Estimating empirical codon hidden Markov models

Evolutionary Shortcuts via Multinucleotide Substitutions and Their Impact on Natural Selection Analyses

Inference and interpretation of evolutionary processes, in particular of the types and targets of natural selection affecting coding sequences, are critically influenced by the assumptions built into statistical models and tests. If certain aspects of the substitution process (even when they are not of direct interest) are presumed absent or are modeled with too crude of a simplification, estimates of key model parameters can become biased, often systematically, and lead to poor statistical performance. Previous work established that failing to accommodate multinucleotide (or multihit, MH) substitutions strongly biases dN/dS-based inference towards false-positive inferences of diversifying episodic selection, as does failing to model variation in the rate of synonymous substitution (SRV) among sites. Here, we develop an integrated analytical framework and software tools to simultaneously incorporate these sources of evolutionary complexity into selection analyses. We found that both MH and SRV are ubiquitous in empirical alignments, and incorporating them has a strong effect on whether or not positive selection is detected (1.4-fold reduction) and on the distributions of inferred evolutionary rates. With simulation studies, we show that this effect is not attributable to reduced statistical power caused by using a more complex model. After a detailed examination of 21 benchmark alignments and a new high-resolution analysis showing which parts of the alignment provide support for positive selection, we show that MH substitutions occurring along shorter branches in the tree explain a significant fraction of discrepant results in selection detection. Our results add to the growing body of literature which examines decades-old modeling assumptions (including MH) and finds them to be problematic for comparative genomic data analysis. Because multinucleotide substitutions have a significant impact on natural selection detection even at the level of an entire gene, we recommend that selection analyses of this type consider their inclusion as a matter of routine. To facilitate this procedure, we developed, implemented, and benchmarked a simple and well-performing model testing selection detection framework able to screen an alignment for positive selection with two biologically important confounding processes: site-to-site synonymous rate variation, and multinucleotide instantaneous substitutions.

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.

Mutation Rates and Selection on Synonymous Mutations in SARS-CoV-2

The COVID-19 pandemic has seen an unprecedented response from the sequencing community. Leveraging the sequence data from more than 140,000 SARS-CoV-2 genomes, we study mutation rates and selective pressures affecting the virus. Understanding the processes and effects of mutation and selection has profound implications for the study of viral evolution, for vaccine design, and for the tracking of viral spread. We highlight and address some common genome sequence analysis pitfalls that can lead to inaccurate inference of mutation rates and selection, such as ignoring skews in the genetic code, not accounting for recurrent mutations, and assuming evolutionary equilibrium. We find that two particular mutation rates, G →U and C →U, are similarly elevated and considerably higher than all other mutation rates, causing the majority of mutations in the SARS-CoV-2 genome, and are possibly the result of APOBEC and ROS activity. These mutations also tend to occur many times at the same genome positions along the global SARS-CoV-2 phylogeny (i.e., they are very homoplasic). We observe an effect of genomic context on mutation rates, but the effect of the context is overall limited. Although previous studies have suggested selection acting to decrease U content at synonymous sites, we bring forward evidence suggesting the opposite.

Extra base hits: Widespread empirical support for instantaneous multiple-nucleotide changes

Despite many attempts to introduce evolutionary models that permit substitutions to instantly alter more than one nucleotide in a codon, the prevailing wisdom remains that such changes are rare and generally negligible or are reflective of non-biological artifacts, such as alignment errors. Codon models continue to posit that only single nucleotide change have non-zero rates. Here, we develop and test a simple hierarchy of codon-substitution models with non-zero evolutionary rates for only one-nucleotide (1H), one- and two-nucleotide (2H), or any (3H) codon substitutions. Using over 42, 000 empirical alignments, we find widespread statistical support for multiple hits: 61% of alignments prefer models with 2H allowed, and 23%-with 3H allowed. Analyses of simulated data suggest that these results are not likely to be due to simple artifacts such as model misspecification or alignment errors. Further modeling reveals that synonymous codon island jumping among codons encoding serine, especially along short branches, contributes significantly to this 3H signal. While serine codons were prominently involved in multiple-hit substitutions, there were other common exchanges contributing to better model fit. It appears that a small subset of sites in most alignments have unusual evolutionary dynamics not well explained by existing model formalisms, and that commonly estimated quantities, such as dN/dS ratios may be biased by model misspecification. Our findings highlight the need for continued evaluation of assumptions underlying workhorse evolutionary models and subsequent evolutionary inference techniques. We provide a software implementation for evolutionary biologists to assess the potential impact of extra base hits in their data in the HyPhy package and in the Datamonkey.org server.

