Comparative sequence analysis and patterns of covariation in RNA secondary structures

A novel method of RNA secondary structure prediction based on a comparison of nucleotide sequences is described. This method correctly predicts nearly all evolutionarily conserved secondary structures of five different RNAs: tRNA, 5S rRNA, bacterial ribonuclease P (RNase P) RNA, eukaryotic small subunit rRNA, and the 3' untranslated region (UTR) of the Drosophila bicoid (bcd) mRNA. Furthermore, covariations occurring in the helices of these conserved RNA structures are analyzed. Two physical parameters are found to be important determinants of the evolution of compensatory mutations: the length of a helix and the distance between base-pairing nucleotides. For the helices of bcd 3' UTR mRNA and RNase P RNA, a positive correlation between the rate of compensatory evolution and helix length is found. The analysis of Drosophila bcd 3' UTR mRNA further revealed that the rate of compensatory evolution decreases with the physical distance between base-pairing residues. This result is in qualitative agreement with Kimura's model of compensatory fitness interactions, which assumes that mutations occurring in RNA helices are individually deleterious but become neutral in appropriate combinations.     

Predicting Secondary Structural Folding Kinetics for Nucleic Acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.     

Multiple functions of Saccharomyces cerevisiae splicing protein Prp24 in U6 RNA structural rearrangements.

U6 spliceosomal RNA has a complex secondary structure that includes a highly conserved stemloop near the 3' end. The 3' stem is unwound when U6 RNA base-pairs with U4 RNA during spliceosome assembly, but likely reforms when U4 RNA leaves the spliceosome prior to the catalysis of splicing. A mutation in yeast U6 RNA that hyperstabilizes the 3' stem confers cold sensitivity and inhibits U4/U6 assembly as well as a later step in splicing. Here we show that extragenic suppressors of the 3' stem mutation map to the gene coding for splicing factor Prp24. The suppressor mutations are located in the second and third of three RNA-recognition motifs (RRMs) in Prp24 and are predicted to disrupt RNA binding. Mutations in U6 RNA predicted to destabilize a novel helix adjacent to the 3' stem also suppress the 3' stem mutation and enhance the growth defect of a suppressor mutation in RRM2 of Prp24. Both phenotypes are reverted by a compensatory mutation that restores pairing in the novel helix. These results are best explained by a model in which RRMs 2 and 3 of Prp24 stabilize an extended intramolecular structure in U6 RNA that competes with the U4/U6 RNA interaction, and thus influence both association and dissociation of U4 and U6 RNAs during the splicing cycle.     

Coupled nucleotide covariations reveal dynamic RNA interaction patterns

Evolutionarily conserved structures in related RNA molecules contain coordinated variations (covariations) of paired nucleotides. Analysis of covariations is a very powerful approach to deduce phylogenetically conserved (i.e., functional) conformations, including tertiary interactions. Here we discuss conserved RNA folding pathways that are revealed by covariation patterns. In such pathways, structural requirements for alternative pairings cause some nucleotides to covary with two different partners. Such "coupled" covariations between three or more nucleotides were found in various types of RNAs. The analysis of coupled covariations can unravel important features of RNA folding dynamics and improve phylogeny reconstruction in some cases. Importantly, it is necessary to distinguish between multiple covariations determined by mutually exclusive structures and those determined by tertiary contacts.     

A non-directed, hydroxylamine-generated suppressor mutation in the P3 pairing region of the bacteriophage T4 td intron partially restores self-splicing capability

Hydroxylamine (HA) mutagenesis of an HA-induced splicing-defective bacteriophage T4 td intron mutant with a mutation in the intron P3 RNA pairing region was used to generate pseudorevertants. Because HA can only cause GC to AT transitions, the original mutant (H104A) could not undergo true reversion, yet the compensatory mutation on the opposite side of the P3 helix, which was complementary to the original H104A mutation, could occur. A pseudorevertant was isolated that contained both the original H104A mutation and the compensatory mutation HS9. By phenotypic and molecular genetic criteria, this double mutant (H104A-HS9) was shown to be able to undergo significant RNA splicing, thus confirming the existence and functional importance of the long-range P3 pairing region in this phage intron. The second-site suppressor mutation (HS9) was isolated by phage cross and also exhibited some self-splicing ability. A correlation exists between the strength of P3 helix Watson-Crick base pairing and the apparent level of splicing when wild-type, H104A, HS9, and H104A-HS9 are compared. This suggests that the primary role of the P3 RNA pairing region in the T4 td intron is structural in contributing to the critical RNA secondary structure.     

