Overdispersion of the molecular clock varies between yeast, Drosophila and mammals

Although protein evolution can be approximated as a "molecular evolutionary clock," it is well known that sequence change departs from a clock-like Poisson expectation. Through studying the deviations from a molecular clock, insight can be gained into the forces shaping evolution at the level of proteins. Generally, substitution patterns that show greater variance than the Poisson expectation are said to be "overdispersed." Overdispersion of sequence change may result from temporal variation in the rate at which amino acid substitutions occur on a phylogeny. By comparing the genomes of four species of yeast, five species of Drosophila, and five species of mammals, we show that the extent of overdispersion shows a strong negative correlation with the effective population size of these organisms. Yeast proteins show very little overdispersion, while mammalian proteins show substantial overdispersion. Additionally, X-linked genes, which have reduced effective population size, have gene products that show increased overdispersion in both Drosophila and mammals. Our research suggests that mutational robustness is more pervasive in organisms with large population sizes and that robustness acts to stabilize the molecular evolutionary clock of sequence change.     

Modeling amino acid substitution patterns in orthologous and paralogous genes

We study to what degree patterns of amino acid substitution vary between genes using two models of protein-coding gene evolution. The first divides the amino acids into groups, with one substitution rate for pairs of residues in the same group and a second for those in differing groups. Unlike previous applications of this model, the groups themselves are estimated from data by simulated annealing. The second model makes substitution rates a function of the physical and chemical similarity between two residues. Because we model the evolution of coding DNA sequences as opposed to protein sequences, artifacts arising from the differing numbers of nucleotide substitutions required to bring about various amino acid substitutions are avoided. Using 10 alignments of related sequences (five of orthologous genes and five gene families), we do find differences in substitution patterns. We also find that, although patterns of amino acid substitution vary temporally within the history of a gene, variation is not greater in paralogous than in orthologous genes. Improved understanding of such gene-specific variation in substitution patterns may have implications for applications such as sequence alignment and phylogenetic inference.     

Partitioning the variation in mammalian substitution rates

We have used analysis of variance to partition the variation in synonymous and amino acid substitution rates between three effects (gene, lineage, and a gene-by-lineage interaction) in mammalian nuclear and mitochondrial genes. We find that gene effects are stronger for amino acid substitution rates than for synonymous substitution rates and that lineage effects are stronger for synonymous substitution rates than for amino acid substitution rates. Gene-by-lineage interactions, equivalent to overdispersion corrected for lineage effects, are found in amino acid substitutions but not in synonymous substitutions. The variance in the ratio of amino acid and synonymous substitution rates is dominated by gene effects, but there is also a significant gene-by-lineage interaction.     

Statistical models of the overdispersed molecular clock

The most commonly used statistical model to describe the rate constancy of molecular evolution (molecular clock) is a simple Poisson process in which the variance of the number of amino acid or nucleotide substitutions in a particular gene should be equal to the mean and henceforth the dispersion index, the ratio of the variance to the mean, should be equal to one. Recent sequence data, however, have shown that the substitutional process in molecular evolution is often considerably overdispersed and have called into question the generality of using a simple Poisson process. Several efforts have been made to develop more realistic models of molecular evolution. In this paper, I will show that the spatial (site-specific) variation in the rate of molecular evolution is an improbable cause of the overdispersion and then review various statistical models which take the temporal variation into account. Although these models do not immediately specify what the mechanisms of molecular evolution might be, they do make qualitatively different predictions and give some insight into their inference. One way to distinguish them is suggested. In addition, effects of selected substitutions that presumably occur after a major change in a molecule are quasi-quantitatively examined. It is most likely that the overdispersion of molecular clock is due either to a major molecular reconfiguration (fluctuating neutral space) led by a series of subliminal neutral changes or to selected substitutions fine-tuning a molecule after a major molecular change. Although the latter possibility, of course, violates the simplest neutrality assumption, it would not impair the neutral theory as a whole.     

