Molecular evolution, mutation size and gene pleiotropy: a geometric reexamination

The influence of phenotypic effects of genetic mutations on molecular evolution is not well understood. Neutral and nearly neutral theories of molecular evolution predict a negative relationship between the evolutionary rate of proteins and their functional importance; nevertheless empirical studies seeking relationships between evolutionary rate and the phenotypic role of proteins have not produced conclusive results. In particular, previous studies have not found the expected negative correlation between evolutionary rate and gene pleiotropy. Here, we studied the effect of gene pleiotropy and the phenotypic size of mutations on the evolutionary rate of genes in a geometrical model, in which gene pleiotropy was characterized by n molecular phenotypes that affect organismal fitness. For a nearly neutral process, we found a negative relationship between evolutionary rate and mutation size but pleiotropy did not affect the evolutionary rate. Further, for a selection model, where most of the substitutions were fixed by natural selection in a randomly fluctuating environment, we also found a negative relationship between evolutionary rate and mutation size, but interestingly, gene pleiotropy increased the evolutionary rate as √n. These findings may explain part of the disagreement between empirical data and traditional expectations.     

The Rate of Compensatory Evolution

A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, k(c), is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, k(c) depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, k(c) is given by the rate at which favorable combinations of double mutants are produced by compensatory mutation. For r>0, k(c) decreases exponentially with r. In contrast, k(c) becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to WRIGHT's shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.     

Compensatory vs. pseudocompensatory evolution in molecular and developmental interactions

The evolution of molecules, developmental circuits, and new species are all characterized by the accumulation of incompatibilities between ancestors and descendants. When specific interactions between components are necessary at any of these levels, this requires compensatory coevolution. Theoretical treatments of compensatory evolution that only consider the endpoints predict that it should be rare because intermediate states are deleterious. However, empirical data suggest that compensatory evolution is common at all levels of molecular interaction. A general solution to this paradox is provided by plausible neutral or nearly neutral intermediates that possess informational redundancy. These intermediates provide an evolutionary path between coadapted allelic combinations. Although they allow incompatible end points to evolve, at no point was a deleterious mutation ever in need of compensation. As a result, what appears to be compensatory evolution may often actually be “pseudocompensatory.” Both theoretical and empirical studies indicate that pseudocompensation can speed the evolution of intergenic incompatibility, especially when driven by adaptation. However, under strong stabilizing selection the rate of pseudocompensatory evolution is still significant. Important examples of this process at work discussed here include the evolution of rRNA secondary structures, intra- and inter-protein interactions, and developmental genetic pathways. Future empirical work in this area should focus on comparing the details of intra- and intergenic interactions in closely related organisms.     

Weak selection and protein evolution

The "nearly neutral" theory of molecular evolution proposes that many features of genomes arise from the interaction of three weak evolutionary forces: mutation, genetic drift, and natural selection acting at its limit of efficacy. Such forces generally have little impact on allele frequencies within populations from generation to generation but can have substantial effects on long-term evolution. The evolutionary dynamics of weakly selected mutations are highly sensitive to population size, and near neutrality was initially proposed as an adjustment to the neutral theory to account for general patterns in available protein and DNA variation data. Here, we review the motivation for the nearly neutral theory, discuss the structure of the model and its predictions, and evaluate current empirical support for interactions among weak evolutionary forces in protein evolution. Near neutrality may be a prevalent mode of evolution across a range of functional categories of mutations and taxa. However, multiple evolutionary mechanisms (including adaptive evolution, linked selection, changes in fitness-effect distributions, and weak selection) can often explain the same patterns of genome variation. Strong parameter sensitivity remains a limitation of the nearly neutral model, and we discuss concave fitness functions as a plausible underlying basis for weak selection.     

