer specific for human alpha-thrombin. This was achieved by constructing a ribozyme variant harboring an RNA sequence complementary to the aptamer, to which the aptamer can hybridize forming a heteroduplex. In this way, the DNA aptamer completely abolishes the catalytic activity of the ribozyme, due to the formation of an inactive ribozyme conformation. However, in the presence of the aptamer's target protein human alpha-thrombin, the inhibitory effect of the DNA aptamer is competitively neutralized and the ribozyme is activated in a highly specific fashion. Protein-responsive allosteric ribozymes are proposed to act as tools with potential applications in medicine where fast detection of clinically relevant targets is required.

RNA folding and the origins of catalytic activity in the hairpin ribozyme

The nucleolytic ribozymes catalyse site-specific phosphodiester cleavage and ligation transesterification reactions in RNA. The hairpin ribozyme folds to generate an intimate loop-loop interaction to create the local environment in which catalysis can proceed. We have studied the ion-induced folding using single-molecule FRET experiments, showing that the four-way helical junction accelerates the folding 500-fold by introducing a discrete intermediate that juxtaposes the loops. Using FRET we can observe individual hairpin ribozyme molecules as they undergo multiple cycles of cleavage and ligation, and measure the rates of the internal reactions, free of uncertainties in the contributions of docking and substrate dissociation processes. On average, the cleaved ribozyme undergoes several docking-undocking events before a ligation reaction occurs. On the basis of these experiments, we have explored the role of the nucleobases G8 and A38 in the catalysis. Both cleavage and ligation reactions are pH dependent, corresponding to the titration of a group with pKa=6.2. We have used a novel ribonucleoside in which these bases are replaced by imidazole to investigate the role of acid-base catalysis in this ribozyme. We observe significant rates of cleavage and ligation, and a bell-shaped pH dependence for both.

The interaction networks of structured RNAs

All pairwise interactions occurring between bases which could be detected in three-dimensional structures of crystallized RNA molecules are annotated on new planar diagrams. The diagrams attempt to map the underlying complex networks of base–base interactions and, especially, they aim at conveying key relationships between helical domains: co-axial stacking, bending and all Watson–Crick as well as non-Watson–Crick base pairs. Although such wiring diagrams cannot replace full stereographic images for correct spatial understanding and representation, they reveal structural similarities as well as the conserved patterns and distances between motifs which are present within the interaction networks of folded RNAs of similar or unrelated functions. Finally, the diagrams could help devising methods for meaningfully transforming RNA structures into graphs amenable to network analysis.

Structural basis of glmS ribozyme activation by glucosamine-6-phosphate

The glmS ribozyme is the only natural catalytic RNA known to require a small-molecule activator for catalysis. This catalytic RNA functions as a riboswitch, with activator-dependent RNA cleavage regulating glmS messenger RNA expression. We report crystal structures of the glmS ribozyme in precleavage states that are unliganded or bound to the competitive inhibitor glucose-6-phosphate and in the postcleavage state. All structures superimpose closely, revealing a remarkably rigid RNA that contains a preformed active and coenzyme-binding site. Unlike other riboswitches, the glmS ribozyme binds its activator in an open, solvent-accessible pocket. Our structures suggest that the amine group of the glmS ribozyme-bound coenzyme performs general acid-base and electrostatic catalysis.

Computational selection of nucleic acid biosensors via a slip structure model

Aptamers have been shown to undergo ligand-dependent conformational changes, and can be joined to ribozymes to create allosteric ribozymes (aptazymes). An anti-flavin (FMN) aptamer joined to the hammerhead ribozyme yielded an aptazyme that underwent small, FMN-dependent displacements in the helix that joined the aptamer and ribozyme. This 'slip structure' model in which alternative sets of base-pairs are formed in the absence and presence of ligand proved amenable to energetic and computational modeling. Initial successes in modeling the activities of known aptazymes led to the in silico selection of new ligand-dependent aptazymes from virtual pools that contained millions of members. Those aptazymes that were predicted to best fit the slip structure model were synthesized and assayed, and the best-designed aptazyme was activated 60-fold by FMN. The slip structure model proved to be generalizable, and could be applied with equal facility to computationally generate aptazymes that proved to be experimentally activated by other ligands (theophylline) or that contained other catalytic cores (hairpin ribozyme). Moreover, the slip structure model could be applied to the prediction of a ligand-dependent aptamer beacon biosensor in which the addition of the protein vascular endothelial growth factor (VegF) led to a 10-fold increase in fluorescent signal.

Trapped water molecules are essential to structural dynamics and function of a ribozyme

Ribozymes are catalytically competent examples of highly structured noncoding RNAs, which are ubiquitous in the processing and regulation of genetic information. Combining explicit-solvent molecular dynamics simulation and single molecule fluorescence spectroscopy approaches, we find that a ribozyme from a subviral plant pathogen exhibits a coupled hydrogen bonding network that communicates dynamic structural rearrangements throughout the catalytic core in response to site-specific chemical modification. Trapped long-residency water molecules are critical for this network and only occasionally exchange with bulk solvent as they pass through a breathing interdomain base stack. These highly structured water molecules line up in a string that may potentially also be involved in specific base catalysis. Our observations suggest important, still underappreciated roles for specifically bound water molecules in the structural dynamics and function of noncoding RNAs.

