Statistical potentials for hairpin and internal loops improve the accuracy of the predicted RNA structure

RNA is directly associated with a growing number of functions within the cell. The accurate prediction of different RNA higher-order structures from their nucleic acid sequences will provide insight into their functions and molecular mechanics. We have been determining statistical potentials for a collection of structural elements that is larger than the number of structural elements determined with experimentally determined energy values. The experimentally derived free energies and the statistical potentials for canonical base-pair stacks are analogous, demonstrating that statistical potentials derived from comparative data can be used as an alternative energetic parameter. A new computational infrastructure—RNA Comparative Analysis Database (rCAD)—that utilizes a relational database was developed to manipulate and analyze very large sequence alignments and secondary-structure data sets. Using rCAD, we determined a richer set of energetic parameters for RNA fundamental structural elements including hairpin and internal loops. A new version of RNAfold was developed to utilize these statistical potentials. Overall, these new statistical potentials for hairpin and internal loops integrated into the new version of RNAfold demonstrated significant improvements in the prediction accuracy of RNA secondary structure.     

Analysis of Four-Way Junctions in RNA Structures

RNA secondary structures can be divided into helical regions composed of canonical Watson-Crick and related base pairs, as well as single-stranded regions such as hairpin loops, internal loops, and junctions. These elements function as building blocks in the design of diverse RNA molecules with various fundamental functions in the cell. To better understand the intricate architecture of three-dimensional (3D) RNAs, we analyze existing RNA four-way junctions in terms of base-pair interactions and 3D configurations. Specifically, we identify nine broad junction families according to coaxial stacking patterns and helical configurations. We find that helices within junctions tend to arrange in roughly parallel and perpendicular patterns and stabilize their conformations using common tertiary motifs such as coaxial stacking, loop-helix interaction, and helix packing interaction. Our analysis also reveals a number of highly conserved base-pair interaction patterns and novel tertiary motifs such as A-minor-coaxial stacking combinations and sarcin/ricin motif variants. Such analyses of RNA building blocks can ultimately help in the difficult task of RNA 3D structure prediction.     

Extracting stacking interaction parameters for RNA from the data set of native structures

A crucial step in the determination of the three-dimensional native structures of RNA is the prediction of their secondary structures, which are stable independent of the tertiary fold. Accurate prediction of the secondary structure requires context-dependent estimates of the interaction parameters. We have exploited the growing database of natively folded RNA structures in the Protein Data Bank (PDB) to obtain stacking interaction parameters using a knowledge-based approach. Remarkably, the calculated values of the resulting statistical potentials (SPs) are in excellent agreement with the parameters determined using measurements in small oligonucleotides. We validate the SPs by predicting 74% of the base-pairs in a dataset of structures using the ViennaRNA package. Interestingly, this number is similar to that obtained using the measured thermodynamic parameters. We also tested the efficacy of the SP in predicting secondary structure by using gapless threading, which we advocate as an alternative method for rapidly predicting RNA structures. For RNA molecules with less than 700 nucleotides, about 70% of the native base-pairs are correctly predicted. As a further validation of the SPs we calculated Z-scores, which measure the relative stability of the native state with respect to a manifold of higher free energy states. The computed Z-scores agree with estimates made using calorimetric measurements for a few RNA molecules. Structural analysis was used to rationalize the success and failures of SP and experimentally determined parameters. First, from the near perfect linear relationship between the number of native base-pairs and sequence length, we show that nearly 46% of nucleotides are not in stacks. Second, by analyzing the suboptimal structures that are generated in gapless threading we show that the SPs and experimentally determined parameters are most successful in predicting stacks that end in hairpins. These results show that further improvement in secondary structure prediction requires reliable estimates of interaction parameters for loops, bulges, and stacks that do not end in hairpins.     

