Genome bias influences amino acid choices: analysis of amino acid substitution and re-compilation of substitution matrices exclusive to an AT-biased genome

The genomic era has seen a remarkable increase in the number of genomes being sequenced and annotated. Nonetheless, annotation remains a serious challenge for compositionally biased genomes. For the preliminary annotation, popular nucleotide and protein comparison methods such as BLAST are widely employed. These methods make use of matrices to score alignments such as the amino acid substitution matrices. Since a nucleotide bias leads to an overall bias in the amino acid composition of proteins, it is possible that a genome with nucleotide bias may have introduced atypical amino acid substitutions in its proteome. Consequently, standard matrices fail to perform well in sequence analysis of these genomes. To address this issue, we examined the amino acid substitution in the AT-rich genome of Plasmodium falciparum, chosen as a reference and reconstituted a substitution matrix in the genome's context. The matrix was used to generate protein sequence alignments for the parasite proteins that improved across the functional regions. We attribute this to the consistency that may have been achieved amid the target and background frequencies calculated exclusively in our study. This study has important implications on annotation of proteins that are of experimental interest but give poor sequence alignments with standard conventional matrices.     

Estimation of amino acid residue substitution rates at local spatial regions and application in protein function inference: a Bayesian Monte Carlo approach

The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important because the rate matrix can be used to develop scoring matrices for sequence alignment. Here we use a continuous time Markov process to model the substitution rates of residues and develop a Bayesian Markov chain Monte Carlo method for rate estimation. We validate our method using simulated artificial protein sequences. Because different local regions such as binding surfaces and the protein interior core experience different selection pressures due to functional or stability constraints, we use our method to estimate the substitution rates of local regions. Our results show that the substitution rates are very different for residues in the buried core and residues on the solvent-exposed surfaces. In addition, the rest of the proteins on the binding surfaces also have very different substitution rates from residues. Based on these findings, we further develop a method for protein function prediction by surface matching using scoring matrices derived from estimated substitution rates for residues located on the binding surfaces. We show with examples that our method is effective in identifying functionally related proteins that have overall low sequence identity, a task known to be very challenging.     

Selective constraints on amino acids estimated by a mechanistic codon substitution model with multiple nucleotide changes

Background

Empirical substitution matrices represent the average tendencies of substitutions over various protein families by sacrificing gene-level resolution. We develop a codon-based model, in which mutational tendencies of codon, a genetic code, and the strength of selective constraints against amino acid replacements can be tailored to a given gene. First, selective constraints averaged over proteins are estimated by maximizing the likelihood of each 1-PAM matrix of empirical amino acid (JTT, WAG, and LG) and codon (KHG) substitution matrices. Then, selective constraints specific to given proteins are approximated as a linear function of those estimated from the empirical substitution matrices.

Results

Akaike information criterion (AIC) values indicate that a model allowing multiple nucleotide changes fits the empirical substitution matrices significantly better. Also, the ML estimates of transition-transversion bias obtained from these empirical matrices are not so large as previously estimated. The selective constraints are characteristic of proteins rather than species. However, their relative strengths among amino acid pairs can be approximated not to depend very much on protein families but amino acid pairs, because the present model, in which selective constraints are approximated to be a linear function of those estimated from the JTT/WAG/LG/KHG matrices, can provide a good fit to other empirical substitution matrices including cpREV for chloroplast proteins and mtREV for vertebrate mitochondrial proteins.

Conclusions/Significance

The present codon-based model with the ML estimates of selective constraints and with adjustable mutation rates of nucleotide would be useful as a simple substitution model in ML and Bayesian inferences of molecular phylogenetic trees, and enables us to obtain biologically meaningful information at both nucleotide and amino acid levels from codon and protein sequences.     

Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles

We review and further develop an analytical model that describes how thermodynamic constraints on the stability of the native state influence protein evolution in a site-specific manner. To this end, we represent both protein sequences and protein structures as vectors: structures are represented by the principal eigenvector (PE) of the protein contact matrix, a quantity that resembles closely the effective connectivity of each site; sequences are represented through the "interactivity" of each amino acid type, using novel parameters that are correlated with hydropathy scales. These interactivity parameters are more strongly correlated than the other hydropathy scales that we examine with: (1) the change upon mutations of the unfolding free energy of proteins with two-states thermodynamics; (2) genomic properties as the genome-size and the genome-wide GC content; (3) the main eigenvectors of the substitution matrices. The evolutionary average of the interactivity vector correlates very strongly with the PE of a protein structure. Using this result, we derive an analytic expression for site-specific distributions of amino acids across protein families in the form of Boltzmann distributions whose "inverse temperature" is a function of the PE component. We show that our predictions are in agreement with site-specific amino acid distributions obtained from the Protein Data Bank, and we determine the mutational model that best fits the observed site-specific amino acid distributions. Interestingly, the optimal model almost minimizes the rate at which deleterious mutations are eliminated by natural selection.     

