The evolution and evolutionary consequences of marginal thermostability in proteins

Substitution Rates Predicted by Stability-Constrained Models of Protein Evolution Are Not Consistent with Empirical Data

Protein structures strongly influence molecular evolution. In particular, the evolutionary rate of a protein site depends on the number of its native contacts. Stability-constrained models of protein evolution consider this influence of protein structure on evolution by predicting the effect of mutations on the stability of the native state, but they currently neglect how mutations affect the protein structure. These models predict that buried protein sites with more native contacts are more constrained by natural selection and less variable, as observed. Nevertheless, previous work did not consider the stability against compact misfolded conformations, although it is known that the negative design that destabilizes these misfolded conformations influences protein evolution significantly. Here, we show that stability-constrained models that consider misfolding predict that site-specific sequence entropy and substitution rate peak at amphiphilic sites with an intermediate number of contacts, as these sites are less constrained than exposed sites with few contacts whose hydrophobicity must be limited. This result holds both for a mean-field model with independent sites and for a pairwise model that takes as a reference the wild-type sequence, but it contrasts with the observations that indicate that the entropy and the substitution rate decrease monotonically with the number of contacts. Our work suggests that stability-constrained models overestimate the tolerance of amphiphilic sites against mutations, either because of the limits of the free energy function or, more importantly in our opinion, because they do not consider how mutations perturb the native protein structure.

Structural analyses of adenylate kinases from Antarctic and tropical fishes for understanding cold adaptation of enzymes

Psychrophiles are extremophilic organisms capable of thriving in cold environments. Proteins from these cold-adapted organisms can remain physiologically functional at low temperatures, but are structurally unstable even at moderate temperatures. Here, we report the crystal structure of adenylate kinase (AK) from the Antarctic fish Notothenia coriiceps, and identify the structural basis of cold adaptation by comparison with homologues from tropical fishes including Danio rerio. The structure of N. coriiceps AK (AKNc) revealed suboptimal hydrophobic packing around three Val residues in its central CORE domain, which are replaced with Ile residues in D. rerio AK (AKDr). The Val-to-Ile mutations that improve hydrophobic CORE packing in AKNc increased stability at high temperatures but decreased activity at low temperatures, suggesting that the suboptimal hydrophobic CORE packing is important for cold adaptation. Such linkage between stability and activity was also observed in AKDr. Ile-to-Val mutations that destabilized the tropical AK resulted in increased activity at low temperatures. Our results provide the structural basis of cold adaptation of a psychrophilic enzyme from a multicellular, eukaryotic organism, and highlight the similarities and differences in the structural adjustment of vertebrate and bacterial psychrophilic AKs during cold adaptation.

Highly expressed genes evolve under strong epistasis from a proteome-wide scan in E. coli

Epistasis or the non-additivity of mutational effects is a major force in protein evolution, but it has not been systematically quantified at the level of a proteome. Here, we estimated the extent of epistasis for 2,382 genes in E. coli using several hundreds of orthologs for each gene within the class Gammaproteobacteria. We found that the average epistasis is ~41% across genes in the proteome and that epistasis is stronger among highly expressed genes. This trend is quantitatively explained by the prevailing model of sequence evolution based on minimizing the fitness cost of protein unfolding and aggregation. The genes with the highest epistasis are also functionally involved in the maintenance of proteostasis, translation and central metabolism. In contrast, genes evolving with low epistasis mainly encode for membrane proteins and are involved in transport activity. Our results highlight the coupling between selection and epistasis in the long-term evolution of a proteome.

Sequence entropy of folding and the absolute rate of amino acid substitutions

Adequate representations of protein evolution should consider how the acceptance of mutations depends on the sequence context in which they arise. However, epistatic interactions among sites in a protein result in time and spatial substitution rate heterogeneity beyond the capabilities of current models. Here, we exploit parallels between amino acid substitutions and chemical reaction kinetics to develop an improved theory of protein evolution. We constructed a mechanistic framework for modelling amino acid substitution rates that employs the formalisms of statistical mechanics, with population genetics principles underlying the analysis. Theoretical analyses and computer simulations of proteins under purifying selection for thermodynamic stability show that substitution rates and the stabilisation of resident amino acids (the ‘evolutionary Stokes shift’) can be predicted from biophysics and the effect of sequence entropy alone. Furthermore, we demonstrate that substitutions predominantly occur when epistatic interactions result in near neutrality; substitution rates are determined by how often epistasis results in such nearly neutral conditions. This theory provides a general framework for modelling protein sequence change under purifying selection, potentially explains patterns of convergence and mutation rates in real proteins that are incompatible with previous models, and provides a better null model for the detection of adaptive changes.