Tertiary contacts distant from the active site prime a ribozyme for catalysis

Minimal hammerhead ribozymes have been characterized extensively by static and time-resolved crystallography as well as numerous biochemical analyses, leading to mutually contradictory mechanistic explanations for catalysis. We present the 2.2 A resolution crystal structure of a full-length Schistosoma mansoni hammerhead ribozyme that permits us to explain the structural basis for its 1000-fold catalytic enhancement. The full-length hammerhead structure reveals how tertiary interactions occurring remotely from the active site prime this ribozyme for catalysis. G-12 and G-8 are positioned consistent with their previously suggested roles in acid-base catalysis, the nucleophile is aligned with a scissile phosphate positioned proximal to the A-9 phosphate, and previously unexplained roles of other conserved nucleotides become apparent within the context of a distinctly new fold that nonetheless accommodates the previous structural studies. These interactions permit us to explain the previously irreconcilable sets of experimental results in a unified, consistent, and unambiguous manner.

Chemical rescue, multiple ionizable groups, and general acid-base catalysis in the HDV genomic ribozyme

In the ribozyme from the hepatitis delta virus (HDV) genomic strand RNA, a cytosine side chain is proposed to facilitate proton transfer in the transition state of the reaction and, thus, act as a general acid-base catalyst. Mutation of this active-site cytosine (C75) reduced RNA cleavage rates by as much as one million-fold, but addition of exogenous cytosine and certain nucleobase or imidazole analogs can partially rescue activity in these mutants. However, pH-rate profiles for the rescued reactions were bell shaped, and only one leg of the pH-rate curve could be attributed to ionization of the exogenous nucleobase or buffer. When a second potential ionizable nucleobase (C41) was removed, one leg of the bell-shaped curve was eliminated in the chemical-rescue reaction. With this construct, the apparent pK(a) determined from the pH-rate profile correlated with the solution pK(a) of the buffer, and the contribution of the buffer to the rate enhancement could be directly evaluated in a free-energy or Brønsted plot. The free-energy relationship between the acid dissociation constant of the buffer and the rate constant for cleavage (Brønsted value, beta, = approximately 0.5) was consistent with a mechanism in which the buffer acted as a general acid-base catalyst. These data support the hypothesis that cytosine 75, in the intact ribozyme, acts as a general acid-base catalyst.

Metal ion dependence, thermodynamics, and kinetics for intramolecular docking of a GAAA tetraloop and receptor connected by a flexible linker

The GAAA tetraloop-receptor motif is a commonly occurring tertiary interaction in RNA. This motif usually occurs in combination with other tertiary interactions in complex RNA structures. Thus, it is difficult to measure directly the contribution that a single GAAA tetraloop-receptor interaction makes to the folding properties of a RNA. To investigate the kinetics and thermodynamics for the isolated interaction, a GAAA tetraloop domain and receptor domain were connected by a single-stranded A(7) linker. Fluorescence resonance energy transfer (FRET) experiments were used to probe intramolecular docking of the GAAA tetraloop and receptor. Docking was induced using a variety of metal ions, where the charge of the ion was the most important factor in determining the concentration of the ion required to promote docking {[Co(NH(3))(6)(3+)] << [Ca(2+)], [Mg(2+)], [Mn(2+)] << [Na(+)], [K(+)]}. Analysis of metal ion cooperativity yielded Hill coefficients of approximately 2 for Na(+)- or K(+)-dependent docking versus approximately 1 for the divalent ions and Co(NH(3))(6)(3+). Ensemble stopped-flow FRET kinetic measurements yielded an apparent activation energy of 12.7 kcal/mol for GAAA tetraloop-receptor docking. RNA constructs with U(7) and A(14) single-stranded linkers were investigated by single-molecule and ensemble FRET techniques to determine how linker length and composition affect docking. These studies showed that the single-stranded region functions primarily as a flexible tether. Inhibition of docking by oligonucleotides complementary to the linker was also investigated. The influence of flexible versus rigid linkers on GAAA tetraloop-receptor docking is discussed.

Structure of the eukaryotic thiamine pyrophosphate riboswitch with its regulatory ligand

Riboswitches are untranslated regions of messenger RNA, which adopt alternate structures depending on the binding of specific metabolites. Such conformational switching regulates the expression of proteins involved in the biosynthesis of riboswitch substrates. Here, we present the 2.9 angstrom-resolution crystal structure of the eukaryotic Arabidopsis thaliana thiamine pyrophosphate (TPP)-specific riboswitch in complex with its natural ligand. The riboswitch specifically recognizes the TPP via conserved residues located within two highly distorted parallel "sensor" helices. The structure provides the basis for understanding the reorganization of the riboswitch fold upon TPP binding and explains the mechanism of resistance to the antibiotic pyrithiamine.

Cation-specific structural accommodation within a catalytic RNA

Metal ions facilitate the folding of the hairpin ribozyme but do not participate directly in catalysis. The metal complex cobalt(III) hexaammine supports folding and activity of the ribozyme and also mediates specific internucleotide photocrosslinks, several of which retain catalytic ability. These crosslinks imply that the active core structure organized by [Co(NH3)6]3+ is different from that organized by Mg2+ and that revealed in the crystal structure [Rupert, P. B., and Ferre-D'Amare, A. R. (2001) Nature 410, 780-786] (1). Residues U+2 and C+3 of the substrate, in particular, adopt different conformations in [Co(NH3)6]3+. U+2 is bulged out of loop A and stacked on residue G36, whereas the nucleotide at position +3 is stacked on G8, a nucleobase crucial for catalysis. Cleavage kinetics performed with +2 variants and a C+3 U variant correlate with the crosslinking observations. Variants that decreased cleavage rates in magnesium up to 70-fold showed only subtle decreases or even increases in observed rates when assayed in [Co(NH3)6]3+. Here, we propose a model of the [Co(NH3)6]3+-mediated catalytic core generated by MC-SYM that is consistent with these data.

