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Corresponding author: Wolfgang Stephan, Department of Biology, University of Rochester, Rochester, NY 14627-0211., stephan{at}troi.cc.rochester.edu (E-mail)
Communicating editor: G. B. GOLDING
 | ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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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.
MOLECULES of RNA have a variety of important functions in biological systems, many of which depend on the RNA folding into a precise structure. For example, protein synthesis requires the participation of tRNAs and rRNAs that have highly conserved structures (
Presently, the most reliable method for predicting secondary structures of large RNAs from primary DNA sequence data is through phylogenetic-comparative analysis of aligned nucleotide sequences (
, is estimated. The relative evolutionary conservation of each predicted pairing is quantified by calculating an LRT statistic. A drawback to the LRT approach has been the requirement to specify the coordinates of potential pairing stems before application of the test. Thus, so far, this method has primarily been used to test structures previously predicted by phylogenetic-comparative analysis (
Here we present a novel method of RNA secondary structure prediction that integrates MUSE's (1995) LRT approach. The method is applied to five different RNA molecules that are known to have conserved, functionally important secondary structures: tRNA, 5S rRNA, bacterial ribonuclease P (RNase P) RNA, the 3' untranslated region (UTR) of the Drosophila bicoid (bcd) mRNA, and eukaryotic small subunit (SSU) rRNA. Furthermore, we analyze the covariations occurring in the helices of these RNA structures. The goal of this analysis is to identify physical parameters that determine the evolution of compensatory mutations. Two parameters are found to be important: the length of a helix and the physical distance between base-pairing nucleotides.
| MATERIALS AND METHODS |
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| TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Sequence collection and alignment:
Aligned, mitochondrial tRNA sequences (UGC anticodon) were downloaded from the tRNA Database (
Aligned 5S rRNA sequences were downloaded from the Berlin RNA Databank (
Aligned RNase P RNA sequences were downloaded from the RNase P Database (
Drosophila bcd sequences were obtained from GenBank (release 108.0). The sequences used (followed by their accession numbers) were D. melanogaster (X07870), D. simulans (M32123), D. sechellia (M32124), D. teissieri (M32121), D. pseudoobscura (X55735), D. subobscura (X78058), D. virilis (M32122), D. picticornis (M32126), and D. heteroneura (M32125). bcd 3' UTR sequences (from stop codon to end of transcript) were aligned using the ClustalX program (
Aligned SSU rRNA sequences were downloaded from the SSU rRNA Database (
Identification of potential RNA helices:
Potential RNA helices that are conserved in the aligned sequences were identified using the novel program PIRANAH. This program represents an extension of the algorithm of
After all helices meeting the specified criteria have been identified, LRT values (
Construction of RNA secondary structure model:
After generating a complete list of potential RNA helices and their respective LRT values with PIRANAH, the helices were assembled into a final RNA secondary structure model using another novel program, GROUPER. This program sorts through the list of helices and determines subsets that are compatible with each other. Two helices are considered compatible if either: (i) there is no overlap between their 5' and 3' coordinates, or (ii) the 5' and 3' coordinates of one helix fall between the 5' and 3' coordinates of a second helix. Thus, several short-range pairings may be nested within one (or more) long-range pairing. Pseudoknots are not permitted. For each compatible set of helices a total LRT value is calculated. This represents the sum of the individual LRTs for each helix in the structure. While the value of total LRT is not necessarily equal to the LRT calculated for the entire structure in toto, previous results suggest that this method produces a reliable estimate (
Significance tests of LRT values:
The distribution of the LRT statistic is ~
2 with one degree of freedom, and it has been demonstrated that this approximation is good for helices 
10 bp in length (2 approximation questionable. In addition, there is a problem of multiple tests, as the helices that were subject to LRT calculations were previously selected to meet certain length and conservation criteria. Thus it is difficult to attach meaningful P values to individual helices. To get around these problems and estimate P values for the helices predicted in our analysis, we used a numerical resampling approach. A similar approach was used by the observed value from the 100 randomizations. In addition, GROUPER was applied to each set of predicted helices from the randomizations to predict total structures. The P value of an observed structure was estimated as the frequency of obtaining a total structure with LRT the observed value from the 100 randomizations.
