Bayesian comparisons of codon substitution models

Next-generation development and application of codon model in evolution

To date, numerous nucleotide, amino acid, and codon substitution models have been developed to estimate the evolutionary history of any sequence/organism in a more comprehensive way. Out of these three, the codon substitution model is the most powerful. These models have been utilized extensively to detect selective pressure on a protein, codon usage bias, ancestral reconstruction and phylogenetic reconstruction. However, due to more computational demanding, in comparison to nucleotide and amino acid substitution models, only a few studies have employed the codon substitution model to understand the heterogeneity of the evolutionary process in a genome-scale analysis. Hence, there is always a question of how to develop more robust but less computationally demanding codon substitution models to get more accurate results. In this review article, the authors attempted to understand the basis of the development of different types of codon-substitution models and how this information can be utilized to develop more robust but less computationally demanding codon substitution models. The codon substitution model enables to detect selection regime under which any gene or gene region is evolving, codon usage bias in any organism or tissue-specific region and phylogenetic relationship between different lineages more accurately than nucleotide and amino acid substitution models. Thus, in the near future, these codon models can be utilized in the field of conservation, breeding and medicine.

An Improved Codon Modeling Approach for Accurate Estimation of the Mutation Bias

Phylogenetic codon models are routinely used to characterize selective regimes in coding sequences. Their parametric design, however, is still a matter of debate, in particular concerning the question of how to account for differing nucleotide frequencies and substitution rates. This problem relates to the fact that nucleotide composition in protein-coding sequences is the result of the interactions between mutation and selection. In particular, because of the structure of the genetic code, the nucleotide composition differs between the three coding positions, with the third position showing a more extreme composition. Yet, phylogenetic codon models do not correctly capture this phenomenon and instead predict that the nucleotide composition should be the same for all three positions. Alternatively, some models allow for different nucleotide rates at the three positions, an approach conflating the effects of mutation and selection on nucleotide composition. In practice, it results in inaccurate estimation of the strength of selection. Conceptually, the problem comes from the fact that phylogenetic codon models do not correctly capture the fixation bias acting against the mutational pressure at the mutation–selection equilibrium. To address this problem and to more accurately identify mutation rates and selection strength, we present an improved codon modeling approach where the fixation rate is not seen as a scalar, but as a tensor. This approach gives an accurate representation of how mutation and selection oppose each other at equilibrium and yields a reliable estimate of the mutational process, while disentangling the mean fixation probabilities prevailing in different mutational directions.

Conditional Approximate Bayesian Computation: A New Approach for Across-Site Dependency in High-Dimensional Mutation-Selection Models

A key question in molecular evolutionary biology concerns the relative roles of mutation and selection in shaping genomic data. Moreover, features of mutation and selection are heterogeneous along the genome and over time. Mechanistic codon substitution models based on the mutation-selection framework are promising approaches to separating these effects. In practice, however, several complications arise, since accounting for such heterogeneities often implies handling models of high dimensionality (e.g., amino acid preferences), or leads to across-site dependence (e.g., CpG hypermutability), making the likelihood function intractable. Approximate Bayesian Computation (ABC) could address this latter issue. Here, we propose a new approach, named Conditional ABC (CABC), which combines the sampling efficiency of MCMC and the flexibility of ABC. To illustrate the potential of the CABC approach, we apply it to the study of mammalian CpG hypermutability based on a new mutation-level parameter implying dependence across adjacent sites, combined with site-specific purifying selection on amino-acids captured by a Dirichlet process. Our proof-of-concept of the CABC methodology opens new modeling perspectives. Our application of the method reveals a high level of heterogeneity of CpG hypermutability across loci and mild heterogeneity across taxonomic groups; and finally, we show that CpG hypermutability is an important evolutionary factor in rendering relative synonymous codon usage. All source code is available as a GitHub repository (https://github.com/Simonll/LikelihoodFreePhylogenetics.git).

