Protein evolution with dependence among codons due to tertiary structure

Markovian models of protein evolution that relax the assumption of independent change among codons are considered. With this comparatively realistic framework, an evolutionary rate at a site can depend both on the state of the site and on the states of surrounding sites. By allowing a relatively general dependence structure among sites, models of evolution can reflect attributes of tertiary structure. To quantify the impact of protein structure on protein evolution, we analyze protein-coding DNA sequence pairs with an evolutionary model that incorporates effects of solvent accessibility and pairwise interactions among amino acid residues. By explicitly considering the relationship between nonsynonymous substitution rates and protein structure, this approach can lead to refined detection and characterization of positive selection. Analyses of simulated sequence pairs indicate that parameters in this evolutionary model can be well estimated. Analyses of lysozyme c and annexin V sequence pairs yield the biologically reasonable result that amino acid replacement rates are higher when the replacements lead to energetically favorable proteins than when they destabilize the proteins. Although the focus here is evolutionary dependence among codons that is associated with protein structure, the statistical approach is quite general and could be applied to diverse cases of evolutionary dependence where surrogates for sequence fitness can be measured or modeled.     

A likelihood approach for comparing synonymous and nonsynonymous nucleotide substitution rates, with application to the chloroplast genome

A model of DNA sequence evolution applicable to coding regions is presented. This represents the first evolutionary model that accounts for dependencies among nucleotides within a codon. The model uses the codon, as opposed to the nucleotide, as the unit of evolution, and is parameterized in terms of synonymous and nonsynonymous nucleotide substitution rates. One of the model's advantages over those used in methods for estimating synonymous and nonsynonymous substitution rates is that it completely corrects for multiple hits at a codon, rather than taking a parsimony approach and considering only pathways of minimum change between homologous codons. Likelihood-ratio versions of the relative-rate test are constructed and applied to data from the complete chloroplast DNA sequences of Oryza sativa, Nicotiana tabacum, and Marchantia polymorpha. Results of these tests confirm previous findings that substitution rates in the chloroplast genome are subject to both lineage-specific and locus-specific effects. Additionally, the new tests suggest tha the rate heterogeneity is due primarily to differences in nonsynonymous substitution rates. Simulations help confirm previous suggestions that silent sites are saturated, leaving no evidence of heterogeneity in synonymous substitution rates.      

A Space-Time Process Model for the Evolution of DNA Sequences

We describe a model for the evolution of DNA sequences by nucleotide substitution, whereby nucleotide sites in the sequence evolve over time, whereas the rates of substitution are variable and correlated over sites. The temporal process used to describe substitutions between nucleotides is a continuous-time Markov process, with the four nucleotides as the states. The spatial process used to describe variation and dependence of substitution rates over sites is based on a serially correlated gamma distribution, i.e., an auto-gamma model assuming Markov-dependence of rates at adjacent sites. To achieve computational efficiency, we use several equal-probability categories to approximate the gamma distribution, and the result is an auto-discrete-gamma model for rates over sites. Correlation of rates at sites then is modeled by the Markov chain transition of rates at adjacent sites from one rate category to another, the states of the chain being the rate categories. Two versions of nonparametric models, which place no restrictions on the distributional forms of rates for sites, also are considered, assuming either independence or Markov dependence. The models are applied to data of a segment of mitochondrial genome from nine primate species. Model parameters are estimated by the maximum likelihood method, and models are compared by the likelihood ratio test. Tremendous variation of rates among sites in the sequence is revealed by the analyses, and when rate differences for different codon positions are appropriately accounted for in the models, substitution rates at adjacent sites are found to be strongly (positively) correlated. Robustness of the results to uncertainty of the phylogenetic tree linking the species is examined.     

