Variation in evolutionary processes at different codon positions

Evolutionary studies commonly model single nucleotide substitutions and assume that they occur as independent draws from a unique probability distribution across the sequence studied. This assumption is violated for protein-coding sequences, and we consider modeling approaches where codon positions (CPs) are treated as separate categories of sites because within each category the assumption is more reasonable. Such "codon-position" models have been shown to explain the evolution of codon data better than homogenous models in previous studies. This paper examines the ways in which codon-position models outperform homogeneous models and characterizes the differences in estimates of model parameters across CPs. Using the PANDIT database of multiple species DNA sequence alignments, we quantify the differences in the evolutionary processes at the 3 CPs in a systematic and comprehensive manner, characterizing previously undescribed features of protein evolution. We relate our findings to the functional constraints imposed by the genetic code, protein function, and the types of mutation that cause synonymous and nonsynonymous codon changes. The results increase our understanding of selective constraints and could be incorporated into phylogenetic analyses or gene-finding techniques in the future. The methods used are extended to an overlapping reading frame data set, and we discover that overlapping reading frames do not necessarily cause more stringent evolutionary constraints.     

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.      

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     

Rates of molecular evolution: the hominoid slowdown

It is proposed that early in phylogeny a large proportion of amino acid substitutions were selectively neutral, but that bursts of adaptive substitutions during major radiations of life so increased selective constraints that most mutations in modern proteins are detrimental. Recent findings on DNA nucleotide sequences indicate that decreasing mutation rates further slowed the rate of molecular evolution in the lineage to humans.     

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.     

Bayesian analysis of amino acid substitution models

Models of amino acid substitution present challenges beyond those often faced with the analysis of DNA sequences. The alignments of amino acid sequences are often small, whereas the number of parameters to be estimated is potentially large when compared with the number of free parameters for nucleotide substitution models. Most approaches to the analysis of amino acid alignments have focused on the use of fixed amino acid models in which all of the potentially free parameters are fixed to values estimated from a large number of sequences. Often, these fixed amino acid models are specific to a gene or taxonomic group (e.g. the Mtmam model, which has parameters that are specific to mammalian mitochondrial gene sequences). Although the fixed amino acid models succeed in reducing the number of free parameters to be estimated--indeed, they reduce the number of free parameters from approximately 200 to 0--it is possible that none of the currently available fixed amino acid models is appropriate for a specific alignment. Here, we present four approaches to the analysis of amino acid sequences. First, we explore the use of a general time reversible model of amino acid substitution using a Dirichlet prior probability distribution on the 190 exchangeability parameters. Second, we then explore the behaviour of prior probability distributions that are'centred' on the rates specified by the fixed amino acid model. Third, we consider a mixture of fixed amino acid models. Finally, we consider constraints on the exchangeability parameters as partitions,similar to how nucleotide substitution models are specified, and place a Dirichlet process prior model on all the possible partitioning schemes.     

Modeling DNA mutation and recombination for directed evolution experiments

Directed evolution experiments rely on the cyclical application of mutagenesis, screening and amplification in a test tube. They have led to the creation of novel proteins for a wide range of applications. However, directed evolution currently requires an uncertain, typically large, number of labor intensive and expensive experimental cycles before proteins with improved function are identified. This paper introduces predictive models for quantifying the outcome of the experiments aiding in the setup of directed evolution for maximizing the chances of obtaining DNA sequences encoding enzymes with improved activities. Two methods of DNA manipulation are analysed: error-prone PCR and DNA recombination. Error-prone PCR is a DNA replication process that intentionally introduces copying errors by imposing mutagenic reaction conditions. The proposed model calculates the probability of producing a specific nucleotide sequence after a number of PCR cycles. DNA recombination methods rely on the mixing and concatenation of genetic material from a number of parent sequences. This paper focuses on modeling a specific DNA recombination protocol, DNA shuffling. Three aspects of the DNA shuffling procedure are modeled: the fragment size distribution after random fragmentation by DNase I, the assembly of DNA fragments, and the probability of assembling specific sequences or combinations of mutations. Results obtained with the proposed models compare favorably with experimental data.     

