Predicting the tolerance of proteins to random amino acid substitution

The effectiveness of selection in a species affects the direction of amino acid frequency evolution

Nearly neutral theory predicts that species with higher effective population size (N e ) are better able to purge slightly deleterious mutations. We compare evolution in high-N e vs. low-N e vertebrates to reveal which amino acid frequencies are subject to subtle selective preferences. We take three complementary approaches, two measuring flux and one measuring outcomes. First, we fit non-stationary substitution models of amino acid flux using maximum likelihood, comparing the high-N e clade of rodents and lagomorphs to its low-N e sister clade of primates and colugos. Second, we compare evolutionary outcomes across a wider range of vertebrates, via correlations between amino acid frequencies and N e . Third, we dissect the details of flux in human, chimpanzee, mouse, and rat, as scored by parsimony - this also enables comparison to a historical paper. All three methods agree on which amino acids are preferred under more effective selection. Preferred amino acids tend to be smaller, less costly to synthesize, and to promote intrinsic structural disorder. Parsimony-induced bias in the historical study produces an apparent reduction in structural disorder, perhaps driven by slightly deleterious substitutions. Within highly exchangeable pairs of amino acids, arginine is strongly preferred over lysine, and valine over isoleucine, consistent with more effective selection preferring a marginally larger free energy of folding. These two preferences match differences between thermophiles and mesophilic relatives. These results reveal the biophysical consequences of mutation-selection-drift balance, and demonstrate the utility of nearly neutral theory for understanding protein evolution.

Recent Progress in the Understanding and Engineering of Coenzyme B12-Dependent Glycerol Dehydratase

Coenzyme B₁₂-dependent glycerol dehydratase (GDHt) catalyzes the dehydration reaction of glycerol in the presence of adenosylcobalamin to yield 3-hydroxypropanal (3-HPA), which can be converted biologically to versatile platform chemicals such as 1,3-propanediol and 3-hydroxypropionic acid. Owing to the increased demand for biofuels, developing biological processes based on glycerol, which is a byproduct of biodiesel production, has attracted considerable attention recently. In this review, we will provide updates on the current understanding of the catalytic mechanism and structure of coenzyme B₁₂-dependent GDHt, and then summarize the results of engineering attempts, with perspectives on future directions in its engineering.

The Impact of Protein Architecture on Adaptive Evolution

Adaptive mutations play an important role in molecular evolution. However, the frequency and nature of these mutations at the intramolecular level are poorly understood. To address this, we analyzed the impact of protein architecture on the rate of adaptive substitutions, aiming to understand how protein biophysics influences fitness and adaptation. Using Drosophila melanogaster and Arabidopsis thaliana population genomics data, we fitted models of distribution of fitness effects and estimated the rate of adaptive amino-acid substitutions both at the protein and amino-acid residue level. We performed a comprehensive analysis covering genome, gene, and protein structure, by exploring a multitude of factors with a plausible impact on the rate of adaptive evolution, such as intron number, protein length, secondary structure, relative solvent accessibility, intrinsic protein disorder, chaperone affinity, gene expression, protein function, and protein-protein interactions. We found that the relative solvent accessibility is a major determinant of adaptive evolution, with most adaptive mutations occurring at the surface of proteins. Moreover, we observe that the rate of adaptive substitutions differs between protein functional classes, with genes encoding for protein biosynthesis and degradation signaling exhibiting the fastest rates of protein adaptation. Overall, our results suggest that adaptive evolution in proteins is mainly driven by intermolecular interactions, with host-pathogen coevolution likely playing a major role.

