RNA secondary structure and compensatory evolution

The classic concept of epistatic fitness interactions between genes has been extended to study interactions within gene regions, especially between nucleotides that are important in maintaining pre-mRNA/mRNA secondary structures. It is shown that the majority of linkage disequilibria found within the Drosophila Adh gene are likely to be caused by epistatic selection operating on RNA secondary structures. A recently proposed method of RNA secondary structure prediction based on DNA sequence comparisons is reviewed and applied to several types of RNAs, including tRNA, rRNA, and mRNA. The patterns of covariation in these RNAs are analyzed based on Kimura's compensatory evolution model. The results suggest that this model describes the substitution process in the pairing regions (helices) of RNA secondary structures well when the helices are evolutionarily conserved and thermodynamically stable, but fails in some other cases. Epistatic selection maintaining pre-mRNA/mRNA secondary structures is compared to weak selective forces that determine features such as base composition and synonymous codon usage. The relationships among these forces and their relative strengths are addressed. Finally, our mutagenesis experiments using the Drosophila Adh locus are reviewed. These experiments analyze long-range compensatory interactions between the 5' and 3' ends of Adh mRNA, the different constraints on secondary structures in introns and exons, and the possible role of secondary structures in RNA splicing.     

A unique secondary folding pattern for 5S RNA corresponds to the lowest energy homologous secondary structure in 17 different prokaryotes.

A general secondary structure is proposed for the 5S RNA of prokaryotic ribosomes, based on helical energy filtering calculations. We have considered all secondary structures that are common to 17 different prokaryotic 5S RNAs and for each 5S sequence calculated the (global) minimum energy secondary structure (300,000 common structures are possible for each sequence). The 17 different minimum energy secondary structures all correspond, with minor differences, to a single, secondary structure model. This is strong evidence that this general 5S folding pattern corresponds to the secondary structure of the functional 5S rRNA. The general 5S secondary structure is forked and in analogy with the cloverleaf of tRNA is named the "wishbone" model. It constant 8 double helical regions; one in the stem, four in the first, or constant arm, and three in the second arm. Four of these double helical regions are present in a model earlier proposed (1) and four additional regions not proposed by them are presented here. In the minimum energy general structure, the four helices in the constant arm are exactly 15 nucleotide pairs long. These helices are stacked in the sequences from gram-positive bacteria and probably stacked in gram-negative sequences as well. In sequences from gram-positive bacteria the length of the constant arm is maintained at 15 stacked pairs by an unusual minimum energy interaction involving a C26-G57 base pair intercalated between two adjacent helical regions.     

Sequences of the 5S rRNAs of Azotobacter vinelandii, Pseudomonas aeruginosa and Pseudomonas fluorescens with some notes on 5S RNA secondary structure

Recently published alignments of available 5 S rRNA sequences have shown that a rigid base pairing pattern, pointing to the existence of a universal five-helix secondary structure for all 5 S RNAs, can be superimposed on such alignments. For a few species, the alignment and the base pairing pattern show distortions with respect to the large majority of sequences. Their 5 S RNAs may form exceptional secondary structures, or there may just be errors in the published sequences. We have examined such a case, Pseudomonas fluorescens, and found the sequence to be in error. The corrected sequence, as well as those of the related species Azotobacter vinelandii and Pseudomonas aeruginosa, fit perfectly in the 5 S RNA sequence alignment and in the five-helix secondary structure model. There exists comparative evidence for the frequent presence of non-standard base pairs at several points of the 5 S RNA secondary structure.     

Phylogenetic analysis and secondary structure of the Bacillus subtilis bacteriophage RNA required for DNA packaging

An unusual RNA molecule encoded by the Bacillus subtilis bacteriophage phi 29 is a structural component of the viral prohead and is required for the ATP-dependent packaging of DNA. Here we report a model of secondary structure for this prohead RNA developed from a phylogenetic analysis of the primary sequences of prohead RNAs of related phages. Twenty-nine phages related to phi 29 were found to produce prohead RNAs. These RNAs were analyzed by their ability to replace phi 29 RNA in in vitro phage assembly, by Northern blot hybridization with a probe complementary to phi 29 RNA, and by partial and complete sequence analyses. These analyses revealed four quite different sequences ranging in length from 161 to 174 residues. The secondary structure deduced from these sequences, in agreement with earlier observations, indicated that prohead RNA is organized into two domains. The larger 5'-domain (Domain I) is composed of 113-117 residues and contains four helices. Three of these helices appear to be organized into a central stem that is interrupted by two unpaired loops and the fourth helix and loop. The smaller 3'-domain (Domain II) is composed of 40-44 residues and consists of two helices. Domains I and II are separated by 8-13 unpaired residues. Nuclease cleavage occurs readily in this single-stranded joining region, and this cleavage allows the subsequent separation of the two RNA domains. The separated Domain I is fully active in DNA packaging in vitro. The functional significance and biological role of Domain II are unknown. The phylogenetic secondary structure model provides a basis for further analysis of the role of this RNA in bacteriophage morphogenesis.     

