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     

SDSE: A software package to simulate the evolution of a pair of DNA sequences

An algorithm to simulate DNA sequence evolution under a generalstochastic model, including as particular cases all the previouslyused schemes of nucleotide substitution, is described. The simulationis carried out on finite, variable length, DNA sequences througha strict stochastic process, according to the particular substitutionrates imposed by each scheme. Five FORTRAN programs, runningon an IBM PC and compatibles, carry out all the tasks neededfor the simulation. They are menu driven and interfaced to thesystem through a principal menu. All sequence data files usedand generated by the SDSE package conform to the standard GenBankdatabase format, thus allowing the use of any sequence retrievedfrom this databank, as well as the application of other packagesto analyse, manipulate or retrieve simulated sequences. Received on August 23, 1988; accepted on November 15, 1988     

An Evolution Model for Sequence Length Based on Residue Insertion–Deletion Independent of Substitution: An Application to the GC Content in Bacterial Genomes

We introduce here a gene evolution model which is an extension of the time-continuous stochastic IDIS model (Lèbre and Michel in J. Comput. Biol. Chem. 34:259-267, 2010) to sequence length. This new IDISL (Insertion Deletion Independent of Substitution based on sequence Length) model gives an analytical expression of the residue occurrence probability p(l) at sequence length l depending on stochastically independent processes of substitution, insertion, and deletion. Furthermore, in contrast to all mathematical models in this research field, the substitution, insertion, and deletion parameters of the IDISL model are independent of each other. For any diagonalizable substitution matrix M, the residue occurrence probability p(l) is given as a function of the eigenvalues of M, the eigenvector matrix of M, a vector r of the residue insertion rates, a deletion rate d (unlike our previous IDIS model), and a vector of the initial residue occurrence probability p(l(0)) at sequence length l(0).As another difference with the classical evolution approaches which mainly focus on sequence alignment, the IDIS class of models allows a mathematical analysis of the behavior of the residue occurrence probability according to either evolution time or sequence length. The length parameter can be associated with any nucleotide regions: genes, genomes, introns, repeats, 5' and 3' regions, etc. Three properties of the IDISL model are given in relation with the sequence length l: parameter scale, inverse evolution, and residue equilibrium distribution. Nucleotide occurrence probabilities are given in the particular case of the IDISL-HKY model, i.e. the IDISL model associated with the HKY asymmetric substitution matrix (Hasegawa et al. in J. Mol. Evol. 22:160-174, 1985).An application of the IDISL model is developed for a massive statistical analysis of GC content in all complete bacterial genomes available to date (894 non-anaerobic and anaerobic genomes). The IDISL-HKY model confirms the increase of the GC content with the genome length for two non-anaerobic taxonomic groups of bacterial genomes. Moreover, the non-linear modelling proposed by the IDISL model outperforms the most recent modelling of GC content in these bacterial genomes (Wang et al. in Biochem. Biophys. Res. Commun. 342:681-684, 2006; Musto et al. in Biochem. Biophys. Res. Commun. 347:1-3, 2006).     

Evolution of DNA base composition under no-strand-bias conditions when the substitution rates are not constant.

The evolution of DNA base composition evolution is simplified to a six-parameter model when there are no strand biases for mutation and selection. We analyzed the dynamics of this model with special attention to the influence of a change in substitution rates. The G + C content of the DNA sequence tends to an equilibrium value that is controlled by four parameters of the model. When the substitution rates are not constant, the G + C equilibrium position is not constant. The DNA sequence base frequencies always tend to a state in which A = T and G = C within a strand, regardless of substitution rates. This is true even when the substitution rates are not constant over time. This provides a simple way of rejecting the model from inspection of present-day DNA base composition.     

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.     

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.     

