Assessing Substitution Variation Across Sites in Grass Chloroplast DNA

We assess the similarity of base substitution processes, described by empirically derived 4 × 4 matrices, using chi-square homogeneity tests. Such significance analyses allow us to assess variation in sequence evolution across sites and we apply them to matrices derived from noncoding sites in different contexts in grass chloroplast DNA. We show that there is statistically significant variation in rates and patterns of mutation among noncoding sites in different contexts and then demonstrate a similar and significant influence of context on substitutions at fourfold degenerate sites of coding regions from grass chloroplast DNA. These results show that context has the same general effect on substitution bias in coding and noncoding DNA: the A+T content of flanking bases is correlated with rate of substitution, transition bias, and GC → AT pressure, while the number of flanking pyrimidines on a single strand is correlated with a mutational bias, or skew, toward pyrimidines. Despite the similarity in general trends, however, when we compare coding and noncoding matrices we find that there is a statistically significant difference between them even when we control for context. Most noticeably, fourfold degenerate sites in coding sequences are undergoing substitution at a higher rate and there are also significant differences in the relationship between pyrimidines skew and the number of flanking pyrimidines. Possible reasons for the differences between coding and noncoding sites are discussed. Furthermore, our analysis illustrates a simple statistical way for comparing substitution processes across sites allowing us to better study variation in evolutionary processes across a genome. [Reviewing Editor: Dr. Martin Kreitman]     

Substitution rates in hepatitis delta virus

Substitution rates were estimated for the coding and noncoding regions of the hepatitis delta virus (HDV). The estimated rates of synonymous substitution in HDV were lower than the rates of substitution at nonsynonymous sites and in the noncoding region. HDV has lower synonymous substitution rates than the hepatitis C virus, though both are RNA viruses. The relatively low rate of synonymous substitution in HDV may be due to a strong preference of G and C nucleotides at third codon positions. Variation in substitution rate among HDV lineages may be correlated with the clinical development of the HDV-induced hepatitis. The phylogenetic tree inferred for 24 HDV strains reveals similarities between lineages isolated from the same geographic region. Correspondence to: W.-H. Li     

Estimation of DNA Sequence Context-dependent Mutation Rates Using Primate Genomic Sequences

It is understood that DNA and amino acid substitution rates are highly sequence context-dependent, e.g., C --> T substitutions in vertebrates may occur much more frequently at CpG sites and that cysteine substitution rates may depend on support of the context for participation in a disulfide bond. Furthermore, many applications rely on quantitative models of nucleotide or amino acid substitution, including phylogenetic inference and identification of amino acid sequence positions involved in functional specificity. We describe quantification of the context dependence of nucleotide substitution rates using baboon, chimpanzee, and human genomic sequence data generated by the NISC Comparative Sequencing Program. Relative mutation rates are reported for the 96 classes of mutations of the form 5' alphabetagamma 3' --> 5' alphadeltagamma 3', where alpha, beta, gamma, and delta are nucleotides and beta not equal delta, based on maximum likelihood calculations. Our results confirm that C --> T substitutions are enhanced at CpG sites compared with other transitions, relatively independent of the identity of the preceding nucleotide. While, as expected, transitions generally occur more frequently than transversions, we find that the most frequent transversions involve the C at CpG sites (CpG transversions) and that their rate is comparable to the rate of transitions at non-CpG sites. A four-class model of the rates of context-dependent evolution of primate DNA sequences, CpG transitions > non-CpG transitions approximately CpG transversions > non-CpG transversions, captures qualitative features of the mutation spectrum. We find that despite qualitative similarity of mutation rates among different genomic regions, there are statistically significant differences.     

Combining phylogenetic and hidden Markov models in biosequence analysis.