A Phenotype-Genotype Codon Model for Detecting Adaptive Evolution

A central objective in biology is to link adaptive evolution in a gene to structural and/or functional phenotypic novelties. Yet most analytic methods make inferences mainly from either phenotypic data or genetic data alone. A small number of models have been developed to infer correlations between the rate of molecular evolution and changes in a discrete or continuous life history trait. But such correlations are not necessarily evidence of adaptation. Here, we present a novel approach called the phenotype-genotype branch-site model (PG-BSM) designed to detect evidence of adaptive codon evolution associated with discrete-state phenotype evolution. An episode of adaptation is inferred under standard codon substitution models when there is evidence of positive selection in the form of an elevation in the nonsynonymous-to-synonymous rate ratio $\omega$ to a value $\omega > 1$. As it is becoming increasingly clear that $\omega > 1$ can occur without adaptation, the PG-BSM was formulated to infer an instance of adaptive evolution without appealing to evidence of positive selection. The null model makes use of a covarion-like component to account for general heterotachy (i.e., random changes in the evolutionary rate at a site over time). The alternative model employs samples of the phenotypic evolutionary history to test for phenomenological patterns of heterotachy consistent with specific mechanisms of molecular adaptation. These include 1) a persistent increase/decrease in $\omega$ at a site following a change in phenotype (the pattern) consistent with an increase/decrease in the functional importance of the site (the mechanism); and 2) a transient increase in $\omega$ at a site along a branch over which the phenotype changed (the pattern) consistent with a change in the site's optimal amino acid (the mechanism). Rejection of the null is followed by post hoc analyses to identify sites with strongest evidence for adaptation in association with changes in the phenotype as well as the most likely evolutionary history of the phenotype. Simulation studies based on a novel method for generating mechanistically realistic signatures of molecular adaptation show that the PG-BSM has good statistical properties. Analyses of real alignments show that site patterns identified post hoc are consistent with the specific mechanisms of adaptation included in the alternate model. Further simulation studies show that the covarion-like component of the PG-BSM plays a crucial role in mitigating recently discovered statistical pathologies associated with confounding by accounting for heterotachy-by-any-cause. [Adaptive evolution; branch-site model; confounding; mutation-selection; phenotype-genotype.].

Extreme variation in rates of evolution in the plastid Clp protease complex

Eukaryotic cells represent an intricate collaboration between multiple genomes, even down to the level of multi-subunit complexes in mitochondria and plastids. One such complex in plants is the caseinolytic protease (Clp), which plays an essential role in plastid protein turnover. The proteolytic core of Clp comprises subunits from one plastid-encoded gene (clpP1) and multiple nuclear genes. TheclpP1 gene is highly conserved across most green plants, but it is by far the fastest evolving plastid-encoded gene in some angiosperms. To better understand these extreme and mysterious patterns of divergence, we investigated the history ofclpP1 molecular evolution across green plants by extracting sequences from 988 published plastid genomes. We find thatclpP1 has undergone remarkably frequent bouts of accelerated sequence evolution and architectural changes (e.g. a loss of introns andRNA-editing sites) within seed plants. AlthoughclpP1 is often assumed to be a pseudogene in such cases, multiple lines of evidence suggest that this is rarely true. We applied comparative native gel electrophoresis of chloroplast protein complexes followed by protein mass spectrometry in two species within the angiosperm genusSilene, which has highly elevated and heterogeneous rates ofclpP1 evolution. We confirmed thatclpP1 is expressed as a stable protein and forms oligomeric complexes with the nuclear-encoded Clp subunits, even in one of the most divergentSilene species. Additionally, there is a tight correlation between amino acid substitution rates inclpP1 and the nuclear-encoded Clp subunits across a broad sampling of angiosperms, suggesting continuing selection on interactions within this complex.