An empirical examination of the utility of codon-substitution models in phylogeny reconstruction

Models of codon substitution have been commonly used to compare protein-coding DNA sequences and are particularly effective in detecting signals of natural selection acting on the protein. Their utility in reconstructing molecular phylogenies and in dating species divergences has not been explored. Codon models naturally accommodate synonymous and nonsynonymous substitutions, which occur at very different rates and may be informative for recent and ancient divergences, respectively. Thus codon models may be expected to make an efficient use of phylogenetic information in protein-coding DNA sequences. Here we applied codon models to 106 protein-coding genes from eight yeast species to reconstruct phylogenies using the maximum likelihood method, in comparison with nucleotide- and amino acid-based analyses. The results appeared to confirm that expectation. Nucleotide-based analysis, under simplistic substitution models, were efficient in recovering recent divergences whereas amino acid-based analysis performed better at recovering deep divergences. Codon models appeared to combine the advantages of amino acid and nucleotide data and had good performance at recovering both recent and deep divergences. Estimation of relative species divergence times using amino acid and codon models suggested that translation of gene sequences into proteins led to information loss of from 30% for deep nodes to 66% for recent nodes. Although computational burden makes codon models unfeasible for tree search in large data sets, we suggest that they may be useful for comparing candidate trees. Nucleotide models that accommodate the differences in evolutionary dynamics at the three codon positions also performed well, at much less computational cost. We discuss the relationship between a model's fit to data and its utility in phylogeny reconstruction and caution against use of overly complex substitution models.     

Substitution bias, rapid saturation, and the use of mtDNA for nematode systematics

Only relatively recently have researchers turned to molecular methods for nematode phylogeny reconstruction. Thus, we lack the extensive literature on evolutionary patterns and phylogenetic usefulness of different DNA regions for nematodes that exists for other taxa. Here, we examine the usefulness of mtDNA for nematode phylogeny reconstruction and provide data that can be used for a priori character weighting or for parameter specification in models of sequence evolution. We estimated the substitution pattern for the mitochondrial ND4 gene from intraspecific comparisons in four species of parasitic nematodes from the family Trichostrongylidae (38-50 sequences per species). The resulting pattern suggests a strong mutational bias toward A and T, and a lower transition/transversion ratio than is typically observed in other taxa. We also present information on the relative rates of substitution at first, second, and third codon positions and on relative rates of saturation of different types of substitutions in comparisons ranging from intraspecific to interordinal. Silent sites saturate extremely quickly, presumably owing to the substitution bias and, perhaps, to an accelerated mutation rate. Results emphasize the importance of using only the most closely related sequences in order to infer patterns of substitution accurately for nematodes or for other taxa having strongly composition-biased DNA. ND4 also shows high amino acid polymorphism at both the intra- and interspecific levels, and in higher level comparisons, there is evidence of saturation at variable amino acid sites. In general, we recommend using mtDNA coding genes only for phylogenetics of relatively closely related nematode species and, even then, using only nonsynonymous substitutions and the more conserved mitochondrial genes (e.g., cytochrome oxidases). On the other hand, the high substitution rate in genes such as ND4 should make them excellent for population genetics studies, identifying cryptic species, and resolving relationships among closely related congeners when other markers show insufficient variation.      

Models of amino acid substitution and applications to mitochondrial protein evolution

Models of amino acid substitution were developed and compared using maximum likelihood. Two kinds of models are considered. "Empirical" models do not explicitly consider factors that shape protein evolution, but attempt to summarize the substitution pattern from large quantities of real data. "Mechanistic" models are formulated at the codon level and separate mutational biases at the nucleotide level from selective constraints at the amino acid level. They account for features of sequence evolution, such as transition-transversion bias and base or codon frequency biases, and make use of physicochemical distances between amino acids to specify nonsynonymous substitution rates. A general approach is presented that transforms a Markov model of codon substitution into a model of amino acid replacement. Protein sequences from the entire mitochondrial genomes of 20 mammalian species were analyzed using different models. The mechanistic models were found to fit the data better than empirical models derived from large databases. Both the mutational distance between amino acids (determined by the genetic code and mutational biases such as the transition-transversion bias) and the physicochemical distance are found to have strong effects on amino acid substitution rates. A significant proportion of amino acid substitutions appeared to have involved more than one codon position, indicating that nucleotide substitutions at neighboring sites may be correlated. Rates of amino acid substitution were found to be highly variable among sites.      