Determination of secondary structure in rabbit globin messenger RNA by thermal denaturation.

The secondary structure of highly purified globin messenger RNA has been investigated by alkaline hydrolysis, nuclease digestion, and thermal denaturation. The thermal denaturation properties of globin messenger have been compared to poly(U), poly (A), and a synthetic random sequence RNA copolymer. From these studies it is concluded that globin mRNA contains considerable secondary structure and that the amount of helical structure is greater than that which occurs with a random sequence polyribonucleotide. Globin mRNA contains, by comparison to the secondary structures of native DNA, tRNAs, or 18S rRNA, helices with involve 55-62% of the bases or 58-68% if a correction is made for the 3'-terminal poly(A) segment. The helices of globin mRNA appear to be unique as differences in the NaCl stabilization of this RNA have been noted when compared to other naturally ooccurring and synthetic RNAs. Comparison of the hyperchromicity maxima, obtained at 260 and 280 nm for globin mRNA and 18S rRNA, indicates that the helices of the two RNAs contain similar numbers of G-C base pairs. Differential analysis of NaCl stabilization curves indicate three discrete thermally denaturable helix types in globin mRNA.     

Natural selection is not required to explain universal compositional patterns in rRNA secondary structure categories

We have encountered an unexpected property of rRNA secondary structures that may generalize to all RNAs. Analysis of 8892 ribosomal RNA sequences and structures from a wide range of species revealed unexpected universal compositional trends. First, different categories of rRNA secondary structure (stems, loops, bulges, and junctions) have distinct, characteristic base compositions. Second, the observed patterns of variation are similar among sequences from large and small rRNA subunits and all domains of life, despite extensive evolutionary divergence. Surprisingly, these differences do not seem to be related to selection for different compositions in different structural categories, but rather relate to the overall composition of the molecule: Randomized RNAs with no evolutionary history show the same structure-dependent compositional biases as rRNAs. These compositional trends may improve the accuracy of RNA secondary structure prediction, because they allow us to compare predicted structures against known compositional preferences. They also suggest caution in interpreting differences in the rate of change of the GC content in different parts of the molecule as evidence of differential selection.     

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.     

An RNA secondary structure workbench

A multiple approach to the study of RNA secondary structure is described which provides for the independent drawing of structures using base-pairing lists, for the generation of local structures in the form of hairpins, and for the generation of global structures by both Monte Carlo and dynamic programming methodologies. User-adjustable parameters provide for limiting the size of hairpin loops, bulges and inner loops, and constraints can be imposed relative to position-dependent base pairing.     

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 RNA 3D structure using a coarse-grain helix-centered model

A 3D model of RNA structure can provide information about its function and regulation that is not possible with just the sequence or secondary structure. Current models suffer from low accuracy and long running times and either neglect or presume knowledge of the long-range interactions which stabilize the tertiary structure. Our coarse-grained, helix-based, tertiary structure model operates with only a few degrees of freedom compared with all-atom models while preserving the ability to sample tertiary structures given a secondary structure. It strikes a balance between the precision of an all-atom tertiary structure model and the simplicity and effectiveness of a secondary structure representation. It provides a simplified tool for exploring global arrangements of helices and loops within RNA structures. We provide an example of a novel energy function relying only on the positions of stems and loops. We show that coupling our model to this energy function produces predictions as good as or better than the current state of the art tools. We propose that given the wide range of conformational space that needs to be explored, a coarse-grain approach can explore more conformations in less iterations than an all-atom model coupled to a fine-grain energy function. Finally, we emphasize the overarching theme of providing an ensemble of predicted structures, something which our tool excels at, rather than providing a handful of the lowest energy structures.     

Comparative sequence analysis as a tool for studying the secondary structure of mRNAs.

Analysis of phylogenetically conserved secondary structure has been important in the development of models for the secondary structure of structural RNAs. In this paper, we apply this type of analysis to several families of informational RNAs to evaluate its usefulness in developing secondary structure models for mRNAs and mRNA precursors. We observed many conserved helices in all mRNA groups analyzed. Three criteria were used to identify potential helices which were not conserved solely because of coding sequence constraints, and may therefore be important for the structure and function of the RNA. These results suggest that this approach will be useful in deriving secondary structure models for informational RNAs when used in conjunction with other complementary techniques, and in designing experiments to determine the functional significance of conserved base pairing interactions.     

An algebraic representation of RNA secondary structures.

