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(ii) A 'positioning element', typically found between 10 and. 30 nt upstream ...... Burset,M. and Guigo,R. (1996) Evaluation of gene structure prediction programs.
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Nucleic Acids Research, 2002, Vol. 30, No. 8 1851–1858

Probabilistic prediction of Saccharomyces cerevisiae mRNA 3′-processing sites Joel H. Graber1,3,*, Gregory D. McAllister2,3 and Temple F. Smith2,3 1Center

for Advanced Biotechnology and 2Biomolecular Engineering Research Center, Boston University, 36 Cummington Street, Boston, MA 02215, USA and 3Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215, USA

Received September 10, 2001; Revised and Accepted February 20, 2002

ABSTRACT We present a tool for the prediction of mRNA 3′ -processing (cleavage and polyadenylation) sites in the yeast Saccharomyces cerevisiae, based on a discrete state-space model or hidden Markov model. Comparison of predicted sites with experimentally verified 3′-processing sites indicates good agreement. All predicted or known yeast genes were analyzed to find probable 3′-processing sites. Known alternative 3′-processing sites, both within the 3′untranslated region and within the protein coding sequence were successfully identified, leading to the possibility of prediction of previously unknown alternative sites. The lack of an apparent 3′-processing site calls into question the validity of some predicted genes. This is specifically investigated for predicted genes with overlapping coding sequences. INTRODUCTION The availability of complete genome sequences has made possible large-scale sequence analysis to identify and model complex biological phenomena such as regulatory control (or signal) sequences (1–7). We are studying the control sequences that determine the position of 3′-processing (cleavage and polyadenylation) of pre-mRNA, in order to develop predictive tools that will locate unknown 3′-processing sites in a genomic sequence. The control sequences involved in 3′-processing in the yeast Saccharomyces cerevisiae have been extensively studied (8–10), yet the creation of a predictive model has remained elusive. Experimental mutagenesis studies have identified many different (though often related) sequences that act as elements in selection and processing of the 3′-ends of yeast mRNA transcripts. Recent computational studies (11,12) of large sets (thousands of sequences) of putative 3′-processing sites have improved our understanding. A general pattern (Fig. 1) of the control sequences required for 3′-processing in yeast has emerged as follows. (i) An ‘efficiency element’, typically found between 35 and 60 nt upstream from the 3′-processing site. Mutagenesis studies and computational analysis have identified the best sequence (word) for this element as UAUAUA. (ii) A ‘positioning element’, typically found between 10 and

30 nt upstream of the 3′-processing site. The best word for this element is AAUAAA (as in mammalian sequences), however, it is commonly described only as ‘A-rich’, since many functional sequences are characterized only by their adenosine content. (iii) A ‘near-upstream element’, typically occurring within 10 nt upstream of the 3 ′-processing site, and best characterized as ‘U-rich’. (iv) A ‘near-downstream element’, typically 10 nt or less downstream of the 3′-processing site and also characterized as ‘U-rich’. (v) The 3′-processing site itself, which has been experimentally shown to consist most commonly of a pyrimidine followed by one or more A residues (13). Significantly, the functionality of the U-rich control elements near the 3′-processing site was first postulated based on computational sequence analysis (11,12), and subsequently verified through laboratory experiments (14). Recent work (15–17) has called the naming conventions of the control elements into question; therefore, in the work reported here, we refer simply to elements 1–4, plus the 3′-processing site. Analysis of verified 3′-processing sites often reveals that one or more of the elements may bear little or no resemblance to its optimal form, yet the complete 3′-processing site is functional. Furthermore, it has been found through mutagenesis studies that the deletion of sequence elements with known function fails to disable 3′-processing of the transcript, but instead reduces its efficiency. It has been postulated (9,18,19) that the complete control sequence acts cooperatively, allowing comparatively ‘strong’ words of some elements to compensate for sub-optimal or missing words in the remaining elements. Alternatively, several ‘weak’ words with acceptable positioning can have an additive effect, giving a net efficiency similar to a single ‘strong’ word. The analysis and prediction of 3′-processing sites in yeast is further complicated by the multiplicity of alternative functional sites. Two forms of alternative polyadenylation of yeast transcripts have been demonstrated: (i) regulatory alternatives (20,21), which are typically separated by hundreds of nucleotides or more; and (ii) apparently non-regulatory alternatives, in which alternative sites are separated by tens of nucleotides or fewer. In one extreme case, 13 separate polyadenylation sites were identified for the yeast HIS3 gene (22). Alternate polyadenylation in animal cells has been reported only as the widely spaced, regulatory form, whereas studies of plant cells have potentially indicated both forms. From our previous studies of yeast 3′-processing sites, we believe that all control elements for a given site are within 100 nt of the 3′-processing