Estimation of DNA Sequence Context-dependent Mutation Rates Using Primate Genomic Sequences

It is understood that DNA and amino acid substitution rates are highly sequence context-dependent, e.g., C --> T substitutions in vertebrates may occur much more frequently at CpG sites and that cysteine substitution rates may depend on support of the context for participation in a disulfide bond. Furthermore, many applications rely on quantitative models of nucleotide or amino acid substitution, including phylogenetic inference and identification of amino acid sequence positions involved in functional specificity. We describe quantification of the context dependence of nucleotide substitution rates using baboon, chimpanzee, and human genomic sequence data generated by the NISC Comparative Sequencing Program. Relative mutation rates are reported for the 96 classes of mutations of the form 5' alphabetagamma 3' --> 5' alphadeltagamma 3', where alpha, beta, gamma, and delta are nucleotides and beta not equal delta, based on maximum likelihood calculations. Our results confirm that C --> T substitutions are enhanced at CpG sites compared with other transitions, relatively independent of the identity of the preceding nucleotide. While, as expected, transitions generally occur more frequently than transversions, we find that the most frequent transversions involve the C at CpG sites (CpG transversions) and that their rate is comparable to the rate of transitions at non-CpG sites. A four-class model of the rates of context-dependent evolution of primate DNA sequences, CpG transitions > non-CpG transitions approximately CpG transversions > non-CpG transversions, captures qualitative features of the mutation spectrum. We find that despite qualitative similarity of mutation rates among different genomic regions, there are statistically significant differences.     

Advantages of a mechanistic codon substitution model for evolutionary analysis of protein-coding sequences

BACKGROUND: A mechanistic codon substitution model, in which each codon substitution rate is proportional to the product of a codon mutation rate and the average fixation probability depending on the type of amino acid replacement, has advantages over nucleotide, amino acid, and empirical codon substitution models in evolutionary analysis of protein-coding sequences. It can approximate a wide range of codon substitution processes. If no selection pressure on amino acids is taken into account, it will become equivalent to a nucleotide substitution model. If mutation rates are assumed not to depend on the codon type, then it will become essentially equivalent to an amino acid substitution model. Mutation at the nucleotide level and selection at the amino acid level can be separately evaluated. RESULTS: The present scheme for single nucleotide mutations is equivalent to the general time-reversible model, but multiple nucleotide changes in infinitesimal time are allowed. Selective constraints on the respective types of amino acid replacements are tailored to each gene in a linear function of a given estimate of selective constraints. Their good estimates are those calculated by maximizing the respective likelihoods of empirical amino acid or codon substitution frequency matrices. Akaike and Bayesian information criteria indicate that the present model performs far better than the other substitution models for all five phylogenetic trees of highly-divergent to highly-homologous sequences of chloroplast, mitochondrial, and nuclear genes. It is also shown that multiple nucleotide changes in infinitesimal time are significant in long branches, although they may be caused by compensatory substitutions or other mechanisms. The variation of selective constraint over sites fits the datasets significantly better than variable mutation rates, except for 10 slow-evolving nuclear genes of 10 mammals. An critical finding for phylogenetic analysis is that assuming variable mutation rates over sites lead to the overestimation of branch lengths.     