Effect of site-directed point mutations on protein misfolding: A simulation study

A Monte Carlo simulation based sequence design method is proposed to investigate the role of site-directed point mutations in protein misfolding. Site-directed point mutations are incorporated in the designed sequences of selected proteins. While most mutated sequences correctly fold to their native conformation, some of them stabilize in other nonnative conformations and thus misfold/unfold. The results suggest that a critical number of hydrophobic amino acid residues must be present in the core of the correctly folded proteins, whereas proteins misfold/unfold if this number of hydrophobic residues falls below the critical limit. A protein can accommodate only a particular number of hydrophobic residues at the surface, provided a large number of hydrophilic residues are present at the surface and critical hydrophobicity of the core is preserved. Some surface sites are observed to be equally sensitive toward site-directed point mutations as the core sites. Point mutations with highly polar and charged amino acids increases the misfold/unfold propensity of proteins. Substitution of natural amino acids at sites with different number of nonbonded contacts suggests that both amino acid identity and its respective site-specificity determine the stability of a protein. A clash-match method is developed to calculate the number of matching and clashing interactions in the mutated protein sequences. While misfolded/unfolded sequences have a higher number of clashing and a lower number of matching interactions, the correctly folded sequences have a lower number of clashing and a higher number of matching interactions. These results are valid for different SCOP classes of proteins.

Biophysical Models of Protein Evolution: Understanding the Patterns of Evolutionary Sequence Divergence

For decades, rates of protein evolution have been interpreted in terms of the vague concept of functional importance. Slowly evolving proteins or sites within proteins were assumed to be more functionally important and thus subject to stronger selection pressure. More recently, biophysical models of protein evolution, which combine evolutionary theory with protein biophysics, have completely revolutionized our view of the forces that shape sequence divergence. Slowly evolving proteins have been found to evolve slowly because of selection against toxic misfolding and misinteractions, linking their rate of evolution primarily to their abundance. Similarly, most slowly evolving sites in proteins are not directly involved in function, but mutating these sites has a large impact on protein structure and stability. In this article, we review the studies in the emerging field of biophysical protein evolution that have shaped our current understanding of sequence divergence patterns. We also propose future research directions to develop this nascent field.

Involvement of a joker mutation in a polymerase-independent lethal mutagenesis escape mechanism

We previously characterized a foot-and-mouth disease virus (FMDV) with three amino acid replacements in its polymerase (3D) that conferred resistance to the mutagenic nucleoside analogue ribavirin. Here we show that passage of this mutant in the presence of high ribavirin concentrations resulted in selection of viruses with the additional replacement I248T in 2C. This 2C substitution alone (even in the absence of replacements in 3D) increased FMDV fitness mainly in the presence of ribavirin, prevented an incorporation bias in favor of A and U associated with ribavirin mutagenesis, and conferred the ATPase activity of 2C decreased sensitivity to ribavirin-triphosphate. Since in previous studies we described that 2C with I248T was selected under different selective pressures, this replacement qualifies as a joker substitution in FMDV evolution. The results have identified a role of 2C in nucleotide incorporation, and have unveiled a new polymerase-independent mechanism of virus escape to lethal mutagenesis.

•

A replacement in FMDV protein 2C confers reduced sensitivity to the mutagen ribavirin.

•

The effect of the replacement is to prevent a mutational bias evoked by ribavirin.

•

2C has an effect in nucleotide incorporation by the FMDV polymerase.

•

We describe a new molecular mechanism of escape to ribavirin-mediated extinction.

High-throughput identification of protein mutant stability computed from a double mutant fitness landscape

The effect of a mutation on protein stability is traditionally measured by genetic construction, expression, purification, and physical analysis using low-throughput methods. This process is tedious and limits the number of mutants able to be examined in a single study. In contrast, functional fitness effects can be measured in a high-throughput manner by various deep mutational scanning tools. Using protein GB 1, we have recently demonstrated the feasibility of estimating the mutational stability effect ( ΔΔG) of single-substitution based on the functional fitness profile of all double-substitutions. The principle is to identify genetic backgrounds that have an exhausted stability margin. The functional effect of an additional substitution on these genetic backgrounds can then be used to compute the mutational ΔΔG based on the biophysical relationship between functional fitness and thermodynamic stability. However, to identify such genetic backgrounds, the approach described in our previous study required a benchmark dataset, which is a set of known mutational ΔΔG. In this study, a benchmark-independent approach is developed. The genetic backgrounds of interest are identified using k-means clustering with the integration of structural information. We further demonstrated that a reasonable approximation of ΔΔG can also be obtained without taking structural information into account. In summary, this study describes a novel method for computing ΔΔG from double-substitution functional fitness profiles alone, without relying on any known mutational ΔΔG as a benchmark.

