Protein biophysics explains why highly abundant proteins evolve slowly

Structure-based analysis of Bacilli and plasmid dihydrofolate reductase evolution

Dihydrofolate reductase (DHFR), a key enzyme in tetrahydrofolate-mediated biosynthetic pathways, has a structural motif known to be highly conserved over a wide range of organisms. Given its critical role in purine and amino acid synthesis, DHFR is a well established therapeutic target for treating a wide range of prokaryotic and eukaryotic infections as well as certain types of cancer. Here we present a structural-based computer analysis of bacterial (Bacilli) and plasmid DHFR evolution. We generated a structure-based sequence alignment using 7 wild-type DHFR x-ray crystal structures obtained from the RCSB Protein Data Bank and 350 chromosomal and plasmid homology models we generated from sequences obtained from the NCBI Protein Database. We used these alignments to compare active site and non-active site conservation in terms of amino acid residues, secondary structure and amino acid residue class. With respect to amino acid sequences and residue classes, active-site positions in both plasmid and chromosomal DHFR are significantly more conserved than non-active site positions. Secondary structure conservation was similar for active site and non-active site positions. Plasmid-encoded DHFR proteins have greater degree of sequence and residue class conservation, particularly in sequence positions associated with a network of concerted protein motions, than chromosomal-encoded DHFR proteins. These structure-based were used to build DHFR specific phylogenetic trees from which evidence for horizontal gene transfer was identified.

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.

Intermediate divergence levels maximize the strength of structure-sequence correlations in enzymes and viral proteins

Structural properties such as solvent accessibility and contact number predict site-specific sequence variability in many proteins. However, the strength and significance of these structure-sequence relationships vary widely among different proteins, with absolute correlation strengths ranging from 0 to 0.8. In particular, two recent works have made contradictory observations. Yeh et al. (Mol. Biol. Evol. 31:135-139, 2014) found that both relative solvent accessibility (RSA) and weighted contact number (WCN) are good predictors of sitewise evolutionary rate in enzymes, with WCN clearly out-performing RSA. Shahmoradi et al. (J. Mol. Evol. 79:130-142, 2014) considered these same predictors (as well as others) in viral proteins and found much weaker correlations and no clear advantage of WCN over RSA. Because these two studies had substantial methodological differences, however, a direct comparison of their results is not possible. Here, we reanalyze the datasets of the two studies with one uniform analysis pipeline, and we find that many apparent discrepancies between the two analyses can be attributed to the extent of sequence divergence in individual alignments. Specifically, the alignments of the enzyme dataset are much more diverged than those of the virus dataset, and proteins with higher divergence exhibit, on average, stronger structure-sequence correlations. However, the highest structure-sequence correlations are observed at intermediate divergence levels, where both highly conserved and highly variable sites are present in the same alignment.

Roles of solvent accessibility and gene expression in modeling protein sequence evolution

Models of protein evolution tend to ignore functional constraints, although structural constraints are sometimes incorporated. Here we propose a probabilistic framework for codon substitution that evaluates joint effects of relative solvent accessibility (RSA), a structural constraint; and gene expression, a functional constraint. First, we explore the relationship between RSA and codon usage at the genomic scale as well as at the individual gene scale. Motivated by these results, we construct our framework by determining how probable is an amino acid, given RSA and gene expression, and then evaluating the relative probability of observing a codon compared to other synonymous codons. We come to the biologically plausible conclusion that both RSA and gene expression are related to amino acid frequencies, but, among synonymous codons, the relative probability of a particular codon is more closely related to gene expression than RSA. To illustrate the potential applications of our framework, we propose a new codon substitution model. Using this model, we obtain estimates of 2N s, the product of effective population size N, and relative fitness difference of allele s. For a training data set consisting of human proteins with known structures and expression data, 2N s is estimated separately for synonymous and nonsynonymous substitutions in each protein. We then contrast the patterns of synonymous and nonsynonymous 2N s estimates across proteins while also taking gene expression levels of the proteins into account. We conclude that our 2N s estimates are too concentrated around 0, and we discuss potential explanations for this lack of variability.