Evolution of the cytochromeb gene of mammals

Summary With the polymerase chain reaction (PCR) and versatile primers that amplify the whole cytochromeb gene (∼ 1140 bp), we obtained 17 complete gene sequences representing three orders of hoofed mammals (ungulates) and dolphins (cetaceans). The fossil record of some ungulate lineages allowed estimation of the evolutionary rates for various components of the cytochromeb DNA and amino acid sequences. The relative rates of substitution at first, second, and third positions within codons are in the ratio 10 to 1 to at least 33. For deep divergences (>5 million years) it appears that both replacements and silent transversions in this mitochondrial gene can be used for phylogenetic inference. Phylogenetic findings include the association of (1) cetaceans, artiodactyls, and perissodactyls to the exclusion of elephants and humans, (2) pronghorn and fallow deer to the exclusion of bovids (i. e., cow, sheep, and goat), (3) sheep and goat to the exclusion of other pecorans (i. e., cow, giraffe, deer, and pronghorn), and (4) advanced ruminants to the exclusion of the chevrotain and other artiodactyls. Comparisons of these cytochromeb sequences support current structure-function models for this membrane-spanning protein. That part of the outer surface which includes the Q_o redox center is more constrained than the remainder of the molecule, namely, the transmembrane segments and the surface that protrudes into the mitochondrial matrix. Many of the amino acid replacements within the transmembrane segments are exchanges between hydrophobic residues (especially leucine, isoleucine, and valine). Replacement changes at first and second positions of codons approximate a negative binomial distribution, similar to other protein-coding sequences. At four-fold degenerate positions of codons, the nucleotide substitutions approximate a Poisson distribution, implying that the underlying mutational spectrum is random with respect to position.     

Hotspots of Biased Nucleotide Substitutions in Human Genes

Genes that have experienced accelerated evolutionary rates on the human lineage during recent evolution are candidates for involvement in human-specific adaptations. To determine the forces that cause increased evolutionary rates in certain genes, we analyzed alignments of 10,238 human genes to their orthologues in chimpanzee and macaque. Using a likelihood ratio test, we identified protein-coding sequences with an accelerated rate of base substitutions along the human lineage. Exons evolving at a fast rate in humans have a significant tendency to contain clusters of AT-to-GC (weak-to-strong) biased substitutions. This pattern is also observed in noncoding sequence flanking rapidly evolving exons. Accelerated exons occur in regions with elevated male recombination rates and exhibit an excess of nonsynonymous substitutions relative to the genomic average. We next analyzed genes with significantly elevated ratios of nonsynonymous to synonymous rates of base substitution (d_N/d_S) along the human lineage, and those with an excess of amino acid replacement substitutions relative to human polymorphism. These genes also show evidence of clusters of weak-to-strong biased substitutions. These findings indicate that a recombination-associated process, such as biased gene conversion (BGC), is driving fixation of GC alleles in the human genome. This process can lead to accelerated evolution in coding sequences and excess amino acid replacement substitutions, thereby generating significant results for tests of positive selection.     

Accelerated Evolution and Molecular Surface of Venom Phospholipase A2 Enzymes

Multiple phospholipase A₂ (PLA₂) isoenzymes found in a single snake venom induce a variety of pharmacological effects. These multiple forms are formed by gene duplication and accelerated evolution of exons. We examined the amino acid sequences of 127 snake venom PLA₂ enzymes and their homologues to study in which location most natural substitutions occur. Our data show that hot spots of amino acid substitutions in this group of proteins occur mostly on the surface. A logistic model correlating the substitution rates of each amino acid residue with their surface accessibility indicates that the probability of natural substitutions occurring in the fully exposed residue is 2.6–3.5 times greater than that of substitutions occurring in buried residues. These surface substitutions play a significant role in the evolution of new PLA₂ isoenzymes by altering the specificity of targeting to various tissues or cells, resulting in distinct pharmacological effects. Thus natural substitutions in PLA₂ enzymes, in contrast to popular belief, are not random substitutions but appear to be directed toward modifying the molecular surface. Received: 11 May 1998 / Accepted: 29 June 1998     