Universal distribution of mutational effects on protein stability, uncoupling of protein robustness from sequence evolution and distinct evolutionary modes of prokaryotic and eukaryotic proteins

Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins.

Synthetic biology for the directed evolution of protein biocatalysts: navigating sequence space intelligently

The amino acid sequence of a protein affects both its structure and its function. Thus, the ability to modify the sequence, and hence the structure and activity, of individual proteins in a systematic way, opens up many opportunities, both scientifically and (as we focus on here) for exploitation in biocatalysis. Modern methods of synthetic biology, whereby increasingly large sequences of DNA can be synthesised de novo, allow an unprecedented ability to engineer proteins with novel functions. However, the number of possible proteins is far too large to test individually, so we need means for navigating the 'search space' of possible protein sequences efficiently and reliably in order to find desirable activities and other properties. Enzymologists distinguish binding (Kd) and catalytic (kcat) steps. In a similar way, judicious strategies have blended design (for binding, specificity and active site modelling) with the more empirical methods of classical directed evolution (DE) for improving kcat (where natural evolution rarely seeks the highest values), especially with regard to residues distant from the active site and where the functional linkages underpinning enzyme dynamics are both unknown and hard to predict. Epistasis (where the 'best' amino acid at one site depends on that or those at others) is a notable feature of directed evolution. The aim of this review is to highlight some of the approaches that are being developed to allow us to use directed evolution to improve enzyme properties, often dramatically. We note that directed evolution differs in a number of ways from natural evolution, including in particular the available mechanisms and the likely selection pressures. Thus, we stress the opportunities afforded by techniques that enable one to map sequence to (structure and) activity in silico, as an effective means of modelling and exploring protein landscapes. Because known landscapes may be assessed and reasoned about as a whole, simultaneously, this offers opportunities for protein improvement not readily available to natural evolution on rapid timescales. Intelligent landscape navigation, informed by sequence-activity relationships and coupled to the emerging methods of synthetic biology, offers scope for the development of novel biocatalysts that are both highly active and robust.

A coarse-grained approach to protein design: learning from design to understand folding

Computational studies have given a great contribution in building our current understanding of the complex behavior of protein molecules; nevertheless, a complete characterization of their free energy landscape still represents a major challenge. Here, we introduce a new coarse-grained approach that allows for an extensive sampling of the conformational space of a large number of sequences. We explicitly discuss its application in protein design, and by studying four representative proteins, we show that the method generates sequences with a relatively smooth free energy surface directed towards the target structures.

Protein structural modularity and robustness are associated with evolvability

Theory suggests that biological modularity and robustness allow for maintenance of fitness under mutational change, and when this change is adaptive, for evolvability. Empirical demonstrations that these traits promote evolvability in nature remain scant however. This is in part because modularity, robustness, and evolvability are difficult to define and measure in real biological systems. Here, we address whether structural modularity and/or robustness confer evolvability at the level of proteins by looking for associations between indices of protein structural modularity, structural robustness, and evolvability. We propose a novel index for protein structural modularity: the number of regular secondary structure elements (helices and strands) divided by the number of residues in the structure. We index protein evolvability as the proportion of sites with evidence of being under positive selection multiplied by the average rate of adaptive evolution at these sites, and we measure this as an average over a phylogeny of 25 mammalian species. We use contact density as an index of protein designability, and thus, structural robustness. We find that protein evolvability is positively associated with structural modularity as well as structural robustness and that the effect of structural modularity on evolvability is independent of the structural robustness index. We interpret these associations to be the result of reduced constraints on amino acid substitutions in highly modular and robust protein structures, which results in faster adaptation through natural selection.

