Adjusting for Selection on Synonymous Sites in Estimates of Evolutionary Distance
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《分子生物学进展》
* Department of Biological Sciences, Stanford University, Stanford, California; Department of Molecular and Cell Biology, University of California, Berkeley
Correspondence: E-mail: hunter@ocf.berkeley.edu.
Abstract
Evolution at silent sites is often used to estimate the pace of selectively neutral processes or to infer differences in divergence times of genes. However, silent sites are subject to selection in favor of preferred codons, and the strength of such selection varies dramatically across genes. Here, we use the relationship between codon bias and synonymous divergence observed in four species of the genus Saccharomyces to provide a simple correction for selection on silent sites.
Key Words: synonymous sites ? codon bias ? evolutionary genomics ? dS ? dN/dS ? selection
Introduction
The number of synonymous nucleotide substitutions per synonymous site, or dS, is central to a variety of analyses in the study of molecular evolution, including the construction of gene genealogies (Nei 1996; Langkjaer et al. 2003), the investigation of mutational processes (Birdsell 2002), and the estimation of the nature and intensity of selection (Suzuki and Gojobori 1999; Yang 2001). In all of these applications, a common assumption is that dS is a measure of evolutionary divergence caused by the selectively neutral processes of mutation and drift. For instance, in the estimation of the strength of selection, the ratio of nonsynonymous to synonymous rates of substitution, dN/dS, is viewed as a measure of the departure from neutrality caused by selection on nonsynonymous sites. However, work on prokaryotes, fungi, C. elegans, Drosophila, and Arabidopsis has shown that selection also operates on synonymous sites, favoring codons that allow for more efficient and accurate translation (reviewed in Akashi [2001]). Our objective here is to use extensive genomic sequence data available for the genus Saccharomyces (Kellis et al. 2003) to provide a simple adjustment of dS that corrects for selection on synonymous mutations, and thereby recovers an evolutionary distance that more accurately reflects the rate of neutral evolution.
Methods
Nucleotide sequences for 3,392 orthologous open reading frames (ORFs) in S. cerevisiae, S. paradoxus, S. mikatae, and S. bayanus were reported by Kellis et al. (2003). In our analysis, only ORFs that were represented in all four species were retained. To remove sequences with authentic or spurious frameshift mutations, which are inconsistent with the model of sequence change underlying maximum-likelihood estimation of dS, all sequences were translated and realigned with ClustalW version 1.8 (Thompson, Higgins, and Gibson 1994) and were then subjected to the following sliding-window filter: an ORF was eliminated from consideration if any single sequence disagreed with the majority-rule consensus protein sequence at five consecutive sites for which the consensus was defined. Visual inspection confirmed that this filter worked well to exclude putative frameshifts. A maximum-likelihood phylogeny based on nucleotide sequences was built for each ORF using PHYLIP version 3.6 (Felsenstein 2003); any ORF that did not exhibit the consensus phylogeny ([S. cerevisiae, S. paradoxus], [S. mikatae, S. bayanus]) was dropped. Synonymous divergence, dS, was then estimated using PAML version 3.12 (Yang 2002), with nine free parameters used to account for codon frequencies (F3x4), as in Dunn, Bielawski, and Yang (2001). Use of 60 free parameters to estimate each codon frequency individually (F61) did not significantly alter the results (for instance, Pearson's correlation coefficient between codon bias and F61 dS was –0.50, very similar to the correlation of –0.58 between codon bias and F3x4 dS [see Results]). Values shown here were estimated under model 0 (one dN/dS ratio for the tree), but results were extremely similar under model 1 (branch-specific dN/dS ratios).
Codon bias, as represented by the codon adaptation index, was calculated for each gene as described (Sharp and Li 1987). The set of optimal codons was taken from the 20 most highly expressed genes in S. cerevisiae (Arava et al. 2003), and bias values for each gene were calculated by averaging the values for all four orthologous copies.