Molecular evolution of the hepatitis B virus genome

The hepatitis B virus (HBV) has a circular DNA genome of about 3,200 base pairs. Economical use of the genome with overlapping reading frames may have led to severe constraints on nucleotide substitutions along the genome and to highly variable rates of substitution among nucleotide sites. Nucleotide sequences from 13 complete HBV genomes were compared to examine such variability of substitution rates among sites and to examine the phylogenetic relationships among the HBV variants. The maximum likelihood method was employed to fit models of DNA sequence evolution that can account for the complexity of the pattern of nucleotide substitution. Comparison of the models suggests that the rates of substitution are different in different genes and codon positions; for example, the third codon position changes at a rate over ten times higher than the second position. Furthermore, substantial variation of substitution rates was detected even after the effects of genes and codon positions were corrected; that is, rates are different at different sites of the same gene or at the same codon position. Such rates after the correction were also found to be positively correlated at adjacent sites, which indicated the existence of conserved and variable domains in the proteins encoded by the viral genome. A multiparameter model validates the earlier finding that the variation in nucleotide conservation is not random around the HBV genome. The test for the existence of a molecular clock suggests that substitution rates are more or less constant among lineages. The phylogenetic relationships among the viral variants were examined. Although the data do not seem to contain sufficient information to resolve the details of the phylogeny, it appears quite certain that the serotypes of the viral variants do not reflect their genetic relatedness. Correspondence to: Z. Yang     

A population genetic model of selection that maintains specific trinucleotides at a specific location

Summary Periodic appearances of specific trinucleotides along the DNA sequence have been reported in the chicken core DNA and the phenomenon has been suggested to be related to the supercoiling of DNA around nucleosomes. A population genetic model is constructed in which selection is operating to maintain specific trinucleotides at a specific location on the DNA sequence. Assuming low mutation rates, equilibrium probabilities of the appearances of respective trinucleotides were computed. Vague patterns appeared if the product of the effective size and the selection coefficient was 0.1–2.0. The genetic load and substitution rates in the equilibrium state were also computed. When the model was applied to the chicken DNA data, the product of the effective size and the selection coefficient was estimated to be 0.1–0.2. With this intensity of selection, the substitution rate was hardly different from that in the case without selection. However, the genetic load became fairly large. Considering the large number of times that DNA coils about nucleosomes, the number of trinucleotide sites must be very large, and thus the total load might be too large. Epistasis among these sites to reduce the total load is suggested to exist if selection is responsible for this periodic pattern observed in the chicken core DNA.     

The impact of the nucleosome code on protein-coding sequence evolution in yeast

Coding sequence evolution was once thought to be the result of selection on optimal protein function alone. Selection can, however, also act at the RNA level, for example, to facilitate rapid translation or ensure correct splicing. Here, we ask whether the way DNA works also imposes constraints on coding sequence evolution. We identify nucleosome positioning as a likely candidate to set up such a DNA-level selective regime and use high-resolution microarray data in yeast to compare the evolution of coding sequence bound to or free from nucleosomes. Controlling for gene expression and intra-gene location, we find a nucleosome-free "linker" sequence to evolve on average 5-6% slower at synonymous sites. A reduced rate of evolution in linker is especially evident at the 5' end of genes, where the effect extends to non-synonymous substitution rates. This is consistent with regular nucleosome architecture in this region being important in the context of gene expression control. As predicted, codons likely to generate a sequence unfavourable to nucleosome formation are enriched in linker sequence. Amino acid content is likewise skewed as a function of nucleosome occupancy. We conclude that selection operating on DNA to maintain correct positioning of nucleosomes impacts codon choice, amino acid choice, and synonymous and non-synonymous rates of evolution in coding sequence. The results support the exclusion model for nucleosome positioning and provide an alternative interpretation for runs of rare codons. As the intimate association of histones and DNA is a universal characteristic of genic sequence in eukaryotes, selection on coding sequence composition imposed by nucleosome positioning should be phylogenetically widespread.     