| RESULTS |
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| TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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RNA secondary structure prediction:
tRNA:
The well-known cloverleaf structure of tRNA molecules has been established through both structural and comparative analyses (
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5S rRNA:
5S rRNA is a small RNA (typically 121 bases) that associates with 23S rRNA and ribosomal proteins to form the large ribosomal subunit (
RNase P RNA:
RNase P is an RNA-protein complex that produces mature tRNAs by cleaving the 5' ends of precursor tRNA molecules. The RNA has been shown to be the catalytic subunit (3 (excluding pseudoknots and helices not present in Bacillus species), all of which were predicted by our method, with only one potential false positive.
bcd 3' UTR:
bcd is a maternal effect gene that plays a crucial role in the early development of D. melanogaster. Proper localization of bcd mRNA to the anterior pole of the developing embryo is required for formation of head and thoracic segments (3 that are conserved in the nine Drosophila species, all of which were identified in our analysis.
SSU rRNA:
SSU rRNA is an integral part of the translational machinery of the cell and has a highly conserved structure in Bacteria, Eukarya, and Archaea (5), we used a hierarchical approach for final structure prediction by GROUPER. An original structure was generated using helices of length 6, LRT > 25, and at least one WC covariation. Helices with length 5, LRT > 20, and at least one WC covariation that were compatible with the helices determined above were then added to the structure. The final structure was composed of 16 helices (Table 1), 13 of which are consistent with previous models of eukaryotic SSU rRNA structure (Figure 1E; 5 that meet the conservation criteria used in our analysis. Thus our method detected 87% of the consensus helices, with three potential false positives. One consensus helix that was not included in our final structure is a 5-bp helix, 1588-1592/2295-2299, which contains an internal GU wobble pair in all five species. The LRT value for this helix was 13.72; thus it did not meet our condition of LRT > 20. The reason for this low LRT value is that in MUSE's (1995) algorithm GU wobble pairs are considered as mismatches. The other consensus helix that was not included in our final structure is a 7-bp helix, 1575-1581/2339-2345, which has a 1-base gap in the S. stercoralis sequence, but is otherwise perfectly conserved. This helix did have a relatively high LRT (40.52) but was not included in the final structure due to its lack of WC covariations. Each of the three potential false positives (helices 539-547/2360-2368, 1528-1532/1639-1643, and 1279-1283/1390-1394) is supported by only a single WC covariation occurring in one out of the five species.
Analysis of covariations:
In this section we investigate whether the patterns of covariations observed in the inferred helices can be described by simple parameters. One interesting parameter that may affect the rate of compensatory molecular evolution is the length of helices in which compensatory substitutions occur. Thus, for each helix in the final secondary structure models, we determined the number of WC and wobble covariations present in the aligned sequences (Table 1). As terminal pairings at either end of a helix may be under different selective constraints than internal pairings, we also determined the number of internal covariations.
Table 3 summarizes the results of our regression analyses. Highly significant correlations between the number of WC covariations per pair and stem length were found for the Drosophila bcd 3' UTR mRNA and for the bacterial RNase P RNA, although in both cases only eight helices were identified. Both correlations are tighter for the internal covariations. A significant correlation was also observed for the internal covariations occurring in tRNA (which consists of four helices), but not for all covariations. For the ribosomal RNAs (both 5S and SSU), however, correlations between stem length and the number of covariations per pair were not found.
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In Figure 3A, the number of internal covariations per pair is plotted against stem length for the bcd 3' UTR mRNA helices. To increase the data set, two Adh pre-mRNA helices were included. The latter two helices were identified in the adult intron and in intron 1 of Drosophila Adh and are well supported statistically (
4) show no internal covariations, however, so that the regression lines of Figure 3A and Figure B, intersect with the x-axis at positive values.
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Our results suggest that compensatory evolution in the Drosophila mRNA and bacterial RNase P RNA structures occurs faster in longer helices. The most likely explanation for this observation is that selective constraints are relaxed in longer helices, because mutations occurring in longer stems result in less helix destabilization than those occurring in shorter stems. This hypothesis can be investigated further by defining a normalized number of covariations per pair for longer helices such that the number of covariations in a helix is scaled by the square of the stem length (instead of the stem length, as above). This definition is suggested by the proportionality between the number of covariations per pair and stem length for longer helices (see Figure 3A and Figure B). Thus, the normalized number of covariations per pair is expected to be nearly independent of differences in selective pressure for helices of different lengths. For pairings in RNA helices that are subjected to similar selection pressure, KIMURA's (1985) model of compensatory evolution predicts that the rate of compensatory changes depends critically on the physical distance between the interacting nucleotides. If selection against mutations that destabilize a helix is much stronger than genetic drift, the rate of compensatory evolution is expected to decrease with physical distance (
We explored this prediction for the Drosophila mRNA and the bacterial RNase P RNA structures. In Figure 4A and Figure B, we plotted the total number of covariations (divided by the square of the stem length) for the longer helices of the Drosophila mRNA (both bcd 3' UTR and Adh) and the bacterial RNase P RNA structures, respectively. To increase the number of helices containing covariations, the total number of covariations was considered (instead of internal covariations). In both cases, the six helices that exhibit covariations are shown. One longer helix (length = 7 bp) was removed from the bcd data because it did not have any covariations and may thus be under stronger selective constraints. For the Drosophila mRNA helices, a significantly negative correlation between physical distance and the normalized number of covariations per pair was found (R2 = 0.89, P < 0.005); for the bacterial structures, no correlation was observed (R2 = 0.201, not significant). For internal covariations, qualitatively similar results were obtained.
