Estimating the distribution of selection coefficients from phylogenetic data using sitewise mutation-selection models

Estimation of the distribution of selection coefficients of mutations is a long-standing issue in molecular evolution. In addition to population-based methods, the distribution can be estimated from DNA sequence data by phylogenetic-based models. Previous models have generally found unimodal distributions where the probability mass is concentrated between mildly deleterious and nearly neutral mutations. Here we use a sitewise mutation-selection phylogenetic model to estimate the distribution of selection coefficients among novel and fixed mutations (substitutions) in a data set of 244 mammalian mitochondrial genomes and a set of 401 PB2 proteins from influenza. We find a bimodal distribution of selection coefficients for novel mutations in both the mitochondrial data set and for the influenza protein evolving in its natural reservoir, birds. Most of the mutations are strongly deleterious with the rest of the probability mass concentrated around mildly deleterious to neutral mutations. The distribution of the coefficients among substitutions is unimodal and symmetrical around nearly neutral substitutions for both data sets at adaptive equilibrium. About 0.5% of the nonsynonymous mutations and 14% of the nonsynonymous substitutions in the mitochondrial proteins are advantageous, with 0.5% and 24% observed for the influenza protein. Following a host shift of influenza from birds to humans, however, we find among novel mutations in PB2 a trimodal distribution with a small mode of advantageous mutations.     

Fixation of deleterious mutations at critical positions in human proteins

Deleterious mutations associated with human diseases are predominantly found in conserved positions and positions that are essential for the structure and/or function of proteins. However, these mutations are purged from the human population over time and prevented from being fixed. Contrary to this belief, here I show that high proportions of deleterious amino acid changing mutations are fixed at positions critical for the structure and/or function of proteins. Similarly, a high rate of fixation of deleterious mutations was observed in slow-evolving amino acid positions of human proteins. The fraction of deleterious substitutions was found to be two times higher in relatively conserved amino acid positions than in highly variable positions. This study also found fixation of a much higher proportion of radical amino acid changes in primates compared with rodents and artiodactyls in slow-evolving positions. Previous studies observed a higher proportion of nonsynonymous substitutions in humans compared with other mammals, which was taken as indirect evidence for the fixation of deleterious mutations in humans. However, the results of this investigation provide direct evidence for this prediction by suggesting that the excess nonsynonymous mutations fixed in humans are indeed deleterious in nature. Furthermore, these results suggest that studies on disease-associated mutations should consider that a significant fraction of such deleterious mutations has already been fixed in the human genome, and thus, the effects of new mutations at those amino acid positions may not necessarily be deleterious and might even result in reversion to benign phenotypes.     

Selectionism and neutralism in molecular evolution

Charles Darwin proposed that evolution occurs primarily by natural selection, but this view has been controversial from the beginning. Two of the major opposing views have been mutationism and neutralism. Early molecular studies suggested that most amino acid substitutions in proteins are neutral or nearly neutral and the functional change of proteins occurs by a few key amino acid substitutions. This suggestion generated an intense controversy over selectionism and neutralism. This controversy is partially caused by Kimura's definition of neutrality, which was too strict (|2Ns|< or =1). If we define neutral mutations as the mutations that do not change the function of gene products appreciably, many controversies disappear because slightly deleterious and slightly advantageous mutations are engulfed by neutral mutations. The ratio of the rate of nonsynonymous nucleotide substitution to that of synonymous substitution is a useful quantity to study positive Darwinian selection operating at highly variable genetic loci, but it does not necessarily detect adaptively important codons. Previously, multigene families were thought to evolve following the model of concerted evolution, but new evidence indicates that most of them evolve by a birth-and-death process of duplicate genes. It is now clear that most phenotypic characters or genetic systems such as the adaptive immune system in vertebrates are controlled by the interaction of a number of multigene families, which are often evolutionarily related and are subject to birth-and-death evolution. Therefore, it is important to study the mechanisms of gene family interaction for understanding phenotypic evolution. Because gene duplication occurs more or less at random, phenotypic evolution contains some fortuitous elements, though the environmental factors also play an important role. The randomness of phenotypic evolution is qualitatively different from allele frequency changes by random genetic drift. However, there is some similarity between phenotypic and molecular evolution with respect to functional or environmental constraints and evolutionary rate. It appears that mutation (including gene duplication and other DNA changes) is the driving force of evolution at both the genic and the phenotypic levels.     

