Fast formation of the P3-P7 pseudoknot: a strategy for efficient folding of the catalytically active ribozyme

Formation of the P3-P7 pseudoknot structure, the core of group I ribozymes, requires long-range base pairing. Study of the Tetrahymena ribozyme appreciates the hierarchical folding of the large, multidomain RNA, in which the P3-P7 core folds significantly slower than do the other domains. Here we explored the formation of the P3-P7 pseudoknot of the Candida ribozyme that has been reported to concertedly fold to the catalytically active structure with a rate constant of 2 min(-1). We demonstrate that pseudoknot formation occurs during the rapid ribozyme compaction, coincident with formation of many tertiary interactions of the ribozyme. A low physiological concentration of magnesium (1.5 mM) is sufficient to fully support the pseudoknot formation. The presence of nonnative intermediates containing an unfolded P3-P7 region is evident. However, catalysis-based analysis shows these nonnative intermediates are stable and fail to convert to the catalytically active structure, suggesting that rapid pseudoknot formation is essential for folding of the active ribozyme. Interestingly, RNAstructure predicts no stable Alt P3 structure for the Candida ribozyme, but two stable Alt P3s for the Tetrahymena ribozyme, explaining the dramatic difference in folding of the P3-P7 core of these two ribozymes. We propose that rapid formation of the P3-P7 pseudoknot represents a folding strategy ensuring efficient production of the catalytically active structure of group I ribozymes, which sheds new light on the mechanism of effective ribozyme folding in vivo.     

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.     

The impact of dyskeratosis congenita mutations on the structure and dynamics of the human telomerase RNA pseudoknot domain

The pseudoknot domain is a functionally crucial part of telomerase RNA and influences the activity and stability of the ribonucleoprotein complex. Autosomal dominant dyskeratosis congenita (DKC) is an inherited disease that is linked to mutations in telomerase RNA and impairs telomerase function. In this paper, we present a computational prediction of the influence of two base DKC mutations on the structure, dynamics, and stability of the pseudoknot domain. We use molecular dynamics simulations, MM-GBSA free energy calculations, static analysis, and melting simulations analysis. Our results show that the DKC mutations stabilize the hairpin form and destabilize the pseudoknot form of telomerase RNA. Moreover, the P3 region of the predicted DKC-mutated pseudoknot structure is unstable and fails to form as a defined helical stem. We directly compare our predictions with experimental observations by calculating the enthalpy of folding and melting profiles for each structure. The enthalpy values are in very good agreement with values determined by thermal denaturation experiments. The melting simulations and simulations at elevated temperatures show the existence of an intermediate structure, which involves the formation of two UU base pairs observed in the hairpin form of the pseudoknot domain.     

An NMR and mutational analysis of an RNA pseudoknot of Escherichia coli tmRNA involved in trans-translation.

Transfer-messenger RNA (tmRNA) is a unique molecule that combines properties from both tRNA and mRNA, and facilitates a novel translation reaction termed trans -translation. According to phylogenetic sequence analysis among various bacteria and chemical probing analysis, the secondary structure of the 350-400 nt RNA is commonly characterized by a tRNA-like structure, and four pseudoknots with different sizes. A mutational analysis using a number of Escherichia coli tmRNA variants as well as a chemical probing analysis has recently demonstrated not only the presence of the smallest pseudoknot, PK1, upstream of the internal coding region, but also its direct implication in trans -translation. Here, NMR methods were used to investigate the structure of the 31 nt pseudoknot PK1 and its 11 mutants in which nucleotide substitutions are introduced into each of two stems or the linking loops. NMR results provide evidence that the PK1 RNA is folded into a pseudoknot structure in the presence of Mg(2+). Imino proton resonances were observed consistent with formation of two helical stem regions and these stems stacked to each other as often seen in pseudoknot structures, in spite of the existence of three intervening nucleo-tides, loop 3, between the stems. Structural instability of the pseudoknot structure, even in the presence of Mg(2+), was found in the PK1 mutants except in the loop 3 mutants which still maintained the pseudoknot folding. These results together with their biological activities indicate that trans -translation requires the pseudoknot structure stabilized by Mg(2+)and specific residues G61 and G62 in loop 3.     

The Impact of Dyskeratosis Congenita Mutations on the Structure and Dynamics of the Human Telomerase RNA Pseudoknot Domain

Abstract

The pseudoknot domain is a functionally crucial part of telomerase RNA and influences the activity and stability of the ribonucleoprotein complex. Autosomal dominant dyskeratosis congenita (DKC) is an inherited disease that is linked to mutations in telomerase RNA and impairs telomerase function. In this paper, we present a computational prediction of the influence of two base DKC mutations on the structure, dynamics, and stability of the pseudoknot domain. We use molecular dynamics simulations, MM-GBSA free energy calculations, static analysis, and melting simulations analysis. Our results show that the DKC mutations stabilize the hairpin form and destabilize the pseudoknot form of telomerase RNA. Moreover, the P3 region of the predicted DKC-mutated pseudoknot structure is unstable and fails to form as a defined helical stem. We directly compare our predictions with experimental observations by calculating the enthalpy of folding and melting profiles for each structure. The enthalpy values are in very good agreement with values determined by thermal denaturation experiments. The melting simulations and simulations at elevated temperatures show the existence of an intermediate structure, which involves the formation of two UU base pairs observed in the hairpin form of the pseudoknot domain.     