*To whom correspondence should be addressed at present address: Bioinformatics Program, Boston University, 44 Cummington Street, Boston, MA 02215, USA. Tel: +1 617 358 2506; Fax: +1 617 353 4814; Email: [email protected]

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MATERIALS AND METHODS

Figure 1. A simplified representation of the arrangement of control elements (with example sequences) that identify the 3′-processing site in yeast mRNA.

site; therefore, the control sequence of regulatory alternative sites are not likely to overlap, and as such will probably not complicate the development of predictive tools. However, the non-regulatory alternatives will most probably have overlapping control elements, and therefore will complicate prediction. The need to accurately model potentially overlapping control sequences specifically led to the use of the forward or filtering algorithm, as described below. A predictive model for 3′-processing sites has many possible uses. A principal use would be in the enhancement of gene prediction (23–26). Most current gene prediction software uses naïve models for the prediction of 3′-processing sites. The simple models typically are based primarily on a search for the canonical AAUAAA positioning element or its most common variant AUUAAA (27,28). Previous attempts at prediction of 3′-processing sites have focused on mammalian sequences (27–31). While the focus on the positioning element is reasonable for modeling 3′-processing sites in mammalian sequences, it is completely inadequate in describing the control sequences that are observed in either yeast or plants (9,19,32). Improvement of gene prediction algorithms goes hand-inhand with improvement in the annotation of newly generated genomic sequence. Currently, such annotation is typically limited to identification of functional RNA (tRNA and rRNA), coding sequences, and other large-scale phenomena. Improvements in transcript prediction (as opposed to simply coding sequence) will also help in troubleshooting and designing large-scale genetic expression measurements. The probes necessary for such hybridization are primarily generated from the coding sequence. Expression measurements are made on complete transcripts; therefore, knowledge of the genomic limits of the transcript will improve the ability to avoid systematic problems such as cross-hybridization of probes due to similar untranslated region (UTR) sequences. As we have shown previously (11,19), in a large set of aligned 3′-processing sequences, the control elements appear with a distinctly non-random positioning with respect to the 3′-processing site. By plotting the relative frequency of occurrence of all words as a function of position with respect to the 3′-processing site, we can cluster words based on similar distributions. We assume that the different words in each of these clusters perform the same biological function. We present a probabilistic method for prediction of S.cerevisiae 3′-processing sites, based on a discrete state-space model (DSM), which is represented mathematically as a hidden Markov model (HMM), but with designed rather than trained parameters. A web-server interface for our S.cerevisiae 3′-processing site predictions is available at http://bmerc-www.bu.edu/polyA/.