Evolutionary constraints and the neutral theory

Summary The neutral theory of molecular evolution postulates that nucleotide substitutions inherently take place in DNA as a result of point mutations followed by random genetic drift. In the absence of selective constraints, the substitution rate reaches the maximum value set by the mutation rate. The rate in globin pseudogenes is about 5 × 10^–9 substitutions per site per year in mammals. Rates slower than this indicate the presence of constraints imposed by negative (natural) selection, which rejects and discards deleterious mutations.We wish to dedicate this paper to the memory of Professor Jack Lester King     

Weighing the evidence for adaptation at the molecular level

The abundance of genome polymorphism and divergence data has provided unprecedented insight into how mutation, drift and natural selection shape genome evolution. Application of the McDonald-Kreitman (MK) test to such data indicates a pervasive influence of positive selection, particularly in Drosophila species. However, evidence for positive selection in other species ranging from yeast to humans is often weak or absent. Although evidence for positive selection could be obscured in some species, there is also reason to believe that the frequency of adaptive substitutions could be overestimated as a result of epistatic fitness effects or hitchhiking of deleterious mutations. Based on these considerations it is argued that the common assumption of independence among sites must be relaxed before abandoning the neutral theory of molecular evolution.     

Evolution by Gene Duplication and Compensatory Advantageous Mutations

Relaxation of selective constraint is thought to play an important role for evolution by gene duplication, in connection with compensatory advantageous mutant substitutions. Models were investigated by incorporating gene duplication by unequal crossing over, selection, mutation and random genetic drift into Monte Carlo simulations. Compensatory advantageous mutations were introduced, and simulations were carried out with and without relaxation, when genes are redundant on chromosomes. Relaxation was introduced by assuming that deleterious mutants have no effect on fitness, so long as one or more genes free of such mutations remain in the array. Compensatory mutations are characterized by the intermediate deleterious step of their substitutions, and therefore relaxation by gene redundancy is important. Through extensive Monte Carlo simulations, it was found that compensatory mutant substitutions require relaxation in addition to gene duplication, when mutant effects are large. However when mutant effects are small, such that the product of selection coefficient and population size is around unity, evolution by compensatory mutation is enhanced by gene duplication even without relaxation.     

Interplay between Chaperones and Protein Disorder Promotes the Evolution of Protein Networks

Evolution is driven by mutations, which lead to new protein functions but come at a cost to protein stability. Non-conservative substitutions are of interest in this regard because they may most profoundly affect both function and stability. Accordingly, organisms must balance the benefit of accepting advantageous substitutions with the possible cost of deleterious effects on protein folding and stability. We here examine factors that systematically promote non-conservative mutations at the proteome level. Intrinsically disordered regions in proteins play pivotal roles in protein interactions, but many questions regarding their evolution remain unanswered. Similarly, whether and how molecular chaperones, which have been shown to buffer destabilizing mutations in individual proteins, generally provide robustness during proteome evolution remains unclear. To this end, we introduce an evolutionary parameter λ that directly estimates the rate of non-conservative substitutions. Our analysis of λ in Escherichia coli, Saccharomyces cerevisiae, and Homo sapiens sequences reveals how co- and post-translationally acting chaperones differentially promote non-conservative substitutions in their substrates, likely through buffering of their destabilizing effects. We further find that λ serves well to quantify the evolution of intrinsically disordered proteins even though the unstructured, thus generally variable regions in proteins are often flanked by very conserved sequences. Crucially, we show that both intrinsically disordered proteins and highly re-wired proteins in protein interaction networks, which have evolved new interactions and functions, exhibit a higher λ at the expense of enhanced chaperone assistance. Our findings thus highlight an intricate interplay of molecular chaperones and protein disorder in the evolvability of protein networks. Our results illuminate the role of chaperones in enabling protein evolution, and underline the importance of the cellular context and integrated approaches for understanding proteome evolution. We feel that the development of λ may be a valuable addition to the toolbox applied to understand the molecular basis of evolution.     

