New methods for estimating the numbers of synonymous and nonsynonymous substitutions

New methods for estimating the numbers of synonymous and nonsynonymous substitutions per site were developed. The methods are unweighted pathway methods based on Kimura's two-parameter model. Computer simulations were conducted to evaluate the accuracies of the new methods, Nei and Gojobori's (NG) method, Miyata and Yasunaga's (MY) method, Li, Wu, and Luo's (LWL) method, and Pamilo, Bianchi, and Li's (PBL) method. The following results were obtained: (1) The NG, MY, and LWL methods give overestimates of the number of synonymous substitutions and underestimates of the number of nonsynonymous substitutions. The major cause for the biased estimation is that these three methods underestimate the number of synonymous sites and overestimate the number of nonsynonymous sites. (2) The PBL method gives better estimates of the numbers of synonymous and nonsynonymous substitutions than those obtained by the NG, MY, and LWL methods. (3) The new methods also give better estimates of the numbers of synonymous and nonsynonymous substitutions than those obtained by the NG, MY, and LWL methods. In addition, estimates of the numbers of synonymous and nonsynonymous sites obtained by the new methods are reasonably accurate. (4) In some cases, the new methods and the PBL method give biased estimates of substitution numbers. However, from the number of nucleotide substitutions at the third position of codons, we can examine whether estimates obtained by the new methods are good or not, whereas we cannot make an examination of estimates obtained by the PBL method. (5) When there are strong transition/transversion and nucleotide-frequency biases like mitochondrial genes, all of the above methods give biased estimates of substitution numbers. In such cases, Kondo et al.'s method is recommended to be used for estimating the number of synonymous substitutions, although their method cannot estimate the number of nonsynonymous substitutions and is time-consuming. These results, particularly result (1), call for reexaminations of some genes. This is because evolutionary pictures of genes have often been discussed on the basis of results obtained by the NG, MY, and LWL methods, which are favorable for the neutral theory of molecular evolution.     

Estimating synonymous and nonsynonymous substitution rates under realistic evolutionary models

Approximate methods for estimating the numbers of synonymous and nonsynonymous substitutions between two DNA sequences involve three steps: counting of synonymous and nonsynonymous sites in the two sequences, counting of synonymous and nonsynonymous differences between the two sequences, and correcting for multiple substitutions at the same site. We examine complexities involved in those steps and propose a new approximate method that takes into account two major features of DNA sequence evolution: transition/transversion rate bias and base/codon frequency bias. We compare the new method with maximum likelihood, as well as several other approximate methods, by examining infinitely long sequences, performing computer simulations, and analyzing a real data set. The results suggest that when there are transition/transversion rate biases and base/codon frequency biases, previously described approximate methods for estimating the nonsynonymous/synonymous rate ratio may involve serious biases, and the bias can be both positive and negative. The new method is, in general, superior to earlier approximate methods and may be useful for analyzing large data sets, although maximum likelihood appears to always be the method of choice.     

Simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions

Two simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions are presented. Although they give no weights to different types of codon substitutions, these methods give essentially the same results as those obtained by Miyata and Yasunaga's and by Li et al.'s methods. Computer simulation indicates that estimates of synonymous substitutions obtained by the two methods are quite accurate unless the number of nucleotide substitutions per site is very large. It is shown that all available methods tend to give an underestimate of the number of nonsynonymous substitutions when the number is large.      

