Biphasic folding kinetics of RNA pseudoknots and telomerase RNA activity

Computational design and experimental verification of pseudoknotted ribozymes

The design of new RNA sequences that retain the function of a model RNA structure is a challenge in bioinformatics because of the structural complexity of these molecules. RNA can fold into its secondary and tertiary structures by forming stem-loops and pseudoknots. A pseudoknot is a set of base pairs between a region within a stem-loop and nucleotides outside of this stem-loop; this motif is very important for numerous functional structures. It is important for any computational design algorithm to take into account these interactions to give a reliable result for any structures that include pseudoknots. In our study, we experimentally validated synthetic ribozymes designed by Enzymer, which implements algorithms allowing for the design of pseudoknots. Enzymer is a program that uses an inverse folding approach to design pseudoknotted RNAs; we used it in this study to design two types of ribozymes. The ribozymes tested were the hammerhead and the glmS, which have a self-cleaving activity that allows them to liberate the new RNA genome copy during rolling-circle replication or to control the expression of the downstream genes, respectively. We demonstrated the efficiency of Enzymer by showing that the pseudoknotted hammerhead and glmS ribozymes sequences it designed were extensively modified compared to wild-type sequences and were still active.

Thermodynamics of unfolding mechanisms of mouse mammary tumor virus pseudoknot from a coarse-grained loop-entropy model

Pseudoknotted RNA molecules play important biological roles that depend on their folded structure. To understand the underlying principles that determine their thermodynamics and folding/unfolding mechanisms, we carried out a study on a variant of the mouse mammary tumor virus pseudoknotted RNA (VPK), a widely studied model system for RNA pseudoknots. Our method is based on a coarse-grained discrete-state model and the algorithm of PK3D (pseudoknot structure predictor in three-dimensional space), with RNA loops explicitly constructed and their conformational entropic effects incorporated. Our loop entropy calculations are validated by accurately capturing previously measured melting temperatures of RNA hairpins with varying loop lengths. For each of the hairpins that constitutes the VPK, we identified alternative conformations that are more stable than the hairpin structures at low temperatures and predicted their populations at different temperatures. Our predictions were validated by thermodynamic experiments on these hairpins. We further computed the heat capacity profiles of VPK, which are in excellent agreement with available experimental data. Notably, our model provides detailed information on the unfolding mechanisms of pseudoknotted RNA. Analysis of the distribution of base-pairing probability of VPK reveals a cooperative unfolding mechanism instead of a simple sequential unfolding of first one stem and then the other. Specifically, we find a simultaneous "loosening" of both stems as the temperature is raised, whereby both stems become partially melted and co-exist during the unfolding process.

Directed kinetic transition network model

Molecular dynamics simulations contain detailed kinetic information related to the functional states of proteins and macromolecules, but this information is obscured by the high dimensionality of configurational space. Markov state models and transition network models are widely applied to extract kinetic descriptors from equilibrium molecular dynamics simulations. In this study, we developed the Directed Kinetic Transition Network (DKTN)-a graph representation of a master equation which is appropriate for describing nonequilibrium kinetics. DKTN models the transition rate matrix among different states under detailed balance. Adopting the mixing time from the Markov chain, we use the half mixing time as the criterion to identify critical state transition regarding the protein conformational change. The similarity between the master equation and the Kolmogorov equation suggests that the DKTN model can be reformulated into the continuous-time Markov chain model, which is a general case of the Markov chain without a specific lag time. We selected a photo-sensitive protein, vivid, as a model system to illustrate the usage of the DKTN model. Overall, the DKTN model provides a graph representation of the master equation based on chemical kinetics to model the protein conformational change without the underlying assumption of the Markovian property.

A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.