Water in the active site of an all-RNA hairpin ribozyme and effects of Gua8 base variants on the geometry of phosphoryl transfer

The hairpin ribozyme requires functional group contributions from G8 to assist in phosphodiester bond cleavage. Previously, replacement of G8 by a series of nucleobase variants showed little effect on interdomain docking, but a 3-250-fold effect on catalysis. To identify G8 features that contribute to catalysis within the hairpin ribozyme active site, structures for five base variants were determined by X-ray crystallography in a resolution range between 2.3 and 2.7 A. For comparison, a native all-RNA "G8" hairpin ribozyme structure was refined to 2.05 A resolution. The native structure revealed a scissile bond angle (tau) of 158 degrees, which is close to the requisite 180 degrees "in-line" geometry. Mutations G8(inosine), G8(diaminopurine), G8(aminopurine), G8(adenosine), and G8(uridine) folded properly, but exhibited nonideal scissile bond geometries (tau ranging from 118 degrees to 93 degrees) that paralleled their diminished solution activities. A superposition ensemble of all structures, including a previously described hairpin ribozyme-vanadate complex, indicated the scissile bond can adopt a variety of conformations resulting from perturbation of the chemical environment and provided a rationale for how the exocyclic amine of nucleobase 8 promotes productive, in-line geometry. Changes at position 8 also caused variations in the A-1 sugar pucker. In this regard, variants A8 and U8 appeared to represent nonproductive ground states in which their 2'-OH groups mimicked the pro-R, nonbridging oxygen of the vanadate transition-state complex. Finally, the results indicated that ordered water molecules bind near the 2'-hydroxyl of A-1, lending support to the hypothesis that solvent may play an important role in the reaction.

Engineering RNA-based circuits

Nucleic acids can modulate gene function by base-pairing, via the molecular recognition of proteins and metabolites, and by catalysis. This diversity of functions can be combined with the ability to engineer nucleic acids based on Watson-Crick base-pairing rules to create a modular set of molecular "tools" for biotechnological and medical interventions in cellular metabolism. However, these individual RNA-based tools are most powerful when combined into rational logical or regulatory circuits, and the circuits can in turn be evolved for optimal function. Examples of genetic circuits that control translation and transcription are herein detailed, and more complex circuits with medical applications are anticipated.

The exocyclic amine at the RNase P cleavage site contributes to substrate binding and catalysis

Most tRNAs carry a G at their 5' termini, i.e. at position +1. This position corresponds to the position immediately downstream of the site of cleavage in tRNA precursors. Here we studied RNase P RNA-mediated cleavage of substrates carrying substitutions/modifications at position +1 in the absence of the RNase P protein, C5, to investigate the role of G at the RNase P cleavage site. We present data suggesting that the exocyclic amine (2NH2) of G+1 contributes to cleavage site recognition, ground state binding and catalysis by affecting the rate of cleavage. This is in contrast to O6, N7 and 2'OH that are suggested to affect ground state binding and rate of cleavage to significantly lesser extent. We also provide evidence that the effects caused by the absence of 2NH2 at position +1 influenced the charge distribution and conceivably Mg2+ binding at the RNase P cleavage site. These findings are consistent with models where the 2NH2 at the cleavage site (when present) interacts with RNase P RNA and/or influences the positioning of Mg2+ in the vicinity of the cleavage site. Moreover, our data suggest that the presence of the base at +1 is not essential for cleavage but its presence suppresses miscleavage and dramatically increases the rate of cleavage. Together our findings provide reasons why most tRNAs carry a guanosine at their 5' end.

Characteristics of the glmS ribozyme suggest only structural roles for divalent metal ions

The glmS ribozyme is a riboswitch class that occurs in certain Gram-positive bacteria, where it resides within mRNAs encoding glucosamine 6-phosphate synthase. Members of this self-cleaving ribozyme class rapidly catalyze RNA transesterification upon binding GlcN6P, and genetic evidence suggests that this cleavage event is important for down-regulating GlmS protein expression. In this report, we present a refined secondary structure model of the glmS ribozyme and determine the importance of a conserved pseudoknot structure for optimal ribozyme function. Analyses of deletion constructs demonstrate that the pseudoknot, together with other structural elements, permits the ribozyme to achieve maximum rate constants for RNA cleavage at physiologically relevant Mg2+ concentrations. In addition, we show that substantial rate enhancements are supported by an exchange-inert cobalt (III) complex and by molar concentrations of monovalent ions. Our findings indicate that the glmS ribozyme forms a complex structure to employ catalytic strategies that do not require the direct participation of divalent metal ions.

Controlling RNA self-assembly to form filaments

Fundamental control over supra-molecular self-assembly for organization of matter on the nano-scale is a major objective of nanoscience and nanotechnology. 'RNA tectonics' is the design of modular RNA units, called tectoRNAs, that can be programmed to self-assemble into novel nano- and meso-scopic architectures of desired size and shape. We report the three-dimensional design of tectoRNAs incorporating modular 4-way junction (4WJ) motifs, hairpin loops and their cognate loop-receptors to create extended, programmable interaction interfaces. Specific and directional RNA-RNA interactions at these interfaces enable conformational, topological and orientational control of tectoRNA self-assembly. The interacting motifs are precisely positioned within the helical arms of the 4WJ to program assembly from only one helical stacking conformation of the 4WJ. TectoRNAs programmed to assemble with orientational compensation produce micrometer-scale RNA filaments through supra-molecular equilibrium polymerization. As visualized by transmission electron microscopy, these RNA filaments resemble actin filaments from the protein world. This work emphasizes the potential of RNA as a scaffold for designing and engineering new controllable biomaterials mimicking modern cytoskeletal proteins.