Promoting RNA helical stacking via A-minor junctions

RNA molecules take advantage of prevalent structural motifs to fold and assemble into well-defined 3D architectures. The A-minor junction is a class of RNA motifs that specifically controls coaxial stacking of helices in natural RNAs. A sensitive self-assembling supra-molecular system was used as an assay to compare several natural and previously unidentified A-minor junctions by native polyacrylamide gel electrophoresis and atomic force microscopy. This class of modular motifs follows a topological rule that can accommodate a variety of interchangeable A-minor interactions with distinct local structural motifs. Overall, two different types of A-minor junctions can be distinguished based on their functional self-assembling behavior: one group makes use of triloops or GNRA and GNRA-like loops assembling with helices, while the other takes advantage of more complex tertiary receptors specific for the loop to gain higher stability. This study demonstrates how different structural motifs of RNA can contribute to the formation of topologically equivalent helical stacks. It also exemplifies the need of classifying RNA motifs based on their tertiary structural features rather than secondary structural features. The A-minor junction rule can be used to facilitate tertiary structure prediction of RNAs and rational design of RNA parts for nanobiotechnology and synthetic biology.     

The energetics of small internal loops in RNA

The energetics of small internal loops are important for prediction of RNA secondary and tertiary structure, selection of drug target sites, and understanding RNA structure-function relationships. Hydrogen bonding, base stacking, electrostatic interactions, backbone distortion, and base-pair size compatibility all contribute to the energetics of small internal loops. Thus, the sequence dependence of these energetics are idiosyncratic. Current approximations for predicting the free energies of internal loops consider size, asymmetry, closing base pairs, and the potential to form GA, GG, or UU pairs. The database of known three-dimensional structures allows for comparison with the models used for predicting stability from sequence.     

Thermodynamic characterization of RNA 2 × 3 nucleotide internal loops

To better elucidate RNA structure-function relationships and to improve the design of pharmaceutical agents that target specific RNA motifs, an understanding of RNA primary, secondary, and tertiary structure is necessary. The prediction of RNA secondary structure from sequence is an intermediate step in predicting RNA three-dimensional structure. RNA secondary structure is typically predicted using a nearest neighbor model based on free energy parameters. The current free energy parameters for 2 × 3 nucleotide loops are based on a 23-member data set of 2 × 3 loops and internal loops of other sizes. A database of representative RNA secondary structures was searched to identify 2 × 3 nucleotide loops that occur in nature. Seventeen of the most frequent 2 × 3 nucleotide loops in this database were studied by optical melting experiments. Fifteen of these loops melted in a two-state manner, and the associated experimental ΔG°(37,2×3) values are, on average, 0.6 and 0.7 kcal/mol different from the values predicted for these internal loops using the predictive models proposed by Lu, Turner, and Mathews [Lu, Z. J., Turner, D. H., and Mathews, D. H. (2006) Nucleic Acids Res. 34, 4912-4924] and Chen and Turner [Chen, G., and Turner, D. H. (2006) Biochemistry 45, 4025-4043], respectively. These new ΔG°(37,2×3) values can be used to update the current algorithms that predict secondary structure from sequence. To improve free energy calculations for duplexes containing 2 × 3 nucleotide loops that still do not have experimentally determined free energy contributions, an updated predictive model was derived. This new model resulted from a linear regression analysis of the data reported here combined with 31 previously studied 2 × 3 nucleotide internal loops. Most of the values for the parameters in this new predictive model are within experimental error of those of the previous models, suggesting that approximations and assumptions associated with the derivation of the previous nearest neighbor parameters were valid. The updated predictive model predicts free energies of 2 × 3 nucleotide internal loops within 0.4 kcal/mol, on average, of the experimental free energy values. Both the experimental values and the updated predictive model can be used to improve secondary structure prediction from sequence.     