Rates of nucleotide substitution and mammalian nuclear gene evolution. Approximate and maximum-likelihood methods lead to different conclusions

Rates and patterns of synonymous and nonsynonymous substitutions have important implications for the origin and maintenance of mammalian isochores and the effectiveness of selection at synonymous sites. Previous studies of mammalian nuclear genes largely employed approximate methods to estimate rates of nonsynonymous and synonymous substitutions. Because these methods did not account for major features of DNA sequence evolution such as transition/transversion rate bias and unequal codon usage, they might not have produced reliable results. To evaluate the impact of the estimation method, we analyzed a sample of 82 nuclear genes from the mammalian orders Artiodactyla, Primates, and Rodentia using both approximate and maximum-likelihood methods. Maximum-likelihood analysis indicated that synonymous substitution rates were positively correlated with GC content at the third codon positions, but independent of nonsynonymous substitution rates. Approximate methods, however, indicated that synonymous substitution rates were independent of GC content at the third codon positions, but were positively correlated with nonsynonymous rates. Failure to properly account for transition/transversion rate bias and unequal codon usage appears to have caused substantial biases in approximate estimates of substitution rates.     

A method for estimating the numbers of synonymous and nonsynonymous substitutions per site

A method for estimating the numbers of synonymous (Ks) and nonsynonymous (Ka) substitutions per site is proposed. The method is based on the Li's (J Mol. Evol. 36:96–99, 1993) and Pamilo and Bianchi's (Mol. Biol. Evol. 10:271–281, 1993) method, but a putative source of bias is solved. It is proposed that the number of synonymous substitutions that are actually transitions or transversions should be computed by separating the twofold degenerate sites into two types of sites, 2S-fold and 2V-fold, where only transitional and transversional substitutions are synonymous, respectively. Kimura's (J. Mol. Evol. 16:111–120, 1980) two-parameter correcting method for multiple substitutions at a site is then applied using the overall observed synonymous transversion frequency to estimate both the numbers of synonymous transversional (Bs) and transitional (As) substitutions per site. This approach, therefore, also minimizes stochastic errors. Computer simulations indicate that the method presented gives more accurate Ks and Ka estimates than the aforementioned methods. Furthermore, the obtention of confidence intervals for divergence estimates by computer simulation is proposed.     

Molecular evolution of the major capsid protein VP1 of enterovirus 70.

Nucleotide sequences of the genome RNA encoding capsid protein VP1 (918 nucleotides) of 18 enterovirus 70 (EV70) isolates collected from various parts of the world in 1971 to 1981 were determined, and nucleotide substitutions among them were studied. The genetic distances between isolates were calculated by the pairwise comparison of nucleotide difference. Regression analysis of the genetic distances against time of isolation of the strains showed that the synonymous substitution rate was very high at 21.53 x 10(-3) substitution per nucleotide per year, while the nonsynonymous rate was extremely low at 0.32 x 10(-3) substitution per nucleotide per year. The rate estimated by the average value of synonymous and nonsynonymous substitutions (W.-H. Li, C.-C. Wu, and C.-C. Luo, Mol. Biol. Evol. 2:150-174, 1985) was 5.00 x 10(-3) substitution per nucleotide per year. Taking the average value of synonymous and nonsynonymous substitutions as genetic distances between isolates, the phylogenetic tree was inferred by the unweighted pairwise grouping method of arithmetic average and by the neighbor-joining method. The tree indicated that the virus had evolved from one focal place, and the time of emergence was estimated to be August 1967 +/- 15 months, 2 years before first recognition of the pandemic of acute hemorrhagic conjunctivitis. By superimposing every nucleotide substitution on the branches of the phylogenetic tree, we analyzed nucleotide substitution patterns of EV70 genome RNA. In synonymous substitutions, the proportion of transitions, i.e., C<==>U and G<==>A, was found to be extremely frequent in comparison with that reported on other viruses or pseudogenes. In addition, parallel substitutions (independent substitutions at the same nucleotide position on different branches, i.e., different isolates, of the tree) were frequently found in both synonymous and nonsynonymous substitutions. These frequent parallel substitutions and the low nonsynonymous substitution rate despite the very high synonymous substitution rate described above imply a strong restriction on nonsynonymous substitution sites of VP1, probably due to the requirement for maintaining the rigid icosahedral conformation of the virus.     