Ligand requirements for glmS ribozyme self-cleavage

Natural RNA catalysts (ribozymes) perform essential reactions in biological RNA processing and protein synthesis, whereby catalysis is intrinsic to RNA structure alone or in combination with metal ion cofactors. The recently discovered glmS ribozyme is unique in that it functions as a glucosamine-6-phosphate (GlcN6P)-dependent catalyst believed to enable "riboswitch" regulation of amino-sugar biosynthesis in certain prokaryotes. However, it is unclear whether GlcN6P functions as an effector or coenzyme to promote ribozyme self-cleavage. Herein, we demonstrate that ligand is absolutely requisite for glmS ribozyme self-cleavage activity. Furthermore, catalysis both requires and is dependent upon the acid dissociation constant (pKa) of the amine functionality of GlcN6P and related compounds. The data demonstrate that ligand is integral to catalysis, consistent with a coenzyme role for GlcN6P and illustrating an expanded capacity for biological RNA catalysis.

Hairpin ribozyme-catalyzed ligation in water-alcohol solutions

The hairpin ribozyme (HPR) is a naturally existing RNA that catalyzes site-specific RNA cleavage and ligation. At 37 degrees C and in the presence of divalent metal ions (M(2+)), the HPR efficiently cleaves RNA substrates in trans. Here, we show that the HPR can catalyze efficient M(2+)-independent ligation in trans in aqueous solutions containing any of several alcohols, including methanol, ethanol, and isopropanol, and millimolar concentrations of monovalent cations. Ligation proceeds most efficiently in 60% isopropanol at 37 degrees C, whereas the reverse (cleavage) reaction is negligible under these conditions. We suggest that dehydration of the RNA is the key factor promoting HPR activity in water- alcohol solutions. Alcohol-induced ribozyme ligation may have practical applications.

Hydrostatic and osmotic pressure study of the hairpin ribozyme

The recent discovery of numerous catalytically active RNAs in various living species as well as the in vitro selection of a large series of RNA aptamers able to bind specifically various molecules such as metabolites and co-factors, emphasize the adaptability of RNAs through the plasticity of their secondary structure. Furthermore, all these observations give support to the "RNA world" hypothesis as a step in the primitive development of life on Earth. On this background, we used high pressure to study the mechanism of action of a model hairpin ribozyme which exhibits self-cleavage and ligation. The activation volume (DeltaV( not equal)) of the cleavage reaction (34+/-4 ml/mol) indicates that an important compaction of the RNA molecule occurs during the reaction and must be accompanied by a significant movement of water molecules . Indeed, such a release of 78+/-4 water molecules per RNA molecule could be measured by complementary osmotic shock experiments. These results are consistent with the information provided by the structural studies which indicate that two loops of the RNA molecule should come into contact for the reaction to occur . The high pressure study of a modified form of the ribozyme whose activity is strictly dependent on the presence of adenine as a co-factor should bring some information about the structural significance of this important DeltaV( not equal) of activation.

Free energy landscapes of RNA/RNA complexes: with applications to snRNA complexes in spliceosomes

We develop a statistical mechanical model for RNA/RNA complexes with both intramolecular and intermolecular interactions. As an application of the model, we compute the free energy landscapes, which give the full distribution for all the possible conformations, for U4/U6 and U2/U6 in major spliceosome and U4atac/U6atac and U12/U6atac in minor spliceosome. Different snRNA experiments found contrasting structures, our free energy landscape theory shows why these structures emerge and how they compete with each other. For yeast U2/U6, the model predicts that the two distinct experimental structures, the four-helix junction structure and the helix Ib-containing structure, can actually coexist and specifically compete with each other. In addition, the energy landscapes suggest possible mechanisms for the conformational switches in splicing. For instance, our calculation shows that coaxial stacking is essential for stabilizing the four-helix junction in yeast U2/U6. Therefore, inhibition of the coaxial stacking possibly by protein-binding may activate the conformational switch from the four-helix junction to the helix Ib-containing structure. Moreover, the change of the energy landscape shape gives information about the conformational changes. We find multiple (native-like and misfolded) intermediates formed through base-pairing rearrangements in snRNA complexes. For example, the unfolding of the U2/U6 undergoes a transition to a misfolded state which is functional, while in the unfolding of U12/U6atac, the functional helix Ib is found to be the last one to unfold and is thus the most stable structural component. Furthermore, the energy landscape gives the stabilities of all the possible (functional) intermediates and such information is directly related to splicing efficiency.