This paper develops mathematical methods for describing and analyzing RNA secondary structures. It was motivated by the need to develop rigorous yet efficient methods to treat transitions from one secondary structure to another, which we propose here may occur as motions of loops within RNAs having appropriate sequences. In this approach a molecular sequence is described as a vector of the appropriate length. The concept of symmetries between nucleic acid sequences is developed, and the 48 possible different types of symmetries are described. Each secondary structure possible for a particular nucleotide sequence determines a symmetric, signed permutation matrix. The collection of all possible secondary structures is comprised of all matrices of this type whose left multiplication with the sequence vector leaves that vector unchanged. A transition between two secondary structures is given by the product of the two corresponding structure matrices. This formalism provides an efficient method for describing nucleic acid sequences that allows questions relating to secondary structures and transitions to be addressed using the powerful methods of abstract algebra. In particular, it facilitates the determination of possible secondary structures, including those containing pseudoknots. Although this paper concentrates on RNA structure, this formalism also can be applied to DNA.     

Improving protein secondary structure prediction with aligned homologous sequences.

Most recent protein secondary structure prediction methods use sequence alignments to improve the prediction quality. We investigate the relationship between the location of secondary structural elements, gaps, and variable residue positions in multiple sequence alignments. We further investigate how these relationships compare with those found in structurally aligned protein families. We show how such associations may be used to improve the quality of prediction of the secondary structure elements, using the Quadratic-Logistic method with profiles. Furthermore, we analyze the extent to which the number of homologous sequences influences the quality of prediction. The analysis of variable residue positions shows that surprisingly, helical regions exhibit greater variability than do coil regions, which are generally thought to be the most common secondary structure elements in loops. However, the correlation between variability and the presence of helices does not significantly improve prediction quality. Gaps are a distinct signal for coil regions. Increasing the coil propensity for those residues occurring in gap regions enhances the overall prediction quality. Prediction accuracy increases initially with the number of homologues, but changes negligibly as the number of homologues exceeds about 14. The alignment quality affects the prediction more than other factors, hence a careful selection and alignment of even a small number of homologues can lead to significant improvements in prediction accuracy.     

The secondary structure of guide RNA molecules from Trypanosoma brucei.

RNA editing in kinetoplastid organisms is a mitochondrial RNA processing phenomenon that is characterized by the insertion and deletion of uridine nucleotides into incomplete mRNAs. Key molecules in the process are guide RNAs which direct the editing reaction by virtue of their primary sequences in an RNA-RNA interaction with the pre-edited mRNAs. To understand the molecular details of this reaction, especially potential RNA folding and unfolding processes as well as assembly phenomena with mitochondrial proteins, we analyzed the secondary structure of four different guide RNAs from Trypanosoma brucei at physiological conditions. By using structure-sensitive chemical and enzymatic probes in combination with spectroscopic techniques we found that the four molecules despite their different primary sequences, fold into similar structures consisting of two imperfect hairpin loops of low thermodynamic stability. The molecules melt in two-state monomolecular transitions with Tms between 33 and 39 degrees C and transition enthalpies of -32 to -38 kcal/mol. Both terminal ends of the RNAs are single-stranded with the 3' ends possibly adopting a single-stranded, helical conformation. Thus, it appears that the gRNA structures are fine tuned to minimize stability for an optimal annealing reaction to the pre-mRNAs while at the same time maximizing higher order structural features to permit the assembly with other mitochondrial components into the editing machinery.     

Sequences of three molluscan 5 S ribosomal RNAs confirm the validity of a dynamic secondary structure model.

The collection of known 5 S rRNA primary structures is enriched with the sequences from three mollusca, the snails Helix pomatia and Arion rufus, and the mussel Mytilus edulis. The three sequences can be fitted in a five-helix secondary structure model previously shown (De Wachter et al. (1982) Biochimie 64, 311-329) to apply to all 5 S RNAs regardless of their origin. One of the helices in this model can undergo a bulge-internal loop transition. Within the metazoan kingdom, the dimensions of each helix and loop are rigidly conserved, except for one helix which can comprise either 6 or 7 base pairs.     