Conformational changes in transfer RNA. I. Equilibrium theory

We report the results of semi-empirical calculations describing thermodynamic properties of transfer RNA conformations. The most important new features of the procedure are: (1) the use of parameters obtained from model oligoribonucleotides to evaluate the free energy of helical regions and small hairpin loops, and (2) the use of a model which is somewhat more realistic than the freely jointed chain for evaluating internal loops and intermediate size hairpin loops. The new parameters lead to important quantitative and qualitative differences from predictions which would have been made in the past and lead to a priori predictions of tRNA melting temperatures which are within about 6°C of the experimental values. The results suggest the following conclusions: (1) The early melting transition observed in several tRNA's is partly the result of tertiary unfolding, and partly the result of the loss of some secondary structure. (2) The part of the secondary structure which melts during the early transition is different for different tRNA's. For fMet and Tyr from E. coli, the calculations predict that the dihydrouradiene arm melts out early. For yeast Phe the acceptor stem and anticodon helix melt first. (3) The results also suggest the possibility that tertiary unfolding and early secondary structural melting do not occur independently but are coupled, so that the two types of structure are probably mutually stabilizing.     

The lonepair triloop: a new motif in RNA structure

The lonepair triloop (LPTL) is an RNA structural motif that contains a single ("lone") base-pair capped by a hairpin loop containing three nucleotides. The two nucleotides immediately outside of this motif (5' and 3' to the lonepair) are not base-paired to one another, restricting the length of this helix to a single base-pair. Four examples of this motif, along with three tentative examples, were initially identified in the 16S and 23S rRNAs with covariation analysis. An evaluation of the recently determined crystal structures of the Thermus thermophilus 30S and Haloarcula marismortui 50S ribosomal subunits revealed the authenticity for all of these proposed interactions and identified 16 more LPTLs in the 5S, 16S and 23S rRNAs. This motif is found in the T loop in the tRNA crystal structures. The lonepairs are positioned, in nearly all examples, immediately 3' to a regular secondary structure helix and are stabilized by coaxial stacking onto this flanking helix. In all but two cases, the nucleotides in the triloop are involved in a tertiary interaction with another section of the rRNA, establishing an overall three-dimensional function for this motif. Of these 24 examples, 14 occur in multi-stem loops, seven in hairpin loops and three in internal loops. While the most common lonepair, U:A, occurs in ten of the 24 LPTLs, the remaining 14 LPTLs contain seven different base-pair types. Only a few of these lonepairs adopt the standard Watson-Crick base-pair conformations, while the majority of the base-pairs have non-standard conformations. While the general three-dimensional conformation is similar for all examples of this motif, characteristic differences lead to several subtypes present in different structural environments. At least one triloop nucleotide in 22 of the 24 LPTLs in the rRNAs and tRNAs forms a tertiary interaction with another part of the RNA. When a LPTL containing the GNR or UYR triloop sequence forms a tertiary interaction with the first (and second) triloop nucleotide, it recruits a fourth nucleotide to mediate stacking and mimic the tetraloop conformation. Approximately half of the LPTL motifs are in close association with proteins. The majority of these LPTLs are positioned at sites in rRNAs that are conserved in the three phylogenetic domains; a few of these occur in regions of the rRNA associated with ribosomal function, including the presumed site of peptidyl transferase activity in the 23S rRNA.     

Small changes in free energy assignments for unpaired bases do not affect predicted secondary structures in single stranded RNA.

We present extensive calculations of the secondary structure of mRNA which point to its insensitivity to small changes in the free energy assignments of single stranded regions. Truncating the free energies of hairpin loops, bulges, internal loops and multibranched junctions to two significant digits yields structures nearly identical to those generated using three digit values. The results show that one can safely use truncated values in RNA folding calculations. The implementation of these results enabled us to carry out secondary structure calculations on 2600 nucleotides in a single computer run.     

Consensus folding of unaligned RNA sequences revisited.