A few models have appeared in recent years that consider not only the way substitutions occur through evolutionary history at each site of a genome, but also the way the process changes from one site to the next. These models combine phylogenetic models of molecular evolution, which apply to individual sites, and hidden Markov models, which allow for changes from site to site. Besides improving the realism of ordinary phylogenetic models, they are potentially very powerful tools for inference and prediction--for example, for gene finding or prediction of secondary structure. In this paper, we review progress on combined phylogenetic and hidden Markov models and present some extensions to previous work. Our main result is a simple and efficient method for accommodating higher-order states in the HMM, which allows for context-dependent models of substitution--that is, models that consider the effects of neighboring bases on the pattern of substitution. We present experimental results indicating that higher-order states, autocorrelated rates, and multiple functional categories all lead to significant improvements in the fit of a combined phylogenetic and hidden Markov model, with the effect of higher-order states being particularly pronounced.     

The Role of Context-Dependent Mutations in Generating Compositional and Codon Usage Bias in Grass Chloroplast DNA

Abstract The influence of local base composition on mutations in chloroplast DNA (cpDNA) is studied in detail and the resulting, empirically derived, mutation dynamics are used to analyze both base composition and codon usage bias. A 4 × 4 substitution matrix is generated for each of the 16 possible flanking base combinations (contexts) using 17,253 noncoding sites, 1309 of which are variable, from an alignment of three complete grass chloroplast genome sequences. It is shown that substitution bias at these sites is correlated with flanking base composition and that the A+T content of these flanking sites as well as the number of flanking pyrimidines on the same strand appears to have general influences on substitution properties. The context-dependent equilibrium base frequencies predicted from these matrices are then applied to two analyses. The first examines whether or not context dependency of mutations is sufficient to generate average compositional differences between noncoding cpDNA and silent sites of coding sequences. It is found that these two classes of sites exist, on average, in very different contexts and that the observed mutation dynamics are expected to generate significant differences in overall composition bias that are similar to the differences observed in cpDNA. Context dependency, however, cannot account for all of the observed differences: although silent sites in coding regions appear to be at the equilibrium predicted, noncoding cpDNA has a significantly lower A+T content than expected from its own substitution dynamics, possibly due to the influence of indels. The second study examines the codon usage of low-expression chloroplast genes. When context is accounted for, codon usage is very similar to what is predicted by the substitution dynamics of noncoding cpDNA. However, certain codon groups show significant deviation when followed by a purine in a manner suggesting some form of weak selection other than translation efficiency. Overall, the findings indicate that a full understanding of mutational dynamics is critical to understanding the role selection plays in generating composition bias and sequence structure.     

Not so different after all: a comparison of methods for detecting amino acid sites under selection

We consider three approaches for estimating the rates of nonsynonymous and synonymous changes at each site in a sequence alignment in order to identify sites under positive or negative selection: (1) a suite of fast likelihood-based "counting methods" that employ either a single most likely ancestral reconstruction, weighting across all possible ancestral reconstructions, or sampling from ancestral reconstructions; (2) a random effects likelihood (REL) approach, which models variation in nonsynonymous and synonymous rates across sites according to a predefined distribution, with the selection pressure at an individual site inferred using an empirical Bayes approach; and (3) a fixed effects likelihood (FEL) method that directly estimates nonsynonymous and synonymous substitution rates at each site. All three methods incorporate flexible models of nucleotide substitution bias and variation in both nonsynonymous and synonymous substitution rates across sites, facilitating the comparison between the methods. We demonstrate that the results obtained using these approaches show broad agreement in levels of Type I and Type II error and in estimates of substitution rates. Counting methods are well suited for large alignments, for which there is high power to detect positive and negative selection, but appear to underestimate the substitution rate. A REL approach, which is more computationally intensive than counting methods, has higher power than counting methods to detect selection in data sets of intermediate size but may suffer from higher rates of false positives for small data sets. A FEL approach appears to capture the pattern of rate variation better than counting methods or random effects models, does not suffer from as many false positives as random effects models for data sets comprising few sequences, and can be efficiently parallelized. Our results suggest that previously reported differences between results obtained by counting methods and random effects models arise due to a combination of the conservative nature of counting-based methods, the failure of current random effects models to allow for variation in synonymous substitution rates, and the naive application of random effects models to extremely sparse data sets. We demonstrate our methods on sequence data from the human immunodeficiency virus type 1 env and pol genes and simulated alignments.     