Multiple Factors Confounding Phylogenetic Detection of Selection on Codon Usage

Detecting selection on codon usage (CU) is a difficult task, since CU can be shaped by both the mutational process and selective constraints operating at the DNA, RNA, and protein levels. Yang and Nielsen (2008) developed a test (which we call CUYN) for detecting selection on CU using two competing mutation-selection models of codon substitution. The null model assumes that CU is determined by the mutation bias alone, whereas the alternative model assumes that both mutation bias and/or selection act on CU. In applications on mammalian-scale alignments, the CUYN test detects selection on CU for numerous genes. This is surprising, given the small effective population size of mammals, and prompted us to use simulations to evaluate the robustness of the test to model violations. Simulations using a modest level of CpG hypermutability completely mislead the test, with 100% false positives. Surprisingly, a high level of false positives (56.1%) resulted simply from using the HKY mutation-level parameterization within the CUYN test on simulations conducted with a GTR mutation-level parameterization. Finally, by using a crude optimization procedure on a parameter controlling the CpG hypermutability rate, we find that this mutational property could explain a very large part of the observed mammalian CU. Altogether, our work emphasizes the need to evaluate the potential impact of model violations on statistical tests in the field of molecular phylogenetic analysis. The source code of the simulator and the mammalian genes used are available as a GitHub repository (https://github.com/Simonll/LikelihoodFreePhylogenetics.git).

Using the Mutation-Selection Framework to Characterize Selection on Protein Sequences

When mutational pressure is weak, the generative process of protein evolution involves explicit probabilities of mutations of different types coupled to their conditional probabilities of fixation dependent on selection. Establishing this mechanistic modeling framework for the detection of selection has been a goal in the field of molecular evolution. Building on a mathematical framework proposed more than a decade ago, numerous methods have been introduced in an attempt to detect and measure selection on protein sequences. In this review, we discuss the structure of the original model, subsequent advances, and the series of assumptions that these models operate under.

Genomic Insights into Evolution of AdpA Family Master Regulators of Morphological Differentiation and Secondary Metabolism in Streptomyces

The AdpA protein from a streptomycin producer Streptomyces griseus is a founding member of the AdpA family of pleiotropic regulators, known to be ubiquitously present in streptomycetes. Functional genomic approaches revealed a huge number of AdpA targets, leading to the claim that the AdpA regulon is the largest one in bacteria. The expression of adpA is limited at the level of translation of the rare leucyl UUA codon. All known properties of AdpA regulators were discovered on a few streptomycete strains. There are open questions about the true abundance and diversity of AdpA across actinobacterial taxa (and beyond) and about the possible evolutionary forces that shape the AdpA orthologous group in Streptomyces. Here we show that, with respect to the TTA codon, streptomycete adpA is more diverse than has been previously thought, as the genes differ in presence/position of this codon. Reciprocal best hits to AdpA can be found in many actinobacterial orders, with a domain organization resembling that of the prototypical AdpA, but other configurations also exist. Diversifying positive selection was detected within the DNA-binding (AraC) domain in adpA of Streptomyces origin, most likely affecting residues enabling AdpA to recognize a degenerate operator. Sequence coding for putative glutamine amidotransferase (GATase-1) domain also shows signs of positive selection. The two-domain organization of AdpA most likely arose from a fusion of genes encoding separate GATase-1 and AraC domains. Indeed, we show that the AraC domain retains a biological function in the absence of the GATase-1 part. We suggest that acquisition of the regulatory role by TTA codon is a relatively recent event in the evolution of AdpA, which coincided with the rise of the Streptomycetales clade and, at present, is under relaxed selective constraints. Further experimental scrutiny of our findings is invited, which should provide new insights into the evolution and prospects for engineering of an AdpA-centered regulatory network.