Prediction of RNA secondary structure based on helical regions distribution

MOTIVATION: RNAs play an important role in many biological processes and knowing their structure is important in understanding their function. Due to difficulties in the experimental determination of RNA secondary structure, the methods of theoretical prediction for known sequences are often used. Although many different algorithms for such predictions have been developed, this problem has not yet been solved. It is thus necessary to develop new methods for predicting RNA secondary structure. The most-used at present is Zuker's algorithm which can be used to determine the minimum free energy secondary structure. However many RNA secondary structures verified by experiments are not consistent with the minimum free energy secondary structures. In order to solve this problem, a method used to search a group of secondary structures whose free energy is close to the global minimum free energy was developed by Zuker in 1989. When considering a group of secondary structures, if there is no experimental data, we cannot tell which one is better than the others. This case also occurs in combinatorial and heuristic methods. These two kinds of methods have several weaknesses. Here we show how the central limit theorem can be used to solve these problems. RESULTS: An algorithm for predicting RNA secondary structure based on helical regions distribution is presented, which can be used to find the most probable secondary structure for a given RNA sequence. It consists of three steps. First, list all possible helical regions. Second, according to central limit theorem, estimate the occurrence probability of every helical region based on the Monte Carlo simulation. Third, add the helical region with the biggest probability to the current structure and eliminate the helical regions incompatible with the current structure. The above processes can be repeated until no more helical regions can be added. Take the current structure as the final RNA secondary structure. In order to demonstrate the confidence of the program, a test on three RNA sequences: tRNAPhe, Pre-tRNATyr, and Tetrahymena ribosomal RNA intervening sequence, is performed. AVAILABILITY: The program is written in Turbo Pascal 7.0. The source code is available upon request. CONTACT: Wujj@nic.bmi.ac.cn or Liwj@mail.bmi.ac.cn      

RNA folding with soft constraints: reconciliation of probing data and thermodynamic secondary structure prediction

Thermodynamic folding algorithms and structure probing experiments are commonly used to determine the secondary structure of RNAs. Here we propose a formal framework to reconcile information from both prediction algorithms and probing experiments. The thermodynamic energy parameters are adjusted using 'pseudo-energies' to minimize the discrepancy between prediction and experiment. Our framework differs from related approaches that used pseudo-energies in several key aspects. (i) The energy model is only changed when necessary and no adjustments are made if prediction and experiment are consistent. (ii) Pseudo-energies remain biophysically interpretable and hold positional information where experiment and model disagree. (iii) The whole thermodynamic ensemble of structures is considered thus allowing to reconstruct mixtures of suboptimal structures from seemingly contradicting data. (iv) The noise of the energy model and the experimental data is explicitly modeled leading to an intuitive weighting factor through which the problem can be seen as folding with 'soft' constraints of different strength. We present an efficient algorithm to iteratively calculate pseudo-energies within this framework and demonstrate how this approach can be used in combination with SHAPE chemical probing data to improve secondary structure prediction. We further demonstrate that the pseudo-energies correlate with biophysical effects that are known to affect RNA folding such as chemical nucleotide modifications and protein binding.     

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.     

Nucleotide sequence, secondary structure and evolution of the 5S ribosomal RNA from five bacterial species

The nucleotide sequences of the 5S ribosomal RNAs of the bacteria Agrobacterium tumefaciens, Alcaligenes faecalis, Pseudomonas cepacia, Aquaspirillum serpens and Acinetobacter calcoaceticus have been determined. The sequences fit in a generally accepted model for 5S RNA secondary structure. However, a closer comparative examination of these and other bacterial 5S RNA primary structures reveals the potential of additional base pairing and of multiple equilibria between a set of slightly different alternative secondary structures in one area of the molecule. The phylogenetic position of the examined bacteria is derived from a 5S RNA sequence alignment by a clustering method and compared with the position derived on the basis of 16S ribosomal RNA oligonucleotide catalogs.     

Secondary structure of the central region of bacteriophage MS2 RNA. Conservation and biological significance

The RNA of the Escherichia coli RNA phages is highly structured with 75% of the nucleotides estimated to take part in base-pairing. We have used enzymatic and chemical sensitivity of nucleotides, phylogenetic sequence comparison and the phenotypes of constructed mutants to develop a secondary structure model for the central region (900 nucleotides) of the group I phage MS2. The RNA folds into a number of, mostly irregular, helices and is further condensed by several long-distance interactions. There is substantial conservation of helices between the related groups I and II, attesting to the relevance of discrete RNA folding. In general, the secondary structure is thought to be needed to prevent annealing of plus and minus strand and to confer protection against RNase. Superimposed, however, are features required to regulate translation and replication. The MS2 RNA section studied here contains three translational start sites, as well as the binding sites for the coat protein and the replicase enzyme. Considering the density of helices along the RNA, it is not unexpected to find that all these sites lie in helical regions. This fact, however, does not mean that these sites are recognized as secondary structure elements by their interaction partners. This holds true only for the coat protein binding site. The other four sites function in the unfolded state and the stability of the helix in which they are contained serves to negatively control their accessibility. Mutations that stabilize helices containing ribosomal binding sites reduce their efficiency and vice versa. Comparison of homologous helices in different phage RNAs indicates that base substitutions have occurred in such a way that the thermodynamic stability of the helix is maintained. The evolution of individual helices shows several distinct size-reduction patterns. We have observed codon deletions from loop areas and shortening of hairpins by base-pair deletions from either the bottom, the middle or the top of stem structures. Evidence for the coaxial stacking of some helical segments is discussed.