Results and Discussion
If all synonymous sites were under equivalent selective pressure, departure from absolute neutrality would not compromise the utility of dS for comparing genes to assess relative divergence times, mutation rates, or nonsynonymous evolutionary rates (e.g., Lynch and Conery 2000). However, the strength of selection appears to vary widely across synonymous sites, both because the fitness penalty of inaccurate translation varies across sites (Akashi 1994) and because the optimal rate of expression varies across genes (Sharp and Li 1987; Akashi 1994; Coghlan and Wolfe 2000; Akashi 2001). Because selection in favor of preferred codons is expected to increase observable bias and to reduce the fraction of truly neutral mutations at synonymous sites, we would expect genes of higher bias to show a reduced rate of divergence at synonymous sites. This expectation is confirmed in figure 1a, in which each gene's synonymous divergence in a phylogeny of four species of Saccharomyces is plotted against that gene's average codon bias (n = 3,036 genes, each represented by a point in figure 1a; Pearson's correlation coefficient r = –0.58; P < 10–269). The variance in dS was independent of each gene's codon bias (not shown), consistent with the assumptions inherent in linear regression.
FIG. 1.— (a) The relationship between synonymous evolutionary divergence, dS, and codon bias, c. Points represent dS values summed over the complete, four-species phylogeny ([S. cerevisiae, S. paradoxus], [S. mikatae, S. bayanus]), plotted against the codon adaptation index averaged across all four species (n = 3,036, Pearson correlation coefficient r = –0.58, P < 10–269). The solid line represents the best fit to these points (dS = –2.02c + 2.13). The dashed lines represent best-fit relationships between dS and c for each of the four yeast species individually. The lines, in order of decreasing dS-axis intercept, represent: S. bayanus, S. mikatae, S. cerevisiae, and S. paradoxus. Under the linear model relating dS to c, the slope of these lines, which estimates k1t (see text) is expected to decrease in proportion to increases in their intercept, which estimates the neutral divergence, r0t. As shown in (b), this is indeed the case (slope, k2 = –0.90, dS0 = –0.016; r = 0.99).
The relationship shown in figure 1a is approximately linear (best fit line r2 = 0.33; best fit quadratic function r2 = 0.34), suggesting that the rate of synonymous evolution is reduced by an amount that is linearly proportional to the level of codon bias. We, therefore, adopt the simple linear model, dS = (r0 + k1c)t, where c is codon bias, k1 (k1 < 0) is a constant, t is the total time of divergence, and r0 is the rate of neutral evolution—that is, the rate of evolution at synonymous sites exhibiting zero bias. The quantities k1t and r0t are estimated by the slope (m) and intercept (dS0) of the best-fit line relating dS to c for a given total divergence time t. For the complete tree of four yeast species, m = –2.02 and dS0 = 2.14 (fig. 1a, solid line). If the linear model is appropriate, the slope m of the relationship between bias and divergence should decrease from zero in proportion to increases in neutral divergence dS0, because both of these quantities estimate parameters that are proportional to the total divergence time t. That is, starting from slope k1t = 0 at divergence time t = 0, the line relating bias to divergence is expected to rotate clockwise around the fixed point c = 1, dS = 0 because a sequence with perfect codon bias undergoes zero neutral divergence. We test this prediction by obtaining the best-fit line relating dS to c for each of the independent terminal branches of the four-species tree. These lines are shown in figure 1a (dashed lines). The yeast species they represent are, in order of decreasing dS0, S. bayanus, S. mikatae, S. cerevisiae, and S. paradoxus. In figure 1b, the slope m of each species' line, estimating k1t, is plotted against its intercept dS0, estimating r0t. As expected under the simple linear model, m does indeed decrease in direct proportion to neutral divergence (best-fit line in figure 1b: slope = –0.90; r = 0.99). In addition, the intercept of this relationship is not significantly different from 0 (dS0 = 0.016; P = 0.62), in accordance with the fact that the line relating dS to c begins decreasing its slope from k1t = 0 at time t = 0.