Predicting Cotranscriptional Folding Kinetics For Riboswitch

On the basis of a helix-based transition rate model, we developed a new method for sampling cotranscriptional RNA conformational ensemble and the prediction of cotranscriptional folding kinetics. Applications to E. coli. SRP RNA and pbuE riboswitch indicate that the model may provide reliable predictions for the cotranscriptional folding pathways and population kinetics. For E. coli. SRP RNA, the predicted population kinetics and the folding pathway are consistent with the SHAPE profiles in the recent cotranscriptional SHAPE-seq experiments. For the pbuE riboswitch, the model predicts the transcriptional termination efficiency as a function of the force. The theoretical results show (a) a force-induced transition from the aptamer (antiterminator) to the terminator structure and (b) the different folding pathways for the riboswitch with and without the ligand (adenine). More specifically, without adenine, the aptamer structure emerges as a short-lived kinetic transient state instead of a thermodynamically stable intermediate state. Furthermore, from the predicted extension-time curves, the model identifies a series of conformational switches in the pulling process, where the predicted relative residence times for the different structures are in accordance with the experimental data. The model may provide a new tool for quantitative predictions of cotranscriptional folding kinetics, and results can offer useful insights into cotranscriptional folding-related RNA functions such as regulation of gene expression with riboswitches.

Ensemble simulations: folding, unfolding and misfolding of a high-efficiency frameshifting RNA pseudoknot

Massive all-atom molecular dynamics simulations were conducted across a distributed computing network to study the folding, unfolding, misfolding and conformational plasticity of the high-efficiency frameshifting double mutant of the 26 nt potato leaf roll virus RNA pseudoknot. Our robust sampling, which included over 40 starting structures spanning the spectrum from the extended unfolded state to the native fold, yielded nearly 120 μs of cumulative sampling time. Conformational microstate transitions on the 1.0 ns to 10.0 μs timescales were observed, with post-equilibration sampling providing detailed representations of the conformational free energy landscape and the complex folding mechanism inherent to the pseudoknot motif. Herein, we identify and characterize two alternative native structures, three intermediate states, and numerous misfolded states, the latter of which have not previously been characterized via atomistic simulation techniques. While in line with previous thermodynamics-based models of a general RNA folding mechanism, our observations indicate that stem-strand-sequence-separation may serve as an alternative predictor of the order of stem formation during pseudoknot folding. Our results contradict a model of frameshifting based on structural rigidity and resistance to mechanical unfolding, and instead strongly support more recent studies in which conformational plasticity is identified as a determining factor in frameshifting efficiency.

Mimicking Ribosomal Unfolding of RNA Pseudoknot in a Protein Channel

Pseudoknots are a fundamental RNA tertiary structure with important roles in regulation of mRNA translation. Molecular force spectroscopic approaches such as optical tweezers can track the pseudoknot's unfolding intermediate states by pulling the RNA chain from both ends, but the kinetic unfolding pathway induced by this method may be different from that in vivo, which occurs during translation and proceeds from the 5' to 3' end. Here we developed a ribosome-mimicking, nanopore pulling assay for dissecting the vectorial unfolding mechanism of pseudoknots. The pseudoknot unfolding pathway in the nanopore, either from the 5' to 3' end or in the reverse direction, can be controlled by a DNA leader that is attached to the pseudoknot at the 5' or 3' ends. The different nanopore conductance between DNA and RNA translocation serves as a marker for the position and structure of the unfolding RNA in the pore. With this design, we provided evidence that the pseudoknot unfolding is a two-step, multistate, metal ion-regulated process depending on the pulling direction. Most notably, unfolding in both directions is rate-limited by the unzipping of the first helix domain (first step), which is Helix-1 in the 5' → 3' direction and Helix-2 in the 3' → 5' direction, suggesting that the initial unfolding step in either pulling direction needs to overcome an energy barrier contributed by the noncanonical triplex base-pairs and coaxial stacking interactions for the tertiary structure stabilization. These findings provide new insights into RNA vectorial unfolding mechanisms, which play an important role in biological functions including frameshifting.

Free energy landscape and multiple folding pathways of an H-type RNA pseudoknot

How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA.