The RNA-Cleaving Bipartite DNAzyme Is a Distinctive Metalloenzyme

Much interest has focused on the mechanisms of the five naturally occurring self-cleaving ribozymes, which, in spite of catalyzing the same reaction, adopt divergent strategies. These ribozymes, with the exception of the recently described glmS ribozyme, do not absolutely require divalent metal ions for their catalytic chemistries in vitro. A mechanistic investigation of an in vitro-selected, RNA-cleaving DNA enzyme, the bipartite, which catalyzes the same chemistry as the five natural self-cleaving ribozymes, found a mechanism of significant complexity. The DNAzyme showed a bell-shaped pH profile. A dissection of metal usage indicated the involvement of two catalytically relevant magnesium ions for optimal activity. The DNAzyme was able to utilize manganese(II) as well as magnesium; however, with manganese it appeared to function complexed to either one or two of those cations. Titration with hexaamminecobalt(III) chloride inhibited the activity of the bipartite; this suggests that it is a metalloenzyme that utilizes metal hydroxide as a general base for activation of its nucleophile. Overall, the bipartite DNAzyme appeared to be kinetically distinct not only from the self-cleaving ribozymes but also from other in vitro-selected, RNA-cleaving deoxyribozymes, such as the 8-17, 10-23, and 614.

Efficient RNA ligation by reverse-joined hairpin ribozymes and engineering of twin ribozymes consisting of conventional and reverse-joined hairpin ribozyme units

In recent years major progress has been made in elucidating the mechanism and structure of catalytic RNA molecules, and we are now beginning to understand ribozymes well enough to turn them into useful tools. Work in our laboratory has focused on the development of twin ribozymes for site-specific RNA sequence alteration. To this end, we followed a strategy that relies on the combination of two ribozyme units into one molecule (hence dubbed twin ribozyme). Here, we present reverse-joined hairpin ribozymes that are structurally optimized and which, in addition to cleavage, catalyse efficient RNA ligation. The most efficient variant ligated its appropriate RNA substrate with a single turnover rate constant of 1.1 min(-1) and a final yield of 70%. We combined a reverse-joined hairpin ribozyme with a conventional hairpin ribozyme to create a twin ribozyme that mediates the insertion of four additional nucleotides into a predetermined position of a substrate RNA, and thus mimics, at the RNA level, the repair of a short deletion mutation; 17% of the initial substrate was converted to the insertion product.

Competitive regulation of modular allosteric aptazymes by a small molecule and oligonucleotide effector

The hairpin ribozyme can catalyze the cleavage of RNA substrates by employing its conformational flexibility. To form a catalytic complex, the two domains A and B of the hairpin-ribozyme complex must interact with one another in a folding step called docking. We have constructed hairpin ribozyme variants harboring an aptamer sequence that can be allosterically induced by flavin mononucleotide (FMN). Domains A and B are separated by distinct bridge sequences that communicate the formation of the FMN-aptamer complex to domains A and B, facilitating their docking. In the presence of a short oligonucleotide that is complementary to the aptamer, catalytic activity of the ribozyme is completely abolished, due to the formation of an extended conformer that cannot perform catalysis. However, in the presence of the small molecule effector FMN, the inhibitory effect of the oligonucleotide is competitively neutralized and the ribozyme is activated 150-fold. We thus have established a new principle for the regulation of ribozyme catalysis in which two regulatory factors (an oligonucleotide and a small molecule) that switch the ribozyme's activity in opposite directions compete for the same binding site in the aptamer domain.

Structural dynamics of precursor and product of the RNA enzyme from the hepatitis delta virus as revealed by molecular dynamics simulations

The hepatitis delta virus (HDV) ribozyme is a self-cleaving RNA enzyme involved in the replication of a human pathogen, the hepatitis delta virus. Recent crystal structures of the precursor and product of self-cleavage, together with detailed kinetic analyses, have led to hypotheses on the catalytic strategies employed by the HDV ribozyme. We report molecular dynamics (MD) simulations (approximately 120 ns total simulation time) to test the plausibility that specific conformational rearrangements are involved in catalysis. Site-specific self-cleavage requires cytidine in position 75 (C75). A precursor simulation with unprotonated C75 reveals a rather weak dynamic binding of C75 in the catalytic pocket with spontaneous, transient formation of a H-bond between U-1(O2') and C75(N3). This H-bond would be required for C75 to act as the general base. Upon protonation in the precursor, C75H+ has a tendency to move towards its product location and establish a firm H-bonding network within the catalytic pocket. However, a C75H+(N3)-G1(O5') H-bond, which would be expected if C75 acted as a general acid catalyst, is not observed on the present simulation timescale. The adjacent loop L3 is relatively dynamic and may serve as a flexible structural element, possibly gated by the closing U20.G25 base-pair, to facilitate a conformational switch induced by a protonated C75H+. L3 also controls the electrostatic environment of the catalytic core, which in turn may modulate C75 base strength and metal ion binding. We find that a distant RNA tertiary interaction involving a protonated cytidine (C41) becomes unstable when left unprotonated, leading to disruptive conformational rearrangements adjacent to the catalytic core. A Na ion temporarily compensates for the loss of the protonated hydrogen bond, which is strikingly consistent with the experimentally observed synergy between low pH and high Na+ concentrations in mediating residual self-cleavage of the HDV ribozyme in the absence of divalents.

Structure, folding and mechanisms of ribozymes

The past two years have seen exciting developments in RNA catalysis. A completely new ribozyme (possibly two) has come along and several new structures have been determined, including three different group I intron species. Although the origins of catalysis remain incompletely understood, a significant convergence of views has happened in the past year, together with the discovery of new super-fast ribozymes. There is persuasive evidence of general acid-base chemistry in nucleolytic ribozymes, whereas catalysis of peptidyl transfer in the ribosome seems to result largely from orientation and proximity effects. Lastly, important new folding-enhancing elements have been discovered.