Role of an N-terminal extension in stability and catalytic activity of a hyperthermostable α/β hydrolase fold esterase

The carbohydrate esterase family 7 (CE7) enzymes catalyze the deacetylation of acetyl esters of a broad range of alcohols and is unique in its activity towards cephalosporin C. The CE7 fold contains a conserved N-terminal extension that distinguishes it from the canonical α/β hydrolase fold. The hexameric quaternary structure indicates that the N-terminus may affect activity and specificity by controlling access of substrates to the buried active sites via an entrance tunnel. In this context, we characterized the catalytic parameters, conformation and thermal stability of two truncation variants lacking four and ten residues of the N-terminal region of the hyperthermostable Thermotoga maritima CE7 acetyl esterase (TmAcE). The truncations did not affect the secondary structure or the fold but modulated the oligomerization dynamics. A modest increase was observed in substrate specificity for acetylated xylose compared with acetylated glucose. A drastic reduction of ~30-40°C in the optimum temperature for activity of the variants indicated lower thermal stability. The loss of hyperthermostability appears to be an indirect effect associated with an increase in the conformational flexibility of an otherwise rigid neighboring loop containing a catalytic triad residue. The results suggest that the N-terminal extension was evolutionarily selected to preserve the stability of the enzyme.

Stabilization of a nucleotide-binding domain of the cystic fibrosis transmembrane conductance regulator yields insight into disease-causing mutations

Characterization of the second nucleotide-binding domain (NBD2) of the cystic fibrosis transmembrane conductance regulator (CFTR) has lagged behind research into the NBD1 domain, in part because NBD1 contains the F508del mutation, which is the dominant cause of cystic fibrosis. Research on NBD2 has also been hampered by the overall instability of the domain and the difficulty of producing reagents. Nonetheless, multiple disease-causing mutations reside in NBD2, and the domain is critical for CFTR function, because channel gating involves NBD1/NBD2 dimerization, and NBD2 contains the catalytically active ATPase site in CFTR. Recognizing the paucity of structural and biophysical data on NBD2, here we have defined a bioinformatics-based method for manually identifying stabilizing substitutions in NBD2, and we used an iterative process of screening single substitutions against thermal melting points to both produce minimally mutated stable constructs and individually characterize mutations. We present a range of stable constructs with minimal mutations to help inform further research on NBD2. We have used this stabilized background to study the effects of NBD2 mutations identified in cystic fibrosis (CF) patients, demonstrating that mutants such as N1303K and G1349D are characterized by lower stability, as shown previously for some NBD1 mutations, suggesting a potential role for NBD2 instability in the pathology of CF.

Reconstructing Ancient Proteins to Understand the Causes of Structure and Function

A central goal in biochemistry is to explain the causes of protein sequence, structure, and function. Mainstream approaches seek to rationalize sequence and structure in terms of their effects on function and to identify function's underlying determinants by comparing related proteins to each other. Although productive, both strategies suffer from intrinsic limitations that have left important aspects of many proteins unexplained. These limits can be overcome by reconstructing ancient proteins, experimentally characterizing their properties, and retracing their evolution through time. This approach has proven to be a powerful means for discovering how historical changes in sequence produced the functions, structures, and other physical/chemical characteristics of modern proteins. It has also illuminated whether protein features evolved because of functional optimization, historical constraint, or blind chance. Here we review recent studies employing ancestral protein reconstruction and show how they have produced new knowledge not only of molecular evolutionary processes but also of the underlying determinants of modern proteins' physical, chemical, and biological properties.

Evolutionary drivers of thermoadaptation in enzyme catalysis

With early life likely to have existed in a hot environment, enzymes had to cope with an inherent drop in catalytic speed caused by lowered temperature. Here we characterize the molecular mechanisms underlying thermoadaptation of enzyme catalysis in adenylate kinase using ancestral sequence reconstruction spanning 3 billion years of evolution. We show that evolution solved the enzyme's key kinetic obstacle-how to maintain catalytic speed on a cooler Earth-by exploiting transition-state heat capacity. Tracing the evolution of enzyme activity and stability from the hot-start toward modern hyperthermophilic, mesophilic, and psychrophilic organisms illustrates active pressure versus passive drift in evolution on a molecular level, refutes the debated activity/stability trade-off, and suggests that the catalytic speed of adenylate kinase is an evolutionary driver for organismal fitness.