A U⋅U Pair-to-U⋅C Pair Mutation-Induced RNA Native Structure Destabilisation and Stretching-Force-Induced RNA Misfolding

Little is known about how a non-Watson-Crick pair affects the RNA folding dynamics. We studied the effects of a U⋅U-to-U⋅C pair mutation on the folding of a hairpin in human telomerase RNA. The ensemble thermal melting of the hairpins shows an on-pathway intermediate with the disruption of the internal loop structure containing the U⋅U/U⋅C pairs. By using optical tweezers, we applied a stretching force on the terminal ends of the hairpins to probe directly the non-nearest-neighbour effects upon the mutations. The single U⋅U to U⋅C mutations are observed to 1) lower the mechanical unfolding force by approximately 1 picoNewton (pN) per mutation without affecting the unfolding reaction transition-state position (thus suggesting that removing a single hydrogen bond affects the structural dynamics at least two base pairs away), 2) result in more frequent misfolding into a small hairpin at approximately 10 pN and 3) shift the folding reaction transition-state position towards the native hairpin structure and slightly increase the mechanical folding kinetics (thus suggesting that untrapping from the misfolded state is not the rate-limiting step).

Single-molecule fluorescence resonance energy transfer studies of the human telomerase RNA pseudoknot: temperature-/urea-dependent folding kinetics and thermodynamics

The ribonucleoprotein telomerase is an RNA-dependent DNA polymerase that catalyzes the repetitive addition of a short, species-specific, DNA sequence to the ends of linear eukaryotic chromosomes. The single RNA component of telomerase contains both the template sequence for DNA synthesis and a functionally critical pseudoknot motif, which can also exist as a less stable hairpin. Here we use a minimal version of the human telomerase RNA pseudoknot to study this hairpin-pseudoknot structural equilibrium using temperature-controlled single-molecule fluorescence resonance energy transfer (smFRET) experiments. The urea dependence of these experiments aids in determination of the folding kinetics and thermodynamics. The wild-type pseudoknot behavior is compared and contrasted to a mutant pseudoknot sequence implicated in a genetic disorder-dyskeratosis congenita. These findings clearly identify that this 2nt noncomplementary mutation destabilizes the folding of the wild-type pseudoknot by substantially reducing the folding rate constant (≈ 400-fold) while only nominally increasing the unfolding rate constant (≈ 5-fold). Furthermore, the urea dependence of the equilibrium and rate constants is used to develop a free energy landscape for this unimolecular equilibrium and propose details about the structure of the transition state. Finally, the urea-dependent folding experiments provide valuable physical insights into the mechanism for destabilization of RNA pseudoknots by such chemical denaturants.

Analysing RNA-kinetics based on folding space abstraction

BACKGROUND

RNA molecules, especially non-coding RNAs, play vital roles in the cell and their biological functions are mostly determined by structural properties. Often, these properties are related to dynamic changes in the structure, as in the case of riboswitches, and thus the analysis of RNA folding kinetics is crucial for their study. Exact approaches to kinetic folding are computationally expensive and, thus, limited to short sequences. In a previous study, we introduced a position-specific abstraction based on helices which we termed helix index shapes (hishapes) and a hishape-based algorithm for near-optimal folding pathway computation, called HiPath. The combination of these approaches provides an abstract view of the folding space that offers information about the global features.

RESULTS

In this paper we present HiKinetics, an algorithm that can predict RNA folding kinetics for sequences up to several hundred nucleotides long. This algorithm is based on RNAHeliCes, which decomposes the folding space into abstract classes, namely hishapes, and an improved version of HiPath, namely HiPath2, which estimates plausible folding pathways that connect these classes. Furthermore, we analyse the relationship of hishapes to locally optimal structures, the results of which strengthen the use of the hishape abstraction for studying folding kinetics. Finally, we show the application of HiKinetics to the folding kinetics of two well-studied RNAs.

CONCLUSIONS

HiKinetics can calculate kinetic folding based on a novel hishape decomposition. HiKinetics, together with HiPath2 and RNAHeliCes, is available for download at http://www.cyanolab.de/software/RNAHeliCes.htm.

