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.      

Markovian and non-Markovian protein sequence evolution: aggregated Markov process models

Over the years, there have been claims that evolution proceeds according to systematically different processes over different timescales and that protein evolution behaves in a non-Markovian manner. On the other hand, Markov models are fundamental to many applications in evolutionary studies. Apparent non-Markovian or time-dependent behavior has been attributed to influence of the genetic code at short timescales and dominance of physicochemical properties of the amino acids at long timescales. However, any long time period is simply the accumulation of many short time periods, and it remains unclear why evolution should appear to act systematically differently across the range of timescales studied. We show that the observed time-dependent behavior can be explained qualitatively by modeling protein sequence evolution as an aggregated Markov process (AMP): a time-homogeneous Markovian substitution model observed only at the level of the amino acids encoded by the protein-coding DNA sequence. The study of AMPs sheds new light on the relationship between amino acid-level and codon-level models of sequence evolution, and our results suggest that protein evolution should be modeled at the codon level rather than using amino acid substitution models.     

Codon substitution models based on residue similarity and their applications

Codon models are now widely used to draw evolutionary inferences from alignments of homologous sequence data. Incorporating physicochemical properties of amino acids into codon models, two novel codon substitution models describing the evolution of protein-coding DNA sequences are presented based on the similarity scores of amino acids. To describe substitutions between codons a continue-time Markov process is used. Transition/transversion rate bias and nonsynonymous codon usage bias are allowed in the models. In our implementation, the parameters are estimated by maximum-likelihood (ML) method as in previous studies. Furthermore, instantaneous mutations involving more than one nucleotide position of a codon are considered in the second model. Then the two suggested models are applied to five real data sets. The analytic results indicate that the new codon models considering physicochemical properties of amino acids can provide a better fit to the data comparing with existing codon models, and then produce more reliable estimates of certain biologically important measures than existing methods.     

A combined empirical and mechanistic codon model

The evolutionary selection forces acting on a protein are commonly inferred using evolutionary codon models by contrasting the rate of synonymous to nonsynonymous substitutions. Most widely used models are based on theoretical assumptions and ignore the empirical observation that distinct amino acids differ in their replacement rates. In this paper, we develop a general method that allows assimilation of empirical amino acid replacement probabilities into a codon-substitution matrix. In this way, the resulting codon model takes into account not only the transition-transversion bias and the nonsynonymous/synonymous ratio, but also the different amino acid replacement probabilities as specified in empirical amino acid matrices. Different empirical amino acid replacement matrices, such as secondary structure-specific matrices or organelle-specific matrices (e.g., mitochondria and chloroplasts), can be incorporated into the model, making it context dependent. Using a diverse set of coding DNA sequences, we show that the novel model better fits biological data as compared with either mechanistic or empirical codon models. Using the suggested model, we further analyze human immunodeficiency virus type 1 protease sequences obtained from drug-treated patients and reveal positive selection in sites that are known to confer drug resistance to the virus.     

Amino acid substitutions in the human genome: evolutionary implications of single nucleotide polymorphisms

Functional differences between amino acids have long been of interest in understanding protein evolution. Several indices exist for comparing residues on the basis of their physicochemical properties and frequencies of occurrence in conserved protein alignments. Here we present a residue dissimilarity index based on coding single nucleotide polymorphisms (SNPs) in the human genome. The index represents an average, organism-wide set of differences between residues and provides important insight into evolutionary restraints on residue substitutions in the human genome. Unlike previous models, it is not restricted to highly conserved protein structures, nor confounded by evolutionary differences between species. Our results confirm earlier observations regarding residue mutabilities but also suggest that in addition to the established key properties, such as size and polarity, charge conservation may be an important and currently underestimated factor in protein evolution. We also estimate that less than 51% of amino acid substitutions occurring in the human genome are evolutionarily neutral.     