Allele frequency divergence reveals ubiquitous influence of positive selection in Drosophila

Resolving the role of natural selection is a basic objective of evolutionary biology. It is generally difficult to detect the influence of selection because ubiquitous non-selective stochastic change in allele frequencies (genetic drift) degrades evidence of selection. As a result, selection scans typically only identify genomic regions that have undergone episodes of intense selection. Yet it seems likely such episodes are the exception; the norm is more likely to involve subtle, concurrent selective changes at a large number of loci. We develop a new theoretical approach that uncovers a previously undocumented genome-wide signature of selection in the collective divergence of allele frequencies over time. Applying our approach to temporally resolved allele frequency measurements from laboratory and wild Drosophila populations, we quantify the selective contribution to allele frequency divergence and find that selection has substantial effects on much of the genome. We further quantify the magnitude of the total selection coefficient (a measure of the combined effects of direct and linked selection) at a typical polymorphic locus, and find this to be large (of order 1%) even though most mutations are not directly under selection. We find that selective allele frequency divergence is substantially elevated at intermediate allele frequencies, which we argue is most parsimoniously explained by positive—not negative—selection. Thus, in these populations most mutations are far from evolving neutrally in the short term (tens of generations), including mutations with neutral fitness effects, and the result cannot be explained simply as an ongoing purging of deleterious mutations.     

On the unique function of selenocysteine — Insights from the evolution of selenoproteins

The process of natural selection leaves signatures in our genome that can be used to identify functionally important amino acid changes in proteins. In natural populations, amino acids that are better adapted to local conditions might increase in frequency, whereas moderately to severely deleterious protein mutations tend to be eliminated and do not contribute to protein differences between species. Amino acid mutations with no fitness consequences are, however, lost or fixed without regard to natural selection. Looking for evidence of natural selection is, therefore, an attractive strategy for characterizing the contribution of a residue to protein function. Because the majority of identified selenoproteins have now been found in Cys-form, the extent of exchangeability between Sec and Cys residues can be measured in proteins over long periods of time. The statistical analysis of the pattern of Sec/Cys exchanges in diversity (within species) and divergence (between species) data, provides robust inferences of the strength and mode of natural selection acting on these protein sites. Such inferences inform us not only of the long-term exchangeability between Sec and Cys residues, but also of the nature of the selective factors shaping Sec usage in proteins.     

Intense neutral drifts yield robust and evolvable consensus proteins

What changes occur when a natural protein that had been under low mutation rates is subjected to a neutral drift at high mutational loads, thus generating genetically diverse (polymorphic) gene ensembles that all maintain the protein's original function and structure? To address this question we subjected large populations of TEM-1 beta-lactamase to a prolonged neutral drift, applying high mutation rates and purifying selection to maintain TEM-1's existing penicillinase activity. Purging of deleterious mutations and enrichment of beneficial ones maintained the sequence of these ensembles closer to TEM-1's family consensus and inferred ancestor. In particular, back-to-consensus/ancestor mutations that increase TEM-1's kinetic and thermodynamic stability were enriched. These acted as global suppressors and enabled the tolerance of a broad range of deleterious mutations, thus further increasing the genetic diversity of the drifting populations. The probability of a new function emerging (cefotaxime degradation) was also substantially increased in these ensembles owing to the presence of many gene variants carrying the global suppressors. Our findings indicate the unique features of large, polymorphic neutral ensembles generated under high mutational loads and prompt the speculation that the progenitors of today's proteins may have evolved under high mutational loads. The results also suggest that predictable back-to-consensus/ancestor changes can be used in the laboratory to generate highly diverse and evolvable gene libraries.     