Molecular dynamics simulation of RNA pseudoknot unfolding pathway

Many biological functions of RNA molecules are related to their pseudoknot structures. It is significant for predicting the structure and function of RNA that learning about the stability and the process of RNA pseudoknot folding and unfolding. The structural features of mouse mammary tumor virus (MMTV) RNA pseudoknot in different ion concentration, the unfolding process of the RNA pseudoknot, and the two hairpin helices that constitute the RNA pseudoknot were studied with all atom molecule dynamics simulation method in this paper. We found that the higher cation concentration can cause structure of the RNA molecules more stable, and ions played an indispensable role in keeping the structure of RNA molecules stable; the unfolding process of hairpin structure was corresponding to the antiprocess of its folding process. The main pathway of pseudoknot unfolding was that the inner base pair opened first, and then, the two helices, which formed the RNA pseudoknot opened decussately, while the folding pathway of the RNA pseudoknot was a helix folding after formation of the other helix. Therefore, the unfolding process of RNA pseudoknot is different from the antiprocess of its folding process, and the unfolding process of each helix in the RNA pseudoknot is similar to the hairpin structure’s unfolding process, which means that both are the unzipping process.

Statistical mechanical modeling of RNA folding: from free energy landscape to tertiary structural prediction

In spite of the success of computational methods for predicting RNA secondary structure, the problem of predicting RNA tertiary structure folding remains. Low-resolution structural models show promise as they allow for rigorous statistical mechanical computation for the conformational entropies, free energies, and the coarse-grained structures of tertiary folds. Molecular dynamics refinement of coarse-grained structures leads to all-atom 3D structures. Modeling based on statistical mechanics principles also has the unique advantage of predicting the full free energy landscape, including local minima and the global free energy minimum. The energy landscapes combined with the 3D structures form the basis for quantitative predictions of RNA functions. In this chapter, we present an overview of statistical mechanical models for RNA folding and then focus on a recently developed RNA statistical mechanical model -- the Vfold model. The main emphasis is placed on the physics underpinning the models, the computational strategies, and the connections to RNA biology.

Telomere lengthening and other functions of telomerase

Telomerase is an enzyme that maintains the length of the telomere. The telomere length specifies the number of divisions a cell can undergo before it finally dies (i.e. the proliferative potential of cells). For example, telomerase is activated in embryonic cell lines and the telomere length is maintained at a constant level; therefore, these cells have an unlimited fission potential. Stem cells are characterized by a lower telomerase activity, which enables only partial compensation for the shortening of telomeres. Somatic cells are usually characterized by the absence of telomerase activity. Telomere shortening leads to the attainment of the Hayflick limit, the transition of cells to a state of senescence. The cells subsequently enter a state of crisis, accompanied by massive cell death. The surviving cells become cancer cells, which are capable both of dividing indefinitely and maintaining telomere length (usually with the aid of telomerase). Telomerase is a reverse transcriptase. It consists of two major components: telomerase RNA (TER) and reverse transcriptase (TERT). TER is a non-coding RNA, and it contains the region which serves as a template for telomere synthesis. An increasing number of articles focussing on the alternative functions of telomerase components have recently started appearing. The present review summarizes data on the structure, biogenesis, and functions of telomerase.

A domain-based model for predicting large and complex pseudoknotted structures

Pseudoknotted structures play important structural and functional roles in RNA cellular functions at the level of transcription, splicing and translation. However, the problem of computational prediction for large pseudoknotted folds remains. Here we develop a domain-based method for predicting complex and large pseudoknotted structures from RNA sequences. The model is based on the observation that large RNAs can be separated into different structural domains. The basic idea is to first identify the domains and then predict the structures for each domain. Assembly of the domain structures gives the full structure. The use of the domain-based approach leads to a reduction of computational time by a factor of about ~N ( 2) for an N-nt sequence. As applications of the model, we predict structures for a variety of RNA systems, such as regions in human telomerase RNA (hTR), internal ribosome entry site (IRES) and HIV genome. The lengths of these sequences range from 200-nt to 400-nt. The results show good agreements with the experiments.

Fast folding of RNA pseudoknots initiated by laser temperature-jump

RNA pseudoknots are examples of minimal structural motifs in RNA with tertiary interactions that stabilize the structures of many ribozymes. They also play an essential role in a variety of biological functions that are modulated by their structure, stability, and dynamics. Therefore, understanding the global principles that determine the thermodynamics and folding pathways of RNA pseudoknots is an important problem in biology, both for elucidating the folding mechanisms of larger ribozymes as well as addressing issues of possible kinetic control of the biological functions of pseudoknots. We report on the folding/unfolding kinetics of a hairpin-type pseudoknot obtained with microsecond time-resolution in response to a laser temperature-jump perturbation. The kinetics are monitored using UV absorbance as well as fluorescence of extrinsically attached labels as spectroscopic probes of the transiently populated RNA conformations. We measure folding times of 1-6 ms at 37 °C, which are at least 100-fold faster than previous observations of very slow folding pseudoknots that were trapped in misfolded conformations. The measured relaxation times are remarkably similar to predictions of a computational study by Thirumalai and co-workers (Cho, S. S.; Pincus, D.L.; Thirumalai, D. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 17349-17354). Thus, these studies provide the first observation of a fast-folding pseudoknot and present a benchmark against which computational models can be refined.