Strong Epistatic Selection on the RNA Secondary Structure of HIV

A key question in evolutionary genomics is how populations navigate the adaptive landscape in the presence of epistasis, or interactions among loci. This problem can be directly addressed by studying the evolution of RNA secondary structures, for which there is constraint to maintain pairing between Watson-Crick (WC) sites. Replacement of a nucleotide at one site of a WC pair reduces fitness by disrupting binding, which can be restored via a compensatory replacement at the interacting site. Here, I present the first genome-scale analysis of epistasis on the RNA secondary structure of human immunodeficiency virus type 1 (HIV-1). Comparison of polymorphism frequencies at ancestrally conserved sites reveals that selection against replacements is ∼2.7 times stronger at WC than at non-WC sites, such that nearly 50% of constraint can be attributed to epistasis. However, almost all epistatic constraint is due to selection against conversions of WC pairs to unpaired (UP) nucleotides, whereas conversions to GU wobbles are only slightly deleterious. This disparity is also evident in pairs with second-site compensatory replacements; conversions from UP nucleotides to WC pairs increase median fitness by ∼4.2%, whereas conversions from GU wobbles to WC pairs only increase median fitness by ∼0.3%. Moreover, second-site replacements that convert UP nucleotides to GU wobbles also increase median fitness by ∼4%, indicating that such replacements are nearly as compensatory as those that restore WC pairing. Thus, WC peaks of the HIV-1 epistatic adaptive landscape are connected by high GU ridges, enabling the viral population to rapidly explore distant peaks without traversing deep UP valleys.     

Inverse folding with RNA-As-Graphs produces a large pool of candidate sequences with target topologies

We present an RNA-As-Graphs (RAG) based inverse folding algorithm, RAG-IF, to design novel RNA sequences that fold onto target tree graph topologies. The algorithm can be used to enhance our recently reported computational design pipeline (Jain et al., NAR 2018). The RAG approach represents RNA secondary structures as tree and dual graphs, where RNA loops and helices are coarse-grained as vertices and edges, opening the usage of graph theory methods to study, predict, and design RNA structures. Our recently developed computational pipeline for design utilizes graph partitioning (RAG-3D) and atomic fragment assembly (F-RAG) to design sequences to fold onto RNA-like tree graph topologies; the atomic fragments are taken from existing RNA structures that correspond to tree subgraphs. Because F-RAG may not produce the target folds for all designs, automated mutations by RAG-IF algorithm enhance the candidate pool markedly. The crucial residues for mutation are identified by differences between the predicted and the target topology. A genetic algorithm then mutates the selected residues, and the successful sequences are optimized to retain only the minimal or essential mutations. Here we evaluate RAG-IF for 6 RNA-like topologies and generate a large pool of successful candidate sequences with a variety of minimal mutations. We find that RAG-IF adds robustness and efficiency to our RNA design pipeline, making inverse folding motivated by graph topology rather than secondary structure more productive.     

Folding path of P5abc RNA involves direct coupling of secondary and tertiary structures

Folding mechanisms in which secondary structures are stabilized through the formation of tertiary interactions are well documented in protein folding but challenge the folding hierarchy normally assumed for RNA. However, it is increasingly clear that RNA could fold by a similar mechanism. P5abc, a small independently folding tertiary domain of the Tetrahymena thermophila group I ribozyme, is known to fold by a secondary structure rearrangement involving helix P5c. However, the extent of this rearrangement and the precise stage of folding that triggers it are unknown. We use experiments and simulations to show that the P5c helix switches to the native secondary structure late in the folding pathway and is directly coupled to the formation of tertiary interactions in the A-rich bulge. P5c mutations show that the switch in P5c is not rate-determining and suggest that non-native interactions in P5c aid folding rather than impede it. Our study illustrates that despite significant differences in the building blocks of proteins and RNA, there may be common ways in which they self-assemble.     