The relationship between dN/dS and scaled selection coefficients

Numerous computational methods exist to assess the mode and strength of natural selection in protein-coding sequences, yet how distinct methods relate to one another remains largely unknown. Here, we elucidate the relationship between two widely used phylogenetic modeling frameworks: dN/dS models and mutation-selection (MutSel) models. We derive a mathematical relationship between dN/dS and scaled selection coefficients, the focal parameters of MutSel models, and use this relationship to gain deeper insight into the behaviors, limitations, and applicabilities of these two modeling frameworks. We prove that, if all synonymous changes are neutral, standard MutSel models correspond to dN/dS ≤ 1. However, if synonymous codons differ in fitness, dN/dS can take on arbitrarily high values even if all selection is purifying. Thus, the MutSel modeling framework cannot necessarily accommodate positive, diversifying selection, while dN/dS cannot distinguish between purifying selection on synonymous codons and positive selection on amino acids. We further propose a new benchmarking strategy of dN/dS inferences against MutSel simulations and demonstrate that the widely used Goldman-Yang-style dN/dS models yield substantially biased dN/dS estimates on realistic sequence data. In contrast, the less frequently used Muse-Gaut-style models display much less bias. Strikingly, the least-biased and most precise dN/dS estimates are never found in the models with the best fit to the data, measured through both AIC and BIC scores. Thus, selecting models based on goodness-of-fit criteria can yield poor parameter estimates if the models considered do not precisely correspond to the underlying mechanism that generated the data. In conclusion, establishing mathematical links among modeling frameworks represents a novel, powerful strategy to pinpoint previously unrecognized model limitations and strengths.

Detecting the signatures of adaptive evolution in protein-coding genes

The field of molecular evolution, which includes genome evolution, is devoted to finding variation within and between groups of organisms and explaining the processes responsible for generating this variation. Many DNA changes are believed to have little to no functional effect, and a neutral process will best explain their evolution. Thus, a central task is to discover which changes had positive fitness consequences and were subject to Darwinian natural selection during the course of evolution. Due the size and complexity of modern molecular datasets, the field has come to rely extensively on statistical modeling techniques to meet this analytical challenge. For DNA sequences that encode proteins, one of the most powerful approaches is to employ a statistical model of codon evolution. This unit provides a general introduction to the practice of modeling codon evolution using the statistical framework of maximum likelihood. Four real-data analysis activities are used to illustrate the principles of parameter estimation, robustness, hypothesis testing, and site classification. Each activity includes an explicit analytical protocol based on programs provided by the Phylogenetic Analysis by Maximum Likelihood (PAML) package.

CodonPhyML: fast maximum likelihood phylogeny estimation under codon substitution models

Markov models of codon substitution naturally incorporate the structure of the genetic code and the selection intensity at the protein level, providing a more realistic representation of protein-coding sequences compared with nucleotide or amino acid models. Thus, for protein-coding genes, phylogenetic inference is expected to be more accurate under codon models. So far, phylogeny reconstruction under codon models has been elusive due to computational difficulties of dealing with high dimension matrices. Here, we present a fast maximum likelihood (ML) package for phylogenetic inference, CodonPhyML offering hundreds of different codon models, the largest variety to date, for phylogeny inference by ML. CodonPhyML is tested on simulated and real data and is shown to offer excellent speed and convergence properties. In addition, CodonPhyML includes most recent fast methods for estimating phylogenetic branch supports and provides an integral framework for models selection, including amino acid and DNA models.

On the statistical interpretation of site-specific variables in phylogeny-based substitution models

Phylogeny-based modeling of heterogeneity across the positions of multiple-sequence alignments has generally been approached from two main perspectives. The first treats site specificities as random variables drawn from a statistical law, and the likelihood function takes the form of an integral over this law. The second assigns distinct variables to each position, and, in a maximum-likelihood context, adjusts these variables, along with global parameters, to optimize a joint likelihood function. Here, it is emphasized that while the first approach directly enjoys the statistical guaranties of traditional likelihood theory, the latter does not, and should be approached with particular caution when the site-specific variables are high dimensional. Using a phylogeny-based mutation-selection framework, it is shown that the difference in interpretation of site-specific variables explains the incongruities in recent studies regarding distributions of selection coefficients.