RNA Structure: Reading the Ribosome

The crystal structures of the ribosome and its subunits have increased the amount of information about RNA structure by about two orders of magnitude. This is leading to an understanding of the principles of RNA folding and of the molecular interactions that underlie the functional capabilities of the ribosome and other RNA systems. Nearly all of the possible types of RNA tertiary interactions have been found in ribosomal RNA. One of these, an abundant tertiary structural motif called the A-minor interaction, has been shown to participate in both aminoacyl-transfer RNA selection and in peptidyl transferase; it may also play an important role in the structural dynamics of the ribosome.

Folding and catalysis of the hairpin ribozyme

The active form of the hairpin ribozyme is brought about by the interaction of two formally unpaired loops. In a natural molecule, these are present on two adjacent arms of a four-way junction. Although activity can be obtained in molecules lacking this junction, the junction is important in the promotion of the folded state of the ribozyme under physiological conditions, at a rate that is faster than the chemical reaction. Single-molecule fluorescence resonance energy transfer studies show that the junction introduces a discrete intermediate into the folding process, which repeatedly juxtaposes the two loops and thus promotes their docking. Using single-molecule enzymology, the cleavage and ligation rates have been measured directly. The pH dependence of the rates is consistent with a role for nucleobases acting in general acid-base catalysis.

Towards understanding the catalytic core structure of the spliceosome

The spliceosome catalyses the splicing of nuclear pre-mRNA (precursor mRNA) in eukaryotes. Pre-mRNA splicing is essential to remove internal non-coding regions of pre-mRNA (introns) and to join the remaining segments (exons) into mRNA before translation. The spliceosome is a complex assembly of five RNAs (U1, U2, U4, U5 and U6) and many dozens of associated proteins. Although a high-resolution structure of the spliceosome is not yet available, inroads have been made towards understanding its structure and function. There is growing evidence suggesting that U2 and U6 RNAs, of the five, may contribute to the catalysis of pre-mRNA splicing. In this review, recent progress towards understanding the structure and function of U2 and U6 RNAs is summarized.

A peripheral element assembles the compact core structure essential for group I intron self-splicing

The presence of non-conserved peripheral elements in all naturally occurring group I introns underline their importance in ensuring the natural intron function. Recently, we reported that some peripheral elements are conserved in group I introns of IE subgroup. Using self-splicing activity as a readout, our initial screening revealed that one such conserved peripheral elements, P2.1, is mainly required to fold the catalytically active structure of the Candida ribozyme, an IE intron. Unexpectedly, the essential function of P2.1 resides in a sequence-conserved short stem of P2.1 but not in a long-range interaction associated with the loop of P2.1 that stabilizes the ribozyme structure. The P2.1 stem is indispensable in folding the compact ribozyme core, most probably by forming a triple helical interaction with two core helices, P3 and P6. Surprisingly, although the ribozyme lacking the P2.1 stem renders a loosely folded core and the loss of self-splicing activity requires two consecutive transesterifications, the mutant ribozyme efficiently catalyzes the first transesterification reaction. These results suggest that the intron self-splicing demands much more ordered structure than does one independent transesterification, highlighting that the universally present peripheral elements achieve their functional importance by enabling the highly ordered structure through diverse tertiary interactions.

The structure-function dilemma of the hammerhead ribozyme

A powerful approach to understanding protein enzyme catalysis is to examine the structural context of essential amino acid side chains whose deletion or modification negatively impacts catalysis. In principle, this approach can be even more powerful for RNA enzymes, given the wide variety and subtlety of functionally modified nucleotides now available. Numerous recent success stories confirm the utility of this approach to understanding ribozyme function. An anomaly, however, is the hammerhead ribozyme, for which the structural and functional data do not agree well, preventing a unifying view of its catalytic mechanism from emerging. To delineate the hammerhead structure-function comparison, we have evaluated and distilled the large body of biochemical data into a consensus set of functional groups unambiguously required for hammerhead catalysis. By examining the context of these functional groups within available structures, we have established a concise set of disagreements between the structural and functional data. The number and relative distribution of these inconsistencies throughout the hammerhead reaffirms that an extensive conformational rearrangement from the fold observed in the crystal structure must be necessary for cleavage to occur. The nature and energetic driving force of this conformational isomerization are discussed.

The catalytic diversity of RNAs

The natural RNA enzymes catalyse phosphate-group transfer and peptide-bond formation. Initially, metal ions were proposed to supply the chemical versatility that nucleotides lack. In the ensuing decades, structural and mechanistic studies have substantially altered this initial viewpoint. Whereas self-splicing ribozymes clearly rely on essential metal-ion cofactors, self-cleaving ribozymes seem to use nucleotide bases for their catalytic chemistry. Despite the overall differences in chemical features, both RNA and protein enzymes use similar catalytic strategies.

Single-molecule RNA folding

Single-molecule experiments significantly expand our capability to characterize complex dynamics of biological processes. This relatively new approach has contributed significantly to our understanding of the RNA folding problem. Recent single-molecule experiments, together with structural and biochemical characterizations of RNA at the ensemble level, show that RNA molecules typically fold across a highly rugged energy landscape. As a result, long-lived folding intermediates, multiple folding pathways, and heterogeneous conformational dynamics are commonly found for RNA enzymes. While initial results have suggested that stable secondary structures are partly responsible for the rugged energy landscape of RNA, a complete mechanistic understanding of the complex folding behavior has not yet been obtained. A combination of single-molecule experiments, which are well suited to analyze transient and heterogeneous dynamic behaviors, with ensemble characterizations that can provide structural information at a superior resolution will likely provide more answers.