Evolutionary patterns of codon usage in the chloroplast gene rbcL

In this study we reconstruct the evolution of codon usage bias in the chloroplast gene rbcL using a phylogeny of 92 green-plant taxa. We employ a measure of codon usage bias that accounts for chloroplast genomic nucleotide content, as an attempt to limit plausible explanations for patterns of codon bias evolution to selection- or drift-based processes. This measure uses maximum likelihood-ratio tests to compare the performance of two models, one in which a single codon is overrepresented and one in which two codons are overrepresented. The measure allowed us to analyze both the extent of bias in each lineage and the evolution of codon choice across the phylogeny. Despite predictions based primarily on the low G + C content of the chloroplast and the high functional importance of rbcL, we found large differences in the extent of bias, suggesting differential molecular selection that is clade specific. The seed plants and simple leafy liverworts each independently derived a low level of bias in rbcL, perhaps indicating relaxed selectional constraint on molecular changes in the gene. Overrepresentation of a single codon was typically plesiomorphic, and transitions to overrepresentation of two codons occurred commonly across the phylogeny, possibly indicating biochemical selection. The total codon bias in each taxon, when regressed against the total bias of each amino acid, suggested that twofold amino acids play a strong role in inflating the level of codon usage bias in rbcL, despite the fact that twofolds compose a minority of residues in this gene. Those amino acids that contributed most to the total codon usage bias of each taxon are known through amino acid knockout and replacement to be of high functional importance. This suggests that codon usage bias may be constrained by particular amino acids and, thus, may serve as a good predictor of what residues are most important for protein fitness.     

Thermophilic prokaryotes have characteristic patterns of codon usage, amino acid composition and nucleotide content

A number of recent studies have shown that thermophilic prokaryotes have distinguishable patterns of both synonymous codon usage and amino acid composition, indicating the action of natural selection related to thermophily. On the other hand, several other studies of whole genomes have illustrated that nucleotide bias can have dramatic effects on synonymous codon usage and also on the amino acid composition of the encoded proteins. This raises the possibility that the thermophile-specific patterns observed at both the codon and protein levels are merely reflections of a single underlying effect at the level of nucleotide composition. Moreover, such an effect at the nucleotide level might be due entirely to mutational bias. In this study, we have compared the genomes of thermophiles and mesophiles at three levels: nucleotide content, codon usage and amino acid composition. Our results indicate that the genomes of thermophiles are distinguishable from mesophiles at all three levels and that the codon and amino acid frequency differences cannot be explained simply by the patterns of nucleotide composition. At the nucleotide level, we see a consistent tendency for the frequency of adenine to increase at all codon positions within the thermophiles. Thermophiles are also distinguished by their pattern of synonymous codon usage for several amino acids, particularly arginine and isoleucine. At the protein level, the most dramatic effect is a two-fold decrease in the frequency of glutamine residues among thermophiles. These results indicate that adaptation to growth at high temperature requires a coordinated set of evolutionary changes affecting (i) mRNA thermostability, (ii) stability of codon-anticodon interactions and (iii) increased thermostability of the protein products. We conclude that elevated growth temperature imposes selective constraints at all three molecular levels: nucleotide content, codon usage and amino acid composition. In addition to these multiple selective effects, however, the genomes of both thermophiles and mesophiles are often subject to superimposed large changes in composition due to mutational bias.     

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.     

Evolutionary Patterns of Codon Usage in the Chloroplast Gene rbcL

In this study we reconstruct the evolution of codon usage bias in the chloroplast gene rbcL using a phylogeny of 92 green-plant taxa. We employ a measure of codon usage bias that accounts for chloroplast genomic nucleotide content, as an attempt to limit plausible explanations for patterns of codon bias evolution to selection- or drift-based processes. This measure uses maximum likelihood-ratio tests to compare the performance of two models, one in which a single codon is overrepresented and one in which two codons are overrepresented. The measure allowed us to analyze both the extent of bias in each lineage and the evolution of codon choice across the phylogeny. Despite predictions based primarily on the low G+C content of the chloroplast and the high functional importance of rbcL, we found large differences in the extent of bias, suggesting differential molecular selection that is clade specific. The seed plants and simple leafy liverworts each independently derived a low level of bias in rbcL, perhaps indicating relaxed selectional constraint on molecular changes in the gene. Overrepresentation of a single codon was typically plesiomorphic, and transitions to overrepresentation of two codons occurred commonly across the phylogeny, possibly indicating biochemical selection. The total codon bias in each taxon, when regressed against the total bias of each amino acid, suggested that twofold amino acids play a strong role in inflating the level of codon usage bias in rbcL, despite the fact that twofolds compose a minority of residues in this gene. Those amino acids that contributed most to the total codon usage bias of each taxon are known through amino acid knockout and replacement to be of high functional importance. This suggests that codon usage bias may be constrained by particular amino acids and, thus, may serve as a good predictor of what residues are most important for protein fitness. Present address (Joshua T. Herbeck): JBP Center for Comparative Molecular Biology and Evolution, Marine Biological Laboratory, Woods Hole, MA 02543, USA     