There are two distinct contexts in which one may require an adjustment of dS to take into account selection on synonymous sites. In the first context, dS or dN/dS values are compared across genes that share a common divergence time. For instance, to examine functional correlates of evolutionary constraint (e.g., Hirsh and Fraser 2001; Fraser et al. 2002), one would compare dN/dS among the 3,036 genes represented by points in figure 1a; all of these genes share the time of divergence represented by the complete, four-species phylogeny. In this context, the observed synonymous divergence of gene i, dSi, the observed codon bias of gene i, ci, and the best-fit estimate of k1t (given by m) may be used to obtain an adjusted synonymous divergence for gene i, dS'i = dSi – m ci. This adjustment results in a significant reduction in the variance of dN/dS (n = 3,036; dN/dS s2 = 0.0046; dN/dS' s2 = 0.0028; F = 0.60, P < 10–44) and significantly affects the "rank evolutionary constraint," as estimated by rank dN/dS, for a large number of genes (change in rank dN/dS > 50 for 1,553 genes). Table 1 lists the 10 yeast genes for which adjustment of dS has the greatest impact on rank dN/dS; that is, these are the 10 genes for which (rank dN/dS) – (rank dN/dS') is greatest. For most of these genes, the relatively relaxed selective pressure indicated by the uncorrected dN/dS rank is at odds with the encoded protein's biological function. For instance, it seems unlikely that FBA1, which encodes fructose-bisphosphate aldolase, an abundant protein central to glycolysis, should be only the 2875th most constrained gene out of 3,036. Upon correction for codon bias, this gene's dN/dS rank improves to 333.
Table 1 Genes with largest change in dN/dS rank upon adjustment of dS
In another context, one may compare dS or dN/dS values among genes that do not share the same divergence time. For instance, in comparisons of dN/dS among duplicated genes (Lynch and Conery 2000), many paralogs do not share a common date of divergence. In this case, a single best-fit line relating dS to c cannot be used to provide an adjustment of dS, simply because each divergence time corresponds to a line of different slope, k1t. However, the relationship shown in figure 1b, between r0t and k1t, provides the requisite missing information. If we let k2 (k2 < 0) be the slope of the line in figure 1b, then k1t = k2r0t; using this equation and dS = (r0 + k1c) t, we eliminate r0t and solve for the unknown k1t = k2dS/(1+k2c). Substituting for k1t in the equation for corrected synonymous divergence of gene i, dSi' = dSi – k1tci, we obtain dSi' = dSi/(1 + k2ci). This provides a straightforward adjustment for dS, even when genes do not share a common time of divergence.
Whether the simple method of correction that is used here for Saccharomyces can be applied in other groups is not yet clear; a negative linear correlation would be required between dS and codon bias, as we observed for yeast. A negative correlation between synonymous divergence and codon bias has been reported in Drosophila (Shields et al. 1988; Powell and Moriyama 1997), in gene pairs resulting from the genome duplication event in an ancestor of S. cerevisiae (Pal, Papp, and Hurst 2001), and in Escherichia coli (Sharp and Li 1987; Smith and Eyre-Walker 2001). The correlation reported in Drosophila was subsequently found to be insignificant when using maximum-likelihood estimates of dS that account for unequal usage of codons (Dunn, Bielawski, and Yang 2001). Bierne and Eyre-Walker (2003) argued that this result should be revised once again because synonymous evolutionary rate should be measured not in terms of fixations per synonymous mutation, but rather in terms of synonymous fixations per physical nucleotide site. Leaving aside further discussion of the appropriate denominator for measures of synonymous evolutionary rate, we note that, for any given method of estimating dS, the simple correction described here would yield a metric of synonymous substitution rates that has been adjusted for codon bias. The potential problem of unequal codon usage (Dunn, Bielawski, and Yang 2001) does not apply to the relationships shown in figure 1, because we have used maximum-likelihood distance estimates that account for codon usage (Yang 2002).