Multiple global suppressors of protein stability defects facilitate the evolution of extended-spectrum TEM β-lactamases

The introduction of extended-spectrum cephalosporins and β-lactamase inhibitors has driven the evolution of extended-spectrum β-lactamases (ESBLs) that possess the ability to hydrolyze these drugs. The evolved TEM ESBLs from clinical isolates of bacteria often contain substitutions that occur in the active site and alter the catalytic properties of the enzyme to provide an increased hydrolysis of extended-spectrum cephalosporins or an increased resistance to inhibitors. These active-site substitutions often result in a cost in the form of reduced enzyme stability. The evolution of TEM ESBLs is facilitated by mutations that act as global suppressors of protein stability defects in that they allow the enzyme to absorb multiple amino acid changes despite incremental losses in stability associated with the substitutions. The best-studied example is the M182T substitution, which corrects protein stability defects and is commonly found in TEM ESBLs or inhibitor-resistant variants from clinical isolates. In this study, a genetic selection for second-site mutations that could partially restore function to a severely destabilized primary mutant enabled the identification of A184V, T265M, R275Q, and N276D, which are known to occur in TEM ESBLs from clinical isolates, as suppressors of TEM-1 protein stability defects. Further characterization demonstrated that these substitutions increased the thermal stability of TEM-1 and were able to correct the stability defects of two different sets of destabilizing mutations. The acquisition of compensatory global suppressors of stability costs associated with active-site mutations may be a common mechanism for the evolution of novel protein function.

Neutrality and evolvability of designed protein sequences

The effect of foldability on protein's evolvability is analyzed by a two-prong approach consisting of a self-consistent mean-field theory and Monte Carlo simulations. Theory and simulation models representing protein sequences with binary patterning of amino acid residues compatible with a particular foldability criteria are used. This generalized foldability criterion is derived using the high temperature cumulant expansion approximating the free energy of folding. The effect of cumulative point mutations on these designed proteins is studied under neutral condition. The robustness, protein's ability to tolerate random point mutations is determined with a selective pressure of stability (ΔΔG) for the theory designed sequences, which are found to be more robust than that of Monte Carlo and mean-field-biased Monte Carlo generated sequences. The results show that this foldability criterion selects viable protein sequences more effectively compared to the Monte Carlo method, which has a marked effect on how the selective pressure shapes the evolutionary sequence space. These observations may impact de novo sequence design and its applications in protein engineering.

The evolutionary consequences of erroneous protein synthesis

Errors in protein synthesis disrupt cellular fitness, cause disease phenotypes and shape gene and genome evolution. Experimental and theoretical results on this topic have accumulated rapidly in disparate fields, such as neurobiology, protein biosynthesis and degradation and molecular evolution, but with limited communication among disciplines. Here, we review studies of error frequencies, the cellular and organismal consequences of errors and the attendant long-range evolutionary responses to errors. We emphasize major areas in which little is known, such as the failure rates of protein folding, in addition to areas in which technological innovations may enable imminent gains, such as the elucidation of translational missense error frequencies. Evolutionary responses to errors fall into two broad categories: adaptations that minimize errors and their attendant costs and adaptations that exploit errors for the organism's benefit.

Chaperonin overexpression promotes genetic variation and enzyme evolution

Most protein mutations, and mutations that alter protein functions in particular, undermine stability and are therefore deleterious. Chaperones, or heat-shock proteins, are often implicated in buffering mutations, and could thus facilitate the acquisition of neutral genetic diversity and the rate of adaptation. We examined the ability of the Escherichia coli GroEL/GroES chaperonins to buffer destabilizing and adaptive mutations. Here we show that mutational drifts performed in vitro with four different enzymes indicated that GroEL/GroES overexpression doubled the number of accumulating mutations, and promoted the folding of enzyme variants carrying mutations in the protein core and/or mutations with higher destabilizing effects (destabilization energies of >3.5 kcal mol(-)(1), on average, versus approximately 1 kcal mol(-)(1) in the absence of GroEL/GroES). The divergence of modified enzymatic specificity occurred much faster under GroEL/GroES overexpression, in terms of the number of adapted variants (>or=2-fold) and their improved specificity and activity (>or=10-fold). These results indicate that protein stability is a major constraint in protein evolution, and buffering mechanisms such as chaperonins are key in alleviating this constraint.