Detecting Site-Specific Physicochemical Selective Pressures: Applications to the Class I HLA of the Human Major Histocompatibility Complex and the SRK of the Plant Sporophytic Self-Incompatibility System

Models of codon substitution are developed that incorporate physicochemical properties of amino acids. When amino acid sites are inferred to be under positive selection, these models suggest the nature and extent of the physicochemical properties under selection. This is accomplished by first partitioning the codons on the basis of some property of the encoded amino acids. This partition is used to parametrize the rates of property-conserving and property-altering base substitutions at the codon level by means of finite mixtures of Markov models that also account for codon and transition:transversion biases. Here, we apply this method to two positively selected receptors involved in ligand-recognition: the class I alleles of the human major histocompatibility complex (MHC) of known structure and the S-locus receptor kinase (SRK) of the sporophytic self-incompatibility system (SSI) in cruciferous plants (Brassicaceae), whose structure is unknown. Through likelihood ratio tests we demonstrate that at some sites, the positively selected MHC and SRK proteins are under physicochemical selective pressures to alter polarity, volume, polarity and/or volume, and charge to various extents. An empirical Bayes approach is used to identify sites that may be important for ligand recognition in these proteins.Reviewing Editor : Dr. Willie Swanson     

Evaluating the robustness of phylogenetic methods to among-site variability in substitution processes

Computer simulations provide a flexible method for assessing the power and robustness of phylogenetic inference methods. Unfortunately, simulated data are often obviously atypical of data encountered in studies of molecular evolution. Unrealistic simulations can lead to conclusions that are irrelevant to real-data analyses or can provide a biased view of which methods perform well. Here, we present a software tool designed to generate data under a complex codon model that allows each residue in the protein sequence to have a different set of equilibrium amino acid frequencies. The software can obtain maximum-likelihood estimates of the parameters of the Halpern and Bruno model from empirical data and a fixed tree; given an arbitrary tree and a fixed set of parameters, the software can then simulate artificial datasets.We present the results of a simulation experiment using randomly generated tree shapes and substitution parameters estimated from 1610 mammalian cytochrome b sequences.We tested tree inference at the amino acid, nucleotide and codon levels and under parsimony, maximum-likelihood, Bayesian and distance criteria (for a total of more than 650 analyses on each dataset). Based on these simulations, nucleotide-level analyses seem to be more accurate than amino acid and codon analyses. The performance of distance-based phylogenetic methods appears to be quite sensitive to the choice of model and the form of rate heterogeneity used. Further studies are needed to assess the generality of these conclusions. For example, fitting parameters of the Halpern Bruno model to sequences from other genes will reveal the extent to which our conclusions were influenced by the choice of cytochrome b. Incorporating codon bias and more sources heterogeneity into the simulator will be crucial to determining whether the current results are caused by a bias in the current simulation study in favour of nucleotide analyses.     

A codon-based model of nucleotide substitution for protein-coding DNA sequences

A codon-based model for the evolution of protein-coding DNA sequences is presented for use in phylogenetic estimation. A Markov process is used to describe substitutions between codons. Transition/transversion rate bias and codon usage bias are allowed in the model, and selective restraints at the protein level are accommodated using physicochemical distances between the amino acids coded for by the codons. Analyses of two data sets suggest that the new codon-based model can provide a better fit to data than can nucleotide-based models and can produce more reliable estimates of certain biologically important measures such as the transition/transversion rate ratio and the synonymous/nonsynonymous substitution rate ratio.      

On the Evolution of Redundancy in Genetic Codes

We simulate a deterministic population genetic model for the coevolution of genetic codes and protein-coding genes. We use very simple assumptions about translation, mutation, and protein fitness to calculate mutation-selection equilibria of codon frequencies and fitness in a large asexual population with a given genetic code. We then compute the fitnesses of altered genetic codes that compete to invade the population by translating its genes with higher fitness. Codes and genes coevolve in a succession of stages, alternating between genetic equilibration and code invasion, from an initial wholly ambiguous coding state to a diversified frozen coding state. Our simulations almost always resulted in partially redundant frozen genetic codes. Also, the range of simulated physicochemical properties among encoded amino acids in frozen codes was always less than maximal. These results did not require the assumption of historical constraints on the number and type of amino acids available to codes nor on the complexity of proteins, stereochemical constraints on the translational apparatus, nor mechanistic constraints on genetic code change. Both the extent and timing of amino-acid diversification in genetic codes were strongly affected by the message mutation rate and strength of missense selection. Our results suggest that various omnipresent phenomena that distribute codons over sites with different selective requirements—such as the persistence of nonsynonymous mutations at equilibrium, the positive selection of the same codon in different types of sites, and translational ambiguity—predispose the evolution of redundancy and of reduced amino acid diversity in genetic codes. Received: 21 December 2000 / Accepted: 12 March 2001     