Bridging the physical scales in evolutionary biology: from protein sequence space to fitness of organisms and populations

Bridging the gap between the molecular properties of proteins and organismal/population fitness is essential for understanding evolutionary processes. This task requires the integration of the several physical scales of biological organization, each defined by a distinct set of mechanisms and constraints, into a single unifying model. The molecular scale is dominated by the constraints imposed by the physico-chemical properties of proteins and their substrates, which give rise to trade-offs and epistatic (non-additive) effects of mutations. At the systems scale, biological networks modulate protein expression and can either buffer or enhance the fitness effects of mutations. The population scale is influenced by the mutational input, selection regimes, and stochastic changes affecting the size and structure of populations, which eventually determine the evolutionary fate of mutations. Here, we summarize the recent advances in theory, computer simulations, and experiments that advance our understanding of the links between various physical scales in biology.

Evolutionary dynamics of viral escape under antibodies stress: A biophysical model

Viruses constantly face the selection pressure of antibodies, either from innate immune response of the host or from administered antibodies for treatment. We explore the interplay between the biophysical properties of viral proteins and the population and demographic variables in the viral escape. The demographic and population genetics aspect of the viral escape have been explored before; however one important assumption was the a priori distribution of fitness effects (DFE). Here, we relax this assumption by instead considering a realistic biophysics-based genotype-phenotype relationship for RNA viruses escaping antibodies stress. In this model the DFE is itself an evolvable property that depends on the genetic background (epistasis) and the distribution of biophysical effects of mutations, which is informed by biochemical experiments and theoretical calculations in protein engineering. We quantitatively explore in silico the viability of viral populations under antibodies pressure and derive the phase diagram that defines the fate of the virus population (extinction or escape from stress) in a range of viral mutation rates and antibodies concentrations. We find that viruses are most resistant to stress at an optimal mutation rate (OMR) determined by the competition between supply of beneficial mutation to facilitate escape from stressors and lethal mutagenesis caused by excess of destabilizing mutations. We then show the quantitative dependence of the OMR on genome length and viral burst size. We also recapitulate the experimental observation that viruses with longer genomes have smaller mutation rate per nucleotide.

Trends in substitution models of molecular evolution

Substitution models of evolution describe the process of genetic variation through fixed mutations and constitute the basis of the evolutionary analysis at the molecular level. Almost 40 years after the development of first substitution models, highly sophisticated, and data-specific substitution models continue emerging with the aim of better mimicking real evolutionary processes. Here I describe current trends in substitution models of DNA, codon and amino acid sequence evolution, including advantages and pitfalls of the most popular models. The perspective concludes that despite the large number of currently available substitution models, further research is required for more realistic modeling, especially for DNA coding and amino acid data. Additionally, the development of more accurate complex models should be coupled with new implementations and improvements of methods and frameworks for substitution model selection and downstream evolutionary analysis.

Simple Biophysical Model Predicts Faster Accumulation of Hybrid Incompatibilities in Small Populations Under Stabilizing Selection

Speciation is fundamental to the process of generating the huge diversity of life on Earth. However, we are yet to have a clear understanding of its molecular-genetic basis. Here, we examine a computational model of reproductive isolation that explicitly incorporates a map from genotype to phenotype based on the biophysics of protein–DNA binding. In particular, we model the binding of a protein transcription factor to a DNA binding site and how their independent coevolution, in a stabilizing fitness landscape, of two allopatric lineages leads to incompatibilities. Complementing our previous coarse-grained theoretical results, our simulations give a new prediction for the monomorphic regime of evolution that smaller populations should develop incompatibilities more quickly. This arises as (1) smaller populations have a greater initial drift load, as there are more sequences that bind poorly than well, so fewer substitutions are needed to reach incompatible regions of phenotype space, and (2) slower divergence when the population size is larger than the inverse of discrete differences in fitness. Further, we find longer sequences develop incompatibilities more quickly at small population sizes, but more slowly at large population sizes. The biophysical model thus represents a robust mechanism of rapid reproductive isolation for small populations and large sequences that does not require peak shifts or positive selection. Finally, we show that the growth of DMIs with time is quadratic for small populations, agreeing with Orr’s model, but nonpower law for large populations, with a form consistent with our previous theoretical results.