Improved inference of site-specific positive selection under a generalized parametric codon model when there are multinucleotide mutations and multiple nonsynonymous rates

BACKGROUND

An excess of nonsynonymous substitutions, over neutrality, is considered evidence of positive Darwinian selection. Inference for proteins often relies on estimation of the nonsynonymous to synonymous ratio (ω = dN/dS) within a codon model. However, to ease computational difficulties, ω is typically estimated assuming an idealized substitution process where (i) all nonsynonymous substitutions have the same rate (regardless of impact on organism fitness) and (ii) instantaneous double and triple (DT) nucleotide mutations have zero probability (despite evidence that they can occur). It follows that estimates of ω represent an imperfect summary of the intensity of selection, and that tests based on the ω > 1 threshold could be negatively impacted.

RESULTS

We developed a general-purpose parametric (GPP) modelling framework for codons. This novel approach allows specification of all possible instantaneous codon substitutions, including multiple nonsynonymous rates (MNRs) and instantaneous DT nucleotide changes. Existing codon models are specified as special cases of the GPP model. We use GPP models to implement likelihood ratio tests for ω > 1 that accommodate MNRs and DT mutations. Through both simulation and real data analysis, we find that failure to model MNRs and DT mutations reduces power in some cases and inflates false positives in others. False positives under traditional M2a and M8 models were very sensitive to DT changes. This was exacerbated by the choice of frequency parameterization (GY vs. MG), with rates sometimes > 90% under MG. By including MNRs and DT mutations, accuracy and power was greatly improved under the GPP framework. However, we also find that over-parameterized models can perform less well, and this can contribute to degraded performance of LRTs.

CONCLUSIONS

We suggest GPP models should be used alongside traditional codon models. Further, all codon models should be deployed within an experimental design that includes (i) assessing robustness to model assumptions, and (ii) investigation of non-standard behaviour of MLEs. As the goal of every analysis is to avoid false conclusions, more work is needed on model selection methods that consider both the increase in fit engendered by a model parameter and the degree to which that parameter is affected by un-modelled evolutionary processes.

Looking for Darwin in Genomic Sequences: Validity and Success Depends on the Relationship Between Model and Data

Codon substitution models (CSMs) are commonly used to infer the history of natural section for a set of protein-coding sequences, often with the explicit goal of detecting the signature of positive Darwinian selection. However, the validity and success of CSMs used in conjunction with the maximum likelihood (ML) framework is sometimes challenged with claims that the approach might too often support false conclusions. In this chapter, we use a case study approach to identify four legitimate statistical difficulties associated with inference of evolutionary events using CSMs. These include: (1) model misspecification, (2) low information content, (3) the confounding of processes, and (4) phenomenological load, or PL. While past criticisms of CSMs can be connected to these issues, the historical critiques were often misdirected, or overstated, because they failed to recognize that the success of any model-based approach depends on the relationship between model and data. Here, we explore this relationship and provide a candid assessment of the limitations of CSMs to extract historical information from extant sequences. To aid in this assessment, we provide a brief overview of: (1) a more realistic way of thinking about the process of codon evolution framed in terms of population genetic parameters, and (2) a novel presentation of the ML statistical framework. We then divide the development of CSMs into two broad phases of scientific activity and show that the latter phase is characterized by increases in model complexity that can sometimes negatively impact inference of evolutionary mechanisms. Such problems are not yet widely appreciated by the users of CSMs. These problems can be avoided by using a model that is appropriate for the data; but, understanding the relationship between the data and a fitted model is a difficult task. We argue that the only way to properly understand that relationship is to perform in silico experiments using a generating process that can mimic the data as closely as possible. The mutation-selection modeling framework (MutSel) is presented as the basis of such a generating process. We contend that if complex CSMs continue to be developed for testing explicit mechanistic hypotheses, then additional analyses such as those described in here (e.g., penalized LRTs and estimation of PL) will need to be applied alongside the more traditional inferential methods.

