An empirical codon model for protein sequence evolution

In the past, 2 kinds of Markov models have been considered to describe protein sequence evolution. Codon-level models have been mechanistic with a small number of parameters designed to take into account features, such as transition-transversion bias, codon frequency bias, and synonymous-nonsynonymous amino acid substitution bias. Amino acid models have been empirical, attempting to summarize the replacement patterns observed in large quantities of data and not explicitly considering the distinct factors that shape protein evolution. We have estimated the first empirical codon model (ECM). Previous codon models assume that protein evolution proceeds only by successive single nucleotide substitutions, but our results indicate that model accuracy is significantly improved by incorporating instantaneous doublet and triplet changes. We also find that the affiliations between codons, the amino acid each encodes and the physicochemical properties of the amino acids are main factors driving the process of codon evolution. Neither multiple nucleotide changes nor the strong influence of the genetic code nor amino acids' physicochemical properties form a part of standard mechanistic models and their views of how codon evolution proceeds. We have implemented the ECM for likelihood-based phylogenetic analysis, and an assessment of its ability to describe protein evolution shows that it consistently outperforms comparable mechanistic codon models. We point out the biological interpretation of our ECM and possible consequences for studies of selection.     

Mutation-selection models of codon substitution and their use to estimate selective strengths on codon usage

Current models of codon substitution are formulated at the levels of nucleotide substitution and do not explicitly consider the separate effects of mutation and selection. They are thus incapable of inferring whether mutation or selection is responsible for evolution at silent sites. Here we implement a few population genetics models of codon substitution that explicitly consider mutation bias and natural selection at the DNA level. Selection on codon usage is modeled by introducing codon-fitness parameters, which together with mutation-bias parameters, predict optimal codon frequencies for the gene. The selective pressure may be for translational efficiency and accuracy or for fine-tuning translational kinetics to produce correct protein folding. We apply the models to compare mitochondrial and nuclear genes from several mammalian species. Model assumptions concerning codon usage are found to affect the estimation of sequence distances (such as the synonymous rate d(S), the nonsynonymous rate d(N), and the rate at the 4-fold degenerate sites d(4)), as found in previous studies, but the new models produced very similar estimates to some old ones. We also develop a likelihood ratio test to examine the null hypothesis that codon usage is due to mutation bias alone, not influenced by natural selection. Application of the test to the mammalian data led to rejection of the null hypothesis in most genes, suggesting that natural selection may be a driving force in the evolution of synonymous codon usage in mammals. Estimates of selection coefficients nevertheless suggest that selection on codon usage is weak and most mutations are nearly neutral. The sensitivity of the analysis on the assumed mutation model is discussed.     

Intragenomic variation in non-adaptive nucleotide biases causes underestimation of selection on synonymous codon usage

Patterns of non-uniform usage of synonymous codons vary across genes in an organism and between species across all domains of life. This codon usage bias (CUB) is due to a combination of non-adaptive (e.g. mutation biases) and adaptive (e.g. natural selection for translation efficiency/accuracy) evolutionary forces. Most models quantify the effects of mutation bias and selection on CUB assuming uniform mutational and other non-adaptive forces across the genome. However, non-adaptive nucleotide biases can vary within a genome due to processes such as biased gene conversion (BGC), potentially obfuscating signals of selection on codon usage. Moreover, genome-wide estimates of non-adaptive nucleotide biases are lacking for non-model organisms. We combine an unsupervised learning method with a population genetics model of synonymous coding sequence evolution to assess the impact of intragenomic variation in non-adaptive nucleotide bias on quantification of natural selection on synonymous codon usage across 49 Saccharomycotina yeasts. We find that in the absence of a priori information, unsupervised learning can be used to identify genes evolving under different non-adaptive nucleotide biases. We find that the impact of intragenomic variation in non-adaptive nucleotide bias varies widely, even among closely-related species. We show that the overall strength and direction of translational selection can be underestimated by failing to account for intragenomic variation in non-adaptive nucleotide biases. Interestingly, genes falling into clusters identified by machine learning are also physically clustered across chromosomes. Our results indicate the need for more nuanced models of sequence evolution that systematically incorporate the effects of variable non-adaptive nucleotide biases on codon frequencies.     