An expectation maximization algorithm for training hidden substitution models

We derive an expectation maximization algorithm for maximum-likelihood training of substitution rate matrices from multiple sequence alignments. The algorithm can be used to train hidden substitution models, where the structural context of a residue is treated as a hidden variable that can evolve over time. We used the algorithm to train hidden substitution matrices on protein alignments in the Pfam database. Measuring the accuracy of multiple alignment algorithms with reference to BAliBASE (a database of structural reference alignments) our substitution matrices consistently outperform the PAM series, with the improvement steadily increasing as up to four hidden site classes are added. We discuss several applications of this algorithm in bioinformatics.     

Neighboring base composition is strongly correlated with base substitution bias in a region of the chloroplast genome

Nucleotide sequence from a region of the chloroplast genome is presented for 12 species spanning four subfamilies of the grass family. The region contains the coding sequence for the rbcL gene and the intergenic spacer between the gene coding the large subunit of ribulose-1,5-bisphosphate carboxylase/oxygenase rbcL and the photosystem I gene psal. This intergenic spacer contains a pseudogene for rpl23 as well as two noncoding segments with different A+T contents. Using the sequence of rbcL a chloroplast phylogeny of this family was constructed by parsimony. Variable sites of the two noncoding segments were traced onto the phylogeny to study the dynamics of base substitution. This was also performed for the fourfold-degenerate sites of the rbcL gene. A wide variation in transversion/transition is observed between the two noncoding segments and between the noncoding DNA and the fourfold-degenerate sites of rbcL This variation is correlated with regional A+T content. As regional A+T content decreases, the ratio of transversions to transitions also decreases. Substitutions were then scored in relation to neighboring base composition. The composition of the two bases immediately flanking each substitution is highly correlated with the transversion/transition bias. When both the 5 and 3 flanking bases are an A or a T, transversions are observed 2.2 times as frequently as transitions. When either or both neighbors are a C or a G, the opposite trend is found; transitions are observed 1.5 times more frequently than transversions. Correspondence to: Brian R. Morton     

The Influence of Specific Neighboring Bases on Substitution Bias in Noncoding Regions of the Plant Chloroplast Genome

Substitutions occurring in noncoding sequences of the plant chloroplast genome violate the independence of sites that is assumed by substitution models in molecular evolution. The probability that a substitution at a site is a transversion, as opposed to a transition, increases significantly with increasing A + T content of the two adjacent nucleotides. In the present study, this dependency of substitutions on local context is examined further in a number of noncoding regions from the chloroplast genome of members of the grass family (Poaceae). Two features were examined; the influence of specific neighboring bases, as opposed to the general A + T content, on transversion proportion and an influence on substitutions by nucleotides other than the two immediately adjacent to the site of substitution. In both cases, a significant effect was found. In the case of specific nucleotides, transversion proportion is significantly higher at sites with a pyrimidine immediately 5′ on either strand. Substitutions at sites of the type YNR, where N is the site of substitution, have the highest rate of transversion. This specific effect is secondary to the A + T content effect such that, in terms of proportion of substitutions that are transversions, the nucleotides are ranked T > A > C > G as to their effect when they are immediately 5′ to the site of substitution. In the case of nucleotides other than the immediate neighbors, a significant influence on substitution dynamics is observed in the case where the two neighboring bases are both A and/or T. Thus, substitutions are primarily, but not exclusively, influenced by the composition of the two nucleotides that are immediately adjacent. These results indicate that the pattern of molecular evolution of the plant chloroplast genome is extremely complex as a result of a variety of inter-site dependencies. Received: 18 October 1996 / Accepted: 12 April 1997     