Selection Acting on Genomes

Populations evolve as mutations arise in individual organisms and, through hereditary transmission, may become "fixed" (shared by all individuals) in the population. Most mutations are lethal or have negative fitness consequences for the organism. Others have essentially no effect on organismal fitness and can become fixed through the neutral stochastic process known as random drift. However, mutations may also produce a selective advantage that boosts their chances of reaching fixation. Regions of genomes where new mutations are beneficial, rather than neutral or deleterious, tend to evolve more rapidly due to positive selection. Genes involved in immunity and defense are a well-known example; rapid evolution in these genes presumably occurs because new mutations help organisms to prevail in evolutionary "arms races" with pathogens. In recent years genome-wide scans for selection have enlarged our understanding of the genome evolution of various species. In this chapter, we will focus on methods to detect selection on the genome. In particular, we will discuss probabilistic models and how they have changed with the advent of new genome-wide data now available.

Multinucleotide mutations cause false inferences of lineage-specific positive selection

Phylogenetic tests of adaptive evolution, such as the widely used branch-site test, assume that nucleotide substitutions occur singly and independently. But recent research has shown that errors at adjacent sites often occur during DNA replication, and the resulting multinucleotide mutations (MNMs) are overwhelmingly likely to be nonsynonymous. We evaluated whether the branch-site test (BST) might misinterpret sequence patterns produced by MNMs as false support for positive selection. We analyzed two genome-scale datasets– one from mammals and one from flies – and found that codons with multiple differences account for virtually all the support for lineage-specific positive selection in the BST. Simulations under conditions derived from these alignments but without positive selection show that realistic rates of MNMs cause a strong and systematic bias towards false inferences of selection. This bias is sufficient under empirically derived conditions to produce false positive inferences as often as the branch-site test infers positive selection from the empirical data. Although some genes with BST-positive results may have evolved adaptively, the test cannot distinguish sequence patterns produced by authentic positive selection from those caused by neutral fixation of MNMs. Many published inferences of adaptive evolution using this technique may therefore be artifacts of model violation caused by unincorporated neutral mutational processes. We introduce a model that incorporates MNMs and may help to ameliorate this bias.

Non-Markovian effects on protein sequence evolution due to site dependent substitution rates

Background

Many models of protein sequence evolution, in particular those based on Point Accepted Mutation (PAM) matrices, assume that its dynamics is Markovian. Nevertheless, it has been observed that evolution seems to proceed differently at different time scales, questioning this assumption. In 2011 Kosiol and Goldman proved that, if evolution is Markovian at the codon level, it can not be Markovian at the amino acid level. However, it remains unclear up to which point the Markov assumption is verified at the codon level.

Results

Here we show how also the among-site variability of substitution rates makes the process of full protein sequence evolution effectively not Markovian even at the codon level. This may be the theoretical explanation behind the well known systematic underestimation of evolutionary distances observed when omitting rate variability. If the substitution rate variability is neglected the average amino acid and codon replacement probabilities are affected by systematic errors and those with the largest mismatches are the substitutions involving more than one nucleotide at a time. On the other hand, the instantaneous substitution matrices estimated from alignments with the Markov assumption tend to overestimate double and triple substitutions, even when learned from alignments at high sequence identity.

Conclusions

These results discourage the use of simple Markov models to describe full protein sequence evolution and encourage to employ, whenever possible, models that account for rate variability by construction (such as hidden Markov models or mixture models) or substitution models of the type of Le and Gascuel (2008) that account for it explicitly.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1135-1) contains supplementary material, which is available to authorized users.

Gene-wide identification of episodic selection

We present BUSTED, a new approach to identifying gene-wide evidence of episodic positive selection, where the non-synonymous substitution rate is transiently greater than the synonymous rate. BUSTED can be used either on an entire phylogeny (without requiring an a priori hypothesis regarding which branches are under positive selection) or on a pre-specified subset of foreground lineages (if a suitable a priori hypothesis is available). Selection is modeled as varying stochastically over branches and sites, and we propose a computationally inexpensive evidence metric for identifying sites subject to episodic positive selection on any foreground branches. We compare BUSTED with existing models on simulated and empirical data. An implementation is available on www.datamonkey.org/busted, with a widget allowing the interactive specification of foreground branches.