Studying Patterns of Recent Evolution at Synonymous Sites and Intronic Sites in Drosophila melanogaster

Most previous studies of the evolution of codon usage bias (CUB) and intronic GC content (iGC) in Drosophila melanogaster were based on between-species comparisons, reflecting long-term evolutionary events. However, a complete picture of the evolution of CUB and iGC cannot be drawn without knowledge of their more recent evolutionary history. Here, we used a polymorphism dataset collected from Zimbabwe to study patterns of the recent evolution of CUB and iGC. Analyzing coding and intronic data jointly with a model which can simultaneously estimate selection, mutational, and demographic parameters, we have found that: (1) natural selection is probably acting on synonymous codons; (2) a constant population size model seems to be sufficient to explain most of the observed synonymous polymorphism patterns; (3) GC is favored over AT in introns. In agreement with the long-term evolutionary patterns, ongoing selection acting on X-linked synonymous codons is stronger than that acting on autosomal codons. The selective differences between preferred and unpreferred codons tend to be greater than the differences between GC and AT in introns, suggesting that natural selection, not just biased gene conversion, may have influenced the evolution of CUB. Interestingly, evidence for non-equilibrium evolution comes exclusively from the intronic data. However, three different models, an equilibrium model with two classes of selected sites and two non-equilibrium models with changes in either population size or mutational parameters, fit the intronic data equally well. These results show that using inadequate selection (or demographic) models can result in incorrect estimates of demographic (or selection) parameters.     

Inference of Functional Divergence Among Proteins When the Evolutionary Process is Non-stationary

Functional shifts during protein evolution are expected to yield shifts in substitution rate, and statistical methods can test for this at both codon and amino acid levels. Although methods based on models of sequence evolution serve as powerful tools for studying evolutionary processes, violating underlying assumptions can lead to false biological conclusions. It is not unusual for functional shifts to be accompanied by changes in other aspects of the evolutionary process, such as codon or amino acid frequencies. However, models used to test for functional divergence assume these frequencies remain constant over time. We employed simulation to investigate the impact of non-stationary evolution on functional divergence inference. We investigated three likelihood ratio tests based on codon models and found varying degrees of sensitivity. Joint effects of shifts in frequencies and selection pressures can be large, leading to false signals for positive selection. Amino acid-based tests (FunDi and Bivar) were also compromised when several aspects of the substitution process were not adequately modeled. We applied the same tests to a core genome “scan” for functional divergence between light-adapted ecotypes of the cyanobacteria Prochlorococcus, and carried out gene-specific simulations for ten genes. Results of those simulations illustrated how the inference of functional divergence at the genomic level can be seriously impacted by model misspecification. Although computationally costly, simulations motivated by data in hand are warranted when several aspects of the substitution process are either misspecified or not included in the models upon which the statistical tests were built.     

Likelihood-based clustering (LiBaC) for codon models, a method for grouping sites according to similarities in the underlying process of evolution

Models of codon evolution are useful for investigating the strength and direction of natural selection via a parameter for the nonsynonymous/synonymous rate ratio (omega = d(N)/d(S)). Different codon models are available to account for diversity of the evolutionary patterns among sites. Codon models that specify data partitions as fixed effects allow the most evolutionary diversity among sites but require that site partitions are a priori identifiable. Models that use a parametric distribution to express the variability in the omega ratio across site do not require a priori partitioning of sites, but they permit less among-site diversity in the evolutionary process. Simulation studies presented in this paper indicate that differences among sites in estimates of omega under an overly simplistic analytical model can reflect more than just natural selection pressure. We also find that the classic likelihood ratio tests for positive selection have a high false-positive rate in some situations. In this paper, we developed a new method for assigning codon sites into groups where each group has a different model, and the likelihood over all sites is maximized. The method, called likelihood-based clustering (LiBaC), can be viewed as a generalization of the family of model-based clustering approaches to models of codon evolution. We report the performance of several LiBaC-based methods, and selected alternative methods, over a wide variety of scenarios. We find that LiBaC, under an appropriate model, can provide reliable parameter estimates when the process of evolution is very heterogeneous among groups of sites. Certain types of proteins, such as transmembrane proteins, are expected to exhibit such heterogeneity. A survey of genes encoding transmembrane proteins suggests that overly simplistic models could be leading to false signal for positive selection among such genes. In these cases, LiBaC-based methods offer an important addition to a "toolbox" of methods thereby helping to uncover robust evidence for the action of positive selection.     