Folding kinetics for the conformational switch between alternative RNA structures

Transitions between different conformational states, so-called conformational switching, are intrinsic to RNA catalytic and regulatory functions. Often, conformational switching occurs on time scales of several seconds. In combination with the recent real-time NMR experiments (Wenter et al. Angew. Chem. Int. Ed. 2005, 44, 2600; Wenter et al. ChemBioChem 2006, 7, 417) for the transitions between bistable RNA conformations, we combine the master equation method with the kinetic cluster method to investigate the detailed kinetic mechanism and the factors that govern the folding kinetics. We propose that heat capacity change (ΔC(p)) upon RNA folding may be important for RNA folding kinetics. In addition, we find that, for tetraloop hairpins, noncanonical (tertiary) intraloop interactions are important to determine the folding kinetics. Furthermore, through theory-experiment comparisons, we find that the different rate models for the fundamental steps (i.e., formation/disruption of a base pair or stack) can cause contrasting results in the theoretical predictions.

Computing the conformational entropy for RNA folds

We develop a polymer physics-based method to compute the conformational entropy for RNA tertiary folds, namely, conformations consisting of multiple helices connected through (cross-linked) loops. The theory is based on a virtual bond conformational model for the nucleotide chain. A key issue in the calculation of the entropy is how to treat the excluded volume interactions. The weak excluded volume interference between the different loops leads to the decomposition of the whole structure into a number of three-body building blocks, each consisting of a loop and two helices connected to the two ends of the loop. The simple construct of the three-body system allows an accurate computation for the conformational entropy for each building block. The assembly of the building blocks gives the entropy of the whole structure. This approach enables treatment of molten globule-like folds (partially unfolded tertiary structures) for RNAs. Extensive tests against experiments and exact computer enumerations indicate that the method can give accurate results for the entropy. The method developed here provides a solid first step toward a systematic development of a theory for the entropy and free energy landscape for complex tertiary folds for RNAs and proteins.

TRANSAT-- method for detecting the conserved helices of functional RNA structures, including transient, pseudo-knotted and alternative structures

The prediction of functional RNA structures has attracted increased interest, as it allows us to study the potential functional roles of many genes. RNA structure prediction methods, however, assume that there is a unique functional RNA structure and also do not predict functional features required for in vivo folding. In order to understand how functional RNA structures form in vivo, we require sophisticated experiments or reliable prediction methods. So far, there exist only a few, experimentally validated transient RNA structures. On the computational side, there exist several computer programs which aim to predict the co-transcriptional folding pathway in vivo, but these make a range of simplifying assumptions and do not capture all features known to influence RNA folding in vivo. We want to investigate if evolutionarily related RNA genes fold in a similar way in vivo. To this end, we have developed a new computational method, Transat, which detects conserved helices of high statistical significance. We introduce the method, present a comprehensive performance evaluation and show that Transat is able to predict the structural features of known reference structures including pseudo-knotted ones as well as those of known alternative structural configurations. Transat can also identify unstructured sub-sequences bound by other molecules and provides evidence for new helices which may define folding pathways, supporting the notion that homologous RNA sequence not only assume a similar reference RNA structure, but also fold similarly. Finally, we show that the structural features predicted by Transat differ from those assuming thermodynamic equilibrium. Unlike the existing methods for predicting folding pathways, our method works in a comparative way. This has the disadvantage of not being able to predict features as function of time, but has the considerable advantage of highlighting conserved features and of not requiring a detailed knowledge of the cellular environment.