A generalized mechanistic codon model

Models of codon evolution have attracted particular interest because of their unique capabilities to detect selection forces and their high fit when applied to sequence evolution. We described here a novel approach for modeling codon evolution, which is based on Kronecker product of matrices. The 61 × 61 codon substitution rate matrix is created using Kronecker product of three 4 × 4 nucleotide substitution matrices, the equilibrium frequency of codons, and the selection rate parameter. The entities of the nucleotide substitution matrices and selection rate are considered as parameters of the model, which are optimized by maximum likelihood. Our fully mechanistic model allows the instantaneous substitution matrix between codons to be fully estimated with only 19 parameters instead of 3,721, by using the biological interdependence existing between positions within codons. We illustrate the properties of our models using computer simulations and assessed its relevance by comparing the AICc measures of our model and other models of codon evolution on simulations and a large range of empirical data sets. We show that our model fits most biological data better compared with the current codon models. Furthermore, the parameters in our model can be interpreted in a similar way as the exchangeability rates found in empirical codon models.

An experimentally determined evolutionary model dramatically improves phylogenetic fit

All modern approaches to molecular phylogenetics require a quantitative model for how genes evolve. Unfortunately, existing evolutionary models do not realistically represent the site-heterogeneous selection that governs actual sequence change. Attempts to remedy this problem have involved augmenting these models with a burgeoning number of free parameters. Here, I demonstrate an alternative: Experimental determination of a parameter-free evolutionary model via mutagenesis, functional selection, and deep sequencing. Using this strategy, I create an evolutionary model for influenza nucleoprotein that describes the gene phylogeny far better than existing models with dozens or even hundreds of free parameters. Emerging high-throughput experimental strategies such as the one employed here provide fundamentally new information that has the potential to transform the sensitivity of phylogenetic and genetic analyses.

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.

To understand how a protein functions, a critical step is to know which regions in its protein tertiary structure may be functionally important. Functionally important protein regions are typically more conserved than other regions because mutations in these regions are more likely to be deleterious. A number of phylogenetic models have been developed to identify conserved sites or regions in proteins by comparing protein sequences from multiple species. However, most of these methods treat amino acid sites independently and do not consider the spatial clustering of conserved sites in the protein tertiary structure. Therefore, their power of identifying functional protein regions is limited. We develop a new statistical model, GP4Rate, which combines the information from the protein sequences and the protein tertiary structure to infer conserved regions. We demonstrate that GP4Rate outperforms Rate4Site, the most widely used phylogenetic software for inferring functional amino acid sites, via simulations with a case study of B7-1 genes. GP4Rate is a potentially useful tool for guiding mutagenesis experiments or providing insights on the relationship between protein structures and functions.

Linking great apes genome evolution across time scales using polymorphism-aware phylogenetic models

The genomes of related species contain valuable information on the history of the considered taxa. Great apes in particular exhibit variation of evolutionary patterns along their genomes. However, the great ape data also bring new challenges, such as the presence of incomplete lineage sorting and ancestral shared polymorphisms. Previous methods for genome-scale analysis are restricted to very few individuals or cannot disentangle the contribution of mutation rates and fixation biases. This represents a limitation both for the understanding of these forces as well as for the detection of regions affected by selection. Here, we present a new model designed to estimate mutation rates and fixation biases from genetic variation within and between species. We relax the assumption of instantaneous substitutions, modeling substitutions as mutational events followed by a gradual fixation. Hence, we straightforwardly account for shared ancestral polymorphisms and incomplete lineage sorting. We analyze genome-wide synonymous site alignments of human, chimpanzee, and two orangutan species. From each taxon, we include data from several individuals. We estimate mutation rates and GC-biased gene conversion intensity. We find that both mutation rates and biased gene conversion vary with GC content. We also find lineage-specific differences, with weaker fixation biases in orangutan species, suggesting a reduced historical effective population size. Finally, our results are consistent with directional selection acting on coding sequences in relation to exonic splicing enhancers.