Benchmarking Multi-Rate Codon Models

The single rate codon model of non-synonymous substitution is ubiquitous in phylogenetic modeling. Indeed, the use of a non-synonymous to synonymous substitution rate ratio parameter has facilitated the interpretation of selection pressure on genomes. Although the single rate model has achieved wide acceptance, we argue that the assumption of a single rate of non-synonymous substitution is biologically unreasonable, given observed differences in substitution rates evident from empirical amino acid models. Some have attempted to incorporate amino acid substitution biases into models of codon evolution and have shown improved model performance versus the single rate model. Here, we show that the single rate model of non-synonymous substitution is easily outperformed by a model with multiple non-synonymous rate classes, yet in which amino acid substitution pairs are assigned randomly to these classes. We argue that, since the single rate model is so easy to improve upon, new codon models should not be validated entirely on the basis of improved model fit over this model. Rather, we should strive to both improve on the single rate model and to approximate the general time-reversible model of codon substitution, with as few parameters as possible, so as to reduce model over-fitting. We hint at how this can be achieved with a Genetic Algorithm approach in which rate classes are assigned on the basis of sequence information content.     

Evidence for the adaptive evolution of the carbon fixation gene rbcL during diversification in temperature tolerance of a clade of hot spring cyanobacteria

Determining the molecular basis of enzyme adaptation is central to understanding the evolution of environmental tolerance but is complicated by the fact that not all amino acid differences between ecologically divergent taxa are adaptive. Analysing patterns of nucleotide sequence evolution can potentially guide the investigation of protein adaptation by identifying candidate codon sites on which diversifying selection has been operating. Here, I test whether there is evidence for molecular adaptation of the carbon fixation gene rbcL for a clade of hot spring cyanobacteria in the genus Synechococcus that has diverged in thermotolerance. Amino acid replacements during Synechococcus radiation have resulted in an increase in the number of hydrophobic residues in the RbcLs of more thermotolerant strains. A similar increase in hydrophobicity has been observed for many thermostable proteins. Maximum likelihood models which allow for heterogeneity among codon sites in the ratio of nonsynonymous to synonymous nucleotide substitutions estimated a class of amino acid sites as a target of positive selection. Depending on the model, a single amino acid site that interacts with a flexible element involved in the opening and closing of the active site was estimated with either low or moderate support to be a member of this class. Site-directed mutagenesis approaches are being explored in order to directly test its adaptive significance.     

Inferring parameters of mutation, selection and demography from patterns of synonymous site evolution in Drosophila

Selection acting on codon usage can cause patterns of synonymous evolution to deviate considerably from those expected under neutrality. To investigate the quantitative relationship between parameters of mutation, selection, and demography, and patterns of synonymous site divergence, we have developed a novel combination of population genetic models and likelihood methods of phylogenetic sequence analysis. Comparing 50 orthologous gene pairs from Drosophila melanogaster and D. virilis and 27 from D. melanogaster and D. simulans, we show considerable variation between amino acids and genes in the strength of selection acting on codon usage and find evidence for both long-term and short-term changes in the strength of selection between species. Remarkably, D. melanogaster shows no evidence of current selection on codon usage, while its sister species D. simulans experiences only half the selection pressure for codon usage of their common ancestor. We also find evidence for considerable base asymmetries in the rate of mutation, such that the average synonymous mutation rate is 20-30% higher than in noncoding regions. A Bayesian approach is adopted to investigate how accounting for selection on codon usage influences estimates of the parameters of mutation.     