Deleterious mutations in various Drosophila melanogaster strains carrying meiotic mutation c(3)G

In the absence of meiotic recombination, deleterious mutations, decreasing the viability, are accumulated and fixed in small Drosophila populations. Study of the viability of hybrid progenies of three laboratory Drosophila melanogaster strains carrying meiotic mutation c(3)G17 has suggested that the deleterious mutations are negatively synergistic in their interaction. The deleterious mutations localized to the pericentromeric region of chromosome 3 are threefold more efficient as compared with the mutations located in distal regions. Substitution of a new chromosome for the balancer chromosome in a strain with meiotic mutation c(3)G17 partially restores (by approximately 20%) the viability of homozygotes c(3)G17/c(3)G17 over the first 20-30 generations. Further cultivation for 30 generations with the same balancer again decreases the viability to the initial level. An epigenetic nature of deleterious mutations is discussed.     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

Experimental estimate of the abundance and effects of nearly neutral mutations in the RNA virus phi 6

Although the frequency and effects of neutral and nearly neutral mutations are critical to evolutionary patterns and processes governed by genetic drift, the small effects of such mutations make them difficult to study empirically. Here we present the results of a mutation-accumulation experiment designed to assess the frequencies of deleterious mutations with undetectable effects. We promoted the accumulation of spontaneous mutations by subjecting independent lineages of the RNA virus 6 to repeated population bottlenecks of a single individual. We measured fitness following every bottleneck to obtain a complete picture of the timing and effects of the accumulated mutations with detectable effects and sequenced complete genomes to determine the number of mutations that were undetected by the fitness assays. To estimate the effects of the undetected mutations, we implemented a likelihood model developed for quantitative trait locus (QTL) data (Otto and Jones 2000) to estimate the number and effects of the undetected mutations from the measured number and effects of the detected mutations. Using this method we estimated a deleterious mutation rate of U = 0.03 and a gamma effects distribution with mean s=0.093 and coefficient of variation = 0.204. Although our estimates of U and s fall within the range of recent mutation rate and effect estimates in eukaryotes, the fraction of mutations with detectable effects on laboratory fitness (39%) appears to be far higher in 6 than in eukaryotes.     

FURTHER SIMULATION STUDIES ON EVOLUTION BY GENE DUPLICATION

In order to understand the origin of multigene families, Monte Carlo simulations were performed to see how a genetic system evolves under unequal crossing-over, mutation, random genetic drift and natural selection, starting from a single gene copy. Both haploid and diploid models were examined. Beneficial, neutral, and detrimental mutations were incorporated, and “positive” selection favors those chromosomes (haploid) or individuals (diploid) with more beneficial mutations than others. The same model for haploids was previously investigated with special reference to the evolution of gene organization, and the ratio of the numbers of beneficial genes to pseudogenes was found to be a rough indicator of the relative strengths of positive and negative (against deleterious alleles) natural selection (Ohta, 1987b). In the present paper, the evolution of gene organization and of sequence divergence among genes in the multigene family is examined. It is shown that positive selection accelerates the accumulation of arrays containing different beneficial mutations, but that total divergence including both neutral and beneficial mutations is not very sensitive to positive selection, under this model. The proportion of beneficial mutations in the total mutations accumulated is a better indicator of positive selection than is the total divergence. It is pointed out that various observed examples in which amino-acid substitutions are accelerated, as compared with synonymous substitutions in duplicated genes (Li, 1985), may reflect the effect of selection similar to the present scheme. The diploid model is shown to be more efficient for accumulating beneficial mutations in duplicated genes than the haploid one, and the relevance of this finding to the advantage of sexual reproduction is discussed.     

The neutral theory in an infinite population

Selective substitutions at one locus induce stochastic dynamics at a linked neutral locus that resemble genetic drift even when the population size is infinite. This new stochastic force, which is called genetic draft, causes genetic variation at the neutral locus to decrease with population size and the rate of deleterious substitution to increase with population size. The fact that heterozygosities in natural populations are only weakly dependent on population size suggests that genetic draft may be a much more important stochastic force than genetic drift in natural populations. Some of the mathematical properties of genetic draft are explored.     