Insights from modeling protein evolution with context-dependent mutation and asymmetric amino acid selection

We develop an approximate maximum likelihood method to estimate flanking nucleotide context-dependent mutation rates and amino acid exchange-dependent selection in orthologous protein-coding sequences and use it to analyze genome-wide coding sequence alignments from mammals and yeast. Allowing context-dependent mutation provides a better fit to coding sequence data than simpler (context-independent or CpG "hotspot") models and significantly affects selection parameter estimates. Allowing asymmetric (nonreciprocal) selection on amino acid exchanges gives a better fit than simple dN/dS or symmetric selection models. Relative selection strength estimates from our models show good agreement with independent estimates derived from human disease-causing and engineered mutations. Selection strengths depend on local protein structure, showing expected biophysical trends in helical versus nonhelical regions and increased asymmetry on polar-hydrophobic exchanges with increased burial. The more stringent selection that has previously been observed for highly expressed proteins is primarily concentrated in buried regions, supporting the notion that such proteins are under stronger than average selection for stability. Our analyses indicate that a highly parameterized model of mutation and selection is computationally tractable and is a useful tool for exploring a variety of biological questions concerning protein and coding sequence evolution.     

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.     

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.     

Modeling protein evolution with several amino Acid replacement matrices depending on site rates

Most protein substitution models use a single amino acid replacement matrix summarizing the biochemical properties of amino acids. However, site evolution is highly heterogeneous and depends on many factors that influence the substitution patterns. In this paper, we investigate the use of different substitution matrices for different site evolutionary rates. Indeed, the variability of evolutionary rates corresponds to one of the most apparent heterogeneity factors among sites, and there is no reason to assume that the substitution patterns remain identical regardless of the evolutionary rate. We first introduce LG4M, which is composed of four matrices, each corresponding to one discrete gamma rate category (of four). These matrices differ in their amino acid equilibrium distributions and in their exchangeabilities, contrary to the standard gamma model where only the global rate differs from one category to another. Next, we present LG4X, which also uses four different matrices, but leaves aside the gamma distribution and follows a distribution-free scheme for the site rates. All these matrices are estimated from a very large alignment database, and our two models are tested using a large sample of independent alignments. Detailed analysis of resulting matrices and models shows the complexity of amino acid substitutions and the advantage of flexible models such as LG4M and LG4X. Both significantly outperform single-matrix models, providing gains of dozens to hundreds of log-likelihood units for most data sets. LG4X obtains substantial gains compared with LG4M, thanks to its distribution-free scheme for site rates. Since LG4M and LG4X display such advantages but require the same memory space and have comparable running times to standard models, we believe that LG4M and LG4X are relevant alternatives to single replacement matrices. Our models, data, and software are available from http://www.atgc-montpellier.fr/models/lg4x.     

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.     

Physicochemical evolution and molecular adaptation of the cetacean and artiodactyl cytochrome b proteins

Cetaceans have most likely experienced metabolic shifts since evolutionarily diverging from their terrestrial ancestors, shifts that may be reflected in the proteins such as cytochrome b that are responsible for metabolic efficiency. However, accepted statistical methods for detecting molecular adaptation are largely biased against even moderately conservative proteins because the primary criterion involves a comparison of nonsynonymous and synonymous substitution rates (dN/dS); they do not allow for the possibility that adaptation may come in the form of very few amino acid changes. We apply the MM01 model to the possible molecular adaptation of cytochrome b among cetaceans because it does not rely on a dN/dS ratio, instead evaluating positive selection in terms of the amino acid properties that comprise protein phenotypes that selection at the molecular level may act upon. We also apply the codon-degeneracy model (CDM), which focuses on evaluating overall patterns of nucleotide substitution in terms of base exchange, codon position, and synonymy to estimate the overall effect of selection. Using these relatively new models, we characterize the molecular adaptation that has occurred in the cetacean cytochrome b protein by comparing revealed amino acid replacement patterns to those found among artiodactyls, the modern terrestrial mammals found to be most closely related to cetaceans. Our findings suggest that several regions of the cetacean cytochrome b protein have experienced molecular adaptation. Also, these adaptations are spatially associated with domain structure, protein function, and the structure and function of the cytochrome bc(1) complex and its constituents. We also have found a general correlation between the results of the analytical software programs TreeSAAP (which implements the MM01 model) and CDM (which implements the codon-degeneracy model).     

Evaluation of whether accelerated protein evolution in chordates has occurred before, after, or simultaneously with gene duplication

Gene duplication and loss are predicted to be at least of the order of the substitution rate and are key contributors to the development of novel gene function and overall genome evolution. Although it has been established that proteins evolve more rapidly after gene duplication, we were interested in testing to what extent this reflects causation or association. Therefore, we investigated the rate of evolution prior to gene duplication in chordates. Two patterns emerged; firstly, branches, which are both preceded by a duplication and followed by a duplication, display an elevated rate of amino acid replacement. This is reflected in the ratio of nonsynonymous to synonymous substitution (mean nonsynonymous to synonymous nucleotide substitution rate ratio [Ka:Ks]) of 0.44 compared with branches preceded by and followed by a speciation (mean Ka:Ks of 0.23). The observed patterns suggest that there can be simultaneous alteration in the selection pressures on both gene duplication and amino acid replacement, which may be consistent with co-occurring increases in positive selection, or alternatively with concurrent relaxation of purifying selection. The pattern is largely, but perhaps not completely, explained by the existence of certain families that have elevated rates of both gene duplication and amino acid replacement. Secondly, we observed accelerated amino acid replacement prior to duplication (mean Ka:Ks for postspeciation preduplication branches was 0.27). In some cases, this could reflect adaptive changes in protein function precipitating a gene duplication event. In conclusion, the circumstances surrounding the birth of new proteins may frequently involve a simultaneous change in selection pressures on both gene-copy number and amino acid replacement. More precise modeling of the relative importance of preduplication, postduplication, and simultaneous amino acid replacement will require larger and denser genomic data sets from multiple species, allowing simultaneous estimation of lineage-specific fluctuations in mutation rates and adaptive constraints.     