Evidence from simulation studies for selective constraints on the codon usage of the Angiosperm psbA gene

The codon usage of the Angiosperm psbA gene is atypical for flowering plant chloroplast genes but similar to the codon usage observed in highly expressed plastid genes from some other Plantae, particularly Chlorobionta, lineages. The pattern of codon bias in these genes is suggestive of selection for a set of translationally optimal codons but the degree of bias towards these optimal codons is much weaker in the flowering plant psbA gene than in high expression plastid genes from lineages such as certain green algal groups. Two scenarios have been proposed to explain these observations. One is that the flowering plant psbA gene is currently under weak selective constraints for translation efficiency, the other is that there are no current selective constraints and we are observing the remnants of an ancestral codon adaptation that is decaying under mutational pressure. We test these two models using simulations studies that incorporate the context-dependent mutational properties of plant chloroplast DNA. We first reconstruct ancestral sequences and then simulate their evolution in the absence of selection on codon usage by using mutation dynamics estimated from intergenic regions. The results show that psbA has a significantly higher level of codon adaptation than expected while other chloroplast genes are within the range predicted by the simulations. These results suggest that there have been selective constraints on the codon usage of the flowering plant psbA gene during Angiosperm evolution.     

Adaptive evolution after duplication of penaeidin antimicrobial peptides

Penaeidin antimicrobial peptides in penaeid shrimps are an important component of their innate immune system that provides immunity against infection caused by several gram-positive bacteria and filamentous fungal species. Despite the knowledge on the identification and characterization of these peptides in penaeid shrimps, little is known about the evolutionary pattern of these peptides and the underlying genetic mechanisms that maintain high sequence diversities in the penaeidin gene family. Based on the phylogenetic analyses and maximum likelihood-based codon substitution analyses, here we present the convincing evidence that multiple copies of penaeidins have evolved by gene duplication, and positive Darwinian selection (adaptive evolution) is the likely cause of accelerated rate of amino acid substitutions among these duplicated genes. While the average ratio of non-synonymous to synonymous substitutions (omega) for the entire coding region of both active domains is 0.9805, few codon sites showed significantly higher omega (3.73). The likelihood ratio tests that compare models incorporating positive selection (omega>1) at certain codon sites with models not incorporating positive selection (omega<1), failed to reject (p=0) the evidence of positive Darwinian selection. The rapid adaptive evolution of this gene family might be directed by the pathogens and the faster rate of amino acid substitutions in the N-terminal proline-rich and C-terminal cysteine-rich domains could be due to their direct involvement in the protection against pathogens. When the host expose to different habitats/environment an accelerated rate of amino acid substitutions in both the active domains may also be expected.     

Investigating protein-coding sequence evolution with probabilistic codon substitution models

This review is motivated by the true explosion in the number of recent studies both developing and ameliorating probabilistic models of codon evolution. Traditionally parametric, the first codon models focused on estimating the effects of selective pressure on the protein via an explicit parameter in the maximum likelihood framework. Likelihood ratio tests of nested codon models armed the biologists with powerful tools, which provided unambiguous evidence for positive selection in real data. This, in turn, triggered a new wave of methodological developments. The new generation of models views the codon evolution process in a more sophisticated way, relaxing several mathematical assumptions. These models make a greater use of physicochemical amino acid properties, genetic code machinery, and the large amounts of data from the public domain. The overview of the most recent advances on modeling codon evolution is presented here, and a wide range of their applications to real data is discussed. On the downside, availability of a large variety of models, each accounting for various biological factors, increases the margin for misinterpretation; the biological meaning of certain parameters may vary among models, and model selection procedures also deserve greater attention. Solid understanding of the modeling assumptions and their applicability is essential for successful statistical data analysis.     

Gene expression and molecular evolution

The combination of complete genome sequence information and estimates of mRNA abundances have begun to reveal causes of both silent and protein sequence evolution. Translational selection appears to explain patterns of synonymous codon usage in many prokaryotes as well as a number of eukaryotic model organisms (with the notable exception of vertebrates). Relationships between gene length and codon usage bias, however, remain unexplained. Intriguing correlations between expression patterns and protein divergence suggest some general mechanisms underlying protein evolution.     

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.     