BioJazz: in silico evolution of cellular networks with unbounded complexity using rule-based modeling

Systems biologists aim to decipher the structure and dynamics of signaling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. Here we introduce BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for the evolution of cellular networks with unbounded complexity by combining rule-based modeling with an encoding of networks that is akin to a genome. We show that BioJazz can be used to implement biologically realistic selective pressures and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. BioJazz is provided as an open-source tool to facilitate its further development and use. Source code and user manuals are available at: http://oss-lab.github.io/biojazz and http://osslab.lifesci.warwick.ac.uk/BioJazz.aspx.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

Maximum-Likelihood Phylogenetic Inference with Selection on Protein Folding Stability

Despite intense work, incorporating constraints on protein native structures into the mathematical models of molecular evolution remains difficult, because most models and programs assume that protein sites evolve independently, whereas protein stability is maintained by interactions between sites. Here, we address this problem by developing a new mean-field substitution model that generates independent site-specific amino acid distributions with constraints on the stability of the native state against both unfolding and misfolding. The model depends on a background distribution of amino acids and one selection parameter that we fix maximizing the likelihood of the observed protein sequence. The analytic solution of the model shows that the main determinant of the site-specific distributions is the number of native contacts of the site and that the most variable sites are those with an intermediate number of native contacts. The mean-field models obtained, taking into account misfolded conformations, yield larger likelihood than models that only consider the native state, because their average hydrophobicity is more realistic, and they produce on the average stable sequences for most proteins. We evaluated the mean-field model with respect to empirical substitution models on 12 test data sets of different protein families. In all cases, the observed site-specific sequence profiles presented smaller Kullback-Leibler divergence from the mean-field distributions than from the empirical substitution model. Next, we obtained substitution rates combining the mean-field frequencies with an empirical substitution model. The resulting mean-field substitution model assigns larger likelihood than the empirical model to all studied families when we consider sequences with identity larger than 0.35, plausibly a condition that enforces conservation of the native structure across the family. We found that the mean-field model performs better than other structurally constrained models with similar or higher complexity. With respect to the much more complex model recently developed by Bordner and Mittelmann, which takes into account pairwise terms in the amino acid distributions and also optimizes the exchangeability matrix, our model performed worse for data with small sequence divergence but better for data with larger sequence divergence. The mean-field model has been implemented into the computer program Prot_Evol that is freely available at http://ub.cbm.uam.es/software/Prot_Evol.php.

Relationship between protein thermodynamic constraints and variation of evolutionary rates among sites

Evolutionary-rate variation among sites within proteins depends on functional and biophysical properties that constrain protein evolution. It is generally accepted that proteins must be able to fold stably in order to function. However, the relationship between stability constraints and among-sites rate variation is not well understood. Here, we present a biophysical model that links the thermodynamic stability changes due to mutations at sites in proteins ([Formula: see text]) to the rate at which mutations accumulate at those sites over evolutionary time. We find that such a 'stability model' generally performs well, displaying correlations between predicted and empirically observed rates of up to 0.75 for some proteins. We further find that our model has comparable predictive power as does an alternative, recently proposed 'stress model' that explains evolutionary-rate variation among sites in terms of the excess energy needed for mutants to adopt the correct active structure ([Formula: see text]). The two models make distinct predictions, though, and for some proteins the stability model outperforms the stress model and vice versa. We conclude that both stability and stress constrain site-specific sequence evolution in 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.

Nonadaptive Amino Acid Convergence Rates Decrease over Time

Convergence is a central concept in evolutionary studies because it provides strong evidence for adaptation. It also provides information about the nature of the fitness landscape and the repeatability of evolution, and can mislead phylogenetic inference. To understand the role of adaptive convergence, we need to understand the patterns of nonadaptive convergence. Here, we consider the relationship between nonadaptive convergence and divergence in mitochondrial and model proteins. Surprisingly, nonadaptive convergence is much more common than expected in closely related organisms, falling off as organisms diverge. The extent of the convergent drop-off in mitochondrial proteins is well predicted by epistatic or coevolutionary effects in our "evolutionary Stokes shift" models and poorly predicted by conventional evolutionary models. Convergence probabilities decrease dramatically if the ancestral amino acids of branches being compared have diverged, but also drop slowly over evolutionary time even if the ancestral amino acids have not substituted. Convergence probabilities drop-off rapidly for quickly evolving sites, but much more slowly for slowly evolving sites. Furthermore, once sites have diverged their convergence probabilities are extremely low and indistinguishable from convergence levels at randomized sites. These results indicate that we cannot assume that excessive convergence early on is necessarily adaptive. This new understanding should help us to better discriminate adaptive from nonadaptive convergence and develop more relevant evolutionary models with improved validity for phylogenetic inference.