The construction of amino acid substitution matrices for the comparison of proteins with non-standard compositions

MOTIVATION: Amino acid substitution matrices play a central role in protein alignment methods. Standard log-odds matrices, such as those of the PAM and BLOSUM series, are constructed from large sets of protein alignments having implicit background amino acid frequencies. However, these matrices frequently are used to compare proteins with markedly different amino acid compositions, such as transmembrane proteins or proteins from organisms with strongly biased nucleotide compositions. It has been argued elsewhere that standard matrices are not ideal for such comparisons and, furthermore, a rationale has been presented for transforming a standard matrix for use in a non-standard compositional context. RESULTS: This paper presents the mathematical details underlying the compositional adjustment of amino acid or DNA substitution matrices.     

The evolution of electrophoretic mobility of proteins

A model was constructed that predicts the electric charge of a protein and its isoelectric point from its primary and quaternary structures. By using two different patterns of mutation and purifying selection, four schemes of nucleotide substitution were simulated. In the absence of selection for a specific value of pI, proteins are expected to evolve toward a mildly basic pI. Thus, the selection for maintaining extreme values of pI must be stringent, and proteins with extreme pI's will evolve very slowly. This prediction is consistent with observations on the evolution of histones and ubiquitin. The mean charge change is expected to be about 0.005 units pI per nucleotide substitution. The amount of electrophoretically hidden variation is expected to be considerable even for large degrees of divergence at the nucleotide and amino acid levels. Electrophoretic detectability depends on the size of the protein. The longer the protein the larger the amount of variation at the amino acid level that is undetectable by isoelectric focusing. This property may be partially responsible for the imperfect correlation between molecular weight and gene diversity observed for electrophoretic data. Very basic and very acidic proteins are expected to generate less electrophoretic variability than proteins with intermediate pI's. Unequal rates of mutation between nucleotides and asymmetrical patterns of purifying selection have almost no effect on the equilibrium pI of proteins, but affect the rates of change in pI, and increase the amount of electrophoretically hidden variation in comparison to the expectations derived from random patterns of mutation and constant selection. Comparison of detectability of protein differences among four electrophoretical techniques suggests that the best performance is obtained by the sequential electrophoresis method.     

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.     

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.     

Analysis of differences in amino acid substitution patterns, using multilevel G-tests

In this paper, a new algorithm is presented, which makes possible multilevel comparison of BLOSUM protein substitution matrices based on data from different groups of organisms. As an example, a comparison between substitution matrices based on data from two groups of bacterial genomes with different GC content is presented. Our approach includes evaluating the number of amino acid pairs in BLOCKS databases created separately for the two groups of bacteria using protein sequences deposited in the COG database. Differences of distributions of amino acid pair counts are tested using the chi-squared based G-test. Different analysis levels make it possible to distinguish different patterns of amino acid substitution. Application of the algorithm reveals statistically significant differences in amino acid substitution patterns between AT-rich and GC-rich groups of bacterial organisms. The differences are particularly visible in the overall substitution pattern, amino acid conservation pattern and in comparison of substitution patterns for single amino acids. The algorithm presented in this paper can be considered a novel method for multi-level comparison of amino acid substitution patterns. The presented approach is not limited to bacterial organisms and BLOSUM substitution matrices. Statistically significant differences between substitution patterns in the two groups of bacterial organisms with respect to amino acid conservation pattern can be the evidence of different rate of evolutionary change between AT-rich and GC-rich bacterial organisms.     

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.     

Prediction of site-specific amino acid distributions and limits of divergent evolutionary changes in protein sequences

We derive an analytic expression for site-specific stationary distributions of amino acids from the structurally constrained neutral (SCN) model of protein evolution with conservation of folding stability. The stationary distributions that we obtain have a Boltzmann-like shape, and their effective temperature parameter, measuring the limit of divergent evolutionary changes at a given site, can be predicted from a site-specific topological property, the principal eigenvector of the contact matrix of the native conformation of the protein. These analytic results, obtained without free parameters, are compared with simulations of the SCN model and with the site-specific amino acid distributions obtained from the Protein Data Bank. These results also provide new insights into how the topology of a protein fold influences its designability, i.e., the number of sequences compatible with that fold. The dependence of the effective temperature on the principal eigenvector decreases for longer proteins, as a possible consequence of the fact that selection for thermodynamic stability becomes weaker in this case.