Relative rates of evolution in the coding and control regions of African mtDNAs

Reduced median networks of African haplogroup L mitochondrial DNA (mtDNA) sequences were analyzed to determine the pattern of substitutions in both the noncoding control and coding regions. In particular, we attempted to determine the causes of the previously reported (Howell et al. 2004) violation of the molecular clock during the evolution of these sequences. In the coding region, there was a significantly higher rate of substitution at synonymous sites than at nonsynonymous sites as well as in the tRNA and rRNA genes. This is further evidence for the operation of purifying selection during human mtDNA evolution. For most sites in the control region, the relative rate of substitution was similar to the rate of neutral evolution (assumed to be most closely approximated by the substitution rate at 4-fold degenerate sites). However, there are a number of mutational hot spots in the control region, approximately 3% of the total sites, that have a rate of substitution greater than the neutral rate, at some sites by more than an order of magnitude. It is possible either that these sites are evolving under conditions of positive selection or that the substitution rate at some sites in the control region is strongly dependent upon sequence context. Finally, we obtained preliminary evidence for "nonideal" evolution in the control region, including haplogroup-specific substitution patterns and a decoupling between relative rates of substitution in the control and coding regions.     

An evolutionary model for protein-coding regions with conserved RNA structure

Here we present a model of nucleotide substitution in protein-coding regions that also encode the formation of conserved RNA structures. In such regions, apparent evolutionary context dependencies exist, both between nucleotides occupying the same codon and between nucleotides forming a base pair in the RNA structure. The overlap of these fundamental dependencies is sufficient to cause "contagious" context dependencies which cascade across many nucleotide sites. Such large-scale dependencies challenge the use of traditional phylogenetic models in evolutionary inference because they explicitly assume evolutionary independence between short nucleotide tuples. In our model we address this by replacing context dependencies within codons by annotation-specific heterogeneity in the substitution process. Through a general procedure, we fragment the alignment into sets of short nucleotide tuples based on both the protein coding and the structural annotation. These individual tuples are assumed to evolve independently, and the different tuple sets are assigned different annotation-specific substitution models shared between their members. This allows us to build a composite model of the substitution process from components of traditional phylogenetic models. We applied this to a data set of full-genome sequences from the hepatitis C virus where five RNA structures are mapped within the coding region. This allowed us to partition the effects of selection on different structural elements and to test various hypotheses concerning the relation of these effects. Of particular interest, we found evidence of a functional role of loop and bulge regions, as these were shown to evolve according to a different and more constrained selective regime than the nonpairing regions outside the RNA structures. Other potential applications of the model include comparative RNA structure prediction in coding regions and RNA virus phylogenetics.     

A Space-Time Process Model for the Evolution of DNA Sequences

We describe a model for the evolution of DNA sequences by nucleotide substitution, whereby nucleotide sites in the sequence evolve over time, whereas the rates of substitution are variable and correlated over sites. The temporal process used to describe substitutions between nucleotides is a continuous-time Markov process, with the four nucleotides as the states. The spatial process used to describe variation and dependence of substitution rates over sites is based on a serially correlated gamma distribution, i.e., an auto-gamma model assuming Markov-dependence of rates at adjacent sites. To achieve computational efficiency, we use several equal-probability categories to approximate the gamma distribution, and the result is an auto-discrete-gamma model for rates over sites. Correlation of rates at sites then is modeled by the Markov chain transition of rates at adjacent sites from one rate category to another, the states of the chain being the rate categories. Two versions of nonparametric models, which place no restrictions on the distributional forms of rates for sites, also are considered, assuming either independence or Markov dependence. The models are applied to data of a segment of mitochondrial genome from nine primate species. Model parameters are estimated by the maximum likelihood method, and models are compared by the likelihood ratio test. Tremendous variation of rates among sites in the sequence is revealed by the analyses, and when rate differences for different codon positions are appropriately accounted for in the models, substitution rates at adjacent sites are found to be strongly (positively) correlated. Robustness of the results to uncertainty of the phylogenetic tree linking the species is examined.     