The influence of selection for protein stability on dN/dS estimations

Understanding the relative contributions of various evolutionary processes-purifying selection, neutral drift, and adaptation-is fundamental to evolutionary biology. A common metric to distinguish these processes is the ratio of nonsynonymous to synonymous substitutions (i.e., dN/dS) interpreted from the neutral theory as a null model. However, from biophysical considerations, mutations have non-negligible effects on the biophysical properties of proteins such as folding stability. In this work, we investigated how stability affects the rate of protein evolution in phylogenetic trees by using simulations that combine explicit protein sequences with associated stability changes. We first simulated myoglobin evolution in phylogenetic trees with a biophysically realistic approach that accounts for 3D structural information and estimates of changes in stability upon mutation. We then compared evolutionary rates inferred directly from simulation to those estimated using maximum-likelihood (ML) methods. We found that the dN/dS estimated by ML methods (ωML) is highly predictive of the per gene dN/dS inferred from the simulated phylogenetic trees. This agreement is strong in the regime of high stability where protein evolution is neutral. At low folding stabilities and under mutation-selection balance, we observe deviations from neutrality (per gene dN/dS > 1 and dN/dS < 1). We showed that although per gene dN/dS is robust to these deviations, ML tests for positive selection detect statistically significant per site dN/dS > 1. Altogether, we show how protein biophysics affects the dN/dS estimations and its subsequent interpretation. These results are important for improving the current approaches for detecting positive selection.

Merging molecular mechanism and evolution: theory and computation at the interface of biophysics and evolutionary population genetics

The variation among sequences and structures in nature is both determined by physical laws and by evolutionary history. However, these two factors are traditionally investigated by disciplines with different emphasis and philosophy-molecular biophysics on one hand and evolutionary population genetics in another. Here, we review recent theoretical and computational approaches that address the crucial need to integrate these two disciplines. We first articulate the elements of these approaches. Then, we survey their contribution to our mechanistic understanding of molecular evolution, the polymorphisms in coding region, the distribution of fitness effects (DFE) of mutations, the observed folding stability of proteins in nature, and the distribution of protein folds in genomes.

Population size dependence of fitness effect distribution and substitution rate probed by biophysical model of protein thermostability

The predicted effect of effective population size on the distribution of fitness effects and substitution rate is critically dependent on the relationship between sequence and fitness. This highlights the importance of using models that are informed by the molecular biology, biochemistry, and biophysics of the evolving systems. We describe a computational model based on fundamental aspects of biophysics, the requirement for (most) proteins to be thermodynamically stable. Using this model, we find that differences in population size have minimal impact on the distribution of population-scaled fitness effects, as well as on the rate of molecular evolution. This is because larger populations result in selection for more stable proteins that are less affected by mutations. This reduction in the magnitude of the fitness effects almost exactly cancels the greater selective pressure resulting from the larger population size. Conversely, changes in the population size in either direction cause transient increases in the substitution rate. As differences in population size often correspond to changes in population size, this makes comparisons of substitution rates in different lineages difficult to interpret.

Detecting selection on protein stability through statistical mechanical models of folding and evolution

The properties of biomolecules depend both on physics and on the evolutionary process that formed them. These two points of view produce a powerful synergism. Physics sets the stage and the constraints that molecular evolution has to obey, and evolutionary theory helps in rationalizing the physical properties of biomolecules, including protein folding thermodynamics. To complete the parallelism, protein thermodynamics is founded on the statistical mechanics in the space of protein structures, and molecular evolution can be viewed as statistical mechanics in the space of protein sequences. In this review, we will integrate both points of view, applying them to detecting selection on the stability of the folded state of proteins. We will start discussing positive design, which strengthens the stability of the folded against the unfolded state of proteins. Positive design justifies why statistical potentials for protein folding can be obtained from the frequencies of structural motifs. Stability against unfolding is easier to achieve for longer proteins. On the contrary, negative design, which consists in destabilizing frequently formed misfolded conformations, is more difficult to achieve for longer proteins. The folding rate can be enhanced by strengthening short-range native interactions, but this requirement contrasts with negative design, and evolution has to trade-off between them. Finally, selection can accelerate functional movements by favoring low frequency normal modes of the dynamics of the native state that strongly correlate with the functional conformation change.