On the Overdispersed Molecular Clock

Rates of molecular evolution at some loci are more irregular than described by simple Poisson processes. Three situations under which molecular evolution would not follow simple Poisson processes are reevaluated from the viewpoint of the neutrality hypothesis: concomitant or multiple substitutions in a gene, fluctuating substitution rates in time caused by coupled effects of deleterious mutations and bottlenecks, and changes in the degree of selective constraints against a gene (neutral space) caused by successive substitutions. The common underlying assumption that these causes are lineage nonspecific excludes the case where mutation rates themselves change systematically among lineages or taxonomic groups, and severely limits the extent of variation in the number of substitutions among lineages. Even under this stringent condition, however, the third hypothesis, the fluctuating neutral space model, can generate fairly large variation. This is described by a time-dependent renewal process, which does not exhibit any episodic nature of molecular evolution. It is argued that the observed elevated variances in the number of nucleotide or amino acid substitutions do not immediately call for positive Darwinian selection in molecular evolution.     

Molecular evolution of a long wavelength-sensitive opsin in mimetic Heliconius butterflies (Lepidoptera: Nymphalidae)

This study examines the pattern of opsin nucleotide and amino acid substitution among mimetic species 'rings' of Heliconius butterflies that are characterized by divergent wing colour patterns. A long wavelength opsin gene, OPS1 , was sequenced from each of seven species of Heliconius and one species of Dryas (Lepidoptera: Nymphalidae). A parsimony analysis of OPS1 nucleotide and amino acid sequences resulted in a phylogeny that was consistent with that presented by Brower & Egan in 1997, which was based on mitochondrial cytochrome oxidase I and II as well as nuclear wingless genes. Nodes in the OPS1 phylogeny were well supported by bootstrap analysis and decay indices. An analysis of specific sites within the gene indicates that the accumulation of amino acid substitutions has occurred independently of the morphological diversification of Heliconius wing colour patterns. Amino acid substitutions were examined with respect to their location within the opsin protein and their possible interactions with the chromophore and the G-protein. Of the 15 amino acid substitutions identified among the eight species, one nonconservative replacement (A226Q) was identified in a position that may be involved in binding with the G-protein.     

Empirical relationship between the number of nucleotide substitutions and interspecific identity of amino acid sequences in some proteins

There are three different methods of estimating the number of nucleotide substitutions between a pair of species from amino acid sequence data, i.e. the Poisson correction method, random evolutionary hit method, and counting the actual but minimum number of nucleotide substitutions. In this paper the relationships among the estimates obtained by these methods are studied empirically. The results obtained indicate that there is a high correlation among these estimates and in practice any of the three methods may be used for constructing evolutionary trees or relating nucleotide substitutions to evolutionary time. The effects of varying rates of nucleotide substition among different sites on the Poisson correction and random evolutionary hit methods are also studied mathematically. It is shown that these two methods are quite insensitive to the variation of the rate of nucleotide substitution.     

V3 loop of the human immunodeficiency virus type 1 Env protein: interpreting sequence variability.

Two different states of human immunodeficiency virus type 1 are apparent in the asymptomatic and late stages of infection. Important determinants associated with these two states have been found within the V3 loop of the viral Env protein. In this study, two large data sets of published V3 sequences were analyzed to identify patterns of sequence variability that would correspond to these two states of the virus. We were especially interested in the pattern of basic amino acid substitutions, since the presence of basic amino acids in V3 has been shown to change virus tropism in cell culture. Four features of the sequence heterogeneity in V3 were observed: (i) approximately 70% of all nonconservative basic substitutions occur at four positions in V3, and V3 sequences with a basic substitution in at least one of these four positions contain approximately 95% of all nonconservative basic substitutions; (ii) substitution patterns within V3 are influenced by the identity of the amino acid at position 25; (iii) sequence polymorphisms account for a significant fraction of uncharged amino acid substitutions at several positions in V3, and sequence heterogeneity other than these polymorphisms is most significant at two positions near the tip of V3; and (iv) sequence heterogeneity in V3 (in addition to the basic amino acid substitutions) is approximately twofold greater in V3 sequences that contain basic amino acid substitutions. By using this sequence analysis, we were able to identify distinct groups of V3 sequences in infected patients that appear to correspond to these two virus states. The identification of these discrete sequence patterns in vivo demonstrates how the V3 sequence can be used as a genetic marker for studying the two states of human immunodeficiency virus type 1.     