Many non-coding genes exert their function via an RNA structure which starts emerging while the RNA sequence is being transcribed from the genome. The resulting folding pathway is known to depend on a variety of features such as the transcription speed, the concentration of various ions and the binding of proteins and other molecules. Not all of these influences can be adequately captured by the existing computational methods which try to replicate what happens in vivo. So far, it has been challenging to experimentally investigate co-transcriptional folding pathways in vivo and only little data from in vitro experiments exists. In order to investigate if functionally similar RNA sequences from different organisms fold in a similar way, we have developed a new computational method, called Transat, which does not require the detailed computational modeling of the cellular environment. We show in a comprehensive analysis that our method is capable of detecting known structural features and provide evidence that structural features of the in vivo folding pathways have been conserved for several biologically interesting classes of RNA sequences.

Predicting loop-helix tertiary structural contacts in RNA pseudoknots

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

RNA pseudoknots: folding and finding

RNA pseudoknots are important for function. Three-dimensional structural information is available, insights into factors affecting pseudoknot stability are being reported, and computer programs are available for predicting pseudoknots.

Structures of telomerase subunits provide functional insights

BACKGROUND

Telomerase continues to generate substantial attention both because of its pivotal roles in cellular proliferation and aging and because of its unusual structure and mechanism. By replenishing telomeric DNA lost during the cell cycle, telomerase overcomes one of the many hurdles facing cellular immortalization. Functionally, telomerase is a reverse transcriptase, and it shares structural and mechanistic features with this class of nucleotide polymerases. Telomerase is a very unusual reverse transcriptase because it remains stably associated with its template and because it reverse transcribes multiple copies of its template onto a single primer in one reaction cycle.

SCOPE OF REVIEW

Here, we review recent findings that illuminate our understanding of telomerase. Even though the specific emphasis is on structure and mechanism, we also highlight new insights into the roles of telomerase in human biology.

GENERAL SIGNIFICANCE

Recent advances in the structural biology of telomerase, including high resolution structures of the catalytic subunit of a beetle telomerase and two domains of a ciliate telomerase catalytic subunit, provide new perspectives into telomerase biochemistry and reveal new puzzles.

A new computational approach for mechanical folding kinetics of RNA hairpins

Based on an ensemble of kinetically accessible conformations, we propose a new analytical model for RNA folding kinetics. The model gives populational kinetics, kinetic rates, transition states, and pathways from the rate matrix. Applications of the new kinetic model to mechanical folding of RNA hairpins such as trans-activation-responsive RNA reveal distinct kinetic behaviors in different force regimes, from zero force to forces much stronger than the critical force for the folding-unfolding transition. In the absence of force or a low force, folding can be initiated (nucleated) at any position by forming the first base stack and there exist many pathways for the folding process. In contrast, for a higher force, the folding/unfolding would predominantly proceed along a single zipping/unzipping pathway. Studies for different hairpin-forming sequences indicate that depending on the nucleotide sequence, a kinetic intermediate can emerge in the low force regime but disappear in high force regime, and a new kinetic intermediate, which is absent in the low and high force regimes, can emerge in the medium force range. Variations of the force lead to changes in folding cooperativity and rate-limiting steps. The predicted network of pathways for trans-activation-responsive RNA suggests two parallel dominant pathways. The rate-limiting folding steps (at f = 8 pN) are the formation of specific basepairs that are 2-4 basepairs away from the loop. At a higher force (f = 11 pN), the folding rate is controlled by the formation of the bulge loop. The predicted rates and transition states are in good agreement with the experimental data for a broad force regime.

Triplex structures in an RNA pseudoknot enhance mechanical stability and increase efficiency of -1 ribosomal frameshifting

Many viruses use programmed -1 ribosomal frameshifting to express defined ratios of structural and enzymatic proteins. Pseudoknot structures in messenger RNAs stimulate frameshifting in upstream slippery sequences. The detailed molecular determinants of pseudoknot mechanical stability and frameshifting efficiency are not well understood. Here we use single-molecule unfolding studies by optical tweezers, and frameshifting assays to elucidate how mechanical stability of a pseudoknot and its frameshifting efficiency are regulated by tertiary stem-loop interactions. Mechanical unfolding of a model pseudoknot and mutants designed to dissect specific interactions reveals that mechanical stability depends strongly on triplex structures formed by stem-loop interactions. Combining single-molecule and mutational studies facilitates the identification of pseudoknot folding intermediates. Average unfolding forces of the pseudoknot and mutants ranging from 50 to 22 picoNewtons correlated with frameshifting efficiencies ranging from 53% to 0%. Formation of major-groove and minor-groove triplex structures enhances pseudoknot stem stability and torsional resistance, and may thereby stimulate frameshifting. Better understanding of the molecular determinants of frameshifting efficiency may facilitate the development of anti-virus therapeutics targeting frameshifting.