A model of proteostatic energy cost and its use in analysis of proteome trends and sequence evolution

A model of proteome-associated chemical energetic costs of cells is derived from protein-turnover kinetics and protein folding. Minimization of the proteostatic maintenance cost can explain a range of trends of proteomes and combines both protein function, stability, size, proteostatic cost, temperature, resource availability, and turnover rates in one simple framework. We then explore the ansatz that the chemical energy remaining after proteostatic maintenance is available for reproduction (or cell division) and thus, proportional to organism fitness. Selection for lower proteostatic costs is then shown to be significant vs. typical effective population sizes of yeast. The model explains and quantifies evolutionary conservation of highly abundant proteins as arising both from functional mutations and from changes in other properties such as stability, cost, or turnover rates. We show that typical hypomorphic mutations can be selected against due to increased cost of compensatory protein expression (both in the mutated gene and in related genes, i.e. epistasis) rather than compromised function itself, although this compensation depends on the protein's importance. Such mutations exhibit larger selective disadvantage in abundant, large, synthetically costly, and/or short-lived proteins. Selection against increased turnover costs of less stable proteins rather than misfolding toxicity per se can explain equilibrium protein stability distributions, in agreement with recent findings in E. coli. The proteostatic selection pressure is stronger at low metabolic rates (i.e. scarce environments) and in hot habitats, explaining proteome adaptations towards rough environments as a question of energy. The model may also explain several trade-offs observed in protein evolution and suggests how protein properties can coevolve to maintain low proteostatic cost.

Contribution of selection for protein folding stability in shaping the patterns of polymorphisms in coding regions

The patterns of polymorphisms in genomes are imprints of the evolutionary forces at play in nature. In particular, polymorphisms have been extensively used to infer the fitness effects of mutations and their dynamics of fixation. However, the role and contribution of molecular biophysics to these observations remain unclear. Here, we couple robust findings from protein biophysics, enzymatic flux theory, the selection against the cytotoxic effects of protein misfolding, and explicit population dynamics simulations in the polyclonal regime. First, we recapitulate results on the dynamics of clonal interference and on the shape of the DFE, thus providing them with a molecular and mechanistic foundation. Second, we predict that if evolution is indeed under the dynamic equilibrium of mutation-selection balance, the fraction of stabilizing and destabilizing mutations is almost equal among single-nucleotide polymorphisms segregating at high allele frequencies. This prediction is proven true for polymorphisms in the human coding region. Overall, our results show how selection for protein folding stability predominantly shapes the patterns of polymorphisms in coding regions.

Amino acid composition of proteins reduces deleterious impact of mutations

The evolutionary origin of amino acid occurrence frequencies in proteins (composition) is not yet fully understood. We suggest that protein composition works alongside the genetic code to minimize impact of mutations on protein structure. First, we propose a novel method for estimating thermodynamic stability of proteins whose sequence is constrained to a fixed composition. Second, we quantify the average deleterious impact of substituting one amino acid with another. Natural proteome compositions are special in at least two ways: 1) Natural compositions do not generate more stable proteins than the average random composition, however, they result in proteins that are less susceptible to damage from mutations. 2) Natural proteome compositions that result in more stable proteins (i.e. those of thermophiles) are also tuned to have a higher tolerance for mutations. This is consistent with the observation that environmental factors selecting for more stable proteins also enhance the deleterious impact of mutations.

Protein evolution along phylogenetic histories under structurally constrained substitution models

MOTIVATION

Models of molecular evolution aim at describing the evolutionary processes at the molecular level. However, current models rarely incorporate information from protein structure. Conversely, structure-based models of protein evolution have not been commonly applied to simulate sequence evolution in a phylogenetic framework, and they often ignore relevant evolutionary processes such as recombination. A simulation evolutionary framework that integrates substitution models that account for protein structure stability should be able to generate more realistic in silico evolved proteins for a variety of purposes.