Influence of specific mutations on the thermal stability of the td group I intron in vitro and on its splicing efficiency in vivo: a comparative study.

Group I introns constitute excellent systems for analyzing the relationship between RNA tertiary folding and catalysis. Within a hierarchical framework interpretation of RNA folding, secondary structure motifs subtend RNA three-dimensional (3D) architecture. Thus, mutations in two-dimensional motifs are expected to have effects different from those disrupting 3D contacts. Using UV spectroscopy, we have studied the influence of nucleotide substitutions, in both secondary and tertiary structure elements, on the thermal stability of the tertiary folding of the bacteriophage T4 td group I intron. Further, we present a quantitative analysis of the relationship between the splicing efficiency in vivo and the stability of the intron structure as monitored by UV melting curves. We conclude that the stability of the tertiary structure of a group I intron as measured by UV melting is generally a good indication of its ability to splice in vivo.     

Novel and efficient RNA secondary structure prediction using hierarchical folding.

Algorithms for prediction of RNA secondary structure-the set of base pairs that form when an RNA molecule folds-are valuable to biologists who aim to understand RNA structure and function. Improving the accuracy and efficiency of prediction methods is an ongoing challenge, particularly for pseudoknotted secondary structures, in which base pairs overlap. This challenge is biologically important, since pseudoknotted structures play essential roles in functions of many RNA molecules, such as splicing and ribosomal frameshifting. State-of-the-art methods, which are based on free energy minimization, have high run-time complexity (typically Theta(n(5)) or worse), and can handle (minimize over) only limited types of pseudoknotted structures. We propose a new approach for prediction of pseudoknotted structures, motivated by the hypothesis that RNA structures fold hierarchically, with pseudoknot-free (non-overlapping) base pairs forming first, and pseudoknots forming later so as to minimize energy relative to the folded pseudoknot-free structure. Our HFold algorithm uses two-phase energy minimization to predict hierarchically formed secondary structures in O(n(3)) time, matching the complexity of the best algorithms for pseudoknot-free secondary structure prediction via energy minimization. Our algorithm can handle a wide range of biological structures, including kissing hairpins and nested kissing hairpins, which have previously required Theta(n(6)) time.     

Helix Capping in RNA Structure

Helices are an essential element in defining the three-dimensional architecture of structured RNAs. While internal basepairs in a canonical helix stack on both sides, the ends of the helix stack on only one side and are exposed to the loop side, thus susceptible to fraying unless they are protected. While coaxial stacking has long been known to stabilize helix ends by directly stacking two canonical helices coaxially, based on analysis of helix-loop junctions in RNA crystal structures, herein we describe helix capping, topological stacking of a helix end with a basepair or an unpaired nucleotide from the loop side, which in turn protects helix ends. Beyond the topological protection of helix ends against fraying, helix capping should confer greater stability onto the resulting composite helices. Our analysis also reveals that this general motif is associated with the formation of tertiary structure interactions. Greater knowledge about the dynamics at the helix-junctions in the secondary structure should enhance the prediction of RNA secondary structure with a richer set of energetic rules and help better understand the folding of a secondary structure into its three-dimensional structure. These together suggest that helix capping likely play a fundamental role in driving RNA folding.     

Compensatory mutations demonstrate that P8 and P6 are RNA secondary structure elements important for processing of a group I intron.

Compensatory mutations have been constructed which demonstrate that P8 and P6, two of nine proposed base-pairing interactions characteristic of group I introns, exist within the folded structure of the Tetrahymena thermophila rRNA intervening sequence, and that these secondary structure elements are important for splicing in E. coli and self-splicing in vitro. Two-base mutations in the 5' and 3' segments of P8 are predicted to disrupt P8 and a strong splicing-defective phenotype is observed in each case. A compensatory four-base mutation in P8 is predicted to restore pairing, and results in the restoration of splicing activity to nearly wild type levels. Thus, we conclude that P8 exists and is essential for splicing. In contrast to the strong phenotypes generally exhibited by mutations which disrupt RNA secondary structure, a two-base mutation in L8, the loop between P8[5'] and P8[3'], results in only a slight decrease in splicing activity. We also tested P6, a pairing which is proposed to consist of only two base-pairs in this intron. A two-base mutation in P6[3'] reduces splicing activity to a greater extent than does a two-base mutation in P6[5']. Comparison of the activities of these mutants and a compensatory P6 four-base mutant support the existence of P6, and suggest that the P6 pairing may be particularly important in the exon ligation step of splicing.     