The negative correlation between dS and codon bias in E. coli was suggested to be mediated by a mutational effect: if more highly expressed genes exhibit higher bias and suffer fewer mutations, the relationship between bias and dS could emerge without selection on silent sites (Smith and Eyre-Walker 2001). However, work on S. cerevisiae (Datta and Jinks-Robertson 1995; Morey, Greene, and Jinks-Robertson 2000), as well as E. coli (Wright, Longacre, and Reimers 1999; Klapacz and Bhagwat 2002) and Salmonella enterica (Hudson, Bergthorsson, and Ochman 2003), has shown that more highly expressed genes actually suffer higher mutation rates. This association between transcription and mutation would cause a positive correlation between dS and codon bias—the opposite of the one observed here. Thus, if transcription-associated mutation affects the correction we describe here, it is to make the correction somewhat conservative.
Acknowledgements
We are grateful to Dmitri Petrov for prompting this work, to Marc Feldman for advice and support, and to Jerel Davis for comments on the manuscript. This study was supported by NIH grants GM 28016 and 28424 to Marcus W. Feldman (A.E.H. and D.P.W.), by an NSF postdoctoral fellowship in bioinformatics (D.P.W.), and by an NSF predoctoral fellowship (H.B.F.).
References
Akashi, H. 1994. Synonymous codon usage in Drosophila melanogaster: natural selection and translational accuracy. Genetics 136:927–935.
———. 2001. Gene expression and molecular evolution. Curr Opin Genet Dev 11:660–666.
Arava, Y., Y. Wang, J. D. Storey, C. L. Liu, P. O. Brown, and D. Herschlag. 2003. Genome-wide analysis of mRNA translation profiles in Saccharomyces cerevisiae. Proc. Natl. Acad. Sci. USA 100:3889–3894.
Bierne, N., and A. Eyre-Walker. 2003. The problem of counting sites in the estimation of the synonymous and nonsynonymous substitution rates: implications for the correlation between the synonymous substitution rate and codon usage bias. Genetics 165:1587–1597.
Birdsell, J. A. 2002. Integrating genomics, bioinformatics, and classical genetics to study the effects of recombination on genome evolution. Mol. Biol. Evol. 19:1181–1197.
Coghlan, A., and K. H. Wolfe. 2000. Relationship of codon bias to mRNA concentration and protein length in Saccharomyces cerevisiae. Yeast 16:1131–1145.
Datta, A., and S. Jinks-Robertson. 1995. Association of increased spontaneous mutation rates with high levels of transcription in yeast. Science 268:1616–1619.
Dunn, K. A., J. P. Bielawski, and Z. Yang. 2001. Substitution rates in Drosophila nuclear genes: implications for translational selection. Genetics 157:295–305.
Felsenstein, J. 2003. PHYLIP (phylogeny and inference package). Version. 3.6. Distributed by the author, Department of Genetics, University of Washington, Seattle.
Fraser, H. B., A. E. Hirsh, L. M. Steinmetz, C. Scharfe, and M. W. Feldman. 2002. Evolutionary rate in the protein interaction network. Science 296:750–752.
Hirsh, A. E., and H. B. Fraser. 2001. Protein dispensability and rate of evolution. Nature 411:1046–1049.
Hudson, R. E., U. Bergthorsson, and H. Ochman. 2003. Transcription increases multiple spontaneous point mutations in Salmonella enterica. Nucleic Acids Res. 31:4517–4522.
Kellis, M., N. Patterson, M. Endrizzi, B. Birren, and E. S. Lander. 2003. Sequencing and comparison of yeast species to identify genes and regulatory elements. Nature 423:241–254.
Klapacz, J., and A. S. Bhagwat. 2002. Transcription-dependent increase in multiple classes of base substitution mutations in Escherichia coli. J. Bacteriol. 184:6866–6872.