Biological effect of Muller's Ratchet: distant capsid site can affect picornavirus protein processing

Repeated bottleneck passages of RNA viruses result in accumulation of mutations and fitness decrease. Here, we show that clones of foot-and-mouth disease virus (FMDV) subjected to bottleneck passages, in the form of plaque-to-plaque transfers in BHK-21 cells, increased the thermosensitivity of the viral clones. By constructing infectious FMDV clones, we have identified the amino acid substitution M54I in capsid protein VP1 as one of the lesions associated with thermosensitivity. M54I affects processing of precursor P1, as evidenced by decreased production of VP1 and accumulation of VP1 precursor proteins. The defect is enhanced at high temperatures. Residue M54 of VP1 is exposed on the virion surface, and it is close to the B-C loop where an antigenic site of FMDV is located. M54 is not in direct contact with the VP1-VP3 cleavage site, according to the three-dimensional structure of FMDV particles. Models to account for the effect of M54 in processing of the FMDV polyprotein are proposed. In addition to revealing a distance effect in polyprotein processing, these results underline the importance of pursuing at the biochemical level the biological defects that arise when viruses are subjected to multiple bottleneck events.

A framework for evolutionary systems biology

BACKGROUND

Many difficult problems in evolutionary genomics are related to mutations that have weak effects on fitness, as the consequences of mutations with large effects are often simple to predict. Current systems biology has accumulated much data on mutations with large effects and can predict the properties of knockout mutants in some systems. However experimental methods are too insensitive to observe small effects.

RESULTS

Here I propose a novel framework that brings together evolutionary theory and current systems biology approaches in order to quantify small effects of mutations and their epistatic interactions in silico. Central to this approach is the definition of fitness correlates that can be computed in some current systems biology models employing the rigorous algorithms that are at the core of much work in computational systems biology. The framework exploits synergies between the realism of such models and the need to understand real systems in evolutionary theory. This framework can address many longstanding topics in evolutionary biology by defining various 'levels' of the adaptive landscape. Addressed topics include the distribution of mutational effects on fitness, as well as the nature of advantageous mutations, epistasis and robustness. Combining corresponding parameter estimates with population genetics models raises the possibility of testing evolutionary hypotheses at a new level of realism.

CONCLUSION

EvoSysBio is expected to lead to a more detailed understanding of the fundamental principles of life by combining knowledge about well-known biological systems from several disciplines. This will benefit both evolutionary theory and current systems biology. Understanding robustness by analysing distributions of mutational effects and epistasis is pivotal for drug design, cancer research, responsible genetic engineering in synthetic biology and many other practical applications.

Lethal mutagenesis of bacteria

Lethal mutagenesis, the killing of a microbial pathogen with a chemical mutagen, is a potential broad-spectrum antiviral treatment. It operates by raising the genomic mutation rate to the point that the deleterious load causes the population to decline. Its use has been limited to RNA viruses because of their high intrinsic mutation rates. Microbes with DNA genomes, which include many viruses and bacteria, have not been considered for this type of treatment because their low intrinsic mutation rates seem difficult to elevate enough to cause extinction. Surprisingly, models of lethal mutagenesis indicate that bacteria may be candidates for lethal mutagenesis. In contrast to viruses, bacteria reproduce by binary fission, and this property ensures their extinction if subjected to a mutation rate >0.69 deleterious mutations per generation. The extinction threshold is further lowered when bacteria die from environmental causes, such as washout or host clearance. In practice, mutagenesis can require many generations before extinction is achieved, allowing the bacterial population to grow to large absolute numbers before the load of deleterious mutations causes the decline. Therefore, if effective treatment requires rapid population decline, mutation rates >>0.69 may be necessary to achieve treatment success. Implications for the treatment of bacteria with mutagens, for the evolution of mutator strains in bacterial populations, and also for the evolution of mutation rate in cancer are discussed.

The optimal burst of mutation to create a phenotype

Mutagenesis is commonly applied to genes and genomes to create novel variants with desired properties. This paper calculates the level of mutagenesis that maximizes the appearance of favorable mutants, assuming that the mutagenesis is applied in a single episode. The downside of mutagenesis is that a substantial fraction of mutations will destroy gene/genome function. The upside of mutagenesis is the production of beneficial mutations, but the desired phenotype may require that 1, 2 or more beneficial mutations be present simultaneously (the phenotype dimensionality). The optimum level of mutagenesis is sensitive to both properties. In the simplest model, the mutation optimum occurs when number of lethal equivalents per genome equals the phenotype dimensionality, a result first derived by Mundry and Gierer [1958. Production of mutations in tobacco mosaic virus by chemical treatment of its nucleic acid in vitro. Z. Vererbungsl. 89 (4), 614-630]. This level of mutation is shown to be an upper bound for the optimum in various extensions of the model, and the recovery of mutants is also reasonably tolerant to deviations from the optimum.