As one of the earliest problems in computational biology, RNA secondary structure prediction (sometimes referred to as "RNA folding") problem has attracted attention again, thanks to the recent discoveries of many novel non-coding RNA molecules. The two common approaches to this problem are de novo prediction of RNA secondary structure based on energy minimization and the consensus folding approach (computing the common secondary structure for a set of unaligned RNA sequences). Consensus folding algorithms work well when the correct seed alignment is part of the input to the problem. However, seed alignment itself is a challenging problem for diverged RNA families. In this paper, we propose a novel framework to predict the common secondary structure for unaligned RNA sequences. By matching putative stacks in RNA sequences, we make use of both primary sequence information and thermodynamic stability for prediction at the same time. We show that our method can predict the correct common RNA secondary structures even when we are given only a limited number of unaligned RNA sequences, and it outperforms current algorithms in sensitivity and accuracy.     

Statistical and Bayesian approaches to RNA secondary structure prediction

Prediction of RNA secondary structure is a fundamental problem in computational structural biology. For several decades, free energy minimization has been the most popular method for prediction from a single sequence. In recent years, the McCaskill algorithm for computation of partition function and base-pair probabilities has become increasingly appreciated. This paradigm-shifting work has inspired the developments of extended partition function algorithms, statistical sampling and clustering, and application of Bayesian statistical inference. The performance of thermodynamics-based methods is limited by thermodynamic rules and parameters. However, further improvements may come from statistical estimates derived from structural databases for thermodynamics parameters with weak or little experimental data. The Bayesian inference approach appears to be promising in this context.     

Improved RNA secondary structure prediction by maximizing expected pair accuracy

Free energy minimization has been the most popular method for RNA secondary structure prediction for decades. It is based on a set of empirical free energy change parameters derived from experiments using a nearest-neighbor model. In this study, a program, MaxExpect, that predicts RNA secondary structure by maximizing the expected base-pair accuracy, is reported. This approach was first pioneered in the program CONTRAfold, using pair probabilities predicted with a statistical learning method. Here, a partition function calculation that utilizes the free energy change nearest-neighbor parameters is used to predict base-pair probabilities as well as probabilities of nucleotides being single-stranded. MaxExpect predicts both the optimal structure (having highest expected pair accuracy) and suboptimal structures to serve as alternative hypotheses for the structure. Tested on a large database of different types of RNA, the maximum expected accuracy structures are, on average, of higher accuracy than minimum free energy structures. Accuracy is measured by sensitivity, the percentage of known base pairs correctly predicted, and positive predictive value (PPV), the percentage of predicted pairs that are in the known structure. By favoring double-strandedness or single-strandedness, a higher sensitivity or PPV of prediction can be favored, respectively. Using MaxExpect, the average PPV of optimal structure is improved from 66% to 68% at the same sensitivity level (73%) compared with free energy minimization.     

Thermodynamic parameters for loop formation in RNA and DNA hairpin tetraloops.

We determined the melting temperatures (Tm) and thermodynamic parameters of 15 RNA and 19 DNA hairpins at 1 M NaCl, 0.01 M sodium phosphate, 0.1 mM EDTA, at pH 7. All these hairpins have loops of four bases, the most common loop size in 16S and 23S ribosomal RNAs. The RNA hairpins varied in loop sequence, loop-closing base pair (A.U, C.G, or G.C), base sequence of the stem, and stem size (four or five base pairs). The DNA hairpins varied in loop sequence, loop-closing base pair (C.G, or G.C), and base sequence of the four base-pair stem. Thermodynamic properties of a hairpin may be represented by nearest-neighbor interactions of the stem plus contributions from the loop. Thus, we obtained thermodynamic parameters for the formation of RNA and DNA tetraloops. For the tetraloops we studied, a free energy of loop formation (at 37 degrees C) of about +3 kcal/mol is most common for either RNA or DNA. There are extra stable loops with delta G degrees 37 near +1 kcal/mol, but the sequences are not necessarily the same for RNA and DNA. The closing base pair is also important; changing from C.G to G.C lowered the stability of several tetraloops in both RNA and DNA. These values will be useful in predicting RNA and DNA secondary structures.     