Langkjaer, R. B., P. F. Cliften, M. Johnston, and J. Piskur. 2003. Yeast genome duplication was followed by asynchronous differentiation of duplicated genes. Nature 421:848–852.
Lynch, M., and J. S. Conery. 2000. The evolutionary fate and consequences of duplicate genes. Science 290:1151–1155.
Morey, N. J., C. N. Greene, and S. Jinks-Robertson. 2000. Genetic analysis of transcription-associated mutation in Saccharomyces cerevisiae. Genetics 154:109–120.
Nei, M. 1996. Phylogenetic analysis in molecular evolutionary genetics. Ann. Rev. Genet. 30:371–403.
Pal, C., B. Papp, and L. D. Hurst. 2001. Highly expressed genes in yeast evolve slowly. Genetics 158:927–931.
Powell, J. R., and E. N. Moriyama. 1997. Evolution of codon usage bias in Drosophila. Proc. Natl. Acad. Sci. USA 94:7784–7790.
Sharp, P. M., and W. H. Li. 1987. The rate of synonymous substitution in enterobacterial genes is inversely related to codon usage bias. Mol. Biol. Evol. 4:222–230.
Shields, D. C., P. M. Sharp, D. G. Higgins, and F. Wright. 1988. "Silent" sites in Drosophila genes are not neutral: evidence of selection among synonymous codons. Mol. Biol. Evol. 5:704–716.
Smith, N. G., and A. Eyre-Walker. 2001. Nucleotide substitution rate estimation in enterobacteria: approximate and maximum-likelihood methods lead to similar conclusions. Mol. Biol. Evol. 18:2124–2126.
Suzuki, Y., and T. Gojobori. 1999. A method for detecting positive selection at single amino acid sites. Mol. Biol. Evol. 16:1315–1328.
Thompson, J. D., D. G. Higgins, and T. J. Gibson. 1994. CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res. 22:4673–4680.
Wright, B. E., A. Longacre, and J. M. Reimers. 1999. Hypermutation in derepressed operons of Escherichia coli K12. Proc. Natl. Acad. Sci. USA 96:5089–5094.
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———. 2002. Phylogenetic analysis by maximum likelihood. University College, London.(Aaron E. Hirsh*, Hunter B)
Correspondence: E-mail: hunter@ocf.berkeley.edu.
Abstract
Evolution at silent sites is often used to estimate the pace of selectively neutral processes or to infer differences in divergence times of genes. However, silent sites are subject to selection in favor of preferred codons, and the strength of such selection varies dramatically across genes. Here, we use the relationship between codon bias and synonymous divergence observed in four species of the genus Saccharomyces to provide a simple correction for selection on silent sites.
Key Words: synonymous sites ? codon bias ? evolutionary genomics ? dS ? dN/dS ? selection
Introduction
The number of synonymous nucleotide substitutions per synonymous site, or dS, is central to a variety of analyses in the study of molecular evolution, including the construction of gene genealogies (Nei 1996; Langkjaer et al. 2003), the investigation of mutational processes (Birdsell 2002), and the estimation of the nature and intensity of selection (Suzuki and Gojobori 1999; Yang 2001). In all of these applications, a common assumption is that dS is a measure of evolutionary divergence caused by the selectively neutral processes of mutation and drift. For instance, in the estimation of the strength of selection, the ratio of nonsynonymous to synonymous rates of substitution, dN/dS, is viewed as a measure of the departure from neutrality caused by selection on nonsynonymous sites. However, work on prokaryotes, fungi, C. elegans, Drosophila, and Arabidopsis has shown that selection also operates on synonymous sites, favoring codons that allow for more efficient and accurate translation (reviewed in Akashi [2001]). Our objective here is to use extensive genomic sequence data available for the genus Saccharomyces (Kellis et al. 2003) to provide a simple adjustment of dS that corrects for selection on synonymous mutations, and thereby recovers an evolutionary distance that more accurately reflects the rate of neutral evolution.