A new method for estimating synonymous and nonsynonymous rates of nucleotide substitution considering the relative likelihood of nucleotide and codon changes

A new method is proposed for estimating the number of synonymous and nonsynonymous nucleotide substitutions between homologous genes. In this method, a nucleotide site is classified as nondegenerate, twofold degenerate, or fourfold degenerate, depending on how often nucleotide substitutions will result in amino acid replacement; nucleotide changes are classified as either transitional or transversional, and changes between codons are assumed to occur with different probabilities, which are determined by their relative frequencies among more than 3,000 changes in mammalian genes. The method is applied to a large number of mammalian genes. The rate of nonsynonymous substitution is extremely variable among genes; it ranges from 0.004 X 10(-9) (histone H4) to 2.80 X 10(-9) (interferon gamma), with a mean of 0.88 X 10(-9) substitutions per nonsynonymous site per year. The rate of synonymous substitution is also variable among genes; the highest rate is three to four times higher than the lowest one, with a mean of 4.7 X 10(-9) substitutions per synonymous site per year. The rate of nucleotide substitution is lowest at nondegenerate sites (the average being 0.94 X 10(-9), intermediate at twofold degenerate sites (2.26 X 10(-9)). and highest at fourfold degenerate sites (4.2 X 10(-9)). The implication of our results for the mechanisms of DNA evolution and that of the relative likelihood of codon interchanges in parsimonious phylogenetic reconstruction are discussed.     

The ratio of replacement to silent divergence and tests of neutrality

Comparisons of replacement to silent divergence have been used in a variety of studies aimed at detecting selection. Here, such comparisons are shown to be very sensitive to the pattern of rate variation in replacement sites. Saturation may play an important role even at surprisingly low levels of divergence if the substitution rate varies across replacement sites. For example, saturation in replacement sites may be of importance in the evolution of the HIV-1 envelope gene. However, the pattern of saturation in replacement and silent sites may, in itself, provide valuable insight into the causes of DNA evolution. 210 DNA sequences from 15 different loci/systematic groups are analyzed, and evidence for positive selection is demonstrated in at least one of these data sets, through an analysis of the distribution of substitution rates along the sequence.     

Modeling the evolution of the human mitochondrial genome.

Mitochondrial DNA data have been used extensively to study evolution and early human origins. These applications require estimates of the rate at which nucleotide substitutions occur in the DNA sequence. We consider the problem of estimating substitution rates in the presence of site-to-site rate variation. A coalescent model is presented that allows for different substitution rates for purines and pyrimidines, as well as more detailed models that allow fast and slow rates within each of the purine and pyrimidine classes. A method for estimating such rates is presented. Even for these simple models of site heterogeneity, there are, typically, insufficient data to obtain reliable estimates of site-specific substitution rates. However, estimates of the average rate across all sites appear to be relatively stable even in the presence of site heterogeneity. Simulations of models with site-to-site variation in mutation rate show that hypervariable sites can produce peaks in the pairwise difference curves that have previously been attributed to population dynamics.     

Identifying site-specific substitution rates

A maximum likelihood framework for estimating site-specific substitution rates is presented that does not require any prior assumptions about the rate distribution. We show that, when the branching pattern of the underlying tree is known, the analysis of pairs of positions is sufficient to estimate site-specific rates. In the abscense of a known topology, we introduce an iterative procedure to estimate simultaneously the branching pattern, the branch lengths, and site-specific substitution rates. Simulations show that the evolutionary rate of fast-evolving sites can be reliably inferred and that the accuracy of rate estimates depends mainly on the number of sequences in the data set. Thus, large sets of aligned sequences are necessary for reliable site-specific rate estimates. The method is applied to the complete mitochondrial DNA sequence of 53 humans, providing a complete picture of the site-specific substitution rates in human mitochondrial DNA.     