Molecular evolution of the hepatitis B virus genome

The hepatitis B virus (HBV) has a circular DNA genome of about 3,200 base pairs. Economical use of the genome with overlapping reading frames may have led to severe constraints on nucleotide substitutions along the genome and to highly variable rates of substitution among nucleotide sites. Nucleotide sequences from 13 complete HBV genomes were compared to examine such variability of substitution rates among sites and to examine the phylogenetic relationships among the HBV variants. The maximum likelihood method was employed to fit models of DNA sequence evolution that can account for the complexity of the pattern of nucleotide substitution. Comparison of the models suggests that the rates of substitution are different in different genes and codon positions; for example, the third codon position changes at a rate over ten times higher than the second position. Furthermore, substantial variation of substitution rates was detected even after the effects of genes and codon positions were corrected; that is, rates are different at different sites of the same gene or at the same codon position. Such rates after the correction were also found to be positively correlated at adjacent sites, which indicated the existence of conserved and variable domains in the proteins encoded by the viral genome. A multiparameter model validates the earlier finding that the variation in nucleotide conservation is not random around the HBV genome. The test for the existence of a molecular clock suggests that substitution rates are more or less constant among lineages. The phylogenetic relationships among the viral variants were examined. Although the data do not seem to contain sufficient information to resolve the details of the phylogeny, it appears quite certain that the serotypes of the viral variants do not reflect their genetic relatedness. Correspondence to: Z. Yang     

Hypervariable noncoding sequences in Saccharomyces cerevisiae

Compared to protein-coding sequences, the evolution of noncoding sequences and the selective constraints placed on these sequences is not well characterized. To compare the evolution of coding and noncoding sequences, we have conducted a survey for DNA polymorphism at five randomly chosen loci among a diverse collection of 81 strains of Saccharomyces cerevisiae. Average rates of both polymorphism and divergence are 40% lower at noncoding sites and 90% lower at nonsynonymous sites in comparison to synonymous sites. Although noncoding and coding sequences show substantial variability in ratios of polymorphism to divergence, two of the loci, MLS1 and PDR10, show a higher rate of polymorphism at noncoding compared to synonymous sites. The high rate of polymorphism is not accompanied by a high rate of divergence and is limited to a few small regions. These hypervariable regions include sites with three segregating bases at a single site and adjacent polymorphic sites. We show that this clustering of polymorphic sites is significantly greater than one would expect on the basis of the spacing between polymorphic fourfold degenerate sites. Although hypervariable noncoding sequences could result from selection on regulatory mutations, they could also result from transient mutational hotspots.     

Context-Dependent Evolutionary Models for Non-Coding Sequences: An Overview of Several Decades of Research and an Analysis of Laurasiatheria and Primate Evolution

The past decade has seen a growing interest in evolutionary models that relax the assumption of site-independent evolution for non-coding sequences. While phylogenetic inference using such so-called context-dependent models is currently computationally prohibitive, these models have been shown to yield significant increases in model fit compared to site-independent evolutionary models, which remain the most widely used evolutionary models to study substitution patterns and perform phylogenetic inference. Context-dependent models have been shown to be suited to study the spontaneous deamination of cytosine in mammalian sequences. In this paper, I discuss various approaches presented in recent years to model context-dependent evolution. I start with discussing the empirical research and results that have led to the development of these models. To accurately estimate the context-dependent substitution patterns that arise from these models, accurate sampling of substitution histories under such models is required. Further, appropriate model selection techniques to assess model performance has become more important than ever, given the drastic increase in parameters of context-dependent models and the tendency of older model selection techniques to prefer parameter-rich models. I also present new results on two mammalian datasets (Primate and Laurasiatheria data) to shed a light on so-called lineage-dependent context-dependent evolution. I conclude this paper with a discussion on current challenges in the development of context-dependent modeling approaches.     