Methods for selecting fixed-effect models for heterogeneous codon evolution,with comments on their application to gene and genome data

Background

Models of codon evolution have proven useful for investigating the strength and direction of natural selection. In some cases, a priori biological knowledge has been used successfully to model heterogeneous evolutionary dynamics among codon sites. These are called fixed-effect models, and they require that all codon sites are assigned to one of several partitions which are permitted to have independent parameters for selection pressure, evolutionary rate, transition to transversion ratio or codon frequencies. For single gene analysis, partitions might be defined according to protein tertiary structure, and for multiple gene analysis partitions might be defined according to a gene's functional category. Given a set of related fixed-effect models, the task of selecting the model that best fits the data is not trivial.

Results

In this study, we implement a set of fixed-effect codon models which allow for different levels of heterogeneity among partitions in the substitution process. We describe strategies for selecting among these models by a backward elimination procedure, Akaike information criterion (AIC) or a corrected Akaike information criterion (AICc). We evaluate the performance of these model selection methods via a simulation study, and make several recommendations for real data analysis. Our simulation study indicates that the backward elimination procedure can provide a reliable method for model selection in this setting. We also demonstrate the utility of these models by application to a single-gene dataset partitioned according to tertiary structure (abalone sperm lysin), and a multi-gene dataset partitioned according to the functional category of the gene (flagellar-related proteins of Listeria).

Conclusion

Fixed-effect models have advantages and disadvantages. Fixed-effect models are desirable when data partitions are known to exhibit significant heterogeneity or when a statistical test of such heterogeneity is desired. They have the disadvantage of requiring a priori knowledge for partitioning sites. We recommend: (i) selection of models by using backward elimination rather than AIC or AICc, (ii) use a stringent cut-off, e.g., p = 0.0001, and (iii) conduct sensitivity analysis of results. With thoughtful application, fixed-effect codon models should provide a useful tool for large scale multi-gene analyses.

     

Selecting the best-fit model of nucleotide substitution

Despite the relevant role of models of nucleotide substitution in phylogenetics, choosing among different models remains a problem. Several statistical methods for selecting the model that best fits the data at hand have been proposed, but their absolute and relative performance has not yet been characterized. In this study, we compare under various conditions the performance of different hierarchical and dynamic likelihood ratio tests, and of Akaike and Bayesian information methods, for selecting best-fit models of nucleotide substitution. We specifically examine the role of the topology used to estimate the likelihood of the different models and the importance of the order in which hypotheses are tested. We do this by simulating DNA sequences under a known model of nucleotide substitution and recording how often this true model is recovered by the different methods. Our results suggest that model selection is reasonably accurate and indicate that some likelihood ratio test methods perform overall better than the Akaike or Bayesian information criteria. The tree used to estimate the likelihood scores does not influence model selection unless it is a randomly chosen tree. The order in which hypotheses are tested, and the complexity of the initial model in the sequence of tests, influence model selection in some cases. Model fitting in phylogenetics has been suggested for many years, yet many authors still arbitrarily choose their models, often using the default models implemented in standard computer programs for phylogenetic estimation. We show here that a best-fit model can be readily identified. Consequently, given the relevance of models, model fitting should be routine in any phylogenetic analysis that uses models of evolution.     

Genetic robustness and selection at the protein level for synonymous codons

Synonymous codons are neutral at the protein level, therefore natural selection at the protein level should have no effect on their frequencies. Synonymous codons, however, differ in their capacity to reduce the effects of errors: after mutation, certain codons keep on coding for the same amino acid or for amino acids with similar properties, while other synonymous codons produce very different amino acids. Therefore, the impact of errors on a coding sequence (genetic robustness) can be measured by analysing its codon usage. I analyse the codon usage of sequenced nuclear and cytoplasmic genomes and I show that there is an extensive variation in genetic robustness at the DNA sequence level, both among genomes and among genes of the same genome. I also show theoretically that robustness can be adaptive, that is natural selection may lead to a preference for codons that reduce the impact of errors. If selection occurs only among the mutants of a codon (e.g. among the progeny before the adult phase), however, the codons that are more sensitive to the effects of mutations may increase in frequency because they manage to get rid more easily of deleterious mutations. I also suggest other possible explanations for the evolution of genetic robustness at the codon level.     