Putative S.cerevisiae 3′-processing sequences were identified through genomic/EST alignment and analysis as described previously (11). This set totals 1352 3′-processing sites, associated with 861 different genes. Our predictive models are based on the assumption that the functional elements of the 3′-processing control sequence can be identified by their positioning with respect to the 3′-processing site. Based on our previous work, as well as published experimental evidence (9), we have built a probabilistic model to include information from a relative position of –110 to +40 with respect to the 3′-processing site (see Fig. 3). All protein-coding bases in the training set were replaced with Ns so that the resulting models would emphasize the functional elements of the 3′-processing control sequence, rather than the end of the protein coding sequence (CDS). The mathematical structure of the DSM is that of a HMM (33). A HMM models sequence generation as a traversal of a set of discrete states. Each state is defined by emission probabilities, the probability for each of the four nucleotides to be observed in that state, and transitions from any specific state to any other are governed by transition probabilities. We used the filtering, or forward, algorithm (33–36), which computes the probability that a query sequence will be generated by a given model. The smoothing algorithm (34–36) [also referred to as the forward– backward algorithm or posterior decoding (37)] calculates the probability for each model state at each position of the query sequence. Note that the smoothing algorithm will give an answer (in our case, the most likely positions where 3′-processing will occur) regardless of the probability that the model would have produced the query sequence. As shown below, the output of both algorithms is necessary to find 3′-processing sites. The combination of the filtering and smoothing algorithms is a natural choice to compensate for many of the complications described in the Introduction, including non-regulatory alternative 3′-processing sites and multiple, additive elements for a single 3′-processing site. The filtering and smoothing algorithms assess a query sequence by computing all paths through the model that could generate the sequence, in contrast with optimal path methods such as the Viterbi algorithm (37), which use dynamic programming to model only the most likely path through the model. By evaluating all paths, the filtering– smoothing combination allows for and incorporates multiple occurrences of any modeled element, whether it is one of the control elements or the 3′-processing site itself. The presence of multiple 3′-processing sites in a query sequence would be signaled by a high filtering probability and multiple maxima in the conditional probability of the model state associated with the 3′-processing site (Fig. 2, element c). The structure of the model developed for 3′-processing prediction in S.cerevisiae is shown in Figure 2. As shown, the model consists of four hexamer elements (e1–e4) and the 3′-processing site (c), separated by variable length background sequences. Nucleotide emission frequencies for each position in the four control elements (e1, e2, e3, e4) were obtained with the Gibbs sampler (38). In order to optimize the Gibbs Sampler’s ability to locate the elements in question, separate analyses were made for each element, with the input sequences restricted to the region where the element is most likely to

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Figure 2. The structure of the HMM used to model 3′-processing control sequences for yeast. All state-to-state transitions not explicitly labeled have a probability of 1.0. The hexagonal elements are background elements that can take on any length in the given range with equal probability. The functional elements e1– e4 are hexamers, with individual nucleotide probabilities determined through analysis with the Gibbs sampler (38). Probabilities p1–p4 were optimized empirically in analysis of known processing sites. The position of the cleavage and polyadenylation is the center of the c element. Nucleotide probabilities for the c element were obtained from the 1352 training sequences. Complete details, including nucleotide emission probabilities, are available as Supplementary Material.

in Figure 2, the length distributions for these spacer states between functional elements were given a uniform probability over a specified range, and an exponentially decaying upper limit. The minimum distance between the functional elements is fixed as shown, whereas the maximum distance is mediated by the four non-unity transition probabilities p1–p4, which were determined primarily through examination of the data summarized in Figure 3, followed by optimization through testing of known 3′-processing sites. The final values were p1 = 0.8, p2 = 0.65, p3 = 0.5 and p4 = 0.65. Additional knowledge from previous studies was also used, specifically the previously reported minimum distance (10 nt) that can separate functional copies of the first two elements (8,42). The HMM is described in complete detail in the Supplementary Material or at our website. As stated in the Introduction, a principal goal of our work is to aid in the annotation of new genomes and, as such, we need to be able to analyze large sequences (tens or hundreds of thousands of nucleotides). In contrast, the control sequences for which we are searching are limited to ∼150 nt. In order to reconcile this, we have chosen to test the model on a sliding 150 nt-wide window, stepping along the entire sequence, combining the results using the following equation for the score at nucleotide x: S(x) = log10 {[Σ PFw × PSw,x]/[(PFw × PSw,x)bg]} w

Figure 3. The characteristic logarithmic distributions for positioning the four functional elements used in our model of the 3′-processing control sequence, as determined by a k-means clustering of words with similar positioning with respect to the processing site. The elements are normalized to a uniform distribution.