Locating protein-coding sequences under selection for additional, overlapping functions in 29 mammalian genomes

The degeneracy of the genetic code allows protein-coding DNA and RNA sequences to simultaneously encode additional, overlapping functional elements. A sequence in which both protein-coding and additional overlapping functions have evolved under purifying selection should show increased evolutionary conservation compared to typical protein-coding genes--especially at synonymous sites. In this study, we use genome alignments of 29 placental mammals to systematically locate short regions within human ORFs that show conspicuously low estimated rates of synonymous substitution across these species. The 29-species alignment provides statistical power to locate more than 10,000 such regions with resolution down to nine-codon windows, which are found within more than a quarter of all human protein-coding genes and contain ∼2% of their synonymous sites. We collect numerous lines of evidence that the observed synonymous constraint in these regions reflects selection on overlapping functional elements including splicing regulatory elements, dual-coding genes, RNA secondary structures, microRNA target sites, and developmental enhancers. Our results show that overlapping functional elements are common in mammalian genes, despite the vast genomic landscape.

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.

Mechanistic revisions of phenomenological modeling strategies in molecular evolution

The physical sciences have long recognized the distinction between formal descriptions of observations versus explanations for observations, with the canonical example embodied in the axiom statistical mechanics explains thermodynamics. Descriptive models are often said to be phenomenologically motivated whereas explanatory models are said to be mechanistically motivated. In molecular evolutionary modeling the two approaches can typically be classified as dealing with either the inference of phylogenies - the phenomenological approach, lacking particular interest in evolutionary mechanisms per se, or focused on explaining the evolutionary process itself - the mechanistic approach. Here we emphasize that both phenomenological and mechanistic approaches are inherently present in any model. Focusing on the field of codon substitution modeling we point out that this area, traditionally viewed as being mechanistically motivated, has itself been imbued with phenomenological underpinnings. Using practical examples we stress that clarifying phenomenological and mechanistic motivations can help guide model developments, and suggest future work directions.

Mutation-selection models of coding sequence evolution with site-heterogeneous amino acid fitness profiles

Modeling the interplay between mutation and selection at the molecular level is key to evolutionary studies. To this end, codon-based evolutionary models have been proposed as pertinent means of studying long-range evolutionary patterns and are widely used. However, these approaches have not yet consolidated results from amino acid level phylogenetic studies showing that selection acting on proteins displays strong site-specific effects, which translate into heterogeneous amino acid propensities across the columns of alignments; related codon-level studies have instead focused on either modeling a single selective context for all codon columns, or a separate selective context for each codon column, with the former strategy deemed too simplistic and the latter deemed overparameterized. Here, we integrate recent developments in nonparametric statistical approaches to propose a probabilistic model that accounts for the heterogeneity of amino acid fitness profiles across the coding positions of a gene. We apply the model to a dozen real protein-coding gene alignments and find it to produce biologically plausible inferences, for instance, as pertaining to site-specific amino acid constraints, as well as distributions of scaled selection coefficients. In their account of mutational features as well as the heterogeneous regimes of selection at the amino acid level, the modeling approaches studied here can form a backdrop for several extensions, accounting for other selective features, for variable population size, or for subtleties of mutational features, all with parameterizations couched within population-genetic theory.

Models of coding sequence evolution

Probabilistic models of sequence evolution are in widespread use in phylogenetics and molecular sequence evolution. These models have become increasingly sophisticated and combined with statistical model comparison techniques have helped to shed light on how genes and proteins evolve. Models of codon evolution have been particularly useful, because, in addition to providing a significant improvement in model realism for protein-coding sequences, codon models can also be designed to test hypotheses about the selective pressures that shape the evolution of the sequences. Such models typically assume a phylogeny and can be used to identify sites or lineages that have evolved adaptively. Recently some of the key assumptions that underlie phylogenetic tests of selection have been questioned, such as the assumption that the rate of synonymous changes is constant across sites or that a single phylogenetic tree can be assumed at all sites for recombining sequences. While some of these issues have been addressed through the development of novel methods, others remain as caveats that need to be considered on a case-by-case basis. Here, we outline the theory of codon models and their application to the detection of positive selection. We review some of the more recent developments that have improved their power and utility, laying a foundation for further advances in the modeling of coding sequence evolution.