Ribozyme catalysis: not different, just worse

Evolution has resoundingly favored protein enzymes over RNA-based catalysts, yet ribozymes occupy important niches in modern cell biology that include the starring role in catalysis of protein synthesis on the ribosome. Recent results from structural and biochemical studies show that natural ribozymes use an impressive range of catalytic mechanisms, beyond metalloenzyme chemistry and analogous to more chemically diverse protein enzymes. These findings make it increasingly possible to compare details of RNA- and protein-based catalysis.

Linkage between proton binding and folding in RNA: implications for RNA catalysis

Small ribozymes use their nucleobases to catalyse phosphodiester bond cleavage. The hepatitis delta virus ribozyme employs C75 as a general acid to protonate the 5′-bridging oxygen leaving group, and to accomplish this task efficiently, it shifts its pKa towards neutrality. Simulations and thermodynamic experiments implicate linkage between folding and protonation in nucleobase pKa shifting. Even small oligonucleotides are shown to fold in a highly co-operative manner, although they do so in a context-specific fashion. Linkage between protonation and co-operativity of folding may drive pKa shifting and provide for enhanced function in RNA.

The catalytic mechanism of hairpin ribozyme studied by hydrostatic pressure

The discovery of ribozymes strengthened the RNA world hypothesis, which assumes that these precursors of modern life both stored information and acted as catalysts. For the first time among extensive studies on ribozymes, we have investigated the influence of hydrostatic pressure on the hairpin ribozyme catalytic activity. High pressures are of interest when studying life under extreme conditions and may help to understand the behavior of macromolecules at the origins of life. Kinetic studies of the hairpin ribozyme self-cleavage were performed under high hydrostatic pressure. The activation volume of the reaction (34 +/- 5 ml/mol) calculated from these experiments is of the same order of magnitude as those of common protein enzymes, and reflects an important compaction of the RNA molecule during catalysis, associated to a water release. Kinetic studies were also carried out under osmotic pressure and confirmed this interpretation and the involvement of water movements (78 +/- 4 water molecules per RNA molecule). Taken together, these results are consistent with structural studies indicating that loops A and B of the ribozyme come into close contact during the formation of the transition state. While validating baro-biochemistry as an efficient tool for investigating dynamics at work during RNA catalysis, these results provide a complementary view of ribozyme catalytic mechanisms.

Role of an active site adenine in hairpin ribozyme catalysis

The hairpin ribozyme is a small catalytic RNA that accelerates reversible cleavage of a phosphodiester bond. Structural and mechanistic studies suggest that divalent metals stabilize the functional structure but do not participate directly in catalysis. Instead, two active site nucleobases, G8 and A38, appear to participate in catalytic chemistry. The features of A38 that are important for active site structure and chemistry were investigated by comparing cleavage and ligation reactions of ribozyme variants with A38 modifications. An abasic substitution of A38 reduced cleavage and ligation activity by 14,000-fold and 370,000-fold, respectively, highlighting the critical role of this nucleobase in ribozyme function. Cleavage and ligation activity of unmodified ribozymes increased with increasing pH, evidence that deprotonation of some functional group with an apparent pK(a) value near 6 is important for activity. The pH-dependent transition in activity shifted by several pH units in the basic direction when A38 was substituted with an abasic residue, or with nucleobase analogs with very high or low pK(a) values that are expected to retain the same protonation state throughout the experimental pH range. Certain exogenous nucleobases that share the amidine group of adenine restored activity to abasic ribozyme variants that lack A38. The pH dependence of chemical rescue reactions also changed according to the intrinsic basicity of the rescuing nucleobase, providing further evidence that the protonation state of the N1 position of purine analogs is important for rescue activity. These results are consistent with models of the hairpin ribozyme catalytic mechanism in which interactions with A38 provide electrostatic stabilization to the transition state.

Inhibition of viral replication by ribozyme: mutational analysis of the site and mechanism of antiviral activity

A controlled mutational study was used to determine the site and mechanism of the antiviral action of ribozymes that inhibit Sindbis virus replication. A hairpin ribozyme targeting G575 of the Sindbis virus genomic RNA was designed and cloned into a minimized alphavirus amplicon vector. Cells that were stably transfected with this construct expressed low levels of a constitutive transcript containing the ribozyme plus recognition sequences for Sindbis RNA replicase. Upon infection, the ribozyme transcript was amplified to high levels by the viral replicase, resulting in decreased viral production from infected ribozyme-expressing cells. Mutations were then introduced into the viral RNA target sequence to interfere with ribozyme binding, and compensatory changes were generated in the ribozyme recognition sequence. Single mutations in the virus or ribozyme decreased the efficacy of the ribozyme's inhibition of viral replication, and compensatory mutations restored it. To confirm that ribozyme-catalyzed RNA cleavage was actually needed for inhibition, we performed tests with a cell line expressing an inactivated ribozyme and with a virus containing a single nucleotide target mutation that allowed the ribozyme to bind but blocked cleavage at the recognition site. The results show that most of the antiviral activity of ribozymes is due to ribozyme-catalyzed cleavage at the targeted RNA sequence, but some additional inhibition seems to occur through an antisense mechanism.