A pseudoknot-compatible universal site is located in the large ribosomal RNA in the peptidyltransferase center

The RNA secondary structure is not confined to a system of the hairpins and can contain pseudoknots as well as topologically equivalent slipped-loop structure (SLS) conformations. A specific primary structure that directs folding to the pseudoknot or SLS is called SL-palindrome (SLP). Using a computer program for searching the SLP in the genomic sequences, 419 primary structures of large ribosomal RNAs from different kingdoms (prokaryota, eukaryota, archaebacteria) as well as plastids and mitochondria were analyzed. A universal site was found in the peptidyltransferase center (PTC) capable of folding to a pseudoknot of 48 nucleotides in length. Phylogenetic conservation of its helices (concurrent replacements with no violation of base pairing, covariation) has been demonstrated. We suggest the reversible folding-unfolding of the pseudoknot for certain stages of the ribosome functioning.     

Biphasic folding kinetics of RNA pseudoknots and telomerase RNA activity

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

Prediction of RNA pseudoknots using heuristic modeling with mapping and sequential folding

Predicting RNA secondary structure is often the first step to determining the structure of RNA. Prediction approaches have historically avoided searching for pseudoknots because of the extreme combinatorial and time complexity of the problem. Yet neglecting pseudoknots limits the utility of such approaches. Here, an algorithm utilizing structure mapping and thermodynamics is introduced for RNA pseudoknot prediction that finds the minimum free energy and identifies information about the flexibility of the RNA. The heuristic approach takes advantage of the 5' to 3' folding direction of many biological RNA molecules and is consistent with the hierarchical folding hypothesis and the contact order model. Mapping methods are used to build and analyze the folded structure for pseudoknots and to add important 3D structural considerations. The program can predict some well known pseudoknot structures correctly. The results of this study suggest that many functional RNA sequences are optimized for proper folding. They also suggest directions we can proceed in the future to achieve even better results.     

Thermodynamic heuristics with case-based reasoning: combined insights for RNA pseudoknot secondary structure

The secondary structure of RNA pseudoknots has been extensively inferred and scrutinized by computational approaches. Experimental methods for determining RNA structure are time consuming and tedious; therefore, predictive computational approaches are required. Predicting the most accurate and energy-stable pseudoknot RNA secondary structure has been proven to be an NP-hard problem. In this paper, a new RNA folding approach, termed MSeeker, is presented; it includes KnotSeeker (a heuristic method) and Mfold (a thermodynamic algorithm). The global optimization of this thermodynamic heuristic approach was further enhanced by using a case-based reasoning technique as a local optimization method. MSeeker is a proposed algorithm for predicting RNA pseudoknot structure from individual sequences, especially long ones. This research demonstrates that MSeeker improves the sensitivity and specificity of existing RNA pseudoknot structure predictions. The performance and structural results from this proposed method were evaluated against seven other state-of-the-art pseudoknot prediction methods. The MSeeker method had better sensitivity than the DotKnot, FlexStem, HotKnots, pknotsRG, ILM, NUPACK and pknotsRE methods, with 79% of the predicted pseudoknot base-pairs being correct.     

Predicting RNA pseudoknot folding thermodynamics

Based on the experimentally determined atomic coordinates for RNA helices and the self-avoiding walks of the P (phosphate) and C₄ (carbon) atoms in the diamond lattice for the polynucleotide loop conformations, we derive a set of conformational entropy parameters for RNA pseudoknots. Based on the entropy parameters, we develop a folding thermodynamics model that enables us to compute the sequence-specific RNA pseudoknot folding free energy landscape and thermodynamics. The model is validated through extensive experimental tests both for the native structures and for the folding thermodynamics. The model predicts strong sequence-dependent helix-loop competitions in the pseudoknot stability and the resultant conformational switches between different hairpin and pseudoknot structures. For instance, for the pseudoknot domain of human telomerase RNA, a native-like and a misfolded hairpin intermediates are found to coexist on the (equilibrium) folding pathways, and the interplay between the stabilities of these intermediates causes the conformational switch that may underlie a human telomerase disease.     

The computer simulation of RNA folding involving pseudoknot formation.

The algorithm and the program for the prediction of RNA secondary structure with pseudoknot formation have been proposed. The algorithm simulates stepwise folding by generating random structures using Monte Carlo method, followed by the selection of helices to final structure on the basis of both their probabilities of occurrence in a random structure and free energy parameters. The program versions have been tested on ribosomal RNA structures and on RNAs with pseudoknots evidenced by experimental data. It is shown that the simulation of folding during RNA synthesis improves the results. The introduction of pseudoknot formation permits to predict the pseudoknotted structures and to improve the prediction of long-range interactions. The computer program is rather fast and allows to predict the structures for long RNAs without using large memory volumes in usual personal computer.     