Substitution Model of Sequence Evolution for the Human Immunodeficiency Virus Type 1 Subtype B gp120 Gene over the C2-V5 Region

Phylogenetic analyses frequently rely on models of sequence evolution that detail nucleotide substitution rates, nucleotide frequencies, and site-to-site rate heterogeneity. These models can influence hypothesis testing and can affect the accuracy of phylogenetic inferences. Maximum likelihood methods of simultaneously constructing phylogenetic tree topologies and estimating model parameters are computationally intensive, and are not feasible for sample sizes of 25 or greater using personal computers. Techniques that initially construct a tree topology and then use this non-maximized topology to estimate ML substitution rates, however, can quickly arrive at a model of sequence evolution. The accuracy of this two-step estimation technique was tested using simulated data sets with known model parameters. The results showed that for a star-like topology, as is often seen in human immunodeficiency virus type 1 (HIV-1) subtype B sequences, a random starting topology could produce nucleotide substitution rates that were not statistically different than the true rates. Samples were isolated from 100 HIV-1 subtype B infected individuals from the United States and a 620 nt region of the env gene was sequenced for each sample. The sequence data were used to obtain a substitution model of sequence evolution specific for HIV-1 subtype B env by estimating nucleotide substitution rates and the site-to-site heterogeneity in 100 individuals from the United States. The method of estimating the model should provide users of large data sets with a way to quickly compute a model of sequence evolution, while the nucleotide substitution model we identified should prove useful in the phylogenetic analysis of HIV-1 subtype B env sequences. Received: 4 October 2000 / Accepted: 1 March 2001     

What's in a likelihood? Simple models of protein evolution and the contribution of structurally viable reconstructions to the likelihood

Most phylogenetic models of protein evolution assume that sites are independent and identically distributed. Interactions between sites are ignored, and the likelihood can be conveniently calculated as the product of the individual site likelihoods. The calculation considers all possible transition paths (also called substitution histories or mappings) that are consistent with the observed states at the terminals, and the probability density of any particular reconstruction depends on the substitution model. The likelihood is the integral of the probability density of each substitution history taken over all possible histories that are consistent with the observed data. We investigated the extent to which transition paths that are incompatible with a protein's three-dimensional structure contribute to the likelihood. Several empirical amino acid models were tested for sequence pairs of different degrees of divergence. When simulating substitutional histories starting from a real sequence, the structural integrity of the simulated sequences quickly disintegrated. This result indicates that simple models are clearly unable to capture the constraints on sequence evolution. However, when we sampled transition paths between real sequences from the posterior probability distribution according to these same models, we found that the sampled histories were largely consistent with the tertiary structure. This suggests that simple empirical substitution models may be adequate for interpolating changes between observed sequences during phylogenetic inference despite the fact that the models cannot predict the effects of structural constraints from first principles. This study is significant because it provides a quantitative assessment of the biological realism of substitution models from the perspective of protein structure, and it provides insight on the prospects for improving models of protein sequence evolution.     

REvolver: modeling sequence evolution under domain constraints

Simulating the change of protein sequences over time in a biologically realistic way is fundamental for a broad range of studies with a focus on evolution. It is, thus, problematic that typically simulators evolve individual sites of a sequence identically and independently. More realistic simulations are possible; however, they are often prohibited by limited knowledge concerning site-specific evolutionary constraints or functional dependencies between amino acids. As a consequence, a protein's functional and structural characteristics are rapidly lost in the course of simulated evolution. Here, we present REvolver (www.cibiv.at/software/revolver), a program that simulates protein sequence alteration such that evolutionarily stable sequence characteristics, like functional domains, are maintained. For this purpose, REvolver recruits profile hidden Markov models (pHMMs) for parameterizing site-specific models of sequence evolution in an automated fashion. pHMMs derived from alignments of homologous proteins or protein domains capture information regarding which sequence sites remained conserved over time and where in a sequence insertions or deletions are more likely to occur. Thus, they describe constraints on the evolutionary process acting on these sequences. To demonstrate the performance of REvolver as well as its applicability in large-scale simulation studies, we evolved the entire human proteome up to 1.5 expected substitutions per site. Simultaneously, we analyzed the preservation of Pfam and SMART domains in the simulated sequences over time. REvolver preserved 92% of the Pfam domains originally present in the human sequences. This value drops to 15% when traditional models of amino acid sequence evolution are used. Thus, REvolver represents a significant advance toward a realistic simulation of protein sequence evolution on a proteome-wide scale. Further, REvolver facilitates the simulation of a protein family with a user-defined domain architecture at the root.     