occur (based on the results shown in Fig. 3). While the Gibbs sampler was used in this work, any methodology used to assign the nucleotide emission probabilities to the control elements would work, for example MEME (39) or AlignACE (2), or even simple statistical averaging if the training set is large enough. The 3′-processing site was modeled as a pentamer, centered on the cleavage site. Nucleotide emission frequencies for the 3′-processing site, (c), were obtained through direct tabulation of the frequencies of each base in the 5 nt centered on the polyadenylation site in our 1352 training sequences. The nucleotide emission frequencies for each of the elements are available as Supplementary Material or at our website (http:// bmerc-www.bu.edu/polyA/). In order to determine the positioning of the elements, we extended our previous analysis of S.cerevisiae 3′-processing sequences (11), grouping (presumably functionally) similar words with a k-means clustering algorithm (40) based on a Pearson correlation coefficient (41) comparison of their positional distributions. Based on our previous work, we chose to create four clusters representing the four elements. The characteristic distribution of each element was determined by averaging all words clustered into that element. Figure 3 shows the characteristic distributions for the four clusters used in the generation of the yeast 3′-processing predictor. The spaces between the functional elements were modeled as states emitting nucleotides at background sequence frequencies (using statistics for typical yeast mRNA transcripts). As shown

where the summation is over all windows (w) that include nucleotide x. PFw is the filtering algorithm’s probability that our model generates the sequence in the window w. PSw,x is the smoothing algorithm’s probability that nucleotide x is a 3′-processing site in window w. The denominator includes a normalization that makes the average score in a random sequence set (described below) equal to 0. In principle, the model should be tested and combined in all possible windows, however, to reduce computation time, we tested various step sizes between consecutive windows and found that up to 20 nt could be safely used without changing the predictions (data not shown). Specific positions within query sequences are classified as likely 3′-processing sites on the basis of whether or not S(x) exceeds a user-specified threshold value. Statistical assessment of the threshold value for S(x) is discussed below. RESULTS Figure 4 shows examples of the output of our analysis (see Materials and Methods) for three different mRNA sequences, SUA7, RNA14 and BAP2. The plot shown for SUA7 (Fig. 4A) is typical in most ways (see the discussion on regulatory alternative 3′-processing below). The CDS (delineated by the large green arrow) is characterized by either small or negative scores and a few isolated, low value ( r > –0.3 indeterminate and r < –0.3 incorrect. This classification resulted in 150 (70.4%) correct, 30 (14.1%) incorrect and 33 (15.5%) indeterminate calls. On closer examination of the 63 pairs initially classified as either incorrect or indeterminate, we found many cases where the presence of a 3′-processing signal for the unnamed gene could be explained by the presence of a third nearby gene. Re-classification following elimination of such signals resulted in 183 (85.9%) correct, 13 (6.1%) incorrect, and 17 (8.0%) indeterminate calls. In an intriguing case of incorrect classification, the overlapping gene pair YHR022C and ECM12 (YHR021W-A) had r = –2.2, indicating an extreme preference for the unnamed gene YHR022C. A search for homologs of the respective protein sequences revealed that YHR022C is probably a GTPase protein, while ECM12 has no known homologs. We believe that, in this case, the ‘incorrect’ classification based on 3′-processing sequences is a sign of incorrect annotation of the genes. The complete listing of all compared pairs of overlapping genes is available at our website. Predicted 3′-processing sites internal to the CDS can indicate either regulatory alternative 3′-processing of the transcript or false positive predictions of our model. Given the analysis of genes with known internal sites (such as RNA14, Fig. 4B), it is likely that some of these predicted sites are genuine. The number of counted internal peaks is, of course, strongly dependent on the value set for the threshold. Table 1 summarizes the results of this analysis. With a threshold S(x)threshold = 3, we found that 1969 (31.3%) of the ORFs investigated had no internal peaks. If the threshold is raised to 3.8 (the value at which the estimated false positive rate is ∼1 in 1000), there are 4870 (77.5%) genes with no internal sites. The expected total number of internal peaks was computed by multiplying our estimated false positive rate by the total number of coding bases in yeast (8.9 × 106). Note that for all threshold values there are approximately three times fewer internal peaks above threshold counted than would be expected based on a second order Markov chain, possibly indicating a suppression of 3′-processing control sequences within the CDS. In our initial genomic analysis of the yeast ESTs, we identified several ESTs that indicated poly(A) tails internal to the CDS

Figure 7. A comparison of the 3′-processing likelihood for wild-type yeast CYC1 (blue line), and the mutated form CYC1-512 (red line). CYC1-512 has a 38 nt deletion (from position 461 to 499) that greatly reduced 3′-processing efficiency. A gap is inserted into the plot for the CYC1-512 likelihood plot to keep the downstream sequences, and thus the processing sites, correctly aligned. Squares, experimentally determined 3′-processing sites in CYC1; diamonds, the experimentally measured positions in CYC1-512.