Vesicle encapsulation studies reveal that single molecule ribozyme heterogeneities are intrinsic

Single-molecule measurements have revealed that what were assumed to be identical molecules can differ significantly in their static and dynamic properties. One of the most striking examples is the hairpin ribozyme, which was shown to exhibit two to three orders of magnitude variation in folding kinetics between molecules. Although averaged behavior of single molecules matched the bulk solution data, it was not possible to exclude rigorously the possibility that the variations around the mean values arose from different ways of interacting with the surface environment. To test this, we minimized the molecules' interaction with the surface by encapsulating DNA or RNA molecules inside 100- to 200-nm diameter unilamellar vesicles, following the procedures described by Haran and coworkers. Vesicles were immobilized on a supported lipid bilayer via biotin-streptavidin linkages. We observed no direct binding of DNA or RNA on the supported bilayer even at concentrations exceeding 100 nM, indicating that these molecules do not bind stably on the membrane. Since the vesicle diameter is smaller than the resolution of optical microscopy, the lateral mobility of the molecules is severely constrained, allowing long observation periods. We used fluorescence correlation spectroscopy, nuclease digestion, and external buffer exchange to show that the molecules were indeed encapsulated within the vesicles. When contained within vesicles, the natural form of the hairpin ribozyme exhibited 50-fold variation in both folding and unfolding rates in 0.5 mM Mg2+, which is identical to what was observed from the molecules tethered directly on the surface. This strongly indicates that the observed heterogeneity in dynamic properties does not arise as an artifact of surface attachment, but is intrinsic to the nature of the molecules.

Investigation of Mg2+- and temperature-dependent folding of the hairpin ribozyme by photo-crosslinking: effects of photo-crosslinker tether length and chemistry

We have used photo-crosslinking to investigate the structure and dynamics of four-way junction hairpin ribozyme constructs. Four phenylazide photo-crosslinkers were coupled to 2′-NH₂-modified U+2 in the substrate and irradiated at different Mg²⁺ concentrations and temperatures. Consistent with the role of divalent metal ions in hairpin ribozyme folding, we observed more interdomain crosslinks in the presence of Mg²⁺ than in its absence. In general, we observed intradomain crosslinks to nucleotides 2–11 and interdomain crosslinks to the U1A binding loop. Crosslinks to A26 and G36 in domain B were also observed when crosslinking was carried out at −78°C. In contrast to crosslinking results at higher temperatures (0, 25 and 37°C), similar crosslinks were obtained in the presence and absence of Mg²⁺ at −78°C, suggesting Mg²⁺ stabilizes a low-energy hairpin ribozyme conformation. We also evaluated the effects of photo-crosslinker structure and mechanism on crosslinks. First, most crosslinks were to unpaired nucleotides. Second, shorter and longer photo-crosslinkers formed crosslinks to intradomain locations nearer to and farther from photo-crosslinker modification, respectively. Finally, fluorine substitutions on the phenylazide ring did not change the locations of crosslinks, but rather decreased crosslinking efficiency. These findings have implications for the use of phenylazide photo-crosslinkers in structural studies of RNA.

Freely diffusing single hairpin ribozymes provide insights into the role of secondary structure and partially folded states in RNA folding

Single-molecule fluorescence resonance energy transfer studies of freely diffusing hairpin ribozymes with different combinations of helical junction and loop elements reveal striking differences in their folding behavior. We examined a series of six different ribozymes consisting of two-, three- and four-way junction variants, as well as corresponding constructs with one of the two loops removed. Our results highlight the varying contributions of preformed secondary structure elements to tertiary folding of the hairpin ribozyme. Of the three helical junction variants studied, the four-way junction strongly favored folding to a docked conformation of the two loops, required for catalytic activity. Moreover, the four-way junction was uniquely able to fold to a similar compact structure even in the absence of specific loop-loop docking interactions. A key feature of the data is the observation of broadening/tailing in the fluorescence resonance energy transfer histogram peak for a single-loop mutant of the four-way junction at higher Mg(2+) concentrations, not observed for any of the other single-loop variants. This feature is consistent with interconversion between compact and extended structures, which we estimate takes place on the 100-micros timescale using a simple model for the peak shape. This unique ability of the four-way junction ribozyme to populate an undocked conformation with native-like structure (a quasi-docked state) likely contributes to its greater tertiary structure stability, with the quasi-docked state acting as an intermediate and facilitating the subsequent formation of the specific hydrogen bonding network during docking of the two loops. The inability of two- and three-way junction ribozymes to fully populate a docked conformation reveals the importance of correct helical junction geometry as well as loop elements for effective ribozyme folding.

Secondary structure prediction of interacting RNA molecules

Computational tools for prediction of the secondary structure of two or more interacting nucleic acid molecules are useful for understanding mechanisms for ribozyme function, determining the affinity of an oligonucleotide primer to its target, and designing good antisense oligonucleotides, novel ribozymes, DNA code words, or nanostructures. Here, we introduce new algorithms for prediction of the minimum free energy pseudoknot-free secondary structure of two or more nucleic acid molecules, and for prediction of alternative low-energy (sub-optimal) secondary structures for two nucleic acid molecules. We provide a comprehensive analysis of our predictions against secondary structures of interacting RNA molecules drawn from the literature. Analysis of our tools on 17 sequences of up to 200 nucleotides that do not form pseudoknots shows that they have 79% accuracy, on average, for the minimum free energy predictions. When the best of 100 sub-optimal foldings is taken, the average accuracy increases to 91%. The accuracy decreases as the sequences increase in length and as the number of pseudoknots and tertiary interactions increases. Our algorithms extend the free energy minimization algorithm of Zuker and Stiegler for secondary structure prediction, and the sub-optimal folding algorithm by Wuchty et al. Implementations of our algorithms are freely available in the package MultiRNAFold.