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Based on predictions of Kimura's model (
| DISCUSSION |
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| TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Method of RNA secondary structure prediction:
Our approach to RNA secondary structure prediction has proven effective at identifying conserved pairing regions in five types of RNA: tRNA, 5S rRNA, RNase P RNA, Drosophila bcd mRNA, and eukaryotic SSU rRNA. The approach can be summarized as follows. A complete list of potential helices meeting specified length and conservation criteria is generated from an alignment of homologous RNA-encoding sequences. For each helix, the constraint for WC base-pairing is estimated by an LRT statistic (
In four of our examples, tRNA, 5S rRNA, RNase P, and bcd 3' UTR, we identified 100% of the conserved pairings in the established consensus structures. In the fifth example, SSU rRNA, the success rate was 87%. The number of false positives (predicted pairings that are not present in the consensus structure) was quite low for all five RNAs. Perhaps the most striking example of successful structure prediction is that of SSU rRNA. This is by far the longest of the five RNAs (1761–2487 nt depending on the species; 2533 nt in the gapped alignment) and also the one for which we used the fewest representative sequences (five). A previous study using the thermodynamic folding algorithm of
An important consideration when using the above method is the choice of parameter values. Parameters must be chosen for both the initial identification of helices by PIRANAH and the assembly of the final secondary structure by GROUPER. Since the most time-consuming part of the process is LRT calculation during the initial identification step, we chose parameter values that would keep computation time reasonable by limiting the total number of potential helices. In practice, this means increasing the minimum score for LRT calculation and the minimum helix length as sequence length increases. The values we chose for these parameters were quite conservative, however, even for the longer sequences. Thus, the number of helices identified by PIRANAH far exceeded the number of helices included in the final structures of all five RNAs. For example, in the case of SSU rRNA (the longest of the five RNAs) only 4% of the helices identified by PIRANAH were included in the final structure prediction by GROUPER, and many of the helices (73%) had LRT values falling below the LRT cutoff used for final structure assembly. Thus it is very unlikely that any evolutionarily conserved helices were overlooked due to the choice of parameter values in this initial step.
For the second step, assembly of the final secondary structure model, the major parameter value is minimum LRT. Typically, this value must be increased as the sequence length increases. In the case of short sequences, such as tRNA, 5S rRNA, or RNase P RNA, the LRT cutoff may be set relatively low (15 in our examples) because there are few conflicting helices. In these cases, nearly all of the helices in the final structure have LRT values well above the cutoff (see Table 1), so our choice of minimum LRT was a conservative one. In addition, for the two short sequences that were used for randomization simulations (tRNA and 5S rRNA; Table 2) the results were identical for LRT cutoffs of 15 and 10. This suggests that the choice of minimum LRT does not greatly affect the significance of the predicted structure. For very long RNA sequences, the hierarchical approach of the SSU rRNA example may be used. Here the first helices assembled by GROUPER were those that had a high LRT value and a long stem, i.e., helices whose pairing potential was evolutionarily most conserved and that were thermodynamically most stable. In subsequent steps, helices with shorter lengths and lower values of LRT were added to the structure. Also, the number of potential helices may be reduced by requiring that at least one WC covariation be present in each helix. Such constraints can greatly simplify structure prediction in cases where there are many conflicting helices. This approach, however, may lead to structures that are incompatible with each other, depending on what the cutoff value of LRT for individual helices is. It may also overlook helices that are perfectly conserved and thus have no covariations. More work is required to explore this potential problem.