Efficient selection of branch-specific models of sequence evolution

The analysis of extant sequences shows that molecular evolution has been heterogeneous through time and among lineages. However, for a given sequence alignment, it is often difficult to uncover what factors caused this heterogeneity. In fact, identifying and characterizing heterogeneous patterns of molecular evolution along a phylogenetic tree is very challenging, for lack of appropriate methods. Users either have to a priori define groups of branches along which they believe molecular evolution has been similar or have to allow each branch to have its own pattern of molecular evolution. The first approach assumes prior knowledge that is seldom available, and the second requires estimating an unreasonably large number of parameters. Here we propose a convenient and reliable approach where branches get clustered by their pattern of molecular evolution alone, with no need for prior knowledge about the data set under study. Model selection is achieved in a statistical framework and therefore avoids overparameterization. We rely on substitution mapping for efficiency and present two clustering approaches, depending on whether or not we expect neighbouring branches to share more similar patterns of sequence evolution than distant branches. We validate our method on simulations and test it on four previously published data sets. We find that our method correctly groups branches sharing similar equilibrium GC contents in a data set of ribosomal RNAs and recovers expected footprints of selection through dN/dS. Importantly, it also uncovers a new pattern of relaxed selection in a phylogeny of Mantellid frogs, which we are able to correlate to life-history traits. This shows that our programs should be very useful to study patterns of molecular evolution and reveal new correlations between sequence and species evolution. Our programs can run on DNA, RNA, codon, or amino acid sequences with a large set of possible models of substitutions and are available at http://biopp.univ-montp2.fr/forge/testnh.     

CpG site degeneration triggered by the loss of functional constraint created a highly polymorphic macaque drug-metabolizing gene, CYP1A2

Background

Duplicated genes frequently experience asymmetric rates of sequence evolution. Relaxed selective constraints and positive selection have both been invoked to explain the observation that one paralog within a gene-duplicate pair exhibits an accelerated rate of sequence evolution. In the majority of studies where asymmetric divergence has been established, there is no indication as to which gene copy, ancestral or derived, is evolving more rapidly. In this study we investigated the effect of local synteny (gene-neighborhood conservation) and codon usage on the sequence evolution of gene duplicates in the S. cerevisiae genome. We further distinguish the gene duplicates into those that originated from a whole-genome duplication (WGD) event (ohnologs) versus small-scale duplications (SSD) to determine if there exist any differences in their patterns of sequence evolution.

Results

For SSD pairs, the derived copy evolves faster than the ancestral copy. However, there is no relationship between rate asymmetry and synteny conservation (ancestral-like versus derived-like) in ohnologs. mRNA abundance and optimal codon usage as measured by the CAI is lower in the derived SSD copies relative to ancestral paralogs. Moreover, in the case of ohnologs, the faster-evolving copy has lower CAI and lowered expression.

Conclusions

Together, these results suggest that relaxation of selection for codon usage and gene expression contribute to rate asymmetry in the evolution of duplicated genes and that in SSD pairs, the relaxation of selection stems from the loss of ancestral regulatory information in the derived copy.     

Gene expression and protein length influence codon usage and rates of sequence evolution in Populus tremula

Codon bias is generally thought to be determined by a balance between mutation, genetic drift, and natural selection on translational efficiency. However, natural selection on codon usage is considered to be a weak evolutionary force and selection on codon usage is expected to be strongest in species with large effective population sizes. In this paper, I study associations between codon usage, gene expression, and molecular evolution at synonymous and nonsynonymous sites in the long-lived, woody perennial plant Populus tremula (Salicaceae). Using expression data for 558 genes derived from expressed sequence tags (EST) libraries from 19 different tissues and developmental stages, I study how gene expression levels within single tissues as well as across tissues affect codon usage and rates sequence evolution at synonymous and nonsynonymous sites. I show that gene expression have direct effects on both codon usage and the level of selective constraint of proteins in P. tremula, although in different ways. Codon usage genes is primarily determined by how highly expressed a genes is, whereas rates of sequence evolution are primarily determined by how widely expressed genes are. In addition to the effects of gene expression, protein length appear to be an important factor influencing virtually all aspects of molecular evolution in P. tremula.