The Impact of Modelling Rate Heterogeneity among Sites on Phylogenetic Estimates of Intraspecific Evolutionary Rates and Timescales

Phylogenetic analyses of DNA sequence data can provide estimates of evolutionary rates and timescales. Nearly all phylogenetic methods rely on accurate models of nucleotide substitution. A key feature of molecular evolution is the heterogeneity of substitution rates among sites, which is often modelled using a discrete gamma distribution. A widely used derivative of this is the gamma-invariable mixture model, which assumes that a proportion of sites in the sequence are completely resistant to change, while substitution rates at the remaining sites are gamma-distributed. For data sampled at the intraspecific level, however, biological assumptions involved in the invariable-sites model are commonly violated. We examined the use of these models in analyses of five intraspecific data sets. We show that using 6–10 rate categories for the discrete gamma distribution of rates among sites is sufficient to provide a good approximation of the marginal likelihood. Increasing the number of gamma rate categories did not have a substantial effect on estimates of the substitution rate or coalescence time, unless rates varied strongly among sites in a non-gamma-distributed manner. The assumption of a proportion of invariable sites provided a better approximation of the asymptotic marginal likelihood when the number of gamma categories was small, but had minimal impact on estimates of rates and coalescence times. However, the estimated proportion of invariable sites was highly susceptible to changes in the number of gamma rate categories. The concurrent use of gamma and invariable-site models for intraspecific data is not biologically meaningful and has been challenged on statistical grounds; here we have found that the assumption of a proportion of invariable sites has no obvious impact on Bayesian estimates of rates and timescales from intraspecific data.     

Statistical properties of the branch-site test of positive selection

The branch-site test is a likelihood ratio test to detect positive selection along prespecified lineages on a phylogeny that affects only a subset of codons in a protein-coding gene, with positive selection indicated by accelerated nonsynonymous substitutions (with ω = d(N)/d(S) > 1). This test may have more power than earlier methods, which average nucleotide substitution rates over sites in the protein and/or over branches on the tree. However, a few recent studies questioned the statistical basis of the test and claimed that the test generated too many false positives. In this paper, we examine the null distribution of the test and conduct a computer simulation to examine the false-positive rate and the power of the test. The results suggest that the asymptotic theory is reliable for typical data sets, and indeed in our simulations, the large-sample null distribution was reliable with as few as 20-50 codons in the alignment. We examined the impact of sequence length, the strength of positive selection, and the proportion of sites under positive selection on the power of the branch-site test. We found that the test was far more powerful in detecting episodic positive selection than branch-based tests, which average substitution rates over all codons in the gene and thus miss the signal when most codons are under strong selective constraint. Recent claims of statistical problems with the branch-site test are due to misinterpretations of simulation results. Our results, as well as previous simulation studies that have demonstrated the robustness of the test, suggest that the branch-site test may be a useful tool for detecting episodic positive selection and for generating biological hypotheses for mutation studies and functional analyses. The test is sensitive to sequence and alignment errors and caution should be exercised concerning its use when data quality is in doubt.     

Analysis of the overdispersed clock in the short-term evolution of hepatitis C virus: Using the E1/E2 gene sequences to infer infection dates in a single source outbreak

The assumption of a molecular clock for dating events from sequence information is often frustrated by the presence of heterogeneity among evolutionary rates due, among other factors, to positively selected sites. In this work, our goal is to explore methods to estimate infection dates from sequence analysis. One such method, based on site stripping for clock detection, was proposed to unravel the clocklike molecular evolution in sequences showing high variability of evolutionary rates and in the presence of positive selection. Other alternatives imply accommodating heterogeneity in evolutionary rates at various levels, without eliminating any information from the data. Here we present the analysis of a data set of hepatitis C virus (HCV) sequences from 24 patients infected by a single individual with known dates of infection. We first used a simple criterion of relative substitution rate for site removal prior to a regression analysis. Time was regressed on maximum likelihood pairwise evolutionary distances between the sequences sampled from the source individual and infected patients. We show that it is indeed the fastest evolving sites that disturb the molecular clock and that these sites correspond to positively selected codons. The high computational efficiency of the regression analysis allowed us to compare the site-stripping scheme with random removal of sites. We demonstrate that removing the fast-evolving sites significantly increases the accuracy of estimation of infection times based on a single substitution rate. However, the time-of-infection estimations improved substantially when a more sophisticated and computationally demanding Bayesian method was used. This method was used with the same data set but keeping all the sequence positions in the analysis. Consequently, despite the distortion introduced by positive selection on evolutionary rates, it is possible to obtain quite accurate estimates of infection dates, a result of especial relevance for molecular epidemiology studies.     