Compensatory evolution of interacting gene products through multifunctional intermediates

When two mutations are singly deleterious but neutral or beneficial together, compensatory evolution can occur. The accumulation of derived, compensated genotypes contributes to the evolution of genetic incompatibilities between diverging populations or species. Previous two locus/two allele models have shown that compensatory evolution is appreciable only with tight linkage, the possibility of nearly simultaneous mutations, and/or a way to overcome negative selection against the singly mutated genotype. These conditions are often not met. Even when they are met, compensatory evolution is still predicted to be extremely slow, and in many scenarios selective advantage of the compensated genotype does little to accelerate it. Despite these obstacles, empirical studies suggest that it occurs readily. We describe here a set of related two locus/three allele models that invoke plausible neutral intermediates capable of productive interaction with both ancestral and compensated products of the interacting locus. These models are explored with analytical and computer simulation methods. The effect of these stepping-stone alleles on the evolution of ancestor-descendant incompatibilities is often profound, making the difference between evolution and stasis in several situations, including in small populations, when codominance or haploidy prevents shielding of mismatched genotypes, and in the absence of positive selection on the derived genotype. However, in large populations these intermediates can either speed or slow the evolution of incompatible genotypes relative to the two-allele case, depending on the specific fitness model. These results suggest that population size, the source of adaptive benefit, and the structural details of heteromeric gene product complexes interact to influence the path by which intergenic incompatibility evolves.     

Evolutionary rescue by compensatory mutations is constrained by genomic and environmental backgrounds

Since deleterious mutations may be rescued by secondary mutations during evolution, compensatory evolution could identify genetic solutions leading to therapeutic targets. Here, we tested this hypothesis and examined whether these solutions would be universal or would need to be adapted to one's genetic and environmental makeups. We performed experimental evolutionary rescue in a yeast disease model for the Wiskott–Aldrich syndrome in two genetic backgrounds and carbon sources. We found that multiple aspects of the evolutionary rescue outcome depend on the genotype, the environment, or a combination thereof. Specifically, the compensatory mutation rate and type, the molecular rescue mechanism, the genetic target, and the associated fitness cost varied across contexts. The course of compensatory evolution is therefore highly contingent on the initial conditions in which the deleterious mutation occurs. In addition, these results reveal biologically favored therapeutic targets for the Wiskott–Aldrich syndrome, including the target of an unrelated clinically approved drug. Our results experimentally illustrate the importance of epistasis and environmental evolutionary constraints that shape the adaptive landscape and evolutionary rate of molecular networks.     

The Structural Determinants of Intra-Protein Compensatory Substitutions

Compensatory substitutions happen when one mutation is advantageously selected because it restores the loss of fitness induced by a previous deleterious mutation. How frequent such mutations occur in evolution and what is the structural and functional context permitting their emergence remain open questions. We built an atlas of intra-protein compensatory substitutions using a phylogenetic approach and a dataset of 1,630 bacterial protein families for which high-quality sequence alignments and experimentally derived protein structures were available. We identified more than 51,000 positions coevolving by the mean of predicted compensatory mutations. Using the evolutionary and structural properties of the analyzed positions, we demonstrate that compensatory mutations are scarce (typically only a few in the protein history) but widespread (the majority of proteins experienced at least one). Typical coevolving residues are evolving slowly, are located in the protein core outside secondary structure motifs, and are more often in contact than expected by chance, even after accounting for their evolutionary rate and solvent exposure. An exception to this general scheme is residues coevolving for charge compensation, which are evolving faster than noncoevolving sites, in contradiction with predictions from simple coevolutionary models, but similar to stem pairs in RNA. While sites with a significant pattern of coevolution by compensatory mutations are rare, the comparative analysis of hundreds of structures ultimately permits a better understanding of the link between the three-dimensional structure of a protein and its fitness landscape.     

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.     

Function-specific accelerations in rates of sequence evolution suggest predictable epistatic responses to reduced effective population size

