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.     

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.      

Directionality in the evolution of influenza A haemagglutinin

The evolution of haemagglutinin (HA), an important influenza virus antigen, has been the subject of intensive research for more than two decades. Many characteristics of HA's sequence evolution are captured by standard Markov chain substitution models. Such models assign equal fitness to all accessible amino acids at a site. We show, however, that such models strongly underestimate the number of homoplastic amino acid substitutions during the course of HA's evolution, i.e. substitutions that repeatedly give rise to the same amino acid at a site. We develop statistics to detect individual homoplastic events and find that they preferentially occur at positively selected epitopic sites. Our results suggest that the evolution of the influenza A HA, including evolution by positive selection, is strongly affected by the long-term site-specific preferences for individual amino acids.     

Modeling amino acid replacement.

The estimation of amino acid replacement frequencies during molecular evolution is crucial for many applications in sequence analysis. Score matrices for database search programs or phylogenetic analysis rely on such models of protein evolution. Pioneering work was done by Dayhoff et al. (1978) who formulated a Markov model of evolution and derived the famous PAM score matrices. Her estimation procedure for amino acid exchange frequencies is restricted to pairs of proteins that have a constant and small degree of divergence. Here we present an improved estimator, called the resolvent method, that is not subject to these limitations. This extension of Dayhoff's approach enables us to estimate an amino acid substitution model from alignments of varying degree of divergence. Extensive simulations show the capability of the new estimator to recover accurately the exchange frequencies among amino acids. Based on the SYSTERS database of aligned protein families (Krause and Vingron, 1998) we recompute a series of score matrices.     

Amino acid substitution of proteins coded for in mitochondrial DNA during mammalian evolution.

Three Markov models (Dayhoff, Proportional and Poisson models; Hasegawa et al., 1992a) for amino acid substitution during evolution were used for maximum likelihood analyses of proteins coded for in mitochondrial DNA in estimating a phylogenetic tree among human, bovine and murids (mouse and rat) with chicken as an outgroup. It turned out that Dayhoff model is the most appropriate model among the alternatives in approximating the amino acid substitutions of proteins coded for in mitochondrial DNA. In spite of the presence of the complete sequence data of mitochondrial genomes, we could not resolve the trichotomy among human, bovine and murids, probably because the time length separating two branching events among these three lines was short and because chicken is too distant from mammals to be used as an outgroup. It was suggested that the average substitution rate of amino acids coded for in mitochondrial DNA is lower along the bovine line than those along the human or murid lines. Advantages of amino acid sequence analysis over nucleotide sequence analysis in phylogenetic study were discussed.     

Estimating amino acid substitution models for metazoan evolutionary studies

Amino acid substitution models represent the substitution rates among amino acids during the evolution of protein sequences. The models are a prerequisite for maximum likelihood or Bayesian methods to analyse the phylogenetic relationships among species based on their protein sequences. Estimating amino acid substitution models requires large protein datasets and intensive computation. In this paper, we presented the estimation of both time-reversible model (Q.met) and time non-reversible model (NQ.met) for multicellular animals (Metazoa). Analyses showed that the Q.met and NQ.met models were significantly better than existing models in analysing metazoan protein sequences. Moreover, the time non-reversible model NQ.met enables us to reconstruct the rooted phylogenetic tree for Metazoa. We recommend researchers to employ the Q.met and NQ.met models in analysing metazoan protein sequences.     

Eigenvalue analysis of amino acid substitution matrices reveals a sharp transition of the mode of sequence conservation in proteins

The pattern of amino acid substitutions and sequence conservation over many structure-based alignments of protein sequences was analyzed as a function of percentage sequence identity. The statistics of the amino acid substitutions were converted into the form of log-odds amino acid substitution matrices to which eigenvalue decomposition was applied. It was found that the most important component of the substitution matrices exhibited a sharp transition at the sequence identity of 30-35%, which coincides with the twilight zone. Above the transition point, the most dominant component is related to the mutability of amino acids and it acts to disfavor any substitutions, whereas below the transition point, the most dominant component is related to the hydrophobicity of amino acids and substitutions between residues of similar hydrophobic character are positively favored. Implications for protein evolution and sequence analysis are discussed.     