Compositional Heterogeneity and Patterns of Molecular Evolution in the Drosophila Genome

The rates and patterns of molecular evolution in many eukaryotic organisms have been shown to be influenced by the compartmentalization of their genomes into fractions of distinct base composition and mutational properties. We have examined the Drosophila genome to explore relationships between the nucleotide content of large chromosomal segments and the base composition and rate of evolution of genes within those segments. Direct determination of the G + C contents of yeast artificial chromosome clones containing inserts of Drosophila melanogaster DNA ranging from 140-340 kb revealed significant heterogeneity in base composition. The G + C content of the large segments studied ranged from 36.9% G + C for a clone containing the hunchback locus in polytene region 85, to 50.9% G + C for a clone that includes the rosy region in polytene region 87. Unlike other organisms, however, there was no significant correlation between the base composition of large chromosomal regions and the base composition at fourfold degenerate nucleotide sites of genes encompassed within those regions. Despite the situation seen in mammals, there was also no significant association between base composition and rate of nucleotide substitution. These results suggest that nucleotide sequence evolution in Drosophila differs from that of many vertebrates and does not reflect distinct mutational biases, as a function of base composition, in different genomic regions. Significant negative correlations between codon-usage bias and rates of synonymous site divergence, however, provide strong support for an argument that selection among alternative codons may be a major contributor to variability in evolutionary rates within Drosophila genomes.     

Substitution rate variation among sites in hypervariable region 1 of human mitochondrial DNA

More than an order of magnitude difference in substitution rate exists among sites within hypervariable region 1 of the control region of human mitochondrial DNA. A two-rate Poisson mixture and a negative binomial distribution are used to describe the distribution of the inferred number of changes per nucleotide site in this region. When three data sets are pooled, however, the two-rate model cannot explain the data. The negative binomial distribution always fits, suggesting that substitution rates are approximately gamma distributed among sites. Simulations presented here provide support for the use of a biased, yet commonly employed, method of examining rate variation. The use of parsimony in the method to infer the number of changes at each site introduces systematic errors into the analysis. These errors preclude an unbiased quantification of variation in substitution rate but make the method conservative overall. The method can be used to distinguish sites with highly elevated rates, and 29 such sites are identified in hypervariable region 1. Variation does not appear to be clustered within this region. Simulations show that biases in rates of substitution among nucleotides and non-uniform base composition can mimic the effects of variation in rate among sites. However, these factors contribute little to the levels of rate variation observed in hypervariable region 1.     

Negative correlation of G+C content at silent substitution sites between orthologous human and mouse protein-coding sequences.

We conducted a genome-wide analysis of variations in guanine plus cytosine (G+C) content at the third codon position at silent substitution sites of orthologous human and mouse protein-coding nucleotide sequences. Alignments of 3776 human protein-coding DNA sequences with mouse orthologs having >50 synonymous codons were analyzed, and nucleotide substitutions were counted by comparing sequences in the alignments extracted from gap-free regions. The G+C content at silent sites in these pairs of genes showed a strong negative correlation (r = -0.93). Some gene pairs showed significant differences in G+C content at the third codon position at silent substitution sites. For example, human thymine-DNA glycosylase was A+T-rich at the silent substitution sites, while the orthologous mouse sequence was G+C-rich at the corresponding sites. In contrast, human matrix metalloproteinase 23B was G+C-rich at silent substitution sites, while the mouse ortholog was A+T-rich. We discuss possible implications of this significant negative correlation of G+C content at silent sites.     