Mutations in the NAM2 genes of Saccharomyces cerevisiae and S. douglasii are clustered non-randomly as a result of constraints on the nucleic acid sequence and not on the protein

Summary We present a statistical study of the nature and distribution of mutations along the NAM2 gene coding for the mitochondrial leucyl tRNA synthetase in Saccharomyces cerevisiae and S. douglasii (Herbert et al. 1988). Two important facts are observed: (1) the relative frequency of transitions and transversions is the same among silent substitutions and replacements. (2) The two kinds of mutations (silent substitutions and replacements) are distributed in the same way along the gene. This distribution is not random; the mutations are clustered and the clusters are regularly spaced along the gene. The NAM2 gene offers an example spaced along the gene. The NAM2 gene offers an example of recent divergence. We show that, in this case, the fixation of mutations is the result of genetic drift and of constraints on the nucleic acid sequence and not on that of the protein.     

Fitness Effects of Single Amino Acid Insertions and Deletions in TEM-1 β-Lactamase

Short insertions and deletions (InDels) are a common type of mutation found in nature and a useful source of variation in protein engineering. InDel events have important consequences in protein evolution, often opening new pathways for adaptation. However, much less is known about the effects of InDels compared to point mutations and amino acid substitutions. In particular, deep mutagenesis studies on the distribution of fitness effects of mutations have focused almost exclusively on amino acid substitutions. Here, we present a near-comprehensive analysis of the fitness effects of single amino acid InDels in TEM-1 β-lactamase. While we found InDels to be largely deleterious, partially overlapping deletion-tolerant and insertion-tolerant regions were observed throughout the protein, especially in unstructured regions and at the end of helices. The signal sequence of TEM-1 tolerated InDels more than the mature protein. Most regions of the protein tolerated insertions more than deletions, but a few regions tolerated deletions more than insertions. We examined the relationship between InDel tolerance and a variety of measures to help understand its origin. These measures included evolutionary variation in β-lactamases, secondary structure identity, tolerance to amino acid substitutions, solvent accessibility, and side-chain weighted contact number. We found secondary structure, weighted contact number, and evolutionary variation in class A beta-lactamases to be the somewhat predictive of InDel fitness effects.     

Combinatorial mutagenesis of the lamB gene: residues 41 through 43, which are conserved in Escherichia coli outer membrane proteins, are informationally important in maltoporin structure and function.

A new strategy for combinatorial mutagenesis was developed and applied to residues 40 through 60 of LamB protein (maltoporin), with the aim of identifying amino acids important for LamB structure and function. The strategy involved a template containing a stop codon in the target sequence and a pool of random degenerate oligonucleotides covering the region. In vitro mutagenesis followed by selection for function (Dex+, ability to utilize dextrins) corrected the nonsense mutation and simultaneously forced incorporation of a random mutation(s) within the region. The relative importance of each residue within the target was indicated by the frequency and nature of neutral and deleterious mutations recovered at each position. Residues 41 through 43 in LamB accepted few neutral substitutions, whereas residues 55 through 57 were highly flexible in this regard. Consistent with this finding was that the majority of defective mutants were altered at residues 41 to 43. Characterization of these mutants indicated that the nature of residues 41 to 43 influenced the amount of stable protein in the outer membrane. These results, as well as the conserved nature of this stretch of residues among outer membrane proteins, suggest that residues 41 to 43 of LamB play an important role in the process of outer membrane localization.     

Quantifying the slightly deleterious mutation model of molecular evolution

We have attempted to quantify the frequency and effects of slightly deleterious mutations (SDMs), those that have selective effects close to the reciprocal of the effective population size of a species, by comparing the level of selective constraint in protein-coding genes of related species that have different present-day effective population sizes. In our two comparisons, the species with the smaller effective population size showed lower constraint, implying that SDMs had become fixed. The fixation of SDMs was supported by the observation of a higher fraction of radical to conservative amino acid substitutions in species with smaller effective population sizes. The fraction of strongly deleterious mutations (which rarely become fixed) is >70% in most species. Only approximately 10% or fewer of mutations seem to behave as SDMs, but SDMs could comprise a substantial fraction of mutations in protein-coding genes that have a chance of becoming fixed between species.