How RNA unfolds and refolds

Understanding how RNA folds and what causes it to unfold has become more important as knowledge of the diverse functions of RNA has increased. Here we review the contributions of single-molecule experiments to providing answers to questions such as: How much energy is required to unfold a secondary or tertiary structure? How fast is the process? How do helicases unwind double helices? Are the unwinding activities of RNA-dependent RNA polymerases and of ribosomes different from other helicases? We discuss the use of optical tweezers to monitor the unfolding activities of helicases, polymerases, and ribosomes, and to apply force to unfold RNAs directly. We also review the applications of fluorescence and fluorescence resonance energy transfer to measure RNA dynamics.

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

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

Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models

We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot probabilities of the more coarse-grained models with the wormlike model show that the behaviors of the random-flight model are similar to that of DNA molecules in a solution environment with high ionic strengths, whereas the behaviors of the cubic lattice model with excluded volume are akin to that of DNA molecules under low ionic strengths.

Unwinding RNA's secrets: advances in the biology, physics, and modeling of complex RNAs

The rapid development of our understanding of the diverse biological roles fulfilled by non-coding RNA has motivated interest in the basic macromolecular behavior, structure, and function of RNA. We focus on two areas in the behavior of complex RNAs. First, we present advances in the understanding of how RNA folding is accomplished in vivo by presenting a mechanism for the action of DEAD-box proteins. Members of this family are intimately associated with almost all cellular processes involving RNA, mediating RNA structural rearrangements and chaperoning their folding. Next, we focus on advances in understanding, and characterizing the basic biophysical forces that govern the folding of complex RNAs. Ultimately we expect that a confluence and synergy between these approaches will lead to profound understanding of RNA and its biology.

Folding kinetics of large RNAs

We introduce here a heuristic approach to kinetic RNA folding that constructs secondary structures by stepwise combination of building blocks. These blocks correspond to subsequences and their thermodynamically optimal structures. These are determined by the standard dynamic programming approach to RNA folding. Folding trajectories are modeled at base-pair resolution using the Morgan-Higgs heuristic and a barrier tree-based heuristic to connect combinations of the local building blocks. Implemented in the program Kinwalker, the algorithm allows co-transcriptional folding and can be used to fold sequences of up to about 1500 nucleotides in length. A detailed comparison with several well-studied examples from the literature, including the delayed folding of bacteriophage cloverleaf structures, the adenine sensing riboswitch, and the hok RNA, shows an excellent agreement of predicted trajectories and experimental evidence. The software is available as part of the ViennaRNA Package.

Simulating RNA folding kinetics on approximated energy landscapes

We present a general computational approach to simulate RNA folding kinetics that can be used to extract population kinetics, folding rates and the formation of particular substructures that might be intermediates in the folding process. Simulating RNA folding kinetics can provide unique insight into RNA whose functions are dictated by folding kinetics and not always by nucleotide sequence or the structure of the lowest free-energy state. The method first builds an approximate map (or model) of the folding energy landscape from which the population kinetics are analyzed by solving the master equation on the map. We present results obtained using an analysis technique, map-based Monte Carlo simulation, which stochastically extracts folding pathways from the map. Our method compares favorably with other computational methods that begin with a comprehensive free-energy landscape, illustrating that the smaller, approximate map captures the major features of the complete energy landscape. As a result, our method scales to larger RNAs. For example, here we validate kinetics of RNA of more than 200 nucleotides. Our method accurately computes the kinetics-based functional rates of wild-type and mutant ColE1 RNAII and MS2 phage RNAs showing excellent agreement with experiment.

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.