RESULTS

We developed a method to simulate protein evolution that combines models of protein folding stability, such that the fitness depends on the stability of the native state both with respect to unfolding and misfolding, with phylogenetic histories that can be either specified by the user or simulated with the coalescent under complex evolutionary scenarios, including recombination, demographics and migration. We have implemented this framework in a computer program called ProteinEvolver. Remarkably, comparing these models with empirical amino acid replacement models, we found that the former produce amino acid distributions closer to distributions observed in real protein families, and proteins that are predicted to be more stable. Therefore, we conclude that evolutionary models that consider protein stability and realistic evolutionary histories constitute a better approximation of the real evolutionary process.

Resurrection of an Urbilaterian U1A/U2B″/SNF protein

The U1A/U2B″/SNF family of proteins found in the U1 and U2 spliceosomal small nuclear ribonucleoproteins is highly conserved. In spite of the high degree of sequence and structural conservation, modern members of this protein family have unique RNA binding properties. These differences have necessarily resulted from evolutionary processes, and therefore, we reconstructed the protein phylogeny in order to understand how and when divergence occurred and how protein function has been modulated. Contrary to the conventional understanding of an ancient human U1A/U2B″ gene duplication, we show that the last common ancestor of bilaterians contained a single ancestral protein (URB). The gene for URB was synthesized, the protein was overexpressed and purified, and we assessed RNA binding to modern snRNA sequences. We find that URB binds human and Drosophila U1 snRNA SLII and U2 snRNA SLIV with higher affinity than do modern homologs, suggesting that both Drosophila SNF and human U1A/U2B″ have evolved into weaker binders of one RNA or both RNAs.

Stability and rigidity/flexibility-two sides of the same coin?

Protein molecules require both flexibility and rigidity for functioning. The fast and accurate prediction of protein rigidity/flexibility is one of the important problems in protein science. We have determined flexible regions for four homologous pairs from thermophilic and mesophilic organisms by two methods: the fast FoldUnfold which uses amino acid sequence and the time consuming MDFirst which uses three-dimensional structures. We demonstrate that both methods allow determining flexible regions in protein structure. For three of the four thermophile-mesophile pairs of proteins, FoldUnfold predicts practically the same flexible regions which have been found by the MD/First method. As expected, molecular dynamics simulations show that thermophilic proteins are more rigid in comparison to their mesophilic homologues. Analysis of rigid clusters and their decomposition provides new insights into protein stability. It has been found that the local networks of salt bridges and hydrogen bonds in thermophiles render their structure more stable with respect to fluctuations of individual contacts. Such network includes salt bridge triads Agr-Glu-Lys and Arg-Glu-Arg, or salt bridges (such as Arg-Glu) connected with hydrogen bonds. This ionic network connects alpha helices and rigidifies the structure. Mesophiles can be characterized by stand alone salt bridges and hydrogen bonds or small ionic clusters. Such difference in the network of salt bridges results in different flexibility of homologous proteins. Combining both approaches allows characterizing structural features in atomic detail that determine the rigidity/flexibility of a protein structure. This article is a part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Residue mutations and their impact on protein structure and function: detecting beneficial and pathogenic changes

The present review focuses on the evolution of proteins and the impact of amino acid mutations on function from a structural perspective. Proteins evolve under the law of natural selection and undergo alternating periods of conservative evolution and of relatively rapid change. The likelihood of mutations being fixed in the genome depends on various factors, such as the fitness of the phenotype or the position of the residues in the three-dimensional structure. For example, co-evolution of residues located close together in three-dimensional space can occur to preserve global stability. Whereas point mutations can fine-tune the protein function, residue insertions and deletions (‘decorations’ at the structural level) can sometimes modify functional sites and protein interactions more dramatically. We discuss recent developments and tools to identify such episodic mutations, and examine their applications in medical research. Such tools have been tested on simulated data and applied to real data such as viruses or animal sequences. Traditionally, there has been little if any cross-talk between the fields of protein biophysics, protein structure–function and molecular evolution. However, the last several years have seen some exciting developments in combining these approaches to obtain an in-depth understanding of how proteins evolve. For example, a better understanding of how structural constraints affect protein evolution will greatly help us to optimize our models of sequence evolution. The present review explores this new synthesis of perspectives.

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.