Methods
Nucleotide sequences for 3,392 orthologous open reading frames (ORFs) in S. cerevisiae, S. paradoxus, S. mikatae, and S. bayanus were reported by Kellis et al. (2003). In our analysis, only ORFs that were represented in all four species were retained. To remove sequences with authentic or spurious frameshift mutations, which are inconsistent with the model of sequence change underlying maximum-likelihood estimation of dS, all sequences were translated and realigned with ClustalW version 1.8 (Thompson, Higgins, and Gibson 1994) and were then subjected to the following sliding-window filter: an ORF was eliminated from consideration if any single sequence disagreed with the majority-rule consensus protein sequence at five consecutive sites for which the consensus was defined. Visual inspection confirmed that this filter worked well to exclude putative frameshifts. A maximum-likelihood phylogeny based on nucleotide sequences was built for each ORF using PHYLIP version 3.6 (Felsenstein 2003); any ORF that did not exhibit the consensus phylogeny ([S. cerevisiae, S. paradoxus], [S. mikatae, S. bayanus]) was dropped. Synonymous divergence, dS, was then estimated using PAML version 3.12 (Yang 2002), with nine free parameters used to account for codon frequencies (F3x4), as in Dunn, Bielawski, and Yang (2001). Use of 60 free parameters to estimate each codon frequency individually (F61) did not significantly alter the results (for instance, Pearson's correlation coefficient between codon bias and F61 dS was –0.50, very similar to the correlation of –0.58 between codon bias and F3x4 dS [see Results]). Values shown here were estimated under model 0 (one dN/dS ratio for the tree), but results were extremely similar under model 1 (branch-specific dN/dS ratios).
Codon bias, as represented by the codon adaptation index, was calculated for each gene as described (Sharp and Li 1987). The set of optimal codons was taken from the 20 most highly expressed genes in S. cerevisiae (Arava et al. 2003), and bias values for each gene were calculated by averaging the values for all four orthologous copies.
Results and Discussion
If all synonymous sites were under equivalent selective pressure, departure from absolute neutrality would not compromise the utility of dS for comparing genes to assess relative divergence times, mutation rates, or nonsynonymous evolutionary rates (e.g., Lynch and Conery 2000). However, the strength of selection appears to vary widely across synonymous sites, both because the fitness penalty of inaccurate translation varies across sites (Akashi 1994) and because the optimal rate of expression varies across genes (Sharp and Li 1987; Akashi 1994; Coghlan and Wolfe 2000; Akashi 2001). Because selection in favor of preferred codons is expected to increase observable bias and to reduce the fraction of truly neutral mutations at synonymous sites, we would expect genes of higher bias to show a reduced rate of divergence at synonymous sites. This expectation is confirmed in figure 1a, in which each gene's synonymous divergence in a phylogeny of four species of Saccharomyces is plotted against that gene's average codon bias (n = 3,036 genes, each represented by a point in figure 1a; Pearson's correlation coefficient r = –0.58; P < 10–269). The variance in dS was independent of each gene's codon bias (not shown), consistent with the assumptions inherent in linear regression.
FIG. 1.— (a) The relationship between synonymous evolutionary divergence, dS, and codon bias, c. Points represent dS values summed over the complete, four-species phylogeny ([S. cerevisiae, S. paradoxus], [S. mikatae, S. bayanus]), plotted against the codon adaptation index averaged across all four species (n = 3,036, Pearson correlation coefficient r = –0.58, P < 10–269). The solid line represents the best fit to these points (dS = –2.02c + 2.13). The dashed lines represent best-fit relationships between dS and c for each of the four yeast species individually. The lines, in order of decreasing dS-axis intercept, represent: S. bayanus, S. mikatae, S. cerevisiae, and S. paradoxus. Under the linear model relating dS to c, the slope of these lines, which estimates k1t (see text) is expected to decrease in proportion to increases in their intercept, which estimates the neutral divergence, r0t. As shown in (b), this is indeed the case (slope, k2 = –0.90, dS0 = –0.016; r = 0.99).