Quantifying codon usage in signal peptides: Gene expression and amino acid usage explain apparent selection for inefficient codons

The Sec secretion pathway is found across all domains of life. A critical feature of Sec secreted proteins is the signal peptide, a short peptide with distinct physicochemical properties located at the N-terminus of the protein. Previous work indicates signal peptides are biased towards translationally inefficient codons, which is hypothesized to be an adaptation driven by selection to improve the efficacy and efficiency of the protein secretion mechanisms. We investigate codon usage in the signal peptides of E. coli using the Codon Adaptation Index (CAI), the tRNA Adaptation Index (tAI), and the ribosomal overhead cost formulation of the stochastic evolutionary model of protein production rates (ROC-SEMPPR). Comparisons between signal peptides and 5′-end of cytoplasmic proteins using CAI and tAI are consistent with a preference for inefficient codons in signal peptides. Simulations reveal these differences are due to amino acid usage and gene expression – we find these differences disappear when accounting for both factors. In contrast, ROC-SEMPPR, a mechanistic population genetics model capable of separating the effects of selection and mutation bias, shows codon usage bias (CUB) of the signal peptides is indistinguishable from the 5′-ends of cytoplasmic proteins. Additionally, we find CUB at the 5′-ends is weaker than later segments of the gene. Results illustrate the value in using models grounded in population genetics to interpret genetic data. We show failure to account for mutation bias and the effects of gene expression on the efficacy of selection against translation inefficiency can lead to a misinterpretation of codon usage patterns.     

Relative benefits of amino‐acid,codon, degeneracy,DNA, and purine‐pyrimidine character coding for phylogenetic analyses of exons

Both traditional as well as 10 more recent methods of coding characters from exons of protein‐coding genes are reviewed. The more recent methods collectively blur the distinction between nucleotide and amino‐acid coding and enable investigators to carefully quantify the effects of different sources of phylogenetic signal as well as their potential biases. Codon models, which explicitly model silent and replacement substitutions, are a major advance and are expected to be broadly useful for simultaneously inferring recent and ancient divergences, unlike amino‐acid coding. Degeneracy coding, wherein ambiguity codes are used to eliminate silent substitutions at the individual‐nucleotide level, has clear advantages over scoring amino‐acid characters. Nucleotide, codon, and amino‐acid models are now directly comparable with easy‐to‐use programs, and widely used phylogenetics programs can analyze partitioned supermatrices that incorporate all three types of model. Therefore, it should become standard practice to test among these alternative model types before conducting parametric phylogenetic analyses. An earlier study of 78 protein‐coding genes from 360 green‐plant plastid genomes is used as an empirical example with which to quantify the relative performance of alternative character‐coding methods using five quantification measures. Codon models were selected as having the best fit to the data, yet were outperformed by nucleotide models for all five quantification measures. Third‐codon positions were found to be an important source of phylogenetic signal and even outperformed analyses of first and second positions for some measures. Degeneracy coding generally performed at least as well as amino‐acid coding and is an arguably more effective alternative.     

Combining models of protein translation and population genetics to predict protein production rates from codon usage patterns

Genes are often biased in their codon usage. The degree of bias displayed often changes with expression level and intragenic position. Numerous indices, such as the codon adaptation index, have been developed to measure this bias. Although the expression level of a gene and index values are correlated, the heuristic nature of these metrics limits their ability to explain this relationship. As an alternative approach, this study integrates mechanistic models of cellular and population processes in a nested manner to develop a stochastic evolutionary model of a protein's production rate (SEMPPR). SEMPPR assumes that the evolution of codon bias is driven by selection to reduce the cost of nonsense errors and that this selection is counteracted by mutation and drift. Through the application of Bayes' theorem, SEMPPR generates a posterior probability distribution for the protein production rate of a given gene. Conceptually, SEMPPR's predictions are based on the degree of adaptation to reduce the cost of nonsense errors observed in the codon usage pattern of the gene. As an illustration, SEMPPR was parameterized using the Saccharomyces cerevisiae genome and its predictions tested using available empirical data. The results indicate that SEMPPR's predictions are as reliable index based ones. In addition, SEMPPR's output is more easily interpreted and its predictions could be improved through refinements of the models upon which it is built.     

