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.