Amino acid coevolution induces an evolutionary Stokes shift

The process of amino acid replacement in proteins is context-dependent, with substitution rates influenced by local structure, functional role, and amino acids at other locations. Predicting how these differences affect replacement processes is difficult. To make such inference easier, it is often assumed that the acceptabilities of different amino acids at a position are constant. However, evolutionary interactions among residue positions will tend to invalidate this assumption. Here, we use simulations of purple acid phosphatase evolution to show that amino acid propensities at a position undergo predictable change after an amino acid replacement at that position. After a replacement, the new amino acid and similar amino acids tend to become gradually more acceptable over time at that position. In other words, proteins tend to equilibrate to the presence of an amino acid at a position through replacements at other positions. Such a shift is reminiscent of the spectroscopy effect known as the Stokes shift, where molecules receiving a quantum of energy and moving to a higher electronic state will adjust to the new state and emit a smaller quantum of energy whenever they shift back down to the original ground state. Predictions of changes in stability in real proteins show that mutation reversals become less favorable over time, and thus, broadly support our results. The observation of an evolutionary Stokes shift has profound implications for the study of protein evolution and the modeling of evolutionary processes.

Biophysical and structural considerations for protein sequence evolution

BACKGROUND

Protein sequence evolution is constrained by the biophysics of folding and function, causing interdependence between interacting sites in the sequence. However, current site-independent models of sequence evolutions do not take this into account. Recent attempts to integrate the influence of structure and biophysics into phylogenetic models via statistical/informational approaches have not resulted in expected improvements in model performance. This suggests that further innovations are needed for progress in this field.

RESULTS

Here we develop a coarse-grained physics-based model of protein folding and binding function, and compare it to a popular informational model. We find that both models violate the assumption of the native sequence being close to a thermodynamic optimum, causing directional selection away from the native state. Sampling and simulation show that the physics-based model is more specific for fold-defining interactions that vary less among residue type. The informational model diffuses further in sequence space with fewer barriers and tends to provide less support for an invariant sites model, although amino acid substitutions are generally conservative. Both approaches produce sequences with natural features like dN/dS < 1 and gamma-distributed rates across sites.

CONCLUSIONS

Simple coarse-grained models of protein folding can describe some natural features of evolving proteins but are currently not accurate enough to use in evolutionary inference. This is partly due to improper packing of the hydrophobic core. We suggest possible improvements on the representation of structure, folding energy, and binding function, as regards both native and non-native conformations, and describe a large number of possible applications for such a model.

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.

Is evolution deterministic, hence predictable, or stochastic, that is unpredictable? What would happen if one could “replay the tape of evolution”: will the outcomes of evolution be completely different or is evolution so constrained that history will be repeated? Arguably, these questions are among the most intriguing and most difficult in evolutionary biology. In other words, the predictability of evolution depends on the fraction of the trajectories on fitness landscapes that are accessible for evolutionary exploration. Because direct experimental investigation of fitness landscapes is technically challenging, the available studies only explore a minuscule portion of the landscape for individual enzymes. We therefore sought to investigate the topography of fitness landscapes within the framework of a previously developed model of protein folding and evolution where fitness is equated with robustness to misfolding. We show that model-derived and experimental landscapes are significantly smoother than random landscapes and resemble moderately perturbed additive landscapes; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. Thus, the smoothness and substantial deficit of peaks in fitness landscapes of protein evolution could be fundamental consequences of the physics of protein folding.

The evolution of protein structures and structural ensembles under functional constraint

Protein sequence, structure, and function are inherently linked through evolution and population genetics. Our knowledge of protein structure comes from solved structures in the Protein Data Bank (PDB), our knowledge of sequence through sequences found in the NCBI sequence databases (http://www.ncbi.nlm.nih.gov/), and our knowledge of function through a limited set of in-vitro biochemical studies. How these intersect through evolution is described in the first part of the review. In the second part, our understanding of a series of questions is addressed. This includes how sequences evolve within structures, how evolutionary processes enable structural transitions, how the folding process can change through evolution and what the fitness impacts of this might be. Moving beyond static structures, the evolution of protein kinetics (including normal modes) is discussed, as is the evolution of conformational ensembles and structurally disordered proteins. This ties back to a question of the role of neostructuralization and how it relates to selection on sequences for functions. The relationship between metastability, the fitness landscape, sequence divergence, and organismal effective population size is explored. Lastly, a brief discussion of modeling the evolution of sequences of ordered and disordered proteins is entertained.