CodonTest: Modeling Amino Acid Substitution Preferences in Coding Sequences

Codon models of evolution have facilitated the interpretation of selective forces operating on genomes. These models, however, assume a single rate of non-synonymous substitution irrespective of the nature of amino acids being exchanged. Recent developments have shown that models which allow for amino acid pairs to have independent rates of substitution offer improved fit over single rate models. However, these approaches have been limited by the necessity for large alignments in their estimation. An alternative approach is to assume that substitution rates between amino acid pairs can be subdivided into rate classes, dependent on the information content of the alignment. However, given the combinatorially large number of such models, an efficient model search strategy is needed. Here we develop a Genetic Algorithm (GA) method for the estimation of such models. A GA is used to assign amino acid substitution pairs to a series of rate classes, where is estimated from the alignment. Other parameters of the phylogenetic Markov model, including substitution rates, character frequencies and branch lengths are estimated using standard maximum likelihood optimization procedures. We apply the GA to empirical alignments and show improved model fit over existing models of codon evolution. Our results suggest that current models are poor approximations of protein evolution and thus gene and organism specific multi-rate models that incorporate amino acid substitution biases are preferred. We further anticipate that the clustering of amino acid substitution rates into classes will be biologically informative, such that genes with similar functions exhibit similar clustering, and hence this clustering will be useful for the evolutionary fingerprinting of genes.     

On the organizational dynamics of the genetic code

The organization of the canonical genetic code needs to be thoroughly illuminated. Here we reorder the four nucleotides-adenine, thymine, guanine and cytosine-according to their emergence in evolution, and apply the organizational rules to devising an algebraic representation for the canonical genetic code. Under a framework of the devised code, we quantify codon and amino acid usages from a large collection of 917 prokaryotic genome sequences, and associate the usages with its intrinsic structure and classification schemes as well as amino acid physicochemical properties. Our results show that the algebraic representation of the code is structurally equivalent to a content-centric organization of the code and that codon and amino acid usages under different classification schemes were correlated closely with GC content, implying a set of rules governing composition dynamics across a wide variety of prokaryotic genome sequences. These results also indicate that codons and amino acids are not randomly allocated in the code, where the six-fold degenerate codons and their amino acids have important balancing roles for error minimization. Therefore, the content-centric code is of great usefulness in deciphering its hitherto unknown regularities as well as the dynamics of nucleotide, codon, and amino acid compositions.     

The molecular evolution of cytochrome c in eukaryotes

Summary Using many more cytochrome sequences than previously available, we have confirmed: 1, the eukaryotic cytochromes c diverged from a common ancestor; 2, the ancestral eukaryotic cytochrome c was not greatly different in character from those present today; 3, fixations are non-randomly distributed among the codons, there being evidence for at least four classes of variability; 4, there are similar classes of variability when the data are considered according to the nucleotide position within the codon; 5, the number of covarions (concomitantly variable codons) in mammalian cytochrome c genes is about 12 and the same value has been obtained for dicotyledonous plants as well; 6, all of the hyper- and most highly variable codons are for external residues, nearly 60 per cent of the invariable codons are for internal residues and nearly half of the codons for internal residues are invariable; 7, the first nucleotide position of a codon is more likely and the second position less likely to fix mutations than would be expected on the basis of the number of ways that alternative amino acids can be reached; 8, the character of nucleotide replacements is enormously non-random, with GA interchanges representing 42% of those observed in the first nucleotide position, but the observation does not stem from a bias in the DNA strand receiving the mutation, nor from the presence of a compositional equilibrium, nor from a bias in the frequency with which different nucleotides mutate, but rather from a bias in the acceptability of an alternative nucleotide as circumscribed by the functional acceptability of the new amino acid encoded; and 9, the unit evolutionary period is approximately 150 million years/observable (amino acid changing) nucleotide replacement/cytochrome c covarion in two diverging lines.Wherever non-randomness has been observed, it has always been consistent with the consideration that an alternative amino acid at any location is more likely to be acceptable the more closely it resembles the present amino acid in its physico-chemical properties.Finally, in no case did the a priori assumption of a biologically realistic phylogeny lead to any observations or conclusions that were in any way significantly different from those obtained when the phylogeny was based solely upon the sequences, proving that the earlier results were not a consequence of some internal circularity.