A statistical examination of hypervariability in complementarity-determining regions of immunoglobulins

To determine the relative importance of gene conversion followed by natural selection and of natural selection for point mutation in generating variability in immunoglobulins, the numbers of synonymous and nonsynonymous substitutions in immunoglobulin sequences of various subgroups were estimated for complementarity-determining regions (CDRs) and for framework regions (FRs). Both the number of synonymous substitutions and the number of nonsynonymous substitutions in the CDR were found to exceed the corresponding numbers in the FR. Therefore, gene conversion is likely to be an important mechanism for providing variability in the CDR of immunoglobulins. The correlation coefficients between the number of synonymous substitutions and the number of nonsynonymous substitutions and between the substitution number in the CDR and that in the FR were found to be very low. Again, gene conversion is thought to be responsible for this finding.     

A method for detecting positive selection at single amino acid sites

A method was developed for detecting the selective force at single amino acid sites given a multiple alignment of protein-coding sequences. The phylogenetic tree was reconstructed using the number of synonymous substitutions. Then, the neutrality was tested for each codon site using the numbers of synonymous and nonsynonymous changes throughout the phylogenetic tree. Computer simulation showed that this method accurately estimated the numbers of synonymous and nonsynonymous substitutions per site, as long as the substitution number on each branch was relatively small. The false-positive rate for detecting the selective force was generally low. On the other hand, the true-positive rate for detecting the selective force depended on the parameter values. Within the range of parameter values used in the simulation, the true-positive rate increased as the strength of the selective force and the total branch length (namely the total number of synonymous substitutions per site) in the phylogenetic tree increased. In particular, with the relative rate of nonsynonymous substitutions to synonymous substitutions being 5.0, most of the positively selected codon sites were correctly detected when the total branch length in the phylogenetic tree was > or = 2.5. When this method was applied to the human leukocyte antigen (HLA) gene, which included antigen recognition sites (ARSs), positive selection was detected mainly on ARSs. This finding confirmed the effectiveness of the present method with actual data. Moreover, two amino acid sites were newly identified as positively selected in non-ARSs. The three-dimensional structure of the HLA molecule indicated that these sites might be involved in antigen recognition. Positively selected amino acid sites were also identified in the envelope protein of human immunodeficiency virus and the influenza virus hemagglutinin protein. This method may be helpful for predicting functions of amino acid sites in proteins, especially in the present situation, in which sequence data are accumulating at an enormous speed.     

Codon Substitution in Evolution and the "Saturation" of Synonymous Changes

A mathematical model for codon substitution is presented, taking into account unequal mutation rates among different nucleotides and purifying selection. This model is constructed by using a 61 X 61 transition probability matrix for the 61 nonterminating codons. Under this model, a computer simulation is conducted to study the numbers of silent (synonymous) and amino acid-altering (nonsynonymous) nucleotide substitutions when the underlying mutation rates among the four kinds of nucleotides are not equal. It is assumed that the substitution rates are constant over evolutionary time, the codon frequencies being in equilibrium, and, thus, the numbers of synonymous and nonsynonymous substitutions both increase linearly with evolutionary time. It is shown that, when the mutation rates are not equal, the estimate of synonymous substitutions obtained by F. Perler, A. Efstratiadis, P. Lomedico, W. Gilbert, R. Kolodner and J. Dodgson's "Percent Corrected Divergence" method increases nonlinearly, although the true number of synonymous substitutions increases linearly. It is, therefore, possible that the "saturation" of synonymous substitutions observed by Perler et al. is due to the inefficiency of their method to detect all synonymous substitutions.     

Synonymous Substitutions in the Xdh Gene of Drosophila: Heterogeneous Distribution along the Coding Region

The Xdh (rosy) region of Drosophila subobscura has been sequenced and compared to the homologous region of D. pseudoobscura and D. melanogaster. Estimates of the numbers of synonymous substitutions per site (Ks) confirm that Xdh has a high synonymous substitution rate. The distributions of both nonsynonymous and synonymous substitutions along the coding region were found to be heterogeneous. Also, no relationship has been detected between Ks estimates and codon usage bias along the gene, in contrast with the generally observed relationship among genes. This heterogeneous distribution of synonymous substitutions along the Xdh gene, which is expression-level independent, could be explained by a differential selection pressure on synonymous sites along the coding region acting on mRNA secondary structure. The synonymous rate in the Xdh coding region is lower in the D. subobscura than in the D. pseudoobscura lineage, whereas the reverse is true for the Adh gene.     