Sense codon in Escherichia coli are translated in context

The nucleotide frequencies 5' and 3' to the sense codons in highly and weakly expressed genes have been investigated by the chi-squares method. A comparison between the experimental and computer-generated random nucleotide sequences (in which each codon is substituted by a random synonymous one) was made. It was shown that the choice of a particular codon among the synonymous ones in a given position of the gene depends on the three nucleotides 3' and 5' adjacent to the codon in highly expressed genes (the triplet 3' and a single nucleotide 5' to the codons in weakly expressed genes). Concrete patterns for the preferable choice of synonymous codons depending on their contexts are presented. It is suggested that these constraints are related to the efficiency of messenger translation. The constraints on the amino acid sequences of encoded proteins also lead to statistically significant bases in nucleotide frequencies around the sense codons. The biological role of these constraints is discussed.     

Comparative evolution of the mitochondrial cytochrome b gene and nuclear beta-fibrinogen intron 7 in woodpeckers

Most molecular phylogenetic studies of vertebrates have been based on DNA sequences of mitochondrial-encoded genes. MtDNA evolves rapidly and is thus particularly useful for resolving relationships among recently evolved groups. However, it has the disadvantage that all of the mitochondrial genes are inherited as a single linkage group so that only one independent gene tree can be inferred regardless of the number of genes sequenced. Introns of nuclear genes are attractive candidates for independent sources of rapidly evolving DNA: they are pervasive, most of their nucleotides appear to be unconstrained by selection, and PCR primers can be designed for sequences in adjacent exons where nucleotide sequences are conserved. We sequenced intron 7 of the beta-fibrinogen gene (beta-fibint7) for a diversity of woodpeckers and compared the phylogenetic signal and nucleotide substitution properties of this DNA sequence with that of mitochondrial-encoded cytochrome b (cyt b) from a previous study. A few indels (insertions and deletions) were found in the beta-fibint7 sequences, but alignment was not difficult, and the indels were phylogentically informative. The beta-fibint7 and cyt b gene trees were nearly identical to each other but differed in significant ways from the traditional woodpecker classification. Cyt b evolves 2.8 times as fast as beta-fibint7 (14. 0 times as fast at third codon positions). Despite its relatively slow substitution rate, the phylogenetic signal in beta-fibint7 is comparable to that in cyt b for woodpeckers, because beta-fibint7 has less base composition bias and more uniform nucleotide substitution probabilities. As a consequence, compared with cyt b, beta-fibint7 nucleotide sites are expected to enter more distinct character states over the course of evolution and have fewer multiple substitutions and lower levels of homoplasy. Moreover, in contrast to cyt b, in which nearly two thirds of nucleotide sites rarely vary among closely related taxa, virtually all beta-fibint7 nucleotide sites appear free of selective constraints, which increases informative sites per unit sequenced. However, the estimated gamma distribution used to model rate variation among sites suggests constraints on some beta-fibint7 sites. This study suggests that introns will be useful for phylogenetic studies of recently evolved groups.     

SWAPSC: sliding window analysis procedure to detect selective constraints

Sliding-window analysis procedure to detect selective constraints (SWAPSC) is a software system to dissect the constraints on the evolution of protein-coding genes. The program estimates rates of nucleotide substitutions at specific codon regions in each branch of a phylogenetic tree. The program uses several sets of simulated sequence alignments to estimate the probability of synonymous and non-synonymous nucleotide substitutions. Thereafter, a statistical analysis is conducted to determine the optimum window size to detect selective constraints. Finally, the optimum window size is slid along the real alignment and a test for significance of the estimated number of synonymous and non-synonymous nucleotide substitutions in each sliding step is conducted. A number of friendly useful output files is generated. AVAILABILITY: SWAPSC is available at http://www.may.ie/academic/biology/staff/mfmolecevolandbioinf.shtml distribution versions for both Linux and Windows operating systems are available, including manual and example files.     