In silico genetic robustness analysis of microRNA secondary structures: potential evidence of congruent evolution in microRNA

Background

Robustness is a fundamental property of biological systems and is defined as the ability to maintain stable functioning in the face of various perturbations. Understanding how robustness has evolved has become one of the most attractive areas of research for evolutionary biologists, as it is still unclear whether genetic robustness evolved as a direct consequence of natural selection, as an intrinsic property of adaptations, or as congruent correlate of environment robustness. Recent studies have demonstrated that the stem-loop structures of microRNA (miRNA) are tolerant to some structural changes and show thermodynamic stability. We therefore hypothesize that genetic robustness may evolve as a correlated side effect of the evolution for environmental robustness.

Results

We examine the robustness of 1,082 miRNA genes covering six species. Our data suggest the stem-loop structures of miRNA precursors exhibit a significantly higher level of genetic robustness, which goes beyond the intrinsic robustness of the stem-loop structure and is not a byproduct of the base composition bias. Furthermore, we demonstrate that the phenotype of miRNA buffers against genetic perturbations, and at the same time is also insensitive to environmental perturbations.

Conclusion

The results suggest that the increased robustness of miRNA stem-loops may result from congruent evolution for environment robustness. Potential applications of our findings are also discussed.

Phenotypic mutation rates and the abundance of abnormal proteins in yeast

Phenotypic mutations are errors that occur during protein synthesis. These errors lead to amino acid substitutions that give rise to abnormal proteins. Experiments suggest that such errors are quite common. We present a model to study the effect of phenotypic mutation rates on the amount of abnormal proteins in a cell. In our model, genes are regulated to synthesize a certain number of functional proteins. During this process, depending on the phenotypic mutation rate, abnormal proteins are generated. We use data on protein length and abundance in Saccharomyces cerevisiae to parametrize our model. We calculate that for small phenotypic mutation rates most abnormal proteins originate from highly expressed genes that are on average nearly twice as large as the average yeast protein. For phenotypic mutation rates much above 5 × 10⁻⁴, the error-free synthesis of large proteins is nearly impossible and lowly expressed, very large proteins contribute more and more to the amount of abnormal proteins in a cell. This fact leads to a steep increase of the amount of abnormal proteins for phenotypic mutation rates above 5 × 10⁻⁴. Simulations show that this property leads to an upper limit for the phenotypic mutation rate of approximately 2 × 10⁻³ even if the costs for abnormal proteins are extremely low. We also consider the adaptation of individual proteins. Individual genes/proteins can decrease their phenotypic mutation rate by using preferred codons or by increasing their robustness against amino acid substitutions. We discuss the similarities and differences between the two mechanisms and show that they can only slow down but not prevent the rapid increase of the amount of abnormal proteins. Our work allows us to estimate the phenotypic mutation rate based on data on the fraction of abnormal proteins. For S. cerevisiae, we predict that the value for the phenotypic mutation rate is between 2 × 10⁻⁴ and 6 × 10⁻⁴.

A functional protein machinery, built from genetic information, is central to every living organism. Surprisingly, the decoding of genes into amino acid sequences is fairly inaccurate. Errors in this process (phenotypic mutations) are several orders of magnitude more frequent than errors during DNA replication (genotypic mutations). Many researchers have explored the evolution of genotypic mutation rates, but there are as yet few investigations into the evolutionary dynamics of phenotypic mutation rates. Here we present a mathematical model that describes the effect of phenotypic mutation on the amount of abnormal proteins in cells. We parameterize our model using data from yeast (Saccharomyces cerevisiae). We show that for phenotypic mutation rates above 5 × 10⁻⁴ per amino acid, the error-free synthesis of large proteins becomes nearly impossible. We estimate the phenotypic mutation rate of S. cerevisiae to be between 2 × 10⁻⁴ and 6 × 10⁻⁴ per amino acid.