Molecular considerations in the evolution of bacterial genes

Summary Synonymous and nonsynonymous substitution rates at the loci encoding glyceraldehyde-3-phosphate dehydrogenase (gap) and outer membrane protein 3A (ompA) were examined in 12 species of enteric bacteria. By examining homologous sequences in species of varying degrees of relatedness and of known phylogenetic relationships, we analyzed the patterns of synonymous and nonsynonymous substitutions within and among these genes. Although both loci accumulate synonymous substitutions at reduced rates due to codon usage bias, portions of thegap andompA reading frames show significant deviation in synonymous substitution rates not attributable to local codon bias. A paucity of synonymous substitutions in portions of theompA gene may reflect selection for a novel mRNA secondary structure. In addition, these studies allow comparisons of homologous protein-coding sequences (gap) in plants, animals, and bacteria, revealing differences in evolutionary constraints on this glycolytic enzyme in these lineages.     

Evolution of Rh Blood Group Genes Have Experienced Gene Conversions and Positive Selection

There are two tightly linked loci (D and CE) for the human Rh blood group. Their gene products are membrane proteins having 12 transmembrane domains and form a complex with Rh50 glycoprotein on erythrocytes. We constructed phylogenetic networks of human and nonhuman primate Rh genes, and the network patterns suggested the occurrences of gene conversions. We therefore used a modified site-by-site reconstruction method by using two assumed gene trees and detected 9 or 11 converted regions. After eliminating the effect of gene conversions, we estimated numbers of nonsynonymous and synonymous substitutions for each branch of both trees. Whichever gene tree we selected the branch connecting hominoids and Old World monkeys showed significantly higher nonsynonymous than synonymous substitutions, an indication of positive selection. Many other branches also showed higher nonsynonymous than synonymous substitutions; this suggests that the Rh genes have experienced some kind of positive selection. Received: 16 March 1999 / Accepted: 17 June 1999     

Substitution rates in Drosophila nuclear genes: implications for translational selection

The relationships between synonymous and nonsynonymous substitution rates and between synonymous rate and codon usage bias are important to our understanding of the roles of mutation and selection in the evolution of Drosophila genes. Previous studies used approximate estimation methods that ignore codon bias. In this study we reexamine those relationships using maximum-likelihood methods to estimate substitution rates, which accommodate the transition/transversion rate bias and codon usage bias. We compiled a sample of homologous DNA sequences at 83 nuclear loci from Drosophila melanogaster and at least one other species of Drosophila. Our analysis was consistent with previous studies in finding that synonymous rates were positively correlated with nonsynonymous rates. Our analysis differed from previous studies, however, in that synonymous rates were unrelated to codon bias. We therefore conducted a simulation study to investigate the differences between approaches. The results suggested that failure to properly account for multiple substitutions at the same site and for biased codon usage by approximate methods can lead to an artifactual correlation between synonymous rate and codon bias. Implications of the results for translational selection are discussed.     

Comparison of three methods for estimating rates of synonymous and nonsynonymous nucleotide substitutions