Evolutionary models accounting for layers of selection in protein-coding genes and their impact on the inference of positive selection

The selective forces acting on a protein-coding gene are commonly inferred using evolutionary codon models by contrasting the rate of nonsynonymous substitutions to the rate of synonymous substitutions. These models usually assume that the synonymous substitution rate, Ks, is homogenous across all sites, which is justified if synonymous sites are free from selection. However, a growing body of evidence indicates that the DNA and RNA levels of protein-coding genes are subject to varying degrees of selective constraints due to various biological functions encoded at these levels. In this paper, we develop evolutionary models that account for these layers of selection by allowing for both among-site variability of substitution rates at the DNA/RNA level (which leads to Ks variability among protein-coding sites) and among-site variability of substitution rates at the protein level (Ka variability). These models are constructed so that positive selection is either allowed or not. This enables statistical testing of positive selection when variability at the DNA/RNA substitution rate is accounted for. Using this methodology, we show that variability of the baseline DNA/RNA substitution rate is a widespread phenomenon in coding sequence data of mammalian genomes, most likely reflecting varying degrees of selection at the DNA and RNA levels. Additionally, we use simulations to examine the impact that accounting for the variability of the baseline DNA/RNA substitution rate has on the inference of positive selection. Our results show that ignoring this variability results in a high rate of erroneous positive-selection inference. Our newly developed model, which accounts for this variability, does not suffer from this problem and hence provides a likelihood framework for the inference of positive selection on a background of variability in the baseline DNA/RNA substitution rate.     

Substitution rate variation among sites in mitochondrial hypervariable region I of humans and chimpanzees

Mitochondrial D-loop hypervariable region I (HVI) sequences are widely used in human molecular evolutionary studies, and therefore accurate assessment of rate heterogeneity among sites is essential. We used the maximum-likelihood method to estimate the gamma shape parameter alpha for variable substitution rates among sites for HVI from humans and chimpanzees to provide estimates for future studies. The complete data of 839 humans and 224 chimpanzees, as well as many subsets of these data, were analyzed to examine the effect of sequence sampling. The effects of the genealogical tree and the nucleotide substitution model were also examined. The transition/transversion rate ratio (kappa) is estimated to be about 25, although much larger and biased estimates were also obtained from small data sets at low divergences. Estimates of alpha were 0.28-0.39 for human data sets of different sizes and 0.20-0.39 for data sets including different chimpanzee subspecies. The combined data set of both species gave estimates of 0.42-0.45. While all those estimates suggest highly variable substitution rates among sites, smaller samples tend to give smaller estimates of alpha. Possible causes for this pattern were examined, such as biases in the estimation procedure and shifts in the rate distribution along certain lineages. Computer simulations suggest that the estimation procedure is quite reliable for large trees but can be biased for small samples at low divergences. Thus, an alpha of 0.4 appears suitable for both humans and chimpanzees. Estimates of alpha can be affected by the nucleotide sites included in the data, the overall tree length (the amount of sequence divergence), the number of rate classes used for the estimation, and to a lesser extent, the included sequences. The genealogical tree, the substitution model, and demographic processes such as population expansion do not have much effect.     

Evolutionary change of restriction sites under unequal rates of nucleotide substitution among the three positions of codons

Summary Under the assumption of unequal rates of nucleotide substitution among the three positions of codons, mathematical formulas are derived for the probability that a restriction site observed at time 0 in a DNA sequence will be present at time t, the probability that a new restriction site will emerge at a particular place in two descendant sequences, and the proportion of identical restriction sites between two such sequences. All three quantitites are shown to be larger for the case of unequal rates than for the case of equal rates. As a consequence, estimates of nucleotide divergence (2t) between two sequences based on restriction-site data tend to be lower than the actual values of the assumption of equal rates is made but actually does not hold. However, the degree of underestimation is slight if 2t is 0.10 or smaller. The underestimation can be serious when 2t becomes 0.20 or larger, particularly if the substitution rates at the three codon positions are very different or if transitional substitution occurs more frequently than transversional substitution. The underestimation is more serious for four-base enzymes than for sixbase enzymes.