LOW METABOLIC RATES IN SALAMANDERS ARE CORRELATED WITH WEAK SELECTIVE CONSTRAINTS ON MITOCHONDRIAL GENES

Mitochondria are the site for the citric acid cycle and oxidative phosphorylation (OXPHOS), the final steps of ATP synthesis via cellular respiration. Each mitochondrion contains its own genome; in vertebrates, this is a small, circular DNA molecule that encodes 13 subunits of the multiprotein OXPHOS electron transport complexes. Vertebrate lineages vary dramatically in metabolic rates; thus, functional constraints on mitochondrial‐encoded proteins likely differ, potentially impacting mitochondrial genome evolution. Here, we examine mitochondrial genome evolution in salamanders, which have the lowest metabolic requirements among tetrapods. We show that salamanders experience weaker purifying selection on protein‐coding sequences than do frogs, a comparable amphibian clade with higher metabolic rates. In contrast, we find no evidence for weaker selection against mitochondrial genome expansion in salamanders. Together, these results suggest that different aspects of mitochondrial genome evolution (i.e., nucleotide substitution, accumulation of noncoding sequences) are differently affected by metabolic variation across tetrapod lineages.     

Inferring the number of evolutionary events from DNA coding sequence differences

The estimation of the amount of evolutionary divergence that has taken place between two DNA coding sequences depends strongly on the degree of constraint on amino acid replacements. If amino acid replacements are relatively unconstrained, the individual nucleotide is the appropriate unit of analysis and the method of Tajima and Nei can be used. If amino acid replacements are constrained, however, this method is shown to be inapplicable. For sequences with strong amino acid constraints, a method is outlined analogous to the Tajima and Nei method using codons as the unit of analysis. Only synonymous substitutions are used. Codon usage data can be employed to estimate the necessary parameters of the calculation, or a priori models of substitution may be employed. Sequences with significant but intermediate constraints on amino acid replacements are, in principle, unanalyzable.      

Comparative study of the evolution of nuclear ribosomal spacers incorporating secondary structure analyzes within Dodonaeoideae,Hippocastanoideae and Xanthoceroideae (Sapindaceae)

Ribosomal DNA internal transcribed spacers (ITS) and partial external transcribed spacers (ETSf) are popularly used to infer evolutionary hypotheses. However, there is generally little consideration given to the secondary structures of these small RNA molecules and their potential effects on sequence alignment and phylogenetic analyzes. Intergeneric relationships amongst three of the four major lineages in the Sapindaceae, the Dodonaeoideae, Hippcastanoideae and Xanthoceroideae were assessed by firstly, generating secondary structure predictions for ITS and partial ETSf sequences, and then these predictions were used to assist alignment of the sequences. Secondly, the alignment was analyzed using RNA specific models of sequence evolution that account for the variation in nucleotide evolution in the independent loops and covariating stems regions of the ribosomal spacers. These models and phylogeny drawn from these analyzes were compared with that from analyzes using ‘traditional’ 4-state models and previous plastid analyzes. These analyzes identified that paired-site models developed to deal specifically with stem structures in RNA encoding sequences more appropriately account for the evolutionary history of the sequences than traditional 4-state substitution models.     

Different models, different trees: the geographic origin of PTLV-I

Using nucleotide sequences from three genomic regions of the human and simian T-cell lymphotropic virus type I (HTLV-I/STLV-I)-consisting of 69 sequences from a 140-bp segment of the pol region, 98 sequences from a 503-bp segment of the LTR, and 154 sequences from a 386-bp segment of the env region-we tested two hypotheses concerning the geographic origin and evolution of STLV-I and HTLV-I. First, we tested the assumption of equal rates of evolution along STLV-I and HTLV-I lineages using a likelihood ratio test to ascertain whether current levels of genomic diversity can be used to determine ancestry. We demonstrated that unequal rates of evolution along HTLV-I and STLV-I lineages have occurred throughout evolutionary time, thus calling into question the use of pairwise distances to assign ancestry. Second, we constructed phylogenetic trees using multiple phylogenetic techniques to test for the geographic origin of STLV-I and HTLV-I. Using the principle of likelihood, we chose a statistically justified model of evolution for each data set. We demonstrated the utility of the likelihood ratio test to determine which model of evolution should be chosen for phylogenetic analyses, revealing that using different models of evolution produces conflicting results, and neither the hypothesis of an African origin nor the hypothesis of an Asian origin can be rejected statistically. Our best estimates of phylogenetic relationships, however, support an African origin of PTLV for each gene region.