that could not be explained through any of the systematic problems with EST creation (11). Of particular interest was the BAP2 gene, which has a 1939 nt CDS. Three ESTs aligned to the genome identically, in a position that would indicate a 3′-processing site at position 635 in the CDS. Figure 4C shows our analysis for BAP2, along with the 3′-processing sites indicated by EST matches. (There was one EST indicating a full-length coding sequence.) As can be seen, the prediction has a peak very close to the internal EST locations. Based on the combination of the EST evidence and the predictions of our methods, we believe that this is a regulatory alternative 3′-processing site, and not a false positive prediction. As a final test of our ability to identify 3′-processing sites, we analyzed the effects of mutation on 3′-processing likelihood. Many of the earliest reported mutagenesis experiments were on the CYC1 test system (13,42,47–51). Figure 7 shows a comparison of 3′-processing likelihoods for wild-type CYC1 and the CYC1-512 mutant, which had a 38 nt deletion that drastically reduced 3′-processing efficiency. The reduction in S(x) for CYC1-512 represents the loss of efficiency rather well. The CYC1-512 mutant, while greatly reduced in efficiency, did still produce a few processed transcripts at positions as shown in Figure 7. Interestingly, the three sites still correspond to local maxima, though with greatly reduced S(x). Similar tests have been made on other reported mutations, with varying results. These are available for viewing at our website. DISCUSSION We have developed a DSM/HMM method for identification of putative yeast 3′-processing sites, based upon the idea that the 3′-processing control elements have predictable positioning and sequence content. The exact structure of the HMM was created manually from a merging of multiple sources of information, including statistical studies of putative element positioning and previously published reports. It is assumed that these elements act in a cooperative fashion, implying no absolute requirement for the sequence of any single element. While not required, it is assumed that the different 3′-processing elements interact with distinct components of the 3′-processing complex (see figure 3 in ref..52).

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As shown in Figure 5, the choice of threshold for assessing the predictions is a trade-off between sensitivity and specificity. For threshold value 3 and higher, the false positive rate approaches zero, however, the sensitivity, even allowing up to a 10 base error in positioning, also drops. Any sequence with S(x) > 4.0 clearly is extremely unlikely to arise randomly, and is therefore a strong prediction. At lower threshold values, the prediction becomes increasingly tenuous, as the possibility of random occurrences rises. As stated in the Introduction, the ability to identify likely 3′-processing sites has the potential to improve gene predictions. In the inset to Figure 6 some of the predicted genes for S.cerevisiae seemingly lack a 3′-processing control sequence, possibly indicating a non-functional ORF. Our analysis of the pairs of overlapping ORFs demonstrated this more clearly. Using the comparison of strength of putative 3′-processing signals for these pairs of genes, we were able to clearly identify the named gene in 86% of the test cases. In addition, our analysis of the putative 3′-processing sites has called into question the relative merits of the pair of overlapping genes ECM12 and YHR022C. Our analysis can point to alternative 3′-processing sites. Of particular interest is RNA14 (Fig. 4B), which is the yeast homolog of the 77 kDa subunit of cleavage stimulation factor (CstF-77k) and the Drosophila melanogaster protein suppressor of forked Su(f), a known component of the 3′-processing machinery. Studies of the fruit fly gene (53) have indicated a negative self-regulatory effect, in which excessive amounts of Su(f) protein activate an alternative 3′-processing site within the coding sequence that results in a truncated, nonfunctional transcript. In yeast, the alternative sites are differentially activated with changes in growth conditions (20). The alternative site in the fruit fly sequence is intronic, whereas in yeast, the protein is encoded by a single exon. The existence of alternative 3′-processing sites inside the coding sequence for the same gene in different organisms brings up the intriguing possibility of a conserved regulatory mechanism. Searches for similar phenomena in other organisms revealed ESTs that indicated a truncated version of the human CstF-77k mRNA. We also analyzed the sequences of the other known components (9) of the 3′-processing machinery, and found evidence for potential truncated transcripts in CLP1, YSH1, YHH1 and PCF11. In addition, RNA15 and PTA1 have evidence of regulatory alternative 3′-processing sites in the 3′-UTR. The analyses of all 3′-processing genes are available at our website. In our analysis of the complete set of known and predicted yeast genes, the distribution of the predicted maxima (corresponding to the most likely 3′-processing site) implies more genes with long UTRs than were found through EST analysis (Fig. 6). However, we believe that there are reasons that mRNA 3′-processing sites would display a bias towards shorter UTRs. In the presence of multiple possible sites (a relatively common occurrence in yeast), sites that occur closer to the stop codon have a competitive advantage, since they are available for interaction with the 3′-processing factors sooner. ‘Weaker’ sites (as defined by our analysis) can win out over ‘stronger’ sites by arising first. Our model appears to have a number of false positive predictions (dependent on the threshold value) due to inhibitory sequences occurring between control elements. Mutagenesis experiments previously demonstrated that the local sequence