Tertiary Motifs Revealed in Analyses of Higher-Order RNA Junctions

RNA junctions are secondary-structure elements formed when three or more helices come together. They are present in diverse RNA molecules with various fundamental functions in the cell. To better understand the intricate architecture of three-dimensional (3D) RNAs, we analyze currently solved 3D RNA junctions in terms of base-pair interactions and 3D configurations. First, we study base-pair interaction diagrams for solved RNA junctions with 5 to 10 helices and discuss common features. Second, we compare these higher-order junctions to those containing 3 or 4 helices and identify global motif patterns such as coaxial stacking and parallel and perpendicular helical configurations. These analyses show that higher-order junctions organize their helical components in parallel and helical configurations similar to lower-order junctions. Their sub-junctions also resemble local helical configurations found in three- and four-way junctions and are stabilized by similar long-range interaction preferences such as A-minor interactions. Furthermore, loop regions within junctions are high in adenine but low in cytosine, and in agreement with previous studies, we suggest that coaxial stacking between helices likely forms when the common single-stranded loop is small in size; however, other factors such as stacking interactions involving noncanonical base pairs and proteins can greatly determine or disrupt coaxial stacking. Finally, we introduce the ribo-base interactions: when combined with the along-groove packing motif, these ribo-base interactions form novel motifs involved in perpendicular helix-helix interactions. Overall, these analyses suggest recurrent tertiary motifs that stabilize junction architecture, pack helices, and help form helical configurations that occur as sub-elements of larger junction networks. The frequent occurrence of similar helical motifs suggest nature's finite and perhaps limited repertoire of RNA helical conformation preferences. More generally, studies of RNA junctions and tertiary building blocks can ultimately help in the difficult task of RNA 3D structure prediction.     

Statistics of RNA secondary structures

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences. Four nucleotide alphabets are used: two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet. RNA secondary structures are made of structural elements, such as stacks, loops, joints, and free ends. Statistical properties of these elements are computed for small RNA molecules of chain lengths up to 100. The results of RNA structure statistics depend strongly on the particular alphabet chosen. The statistical reference is compared with the data derived from natural RNA molecules with similar base frequencies. Secondary structures are represented as trees. Tree editing provides a quantitative measure for the distance d_t, between two structures. We compute a structure density surface as the conditional probability of two structures having distance t given that their sequences have distance h. This surface indicates that the vast majority of possible minimum free energy secondary structures occur within a fairly small neighborhood of any typical (random) sequence. Correlation lengths for secondary structures in their tree representations are computed from probability densities. They are appropriate measures for the complexity of the sequence-structure relation. The correlation length also provides a quantitative estimate for the mean sensitivity of structures to point mutations. © 1993 John Wiley & Sons, Inc.     

Solution Structure of NPSL2, A Regulatory Element in the oncomiR-1 RNA

The miR-17 ～ 92a polycistron, also known as oncomiR-1, is commonly overexpressed in multiple cancers and has several oncogenic properties. OncomiR-1 encodes six constituent microRNAs (miRs), each enzymatically processed with different efficiencies. However, the structural mechanism that regulates this differential processing remains unclear. Chemical probing of oncomiR-1 revealed that the Drosha cleavage sites of pri-miR-92a are sequestered in a four-way junction. NPSL2, an independent stem loop element, is positioned just upstream of pri-miR-92a and sequesters a crucial part of the sequence that constitutes the basal helix of pri-miR-92a. Disruption of the NPSL2 hairpin structure could promote the formation of a pri-miR-92a structure that is primed for processing by Drosha. Thus, NPSL2 is predicted to function as a structural switch, regulating pri-miR-92a processing. Here, we determined the solution structure of NPSL2 using solution NMR spectroscopy. This is the first high-resolution structure of an oncomiR-1 element. NPSL2 adopts a hairpin structure with a large, but highly structured, apical and internal loops. The 10-bp apical loop contains a pH-sensitive A⁺·C mismatch. Additionally, several adenosines within the apical and internal loops have elevated pK_a values. The protonation of these adenosines can stabilize the NPSL2 structure through electrostatic interactions. Our study provides fundamental insights into the secondary and tertiary structure of an important RNA hairpin proposed to regulate miR biogenesis.     