Evidence for widespread reticulate evolution within human duplicons

Approximately 5% of the human genome consists of segmental duplications that can cause genomic mutations and may play a role in gene innovation. Reticulate evolutionary processes, such as unequal crossing-over and gene conversion, are known to occur within specific duplicon families, but the broader contribution of these processes to the evolution of human duplications remains poorly characterized. Here, we use phylogenetic profiling to analyze multiple alignments of 24 human duplicon families that span >8 Mb of DNA. Our results indicate that none of them are evolving independently, with all alignments showing sharp discontinuities in phylogenetic signal consistent with reticulation. To analyze these results in more detail, we have developed a quartet method that estimates the relative contribution of nucleotide substitution and reticulate processes to sequence evolution. Our data indicate that most of the duplications show a highly significant excess of sites consistent with reticulate evolution, compared with the number expected by nucleotide substitution alone, with 15 of 30 alignments showing a >20-fold excess over that expected. Using permutation tests, we also show that at least 5% of the total sequence shares 100% sequence identity because of reticulation, a figure that includes 74 independent tracts of perfect identity >2 kb in length. Furthermore, analysis of a subset of alignments indicates that the density of reticulation events is as high as 1 every 4 kb. These results indicate that phylogenetic relationships within recently duplicated human DNA can be rapidly disrupted by reticulate evolution. This finding has important implications for efforts to finish the human genome sequence, complicates comparative sequence analysis of duplicon families, and could profoundly influence the tempo of gene-family evolution.     

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.      

Genetic codes as evolutionary filters: subtle differences in the structure of genetic codes result in significant differences in patterns of nucleotide substitution

The codon-degeneracy model (CDM) predicts that patterns of nucleotide substitution in protein-coding genes are largely determined by the relative frequencies of four-fold (4f), two-fold, and non-degenerate sites, the attributes of which are determined by the structure of the governing genetic code. The CDM thus further predicts that genetic codes with alternative structures will "filter" molecular evolution differentially. A method, therefore, is presented by which the CDM may be applied to the unique structure of any genetic code. The mathematical relationship between the proportion of transitions at 4f degenerate nucleotide sites and the transition-to-transversion ratio is described. Predictions for five individual genetic codes, relative to the relationship between code structure and expected patterns of nucleotide substitution, are clearly defined. To test this "filter" hypothesis of genetic codes, simulated DNA sequence data sets were generated with a variety of input parameter values to estimate the relationship between patterns of nucleotide substitution and best-fit estimates of transition bias at 4f degenerate sites for both the universal genetic code and the vertebrate mitochondrial genetic code. These analyses confirm the prediction of the CDM that, all else being equal, even small differences in the structure of alternative genetic codes may result in significant shifts in the overall pattern of nucleotide substitution.     

Pitfalls of the most commonly used models of context dependent substitution

Background  

Neighboring nucleotides exert a striking influence on mutation, with the hypermutability of CpG dinucleotides in many genomes being an exemplar. Among the approaches employed to measure the relative importance of sequence neighbors on molecular evolution have been continuous-time Markov process models for substitutions that treat sequences as a series of independent tuples. The most widely used examples are the codon substitution models. We evaluated the suitability of derivatives of the nucleotide frequency weighted (hereafter NF) and tuple frequency weighted (hereafter TF) models for measuring sequence context dependent substitution. Critical properties we address are their relationships to an independent nucleotide process and the robustness of parameter estimation to changes in sequence composition. We then consider the impact on inference concerning dinucleotide substitution processes from application of these two forms to intron sequence alignments from primates.     

Variation in satellite DNA profiles--causes and effects

Heterochromatic regions of the eukaryotic genome harbour DNA sequences that are repeated many times in tandem, collectively known as satellite DNAs. Different satellite sequences co-exist in the genome, thus forming a set called a satellite DNA library. Within a library, satellite DNAs represent independent evolutionary units. Their evolution can be explained as a result of change in two parameters: copy number and nucleotide sequence, both of them ruled by the same mechanisms of concerted evolution. Individual change in either of these two parameters as well as their simultaneous evolution can lead to the genesis of species-specific satellite profiles. In some cases, changes in satellite DNA profiles can be correlated with chromosomal evolution and could possibly influence the evolution of species.     