The above examples revealed another problem inherent in identifying potential helices by sequence comparisons; that is, the length of homologous pairing regions may differ among species due to internal or terminal mismatches. PIRANAH uses a set of strict rules about mismatches in searching for potential helices and may, for instance, find two helices where there would be only a single one if internal mismatches were allowed (see the bcd 3' UTR example). PIRANAH may also fail to include the terminal base pair of a helix in cases where a mismatch or a GU wobble pair is present (see the SSU rRNA example). It is therefore advisable to inspect the output of PIRANAH before it is subjected to GROUPER. The rule we followed during visual inspection of the PIRANAH output was as follows: a helix was extended by including mismatches or GU wobble pairs only if the extended helix produced a greater value of LRT than the originally predicted helix.
Improvements to our method of secondary structure prediction will certainly be possible as computer processing time becomes less limiting. For example, the criteria used for initial helix identification by PIRANAH may be relaxed, allowing more potential helices to be identified and considered in final structure prediction. It may also be possible to integrate sequence alignment with secondary structure prediction. Currently, alignment and structure prediction are completely separate procedures. Alignments are typically adjusted manually so that potential pairing stems are at corresponding positions in all sequences (
Effect of stem length:
Our analysis of covariations identified two parameters that are important for the evolution of compensatory mutations: the length of a helix and the physical distance between base-pairing residues. Positive correlations between the number of covariations (per pair) and stem length were observed for the Drosophila bcd 3' UTR RNA, bacterial RNase P RNA, and tRNA (Table 3 and Figure 3). The observed correlations may be explained by differences in selective constraints. Selective constraints in longer helices appear to be relaxed because single mutations occurring in these helices result in less helix destabilization than those occurring in short stems.
It is noteworthy that a similar correlation was not found for the ribosomal RNAs, in particular SSU rRNA. A plot (not shown) of the helices of SSU rRNA (which includes also the helices of shorter length that were not considered in our analysis) suggests that there is an increase in the number of covariations for shorter stems and a decrease for longer ones, with a maximum rate for an intermediate stem length (of 6 bp). The increase in the number of covariations with stem length for shorter stems may be due to the relaxation of selective constraints with increasing helix length, as discussed above for the other types of RNA. However, other mechanisms, possibly related to the specific function of this type of RNA, have to be invoked to explain the decrease in the rate of compensatory evolution for longer SSU rRNA helices (
Distance effect:
For the two larger RNAs (Drosophila mRNA and bacterial RNase P RNA) that showed a positive correlation between stem length and the rate of covariation, we found that the number of covariations (per pair) scaled by stem length decreases with the physical distance between base-pairing nucleotides (Figure 4). In contrast to bacterial RNase P RNA, for the Drosophila mRNA helices this negative correlation was found to be highly significant.
KIMURA's (1985) model of compensatory evolution provides a simple explanation for these results. All other things being equal (in particular, selection pressure on base-pairing residues), this model suggests that the difference may be due to a lack of recombination in bacteria. Indeed, using reasonable estimates of Drosophila recombination rates (
This theory suggests that the strength of selection on individual WC pairs, measured by the parameter 2Ns (where s is the selection coefficient), is on average much larger than one for the Drosophila data. On the other hand, the occurrence of wobble pairs and mispairings in the helices (see Figure 2D and Table 1) indicates that the strength of selection may vary substantially among base pairs and that some stem evolution proceeds through slightly deleterious intermediates. A statistical method is needed to estimate the parameter 2Ns directly from comparative sequence data.
| FOOTNOTES |
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1 Present address: Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138-2020. 
2 Present address: Le Moyne College, Syracuse, NY 13214-1499.
| ACKNOWLEDGMENTS |
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We are grateful to K. Han and S. Muse who kindly made their programs and C code available. Furthermore, we thank two reviewers for their critical comments and helpful suggestions. The programs and sequence alignments used in our analyses, as well as additional documentation, are available at http://maple.lemoyne.edu/~braverjm/ss.html. This research was supported in part by a National Science Foundation/Sloan Foundation postdoctoral fellowship to J.M.B., and National Institutes of Health grant GM-58405 to W.S.
Manuscript received June 23, 1999; Accepted for publication October 4, 1999.
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 J. F. Baines, Y. Chen, A. Das, and W. Stephan DNA Sequence Variation at a Duplicated Gene: Excess of Replacement Polymorphism and Extensive Haplotype Structure in the Drosophila melanogasterbicoid Region Mol. Biol. Evol., July 1, 2002; 19(7): 989 - 998. [Abstract] [Full Text] [PDF]
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