Three frequently used methods for estimating the synonymous and nonsynonymous substitution rates (Ks and Ka) were evaluated and compared for their accuracies; these methods are denoted by LWL85, LPB93, and GY94, respectively. For this purpose, we used a codon-evolution model to obtain the expected Ka and Ks values for the above three methods and compared the values with those obtained by the three methods. We also proposed some modifications of LWL85 and LPB93 to increase their accuracies. Our computer simulations under the codon-evolution model showed that for sequences < or =300 codons, the performance of GY94 may not be reliable. For longer sequences, GY94 is more accurate for estimating the Ka/Ks ratio than the modified LPB93 and LWL85 in the majority of the cases studied. This is particularly so when k > or = 3, which is the transition/transversion (mutation) rate ratio. However, when k is approximately 2 and when the sequence divergence is relatively large, the modified LWL85 performed better than GY94 and the modified LPB93. The inferiority of LPB93 to LWL85 is surprising because LPB93 was intended to improve LWL85. Also, it has been thought that the codon-based method of GY94 is better than the heuristic method of LWL85, but our simulation results showed that in many cases, the opposite was true, even though our simulation was based on the codon-evolution model.     

ADAPTSITE: detecting natural selection at single amino acid sites.

ADAPTSITE is a program package for detecting natural selection at single amino acid sites, using a multiple alignment of protein-coding sequences for a given phylogenetic tree. The program infers ancestral codons at all interior nodes, and computes the total numbers of synonymous (c(S)) and nonsynonymous (c(N)) substitutions as well as the average numbers of synonymous (s(S)) and nonsynonymous (s(N)) sites for each codon site. The probabilities of occurrence of synonymous and nonsynonymous substitutions are approximated by s(S) / (s(S) + s(N)) and s(N) / (s(S) + s(N)), respectively. The null hypothesis of selective neutrality is tested for each codon site, assuming a binomial distribution for the probability of obtaining c(S) and c(N). AVAILABILITY: ADAPTSITE is available free of charge at the World-Wide Web sites http://mep.bio.psu.edu/adaptivevol.html and http://www.cib.nig.ac.jp/dda/yossuzuk/welcome.html. The package includes the source code written in C, binary files for UNIX operating systems, manual, and example files.     

Variance and covariances of the numbers of synonymous and nonsynonymous substitutions per site

Nei and Gojobori (1986) developed a simple method to estimate the numbers of synonymous (ds) and nonsynonymous (dN) substitutions per site. In the present paper, we have developed a method for computing variances and covariances of ds's and dN's and of the proportions of synonymous (ps) and nonsynonymous (pN) differences. We also have developed a method for computing the variances of mean dS, dN, pS, pN, without constructing a phylogenetic tree of the genes. We have conducted computer simulations based on simple evolutionary models and have shown that the new method gives good estimates of variances and covariances.      

Rates of Conservative and Radical Nonsynonymous Nucleotide Substitutions in Mammalian Nuclear Genes

To understand the process and mechanism of protein evolution, it is important to know what types of amino acid substitutions are more likely to be under selection and what types are mostly neutral. An amino acid substitution can be classified as either conservative or radical, depending on whether it involves a change in a certain physicochemical property of the amino acid. Assuming Kimura's two-parameter model of nucleotide substitution, I present a method for computing the numbers of conservative and radical nonsynonymous (amino acid altering) nucleotide substitutions per site and estimate these rates for 47 nuclear genes from mammals. The results are as follows. (1) The average radical/conservative rate ratio is 0.81 for charge changes, 0.85 for polarity changes, and 0.49 when both polarity and volume changes are considered. (2) The radical/conservative rate ratio is positively correlated with the nonsynonymous/synonymous rate ratio for charge changes or when both polarity and volume changes are considered. (3) Both the conservative/synonymous rate ratio and the radical/synonymous rate ratio are lower in the rodent lineage than in the primate or artiodactyl lineage, suggesting more intense purifying selection in the rodent lineage, for both conservative and radical nonsynonymous substitutions. (4) Neglecting transition/transversion bias would cause an underestimation of both radical and conservative rates and the ratio thereof. (5) Transversions induce more dramatic genetic alternations than transitions in that transversions produce more amino acid altering changes and among which, more radical changes. Received: 6 April 1999 / Accepted: 16 August 1999     

Synonymous and nonsynonymous substitutions in mammalian genes and the nearly neutral theory