Maximum-likelihood analysis of molecular adaptation in abalone sperm lysin reveals variable selective pressures among lineages and sites

Maximum-likelihood models of codon substitution were used to analyze sperm lysin genes of 25 abalone (HALIOTIS:) species to identify lineages and amino acid sites under diversifying selection. The models used the nonsynonymous/synonymous rate ratio (omega = d(N)/d(S)) as an indicator of selective pressure and allowed the ratio to vary among lineages or sites. Likelihood ratio tests suggested significant variation in selective pressure among lineages. The variable selective pressure provided an explanation for the previous observation that the omega ratio is >1 in comparisons of closely related species and <1 in comparisons of distantly related species. Computer simulations demonstrated that saturation of nonsynonymous substitutions and constraint on lysin structure were unlikely to account for the observed pattern. Lineages linking closely related sympatric species appeared to be under diversifying selection, while lineages separating distantly related species from different geographic locations were associated with low evolutionary rates. The selective pressure indicated by the omega ratio was found to vary greatly among amino acid sites in lysin. Sites under potential diversifying selection were identified. Ancestral lysins were inferred to trace the route of evolution at individual sites and to provide lysin sequences for future laboratory studies.     

Variation in salmonid mitochondrial DNA: Evolutioinary constraints and mechanisms of substitution

Summary Sequence comparisons were made from 2214 bp of mitochondrial DNA cloned from six Pacific salmonid species. These sequences include the genes for ATPase subunit 6, cytochrome oxidase subunit 3, NADH dehydrogenase subunit 3, NADH dehydrogenase subunit 4L, tRNA^GLY, and tRNA^ARG. Variation is found at 338 silent and 12 nonsilent positions of protein coding genes and 10 positions in the two tRNA sequences. A single 3-bp length difference was also detected. In all pairwise comparisons the sequence divergence observed in the fragment was higher than that previously predicted by restriction enzyme analysis of the entire molecule. The inferred evolutionary relationship of these species is consistent between methods. The distribution of silent variation shows a complex pattern with greatly reduced variation at the junctions of genes. The variation in the tRNA sequences is concentrated in the DHU loop. The close relationship of these species and extensive sequence analyzed allows for an analysis of the spectrum of substitutions that includes the frequencies of all 12 possible substitutions. The observed spectrum of substitutions is related to potential pathways of spontaneous substitution. The salmonid sequences show an extremely high ratio of silent to replacement substitutions. In addition the amino acid sequences of the four proteins coded in this fragment show a consistently high level of identity with theXenopus sequences. Taken together these data are consistent with a slower rate of amino acid substitution among the cold-blooded vertebrates when compared to mammals.     

Apparent Selection Intensity for the Cytochrome Oxidase Subunit I Gene Varies with Mode of Reproduction in Echinoderms

When most amino acid substitutions in protein-coding genes are slightly deleterious rather than selectively neutral, life history differences can potentially modify the effective population size or the selective regime, resulting in altered ratios of non-synonymous to synonymous substitutions among taxa. We studied substitution patterns for the mitochondrial cytochrome oxidase subunit I (COI) gene in a sea star genus (Leptasterias spp.) with an obligate brood-protecting mode of reproduction and small-scale population genetic subdivision, and compared the results to available COI sequences in nine other genera of echinoderms with pelagic larvae: three sea stars, five sea urchins and one brittle star. We predicted that this life history difference would be associated with differences in the ratio of non-synonymous (dN) to synonymous (dS) substitution rates. Leptasterias had a significantly greater dN/dS ratio (both between species and within species), a significantly smaller transition/transversion rate ratio, and a significantly lower average nucleotide diversity within species, than did the non-brooding genera. Other explanations for the results, such as altered mutation rates or selective sweeps, were not supported by the data analysis. These findings highlight the potential influence of reproductive traits and other life history factors on patterns of nucleotide substitution within and between species.