The relationship shown in figure 1a is approximately linear (best fit line r2 = 0.33; best fit quadratic function r2 = 0.34), suggesting that the rate of synonymous evolution is reduced by an amount that is linearly proportional to the level of codon bias. We, therefore, adopt the simple linear model, dS = (r0 + k1c)t, where c is codon bias, k1 (k1 < 0) is a constant, t is the total time of divergence, and r0 is the rate of neutral evolution—that is, the rate of evolution at synonymous sites exhibiting zero bias. The quantities k1t and r0t are estimated by the slope (m) and intercept (dS0) of the best-fit line relating dS to c for a given total divergence time t. For the complete tree of four yeast species, m = –2.02 and dS0 = 2.14 (fig. 1a, solid line). If the linear model is appropriate, the slope m of the relationship between bias and divergence should decrease from zero in proportion to increases in neutral divergence dS0, because both of these quantities estimate parameters that are proportional to the total divergence time t. That is, starting from slope k1t = 0 at divergence time t = 0, the line relating bias to divergence is expected to rotate clockwise around the fixed point c = 1, dS = 0 because a sequence with perfect codon bias undergoes zero neutral divergence. We test this prediction by obtaining the best-fit line relating dS to c for each of the independent terminal branches of the four-species tree. These lines are shown in figure 1a (dashed lines). The yeast species they represent are, in order of decreasing dS0, S. bayanus, S. mikatae, S. cerevisiae, and S. paradoxus. In figure 1b, the slope m of each species' line, estimating k1t, is plotted against its intercept dS0, estimating r0t. As expected under the simple linear model, m does indeed decrease in direct proportion to neutral divergence (best-fit line in figure 1b: slope = –0.90; r = 0.99). In addition, the intercept of this relationship is not significantly different from 0 (dS0 = 0.016; P = 0.62), in accordance with the fact that the line relating dS to c begins decreasing its slope from k1t = 0 at time t = 0.
There are two distinct contexts in which one may require an adjustment of dS to take into account selection on synonymous sites. In the first context, dS or dN/dS values are compared across genes that share a common divergence time. For instance, to examine functional correlates of evolutionary constraint (e.g., Hirsh and Fraser 2001; Fraser et al. 2002), one would compare dN/dS among the 3,036 genes represented by points in figure 1a; all of these genes share the time of divergence represented by the complete, four-species phylogeny. In this context, the observed synonymous divergence of gene i, dSi, the observed codon bias of gene i, ci, and the best-fit estimate of k1t (given by m) may be used to obtain an adjusted synonymous divergence for gene i, dS'i = dSi – m ci. This adjustment results in a significant reduction in the variance of dN/dS (n = 3,036; dN/dS s2 = 0.0046; dN/dS' s2 = 0.0028; F = 0.60, P < 10–44) and significantly affects the "rank evolutionary constraint," as estimated by rank dN/dS, for a large number of genes (change in rank dN/dS > 50 for 1,553 genes). Table 1 lists the 10 yeast genes for which adjustment of dS has the greatest impact on rank dN/dS; that is, these are the 10 genes for which (rank dN/dS) – (rank dN/dS') is greatest. For most of these genes, the relatively relaxed selective pressure indicated by the uncorrected dN/dS rank is at odds with the encoded protein's biological function. For instance, it seems unlikely that FBA1, which encodes fructose-bisphosphate aldolase, an abundant protein central to glycolysis, should be only the 2875th most constrained gene out of 3,036. Upon correction for codon bias, this gene's dN/dS rank improves to 333.