Changes in effective population size impinge on patterns of molecular evolution. Notably, slightly deleterious mutations are more likely to drift to fixation in smaller populations, which should typically also lead to an overall acceleration in the rates of evolution. This prediction has been validated empirically for several endosymbiont and island taxa. Here, we first show that rate accelerations are also evident in bacterial pathogens whose recent shifts in virulence make them prime candidates for reduced effective population size: Bacillus anthracis, Bordetella parapertussis, Mycobacterium leprae, Salmonella enterica typhi, Shigella spp., and Yersinia pestis. Using closely related genomes to analyze substitution rate dynamics across six phylogenetically independent bacterial clades, we demonstrate that relative rates of coding sequence evolution are biased according to gene functional category. Notably, genes that buffer against slightly deleterious mutations, such as chaperones, experience stronger rate accelerations than other functional classes at both nonsynonymous and synonymous sites. Although theory predicts altered evolutionary dynamics for buffer loci in the face of accumulating deleterious mutations, to observe even stronger rate accelerations is surprising. We suggest that buffer loci experience elevated substitution rates because the accumulation of deleterious mutations in the remainder of the genome favors compensatory substitutions in trans. Critically, the hyper-acceleration is evident across phylogenetically independent clades, supporting the hypothesis that reductions in effective population size predictably induce epistatic responses in genes that buffer against slightly deleterious mutations.     

Genetic constraints on protein evolution

Evolution requires the generation and optimization of new traits ("adaptation") and involves the selection of mutations that improve cellular function. These mutations were assumed to arise by selection of neutral mutations present at all times in the population. Here we review recent evidence that indicates that deleterious mutations are more frequent in the population than previously recognized and that these mutations play a significant role in protein evolution through continuous positive selection. Positively selected mutations include adaptive mutations, i.e. mutations that directly affect enzymatic function, and compensatory mutations, which suppress the pleiotropic effects of adaptive mutations. Compensatory mutations are by far the most frequent of the two and would allow potentially adaptive but deleterious mutations to persist long enough in the population to be positively selected during episodes of adaptation. Compensatory mutations are, by definition, context-dependent and thus constrain the paths available for evolution. This provides a mechanistic basis for the examples of highly constrained evolutionary landscapes and parallel evolution reported in natural and experimental populations. The present review article describes these recent advances in the field of protein evolution and discusses their implications for understanding the genetic basis of disease and for protein engineering in vitro.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Population size and molecular evolution on islands

The nearly neutral theory predicts that the rate and pattern of molecular evolution will be influenced by effective population size (Ne), because in small populations more slightly deleterious mutations are expected to drift to fixation. This important prediction has not been widely empirically tested, largely because of the difficulty of comparing rates of molecular evolution in sufficient numbers of independent lineages which differ only in Ne. Island endemic species provide an ideal test of the effect of Ne on molecular evolution because species restricted to islands frequently have smaller Ne than closely related mainland species, and island endemics have arisen from mainland lineages many times in a wide range of taxa. We collated a dataset of 70 phylogenetically independent comparisons between island and mainland taxa, including vertebrates, invertebrates and plants, from 19 different island groups. The rate of molecular evolution in these lineages was estimated by maximum likelihood using two measures: overall substitution rate and the ratio of non-synonymous to synonymous substitution rates. We show that island lineages have significantly higher ratios of non-synonymous to synonymous substitution rates than mainland lineages, as predicted by the nearly neutral theory, although overall substitution rates do not differ significantly.     

Emergent neutrality in adaptive asexual evolution

In nonrecombining genomes, genetic linkage can be an important evolutionary force. Linkage generates interference interactions, by which simultaneously occurring mutations affect each other's chance of fixation. Here, we develop a comprehensive model of adaptive evolution in linked genomes, which integrates interference interactions between multiple beneficial and deleterious mutations into a unified framework. By an approximate analytical solution, we predict the fixation rates of these mutations, as well as the probabilities of beneficial and deleterious alleles at fixed genomic sites. We find that interference interactions generate a regime of emergent neutrality: all genomic sites with selection coefficients smaller in magnitude than a characteristic threshold have nearly random fixed alleles, and both beneficial and deleterious mutations at these sites have nearly neutral fixation rates. We show that this dynamic limits not only the speed of adaptation, but also a population's degree of adaptation in its current environment. We apply the model to different scenarios: stationary adaptation in a time-dependent environment and approach to equilibrium in a fixed environment. In both cases, the analytical predictions are in good agreement with numerical simulations. Our results suggest that interference can severely compromise biological functions in an adapting population, which sets viability limits on adaptive evolution under linkage.     