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 reduced amino acid alphabets for phylogenetic inference

We investigate the use of Markov models of evolution for reduced amino acid alphabets or bins of amino acids. The use of reduced amino acid alphabets can ameliorate effects of model misspecification and saturation. We present algorithms for 2 different ways of automating the construction of bins: minimizing criteria based on properties of rate matrices and minimizing criteria based on properties of alignments. By simulation, we show that in the absence of model misspecification, the loss of information due to binning is found to be insubstantial, and the use of Markov models at the binned level is found to be almost as effective as the more appropriate missing data approach. By applying these approaches to real data sets where compositional heterogeneity and/or saturation appear to be causing biased tree estimation, we find that binning can improve topological estimation in practice.     

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.     

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 Bayesian hierarchical model for identifying epitopes in peptide microarray data

Peptide Microarray Immunoassay (PMI for brevity) is a novel technology that enables researchers to map a large number of proteomic measurements at a peptide level, providing information regarding the relationship between antibody response and clinical sensitivity. PMI studies aim at recognizing antigen-specific antibodies from serum samples and at detecting epitope regions of the protein antigen. PMI data present new challenges for statistical analysis mainly due to the structural dependence among peptides. A PMI is made of a complete library of consecutive peptides. They are synthesized by systematically shifting a window of a fixed number of amino acids through the finite sequence of amino acids of the antigen protein as ordered in the primary structure of the protein. This implies that consecutive peptides have a certain number of amino acids in common and hence are structurally dependent. We propose a new flexible Bayesian hierarchical model framework, which allows one to detect recognized peptides and bound epitope regions in a single framework, taking into account the structural dependence between peptides through a suitable latent Markov structure. The proposed model is illustrated using PMI data from a recent study about egg allergy. A simulation study shows that the proposed model is more powerful and robust in terms of epitope detection than simpler models overlooking some of the dependence structure.     

The interface of protein structure, protein biophysics, and molecular evolution

Abstract The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.     

FLU,an amino acid substitution model for influenza proteins

Background  

The amino acid substitution model is the core component of many protein analysis systems such as sequence similarity search, sequence alignment, and phylogenetic inference. Although several general amino acid substitution models have been estimated from large and diverse protein databases, they remain inappropriate for analyzing specific species, e.g., viruses. Emerging epidemics of influenza viruses raise the need for comprehensive studies of these dangerous viruses. We propose an influenza-specific amino acid substitution model to enhance the understanding of the evolution of influenza viruses.     

Protein family classification using sparse markov transducers.

We present a method for classifying proteins into families based on short subsequences of amino acids using a new probabilistic model called sparse Markov transducers (SMT). We classify a protein by estimating probability distributions over subsequences of amino acids from the protein. Sparse Markov transducers, similar to probabilistic suffix trees, estimate a probability distribution conditioned on an input sequence. SMTs generalize probabilistic suffix trees by allowing for wild-cards in the conditioning sequences. Since substitutions of amino acids are common in protein families, incorporating wild-cards into the model significantly improves classification performance. We present two models for building protein family classifiers using SMTs. As protein databases become larger, data driven learning algorithms for probabilistic models such as SMTs will require vast amounts of memory. We therefore describe and use efficient data structures to improve the memory usage of SMTs. We evaluate SMTs by building protein family classifiers using the Pfam and SCOP databases and compare our results to previously published results and state-of-the-art protein homology detection methods. SMTs outperform previous probabilistic suffix tree methods and under certain conditions perform comparably to state-of-the-art protein homology methods.     