Inverse folding of RNA pseudoknot structures

Background  

RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and G-U-base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse folding algorithms, RNAinverse, RNA-SSD as well as INFO-RNA are limited to RNA secondary structures, we present in this paper the inverse folding algorithm Inv which can deal with 3-noncrossing, canonical pseudoknot structures.     

Unusual mRNA pseudoknot structure is recognized by a protein translational repressor

Translation of ribosomal proteins in the alpha operon of E. coli is repressed by one of the encoded proteins, S4; it specifically recognizes an RNA fragment containing the translational initiation site for the first gene in the operon. RNA structure mapping experiments have suggested a pseudoknot structure for the S4 binding site: the loop of a hairpin is base paired to sequences downstream of the hairpin. Here, we systematically test this proposed structure by measuring S4 binding to an extensive set of site-directed mutations that create compensatory base pair changes in potential helices. The pseudoknot folding is confirmed, and two additional, unexpected interactions within the pseudoknot are also detected. The overall structure is an unusual "double pseudoknot" linking a hairpin upstream of the ribosome binding site with sequences 2-10 codons downstream of the initiation codon. Stabilization of this structure by S4 could account for translational repression.     

Practicality and time complexity of a sparsified RNA folding algorithm

Commonly used RNA folding programs compute the minimum free energy structure of a sequence under the pseudoknot exclusion constraint. They are based on Zuker's algorithm which runs in time O(n(3)). Recently, it has been claimed that RNA folding can be achieved in average time O(n(2)) using a sparsification technique. A proof of quadratic time complexity was based on the assumption that computational RNA folding obeys the "polymer-zeta property". Several variants of sparse RNA folding algorithms were later developed. Here, we present our own version, which is readily applicable to existing RNA folding programs, as it is extremely simple and does not require any new data structure. We applied it to the widely used Vienna RNAfold program, to create sibRNAfold, the first public sparsified version of a standard RNA folding program. To gain a better understanding of the time complexity of sparsified RNA folding in general, we carried out a thorough run time analysis with synthetic random sequences, both in the context of energy minimization and base pairing maximization. Contrary to previous claims, the asymptotic time complexity of a sparsified RNA folding algorithm using standard energy parameters remains O(n(3)) under a wide variety of conditions. Consistent with our run-time analysis, we found that RNA folding does not obey the "polymer-zeta property" as claimed previously. Yet, a basic version of a sparsified RNA folding algorithm provides 15- to 50-fold speed gain. Surprisingly, the same sparsification technique has a different effect when applied to base pairing optimization. There, its asymptotic running time complexity appears to be either quadratic or cubic depending on the base composition. The code used in this work is available at: .     

High sensitivity RNA pseudoknot prediction

Most ab initio pseudoknot predicting methods provide very few folding scenarios for a given RNA sequence and have low sensitivities. RNA researchers, in many cases, would rather sacrifice the specificity for a much higher sensitivity for pseudoknot detection. In this study, we introduce the Pseudoknot Local Motif Model and Dynamic Partner Sequence Stacking (PLMM_DPSS) algorithm which predicts all PLM model pseudoknots within an RNA sequence in a neighboring-region-interference-free fashion. The PLM model is derived from the existing Pseudobase entries. The innovative DPSS approach calculates the optimally lowest stacking energy between two partner sequences. Combined with the Mfold, PLMM_DPSS can also be used in predicting complicated pseudoknots. The test results of PLMM_DPSS, PKNOTS, iterated loop matching, pknotsRG and HotKnots with Pseudobase sequences have shown that PLMM_DPSS is the most sensitive among the five methods. PLMM_DPSS also provides manageable pseudoknot folding scenarios for further structure determination.     

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

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

Identification of novel ligands for the RNA pseudoknot that regulate -1 ribosomal frameshifting

In many viruses, -1 ribosomal frameshifting (-1RF) regulates synthesis of proteins and is crucial for virus production. An RNA pseudoknot is one of the essential components of the viral -1RF system. Thermodynamic or kinetic control of pseudoknot folding may be important in regulating the efficiency of -1RF. Thus, small molecules that interact with viral RNA pseudoknots may disrupt the -1RF system and show antiviral activity. In this study, we conducted virtual screening of a chemical database targeting the X-ray crystal structure of RNA pseudoknot complexed with biotin to identify ligands that may regulate an -1RF system containing biotin-aptamer as an RNA pseudoknot component. After docking screening of about 80,000 compounds, 58 high-ranked hits were selected and their activities were examined by in vitro and cell-based -1 frameshifting assays. Six compounds increased the efficiency of -1 frameshifting, and these are novel small molecule compounds that regulate the -1RF.