environment could significantly inhibit sequences that were elsewhere known to be functional (13,49). The model currently has no ability to penalize such inhibitory sequences. We are investigating more sophisticated background models that may improve this performance. Our model is also limited by the fact that we are explicitly modeling sequence elements that define all sites in our training set. There are clearly differences in individual sites, as demonstrated by previously reported instances (20,21,54,55) of regulatory alternative 3′-processing sites. It is a distinct possibility that the poor predictions at position 1500 of RNA14 (a known alternative 3′-processing site) can be explained by regulatory differences in the sequences. A larger training set would give us the ability to generate separate models for regulatory alternative sites. This is not available for yeast, but as we expand our investigations to other organisms with larger amounts of training data, such an approach will become possible. The ever-increasing availability of complete genomic sequences will provide both new data and new systems to study. The tools that we have developed and presented here can be applied to any regulatory sequences that satisfy the requirements defined above: a relatively large data set for training and a regular, predictable positioning of the control elements relative to the processing site. SUPPLEMENTARY MATERIAL Supplementary Material is available at NAR Online. ACKNOWLEDGEMENTS The authors thank the scientists of CAB and BMERC at Boston University, especially Charles Cantor, for continued support and guidance. Jim White, Scott Mohr and Martin Frith provided critical reviews of the manuscript. J.H.G. is partially funded by Sequenom, Inc., and by NSF/KDI grant MCB-9980088. T.F.S. and J.H.G. are supported by NHLBI grant U01 HL66678. REFERENCES 1. Dandekar,T., Beyer,K., Bork,P., Kenealy,M.R., Pantopoulos,K., Hentze,M., Sonntag-Buck,V., Flouriot,G., Gannon,F. and Schreiber,S. (1998) Systematic genomic screening and analysis of mRNA in untranslated regions and mRNA precursors: combining experimental and computational approaches. Bioinformatics, 14, 271–278. 2. Hughes,J.D., Estep,P.W., Tavazoie,S. and Church,G.M. (2000) Computational identification of cis-regulatory elements associated with groups of functionally related genes in Saccharomyces cerevisiae. J. Mol. Biol., 296, 1205–1214. 3. McGuire,A.M., Hughes,J.D. and Church,G.M. (2000) Conservation of DNA regulatory motifs and discovery of new motifs in microbial genomes. Genome Res., 10, 744–757. 4. Wasserman,W.W., Palumbo,M., Thompson,W., Fickett,J.W. and Lawrence,C.E. (2000) Human–mouse genome comparisons to locate regulatory sites. Nature Genet., 26, 225–228. 5. McCue,L., Thompson,W., Carmack,C., Ryan,M.P., Liu,J.S., Derbyshire,V. and Lawrence,C.E. (2001) Phylogenetic footprinting of transcription factor binding sites in proteobacterial genomes. Nucleic Acids Res., 29, 774–782. 6. Wasserman,W.W. and Fickett,J.W. (1998) Identification of regulatory regions which confer muscle-specific gene expression. J. Mol. Biol., 278, 167–181. 7. GuhaThakurta,D. and Stormo,G.D. (2001) Identifying target sites for cooperatively binding factors. Bioinformatics, 17, 608–621. 8. Guo,Z. and Sherman,F. (1996) 3′-end-forming signals of yeast mRNA. Trends Biochem. Sci., 21, 477–481.

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