Choosing appropriate substitution models for the phylogenetic analysis of protein-coding sequences

Although phylogenetic inference of protein-coding sequences continues to dominate the literature, few analyses incorporate evolutionary models that consider the genetic code. This problem is exacerbated by the exclusion of codon-based models from commonly employed model selection techniques, presumably due to the computational cost associated with codon models. We investigated an efficient alternative to standard nucleotide substitution models, in which codon position (CP) is incorporated into the model. We determined the most appropriate model for alignments of 177 RNA virus genes and 106 yeast genes, using 11 substitution models including one codon model and four CP models. The majority of analyzed gene alignments are best described by CP substitution models, rather than by standard nucleotide models, and without the computational cost of full codon models. These results have significant implications for phylogenetic inference of coding sequences as they make it clear that substitution models incorporating CPs not only are a computationally realistic alternative to standard models but may also frequently be statistically superior.     

Phylogenetic Gaussian Process Model for the Inference of Functionally Important Regions in Protein Tertiary Structures

A critical question in biology is the identification of functionally important amino acid sites in proteins. Because functionally important sites are under stronger purifying selection, site-specific substitution rates tend to be lower than usual at these sites. A large number of phylogenetic models have been developed to estimate site-specific substitution rates in proteins and the extraordinarily low substitution rates have been used as evidence of function. Most of the existing tools, e.g. Rate4Site, assume that site-specific substitution rates are independent across sites. However, site-specific substitution rates may be strongly correlated in the protein tertiary structure, since functionally important sites tend to be clustered together to form functional patches. We have developed a new model, GP4Rate, which incorporates the Gaussian process model with the standard phylogenetic model to identify slowly evolved regions in protein tertiary structures. GP4Rate uses the Gaussian process to define a nonparametric prior distribution of site-specific substitution rates, which naturally captures the spatial correlation of substitution rates. Simulations suggest that GP4Rate can potentially estimate site-specific substitution rates with a much higher accuracy than Rate4Site and tends to report slowly evolved regions rather than individual sites. In addition, GP4Rate can estimate the strength of the spatial correlation of substitution rates from the data. By applying GP4Rate to a set of mammalian B7-1 genes, we found a highly conserved region which coincides with experimental evidence. GP4Rate may be a useful tool for the in silico prediction of functionally important regions in the proteins with known structures.     

Accounting for variation of substitution rates through time in Bayesian phylogeny reconstruction of Sapotoideae (Sapotaceae)

We used Bayesian phylogenetic analysis of 5 kb of chloroplast DNA data from 68 Sapotaceae species to clarify phylogenetic relationships within Sapotoideae, one of the two major clades within Sapotaceae. Variation in substitution rates through time was shown to be a very important aspect of molecular evolution for this data set. Relative rates tests indicated that changes in overall rate have taken place in several lineages during the history of the group and Bayes factors strongly supported a covarion model, which allows the rate of a site to vary over time, over commonly used models that only allow rates to vary across sites. Rate variation over time was actually found to be a more important model component than rate variation across sites. The covarion model was originally developed for coding gene sequences and has so far only been tested for this type of data. The fact that it performed so well with the present data set, consisting mainly of data from noncoding spacer regions, suggests that it deserves a wider consideration in model based phylogenetic inference. Repeatability of phylogenetic results was very difficult to obtain with the more parameter rich models, and analyses with identical settings often supported different topologies. Overparameterization may be the reason why the MCMC did not sample from the posterior distribution in these cases. The problem could, however, be overcome by using less parameter rich evolutionary models, and adjusting the MCMC settings. The phylogenetic results showed that two taxa, previously thought to belong in Sapotoideae, are not part of this group. Eberhardtia aurata is the sister of the two major Sapotaceae clades, Chrysophylloideae and Sapotoideae, and Neohemsleya usambarensis belongs in Chrysophylloideae. Within Sapotoideae two clades, Sideroxyleae and Sapoteae, were strongly supported. Bayesian analysis of the character history of some floral morphological traits showed that the ancestral type of flower in Sapotoideae may have been characterized by floral parts (sepals, petals, stamens, and staminodes) in single whorls of five, entire corolla lobes, and seeds with an adaxial hilum.