A neutral theory predicts multigenic aging and increased concentrations of deleterious mutations on the mitochondrial and Y chromosomes

Population genetic forces have molded the constitution of the human genome over evolutionary time, and some of the most important parameters are the initial frequency of the allele, p, the effective population size, Ne, and the selection coefficient, s. There is considerable agreement among evolutionary gerontologists that the amplitude of -s is small for alleles that are Deleterious In Late Life (DILL), and thus DILL traits are effectively neutral and should be fixed in the human population in relationship to Ne and p. Even higher rates of fixation of deleterious mutations are predicted to occur in the two nonrecombinant genomes in humans, i.e., the Y chromosome and the mitochondrial genome, as a consequence of their lower Ne than autosomes, and the predicted higher rate of fixation of deleterious alleles on the Y may explain the reduced average life span of males vs. females. The high probability of fixation of neutral and mildly deleterious mutations in the mitochondrial genome explains in part its fast rate of evolution, the high observed frequency of mitochondrial disease in relationship to this genome's small size, and may be the underlying reason for the transfer of mitochondrial genes over evolutionary time to the nucleus. The predicted higher concentration of deleterious mutations on the mitochondrial genome could have some leverage to cause more dysfunction than that predicted by mitochondrial gene number alone, because of the essential role of mitochondrial gene function in multisubunit complexes, the coupling of mitochondrial functions, the observation that some mtDNA sequences facilitate somatic mutation, and the likelihood of deleterious mutations either increasing the production of or the sensitivity to mitochondrial ROS.     

GroEL/ES Buffering and Compensatory Mutations Promote Protein Evolution by Stabilizing Folding Intermediates

Maintaining stability is a major constraint in protein evolution because most mutations are destabilizing. Buffering and/or compensatory mechanisms that counteract this progressive destabilization during functional adaptation are pivotal for protein evolution as well as protein engineering. However, the interplay of these two mechanisms during a full evolutionary trajectory has never been explored. Here, we unravel such dynamics during the laboratory evolution of a phosphotriesterase into an arylesterase. A controllable GroEL/ES chaperone co-expression system enabled us to vary the selection environment between buffering and compensatory, which smoothened the trajectory along the fitness landscape to achieve a > 10⁴ increase in arylesterase activity. Biophysical characterization revealed that, in contrast to prevalent models of protein stability and evolution, the variants' soluble cellular expression did not correlate with in vitro stability, and compensatory mutations were linked to a stabilization of folding intermediates. Thus, folding kinetics in the cell are a key feature of protein evolvability.     

Testing the neutral fixation of hetero-oligomerism in the archaeal chaperonin CCT

The evolutionary transition from homo-oligomerism to hetero-oligomerism in multimeric proteins and its contribution to function innovation and organism complexity remain to be investigated. Here, we undertake the challenge of contributing to this theoretical ground by investigating the hetero-oligomerism in the molecular chaperonin cytosolic chaperonin containing tailless complex polypeptide 1 (CCT) from archaea. CCT is amenable to this study because, in contrast to eukaryotic CCTs where sub-functionalization after gene duplication has been taken to completion, archaeal CCTs present no evidence for subunit functional specialization. Our analyses yield additional information to previous reports on archaeal CCT paralogy by identifying new duplication events. Analyses of selective constraints show that amino acid sites from 1 subunit have fixed slightly deleterious mutations at inter-subunit interfaces after gene duplication. These mutations have been followed by compensatory mutations in nearby regions of the same subunit and in the interface contact regions of its paralogous subunit. The strong selective constraints in these regions after speciation support the evolutionary entrapment of CCTs as hetero-oligomers. In addition, our results unveil different evolutionary dynamics depending on the degree of CCT hetero-oligomerism. Archaeal CCT protein complexes comprising 3 distinct classes of subunits present 2 evolutionary processes. First, slightly deleterious and compensatory mutations were fixed neutrally at inter-subunit regions. Second, sub-functionalization may have occurred at substrate-binding and adenosine triphosphate-binding regions after the 2nd gene duplication event took place. CCTs with 2 distinct types of subunits did not present evidence of sub-functionalization. Our results provide the 1st in silico evidence for the neutral fixation of hetero-oligomerism in archaeal CCTs and provide information on the evolution of hetero-oligomerism toward sub-functionalization in archaeal CCTs.     