Table 1 Genes with largest change in dN/dS rank upon adjustment of dS
In another context, one may compare dS or dN/dS values among genes that do not share the same divergence time. For instance, in comparisons of dN/dS among duplicated genes (Lynch and Conery 2000), many paralogs do not share a common date of divergence. In this case, a single best-fit line relating dS to c cannot be used to provide an adjustment of dS, simply because each divergence time corresponds to a line of different slope, k1t. However, the relationship shown in figure 1b, between r0t and k1t, provides the requisite missing information. If we let k2 (k2 < 0) be the slope of the line in figure 1b, then k1t = k2r0t; using this equation and dS = (r0 + k1c) t, we eliminate r0t and solve for the unknown k1t = k2dS/(1+k2c). Substituting for k1t in the equation for corrected synonymous divergence of gene i, dSi' = dSi – k1tci, we obtain dSi' = dSi/(1 + k2ci). This provides a straightforward adjustment for dS, even when genes do not share a common time of divergence.
Whether the simple method of correction that is used here for Saccharomyces can be applied in other groups is not yet clear; a negative linear correlation would be required between dS and codon bias, as we observed for yeast. A negative correlation between synonymous divergence and codon bias has been reported in Drosophila (Shields et al. 1988; Powell and Moriyama 1997), in gene pairs resulting from the genome duplication event in an ancestor of S. cerevisiae (Pal, Papp, and Hurst 2001), and in Escherichia coli (Sharp and Li 1987; Smith and Eyre-Walker 2001). The correlation reported in Drosophila was subsequently found to be insignificant when using maximum-likelihood estimates of dS that account for unequal usage of codons (Dunn, Bielawski, and Yang 2001). Bierne and Eyre-Walker (2003) argued that this result should be revised once again because synonymous evolutionary rate should be measured not in terms of fixations per synonymous mutation, but rather in terms of synonymous fixations per physical nucleotide site. Leaving aside further discussion of the appropriate denominator for measures of synonymous evolutionary rate, we note that, for any given method of estimating dS, the simple correction described here would yield a metric of synonymous substitution rates that has been adjusted for codon bias. The potential problem of unequal codon usage (Dunn, Bielawski, and Yang 2001) does not apply to the relationships shown in figure 1, because we have used maximum-likelihood distance estimates that account for codon usage (Yang 2002).
The negative correlation between dS and codon bias in E. coli was suggested to be mediated by a mutational effect: if more highly expressed genes exhibit higher bias and suffer fewer mutations, the relationship between bias and dS could emerge without selection on silent sites (Smith and Eyre-Walker 2001). However, work on S. cerevisiae (Datta and Jinks-Robertson 1995; Morey, Greene, and Jinks-Robertson 2000), as well as E. coli (Wright, Longacre, and Reimers 1999; Klapacz and Bhagwat 2002) and Salmonella enterica (Hudson, Bergthorsson, and Ochman 2003), has shown that more highly expressed genes actually suffer higher mutation rates. This association between transcription and mutation would cause a positive correlation between dS and codon bias—the opposite of the one observed here. Thus, if transcription-associated mutation affects the correction we describe here, it is to make the correction somewhat conservative.
Acknowledgements
We are grateful to Dmitri Petrov for prompting this work, to Marc Feldman for advice and support, and to Jerel Davis for comments on the manuscript. This study was supported by NIH grants GM 28016 and 28424 to Marcus W. Feldman (A.E.H. and D.P.W.), by an NSF postdoctoral fellowship in bioinformatics (D.P.W.), and by an NSF predoctoral fellowship (H.B.F.).
References
Akashi, H. 1994. Synonymous codon usage in Drosophila melanogaster: natural selection and translational accuracy. Genetics 136:927–935.
———. 2001. Gene expression and molecular evolution. Curr Opin Genet Dev 11:660–666.
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Bierne, N., and A. Eyre-Walker. 2003. The problem of counting sites in the estimation of the synonymous and nonsynonymous substitution rates: implications for the correlation between the synonymous substitution rate and codon usage bias. Genetics 165:1587–1597.
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