Nucleotide substitution and recombination at orthologous loci in Staphylococcus aureus

The pattern of nucleotide substitution was examined at 2,129 orthologous loci among five genomes of Staphylococcus aureus, which included two sister pairs of closely related genomes (MW2/MSSA476 and Mu50/N315) and the more distantly related MRSA252. A total of 108 loci were unusual in lacking any synonymous differences among the five genomes; most of these were short genes encoding proteins highly conserved at the amino acid sequence level (including many ribosomal proteins) or unknown predicted genes. In contrast, 45 genes were identified that showed anomalously high divergence at synonymous sites. The latter genes were evidently introduced by homologous recombination from distantly related genomes, and in many cases, the pattern of nucleotide substitution made it possible to reconstruct the most probable recombination event involved. These recombination events introduced genes encoding proteins that differed in amino acid sequence and thus potentially in function. Several of the proteins are known or likely to be involved in pathogenesis (e.g., staphylocoagulase, exotoxin, Ser-Asp fibrinogen-binding bone sialoprotein-binding protein, fibrinogen and keratin-10 binding surface-anchored protein, fibrinogen-binding protein ClfA, and enterotoxin P). Therefore, the results support the hypothesis that exchange of homologous genes among S. aureus genomes can play a role in the evolution of pathogenesis in this species.     

REvolver: modeling sequence evolution under domain constraints

Simulating the change of protein sequences over time in a biologically realistic way is fundamental for a broad range of studies with a focus on evolution. It is, thus, problematic that typically simulators evolve individual sites of a sequence identically and independently. More realistic simulations are possible; however, they are often prohibited by limited knowledge concerning site-specific evolutionary constraints or functional dependencies between amino acids. As a consequence, a protein's functional and structural characteristics are rapidly lost in the course of simulated evolution. Here, we present REvolver (www.cibiv.at/software/revolver), a program that simulates protein sequence alteration such that evolutionarily stable sequence characteristics, like functional domains, are maintained. For this purpose, REvolver recruits profile hidden Markov models (pHMMs) for parameterizing site-specific models of sequence evolution in an automated fashion. pHMMs derived from alignments of homologous proteins or protein domains capture information regarding which sequence sites remained conserved over time and where in a sequence insertions or deletions are more likely to occur. Thus, they describe constraints on the evolutionary process acting on these sequences. To demonstrate the performance of REvolver as well as its applicability in large-scale simulation studies, we evolved the entire human proteome up to 1.5 expected substitutions per site. Simultaneously, we analyzed the preservation of Pfam and SMART domains in the simulated sequences over time. REvolver preserved 92% of the Pfam domains originally present in the human sequences. This value drops to 15% when traditional models of amino acid sequence evolution are used. Thus, REvolver represents a significant advance toward a realistic simulation of protein sequence evolution on a proteome-wide scale. Further, REvolver facilitates the simulation of a protein family with a user-defined domain architecture at the root.     

Clustering of amino acids for protein secondary structure prediction

Simple hidden Markov models are proposed for predicting secondary structure of a protein from its amino acid sequence. Since the length of protein conformation segments varies in a narrow range, we ignore the duration effect of length distribution, and focus on inclusion of short range correlations of residues and of conformation states in the models. Conformation-independent and -dependent amino acid coarse-graining schemes are designed for the models by means of proper mutual information. We compare models of different level of complexity, and establish a practical model with a high prediction accuracy.     

Detecting the coevolution of biosequences--an example of RNA interaction prediction

A probabilistic graphical model is proposed in order to detect the coevolution between different sites in biological sequences. The model extends the continuous-time Markov process of sequence substitution for single nucleic or amino acids and imposes general constraints regarding simultaneous changes on the substitution rate matrix. Given a multiple sequence alignment for each molecule of interest and a phylogenetic tree, the model can predict potential interactions within or between nucleic acids and proteins. Initial validation of the model is carried out using tRNA and 16S rRNA sequence data. The model accurately identifies the secondary interactions of tRNA as well as several known tertiary interactions. In addition, results on 16S rRNA data indicate this general and simple coevolutionary model outperforms several other parametric and nonparametric methods in predicting secondary interactions. Furthermore, the majority of the putative predictions exhibit either direct contact or proximity of the nucleotide pairs in the 3-dimensional structure of the Thermus thermophilus ribosomal small subunit. The results on RNA data suggest a general model of coevolution might be applied to other types of interactions between protein, DNA, and RNA molecules.