The secondary structure of the human immunodeficiency virus type 1 transcript modulates viral splicing and infectivity

Splicing of human immunodeficiency virus type 1 (HIV-1) exon 6D is regulated by the presence of a complex splicing regulatory element (SRE) sequence that interacts with the splicing factors hnRNP H and SC35. In this work, we show that, in the context of the wild-type viral sequence, hnRNP H acts as a repressor of exon 6D inclusion independent of its binding to the SRE. However, hnRNP H binding to the SRE acts as an enhancer of exon 6D inclusion in the presence of a critical T-to-C mutation. These seemingly contrasting functional properties of hnRNP H appear to be caused by a change in the RNA secondary structure induced by the T-to-C mutation that affects the spatial location of bound hnRNP H with respect to the exon 6D splicing determinants. We propose a new regulatory mechanism mediated by RNA folding that may also explain the dual properties of hnRNP H in splicing regulation.     

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.     

Is counterion delocalization responsible for collapse in RNA folding?

Although energetic and phylogenetic methods have been very successful for prediction of nucleic acid secondary structures, arrangement of these secondary structure elements into tertiary structure has remained a difficult problem. Here we explore the packing arrangements of DNA, RNA, and DNA/RNA hybrid molecules in crystals. In the conventional view, the highly charged double helix will be pushed toward isolation by favorable solvation effects; interactions with other like-charged stacks would be strongly disfavored. Contrary to this expectation, we find that most of the cases analyzed ( approximately 80%) exhibit specific, preferential packing between elements of secondary structure, which falls into three categories: (i) interlocking of major grooves of two helices, (ii) side-by-side parallel packing of helices, and (iii) placement of the ribose-phosphate backbone ridge of one helix into the major groove of another. The preponderance of parallel packing motifs is especially surprising. This category is expected to be maximally disfavored by charge repulsion. Instead, it comprises in excess of 50% of all packing interactions in crystals of A-form RNA and has also been observed in crystal structures of large RNA molecules. To explain this puzzle, we introduce a novel model for RNA folding. A simple calculation suggests that the entropy gained by a cloud of condensed cations surrounding the helices more than offsets the Coulombic repulsion of parallel arrangements. We propose that these condensed counterions are responsible for entropy-driven RNA collapse, analogous to the role of the hydrophobic effect in protein folding.     

Evidence for widespread association of mammalian splicing and conserved long-range RNA structures

Pre-mRNA structure impacts many cellular processes, including splicing in genes associated with disease. The contemporary paradigm of RNA structure prediction is biased toward secondary structures that occur within short ranges of pre-mRNA, although long-range base-pairings are known to be at least as important. Recently, we developed an efficient method for detecting conserved RNA structures on the genome-wide scale, one that does not require multiple sequence alignments and works equally well for the detection of local and long-range base-pairings. Using an enhanced method that detects base-pairings at all possible combinations of splice sites within each gene, we now report RNA structures that could be involved in the regulation of splicing in mammals. Statistically, we demonstrate strong association between the occurrence of conserved RNA structures and alternative splicing, where local RNA structures are generally more frequent at alternative donor splice sites, while long-range structures are more associated with weak alternative acceptor splice sites. As an example, we validated the RNA structure in the human SF1 gene using minigenes in the HEK293 cell line. Point mutations that disrupted the base-pairing of two complementary boxes between exons 9 and 10 of this gene altered the splicing pattern, while the compensatory mutations that reestablished the base-pairing reverted splicing to that of the wild-type. There is statistical evidence for a Dscam-like class of mammalian genes, in which mutually exclusive RNA structures control mutually exclusive alternative splicing. In sum, we propose that long-range base-pairings carry an important, yet unconsidered part of the splicing code, and that, even by modest estimates, there must be thousands of such potentially regulatory structures conserved throughout the evolutionary history of mammals.     

All-atom Monte Carlo simulation of GCAA RNA folding

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.