An exact steady state solution of Fisher's geometric model and other models

Because nearly neutral substitutions are thought to contribute substantially to molecular evolution, and much of our insight about the workings of nearly neutral evolution relies on theory, solvable models of this process are of particular interest. Here, I present an analytical method for solving models of nearly neutral evolution at steady state. The steady state solution applies to any constant fitness landscape under a dynamic of successive fixations, each of which occurs on the background of the population's most recent common ancestor. Because this dynamic neglects the effects of polymorphism in the population beyond the mutant allele under consideration, the steady state solution provides a decent approximation of evolutionary dynamics when the population mutation rate is low (Nu<1). To demonstrate the method, I apply it to two examples: Fisher's geometric model (FGM), and a simple model of molecular evolution. Since recent papers have studied the steady state behavior of FGM under this dynamic, I analyze its behavior in detail and compare the results with previous work.     

From bad to good: Fitness reversals and the ascent of deleterious mutations

Deleterious mutations are considered a major impediment to adaptation, and there are straightforward expectations for the rate at which they accumulate as a function of population size and mutation rate. In a simulation model of an evolving population of asexually replicating RNA molecules, initially deleterious mutations accumulated at rates nearly equal to that of initially beneficial mutations, without impeding evolutionary progress. As the mutation rate was increased within a moderate range, deleterious mutation accumulation and mean fitness improvement both increased. The fixation rates were higher than predicted by many population-genetic models. This seemingly paradoxical result was resolved in part by the observation that, during the time to fixation, the selection coefficient (s) of initially deleterious mutations reversed to confer a selective advantage. Significantly, more than half of the fixations of initially deleterious mutations involved fitness reversals. These fitness reversals had a substantial effect on the total fitness of the genome and thus contributed to its success in the population. Despite the relative importance of fitness reversals, however, the probabilities of fixation for both initially beneficial and initially deleterious mutations were exceedingly small (on the order of 10⁻⁵ of all mutations).     

Epistasis and the adaptability of an RNA virus

We have explored the patterns of fitness recovery in the vesicular stomatitis RNA virus. We show that, in our experimental setting, reversions to the wild-type genotype were rare and fitness recovery was at least partially driven by compensatory mutations. We compared compensatory adaptation for genotypes carrying (1) mutations with varying deleterious fitness effects, (2) one or two deleterious mutations, and (3) pairs of mutations showing differences in the strength and sign of epistasis. In all cases, we found that the rate of fitness recovery and the proportion of reversions were positively affected by population size. Additionally, we observed that mutations with large fitness effect were always compensated faster than mutations with small fitness effect. Similarly, compensatory evolution was faster for genotypes carrying a single deleterious mutation than for those carrying pairs of mutations. Finally, for genotypes carrying two deleterious mutations, we found evidence of a negative correlation between the epistastic effect and the rate of compensatory evolution.     

Substitution Processes in Molecular Evolution. III. Deleterious Alleles

The substitution processes for various models of deleterious alleles are examined using computer simulations and mathematical analyses. Most of the work focuses on the house-of-cards model, which is a popular model of deleterious allele evolution. The rate of substitution is shown to be a concave function of the strength of selection as measured by α = 2Nσ, where N is the population size and σ is the standard deviation of fitness. For α<1, the house-of-cards model is essentially a neutral model; for α>4, the model ceases to evolve. The stagnation for large α may be understood by appealing to the theory of records. The house-of-cards model evolves to a state where the vast majority of all mutations are deleterious, but precisely one-half of those mutations that fix are deleterious (the other half are advantageous). Thus, the model is not a model of exclusively deleterious evolution as is frequently claimed. It is argued that there are no biologically reasonable models of molecular evolution where the vast majority of all substitutions are deleterious. Other models examined include the exponential and gamma shift models, the Hartl-Dykhuizen-Dean (HDD) model, and the optimum model. Of all those examined, only the optimum and HDD models appear to be reasonable candidates for silent evolution. None of the models are viewed as good candidates for protein evolution, as none are both biologically reasonable and exhibit the variability in substitutions commonly observed in protein sequence data.