Effects of Mg2+ on the free energy landscape for folding a purine riboswitch RNA

There are potentially several ways Mg2+ might promote formation of an RNA tertiary structure: by causing a general "collapse" of the unfolded ensemble to more compact conformations, by favoring a reorganization of structure within a domain to a form with specific tertiary contacts, and by enhancing cooperative linkages between different sets of tertiary contacts. To distinguish these different modes of action, we have studied Mg2+ interactions with the adenine riboswitch, in which a set of tertiary interactions that forms around a purine-binding pocket is thermodynamically linked to the tertiary "docking" of two hairpin loops in another part of the molecule. Each of four RNA forms with different extents of tertiary structure were characterized by small-angle X-ray scattering. The free energy of interconversion between different conformations in the absence of Mg2+ and the free energy of Mg2+ interaction with each form have been estimated, yielding a complete picture of the folding energy landscape as a function of Mg2+ concentration. At 1 mM Mg2+ (50 mM K+), the overall free energy of stabilization by Mg2+ is large, -9.8 kcal/mol, and about equally divided between its effect on RNA collapse to a partially folded structure and on organization of the binding pocket. A strong cooperative linkage between the two sets of tertiary contacts is intrinsic to the RNA. This quantitation of the effects of Mg2+ on an RNA with two distinct sets of tertiary interactions suggests ways that Mg2+ may work to stabilize larger and more complex RNA structures.     

Non-specific binding of Na+ and Mg2+ to RNA determined by force spectroscopy methods

RNA duplex stability depends strongly on ionic conditions, and inside cells RNAs are exposed to both monovalent and multivalent ions. Despite recent advances, we do not have general methods to quantitatively account for the effects of monovalent and multivalent ions on RNA stability, and the thermodynamic parameters for secondary structure prediction have only been derived at 1M [Na(+)]. Here, by mechanically unfolding and folding a 20 bp RNA hairpin using optical tweezers, we study the RNA thermodynamics and kinetics at different monovalent and mixed monovalent/Mg(2+) salt conditions. We measure the unfolding and folding rupture forces and apply Kramers theory to extract accurate information about the hairpin free energy landscape under tension at a wide range of ionic conditions. We obtain non-specific corrections for the free energy of formation of the RNA hairpin and measure how the distance of the transition state to the folded state changes with force and ionic strength. We experimentally validate the Tightly Bound Ion model and obtain values for the persistence length of ssRNA. Finally, we test the approximate rule by which the non-specific binding affinity of divalent cations at a given concentration is equivalent to that of monovalent cations taken at 100-fold concentration for small molecular constructs.     

RNA structural motifs: building blocks of a modular biomolecule

RNAs are modular biomolecules, composed largely of conserved structural subunits, or motifs. These structural motifs comprise the secondary structure of RNA and are knit together via tertiary interactions into a compact, functional, three-dimensional structure and are to be distinguished from motifs defined by sequence or function. A relatively small number of structural motifs are found repeatedly in RNA hairpin and internal loops, and are observed to be composed of a limited number of common 'structural elements'. In addition to secondary and tertiary structure motifs, there are functional motifs specific for certain biological roles and binding motifs that serve to complex metals or other ligands. Research is continuing into the identification and classification of RNA structural motifs and is being initiated to predict motifs from sequence, to trace their phylogenetic relationships and to use them as building blocks in RNA engineering.