Evolution favors protein mutational robustness in sufficiently large populations

Background

An important question is whether evolution favors properties such as mutational robustness or evolvability that do not directly benefit any individual but can influence the course of future evolution. Functionally similar proteins can differ substantially in their robustness to mutations and capacity to evolve new functions, but it has remained unclear whether any of these differences might be due to evolutionary selection for these properties.

Results

Here, we use laboratory experiments to demonstrate that evolution favors protein mutational robustness if the evolving population is sufficiently large. We neutrally evolve cytochrome P450 proteins under identical selection pressures and mutation rates in populations of different sizes, and show that proteins from the larger and thus more polymorphic population tend towards higher mutational robustness. Proteins from the larger population also evolve greater stability, a biophysical property that is known to enhance both mutational robustness and evolvability. The excess mutational robustness and stability is well described by mathematical theory, and can be quantitatively related to the way that the proteins occupy their neutral network.

Conclusion

Our work is the first experimental demonstration of the general tendency of evolution to favor mutational robustness and protein stability in highly polymorphic populations. We suggest that this phenomenon could contribute to the mutational robustness and evolvability of viruses and bacteria that exist in large populations.

Thermodynamics of neutral protein evolution

Naturally evolving proteins gradually accumulate mutations while continuing to fold to stable structures. This process of neutral evolution is an important mode of genetic change and forms the basis for the molecular clock. We present a mathematical theory that predicts the number of accumulated mutations, the index of dispersion, and the distribution of stabilities in an evolving protein population from knowledge of the stability effects (delta deltaG values) for single mutations. Our theory quantitatively describes how neutral evolution leads to marginally stable proteins and provides formulas for calculating how fluctuations in stability can overdisperse the molecular clock. It also shows that the structural influences on the rate of sequence evolution observed in earlier simulations can be calculated using just the single-mutation delta deltaG values. We consider both the case when the product of the population size and mutation rate is small and the case when this product is large, and show that in the latter case the proteins evolve excess mutational robustness that is manifested by extra stability and an increase in the rate of sequence evolution. All our theoretical predictions are confirmed by simulations with lattice proteins. Our work provides a mathematical foundation for understanding how protein biophysics shapes the process of evolution.

HIV-1 protease catalytic efficiency effects caused by random single amino acid substitutions

Protein evolution has occurred by successive fixation of individual mutations. The probability of fixation depends on the fitness of the mutation, and the arising variant can be deleterious, neutral, or beneficial. Despite its relevance, only few studies have estimated the distribution of fitness effects caused by random single mutations on protein function. The human immunodeficiency virus type 1 (HIV-1) protease was chosen as a model protein to quantify protein's tolerability to random single mutations. After determining the enzymatic activity of 107 single random mutants, we found that 86% of single mutations were deleterious for the enzyme catalytic efficiency and 54% lethal. Only 2% of the mutations significantly increased the catalytic efficiency of the enzyme. These data demonstrate the vulnerability of HIV-1 protease to single random mutations. When a second random mutagenesis library was constructed from an HIV-1 protease carrying a highly deleterious single mutation (D30N), a higher proportion of mutations with neutral or beneficial effect were found, 26% and 9%, respectively. Importantly, antagonist epistasis was observed between deleterious mutations. In particular, the mutation N88D, lethal for the wild-type protease, restored the wild-type catalytic efficiency when combined with the highly deleterious mutation D30N. The low tolerability to single random substitutions shown here for the wild-type HIV-1 protease contrasts with its in vivo ability to generate an adaptive variation. Thus, the antagonist epistasis between deleterious or lethal mutations may be responsible for increasing the protein mutational robustness and evolvability.

Population genetics of translational robustness

Recent work has shown that expression level is the main predictor of a gene's evolutionary rate and that more highly expressed genes evolve slower. A possible explanation for this observation is selection for proteins that fold properly despite mistranslation, in short selection for translational robustness. Translational robustness leads to the somewhat paradoxical prediction that highly expressed genes are extremely tolerant to missense substitutions but nevertheless evolve very slowly. Here, we study a simple theoretical model of translational robustness that allows us to gain analytic insight into how this paradoxical behavior arises.