Model of amino acid substitution in proteins encoded by mitochondrial DNA

Mitochondrial DNA (mtDNA) sequences are widely used for inferring the phylogenetic relationships among species. Clearly, the assumed model of nucleotide or amino acid substitution used should be as realistic as possible. Dependence among neighboring nucleotides in a codon complicates modeling of nucleotide substitutions in protein-encoding genes. It seems preferable to model amino acid substitution rather than nucleotide substitution. Therefore, we present a transition probability matrix of the general reversible Markov model of amino acid substitution for mtDNA-encoded proteins. The matrix is estimated by the maximum likelihood (ML) method from the complete sequence data of mtDNA from 20 vertebrate species. This matrix represents the substitution pattern of the mtDNA-encoded proteins and shows some differences from the matrix estimated from the nuclear-encoded proteins. The use of this matrix would be recommended in inferring trees from mtDNA-encoded protein sequences by the ML method. Received: 3 May 1995 / Accepted: 31 October 1995     

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.     

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.     

GC skew in protein-coding genes between the leading and lagging strands in bacterial genomes: new substitution models incorporating strand bias

The DNA strands in most prokaryotic genomes experience strand-biased spontaneous mutation, especially C→T mutations produced by deamination that occur preferentially in the leading strand. This has often been invoked to account for the asymmetry in nucleotide composition, typically measured by GC skew, between the leading and the lagging strand. Casting such strand asymmetry in the framework of a nucleotide substitution model is important for understanding genomic evolution and phylogenetic reconstruction. We present a substitution model showing that the increased C→T mutation will lead to positive GC skew in one strand but negative GC skew in the other, with greater C→T mutation pressure associated with greater differences in GC skew between the leading and the lagging strand. However, the model based on mutation bias alone does not predict any positive correlation in GC skew between the leading and lagging strands. We computed GC skew for coding sequences collinear with the leading and lagging strands across 339 prokaryotic genomes and found a strong and positive correlation in GC skew between the two strands. We show that the observed positive correlation can be satisfactorily explained by an improved substitution model with one additional parameter incorporating a general trend of C avoidance.     

Comparison of models for nucleotide substitution used in maximum- likelihood phylogenetic estimation

Using real sequence data, we evaluate the adequacy of assumptions made in evolutionary models of nucleotide substitution and the effects that these assumptions have on estimation of evolutionary trees. Two aspects of the assumptions are evaluated. The first concerns the pattern of nucleotide substitution, including equilibrium base frequencies and the transition/transversion-rate ratio. The second concerns the variation of substitution rates over sites. The maximum-likelihood estimate of tree topology appears quite robust to both these aspects of the assumptions of the models, but evaluation of the reliability of the estimated tree by using simpler, less realistic models can be misleading. Branch lengths are underestimated when simpler models of substitution are used, but the underestimation caused by ignoring rate variation over nucleotide sites is much more serious. The goodness of fit of a model is reduced by ignoring spatial rate variation, but unrealistic assumptions about the pattern of nucleotide substitution can lead to an extraordinary reduction in the likelihood. It seems that evolutionary biologists can obtain accurate estimates of certain evolutionary parameters even with an incorrect phylogeny, while systematists cannot get the right tree with confidence even when a realistic, and more complex, model of evolution is assumed.      

Performance of likelihood ratio tests of evolutionary hypotheses under inadequate substitution models.

In recent years, likelihood ratio tests (LRTs) based on DNA and protein sequence data have been proposed for testing various evolutionary hypotheses. Because conducting an LRT requires an evolutionary model of nucleotide or amino acid substitution, which is almost always unknown, it becomes important to investigate the robustness of LRTs to violations of assumptions of these evolutionary models. Computer simulation was used to examine performance of LRTs of the molecular clock, transition/transversion bias, and among-site rate variation under different substitution models. The results showed that when correct models are used, LRTs perform quite well even when the DNA sequences are as short as 300 nt. However, LRTs were found to be biased under incorrect models. The extent of bias varies considerably, depending on the hypotheses tested, the substitution models assumed, and the lengths of the sequences used, among other things. A preliminary simulation study also suggests that LRTs based on parametric bootstrapping may be more sensitive to substitution models than are standard LRTs. When an assumed substitution model is grossly wrong and a more realistic model is available, LRTs can often reject the wrong model; thus, the performance of LRTs may be improved by using a more appropriate model. On the other hand, many factors of molecular evolution have not been considered in any substitution models so far built, and the possibility of an influence of this negligence on LRTs is often overlooked. The dependence of LRTs on substitution models calls for caution in interpreting test results and highlights the importance of clarifying the substitution patterns of genes and proteins and building more realistic models.     

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.