The nearly neutral theory of molecular evolution predicts larger generation-time effects for synonymous than for nonsynonymous substitutions. This prediction is tested using the sequences of 49 single-copy genes by calculating the average and variance of synonymous and nonsynonymous substitutions in mammalian star phylogenies (rodentia, artiodactyla, and primates). The average pattern of the 49 genes supports the prediction of the nearly neutral theory, with some notable exceptions.The nearly neutral theory also predicts that the variance of the evolutionary rate is larger than the value predicted by the completely neutral theory. This prediction is tested by examining the dispersion index (ratio of the variance to the mean), which is positively correlated with the average substitution number. After weighting by the lineage effects, this correlation almost disappears for nonsynonymous substitutions, but not quite so for synonymous substitutions. After weighting, the dispersion indices of both synonymous and nonsynonymous substitutions still exceed values expected under the simple Poisson process. The results indicate that both the systematic bias in evolutionary rate among the lineages and the episodic type of rate variation are contributing to the large variance. The former is more significant to synonymous substitutions than to nonsynonymous substitutions. Isochore evolution may be similar to synonymous substitutions. The rate and pattern found here are consistent with the nearly neutral theory, such that the relative contributions of drift and selection differ between the two types of substitutions. The results are also consistent with Gillespie's episodic selection theory.     

Genome-wide patterns of nucleotide substitution reveal stringent functional constraints on the protein sequences of thermophiles

To test the hypothesis that the proteins of thermophilic prokaryotes are subject to unusually stringent functional constraints, we estimated the numbers of synonymous and nonsynonymous nucleotide substitutions per site between 17,957 pairs of orthologous genes from 22 pairs of closely related species of Archaea and Bacteria. The average ratio of nonsynonymous to synonymous substitutions was significantly lower in thermophiles than in nonthermophiles, and this effect was observed in both Archaea and Bacteria. There was no evidence that this difference could be explained by factors such as nucleotide content bias. Rather, the results support the hypothesis that proteins of thermophiles are subject to unusually strong purifying selection, leading to a reduced overall level of amino acid evolution per mutational event. The results show that genome-wide patterns of sequence evolution can be influenced by natural selection exerted by a species' environment and shed light on a previous observation that relatively few of the mutations arising in a thermophilic archaeon were nucleotide substitutions in contrast to indels.     

Founder virus population related to route of virus transmission: a determinant of intrahost human immunodeficiency virus type 1 evolution?

We and others have shown that in individual human immunodeficiency virus type 1 (HIV-1) infection, the adaptive evolution of HIV-1 is influenced by host immune competence. In this study, we tested the hypothesis that in addition to selective forces operating within the host, transmission bottlenecks have an impact on HIV-1 intrahost evolution. Therefore, we studied the intrahost evolution of the V3 region of the external glycoprotein gp120 of HIV-1 during the 3- and 5-year periods following seroconversion after parenteral versus sexual (male-to-male) transmission in 41 participants of the Amsterdam prospective cohorts of homosexual men (n = 31) and intravenous drug users (IVDUs; n = 10) who were AIDS free and had comparable numbers of CD4+ cells. We observed that HIV-1 strains in homosexual men accumulated over 5 years more nonsynonymous substitutions within the V3 loop than HIV-1 strains in IVDUs as a result of lower rates of nonsynonymous evolution in both the initial 3-year period from seroconversion and the following 2-year period as well as a larger proportion of nonsynonymous back substitutions in IVDUs. The mean numbers of synonymous substitutions did not differ between the two risk groups. Since HIV-1 strains in IVDUs could be distinguished from the viruses of homosexual men based on several nucleotide substitutions of which the most conserved is a synonymous substitution at the tip of the V3 loop (GGC pattern), we studied whether the founder virus population itself has an impact on the intrahost evolution of HIV-1. The mean number of nonsynonymous substitutions accumulated over 5 years within the V3 loop was lower in 10 IVDUs infected by the HIV-1 strains with the GGC signature than in 4 IVDUs infected by HIV-1 strains lacking this pattern, while the mean numbers of synonymous substitutions were similar in the two groups.