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.

Evolutionary dynamics of Rh2 opsins in birds demonstrate an episode of accelerated evolution in the New World warblers (Setophaga)

Low rates of sequence evolution associated with purifying selection can be interrupted by episodic changes in selective regimes. Visual pigments are a unique system in which we can investigate the functional consequences of genetic changes, therefore connecting genotype to phenotype in the context of natural and sexual selection pressures. We study the RH2 and RH1 visual pigments (opsins) across 22 bird species belonging to two ecologically convergent clades, the New World warblers (Parulidae) and Old World warblers (Phylloscopidae) and evaluate rates of evolution in these clades along with data from 21 additional species. We demonstrate generally slow evolution of these opsins: both Rh1 and Rh2 are highly conserved across Old World and New World warblers. However, Rh2 underwent a burst of evolution within the New World genus Setophaga, where it accumulated substitutions at 6 amino acid sites across the species we studied. Evolutionary analyses revealed a significant increase in dN /dS in Setophaga, implying relatively strong selective pressures to overcome long-standing purifying selection. We studied the effects of each substitution on spectral tuning and found they do not cause large spectral shifts. Thus, substitutions may reflect other aspects of opsin function, such as those affecting photosensitivity and/or dark-light adaptation. Although it is unclear what these alterations mean for colour perception, we suggest that rapid evolution is linked to sexual selection, given the exceptional plumage colour diversification in Setophaga.

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.

Protein folding and binding can emerge as evolutionary spandrels through structural coupling

Binding interactions between proteins and other molecules mediate numerous cellular processes, including metabolism, signaling, and gene regulation. These interactions often evolve in response to changes in the protein's chemical or physical environment (such as the addition of an antibiotic). Several recent studies have shown the importance of folding stability in constraining protein evolution. Here we investigate how structural coupling between folding and binding--the fact that most proteins can only bind their targets when folded--gives rise to an evolutionary coupling between the traits of folding stability and binding strength. Using a biophysical and evolutionary model, we show how these protein traits can emerge as evolutionary "spandrels" even if they do not confer an intrinsic fitness advantage. In particular, proteins can evolve strong binding interactions that have no functional role but merely serve to stabilize the protein if its misfolding is deleterious. Furthermore, such proteins may have divergent fates, evolving to bind or not bind their targets depending on random mutational events. These observations may explain the abundance of apparently nonfunctional interactions among proteins observed in high-throughput assays. In contrast, for proteins with both functional binding and deleterious misfolding, evolution may be highly predictable at the level of biophysical traits: adaptive paths are tightly constrained to first gain extra folding stability and then partially lose it as the new binding function is developed. These findings have important consequences for our understanding of how natural and engineered proteins evolve under selective pressure.

Proteome folding kinetics is limited by protein halflife

How heterogeneous are proteome folding timescales and what physical principles, if any, dictate its limits? We answer this by predicting copy number weighted folding speed distribution – using the native topology – for E.coli and Yeast proteome. E.coli and Yeast proteomes yield very similar distributions with average folding times of 100 milliseconds and 170 milliseconds, respectively. The topology-based folding time distribution is well described by a diffusion-drift mutation model on a flat-fitness landscape in free energy barrier between two boundaries: i) the lowest barrier height determined by the upper limit of folding speed and ii) the highest barrier height governed by the lower speed limit of folding. While the fastest time scale of the distribution is near the experimentally measured speed limit of 1 microsecond (typical of barrier-less folders), we find the slowest folding time to be around seconds (8 seconds for Yeast distribution), approximately an order of magnitude less than the fastest halflife (approximately 2 minutes) in the Yeast proteome. This separation of timescale implies even the fastest degrading protein will have moderately high (96%) probability of folding before degradation. The overall agreement with the flat-fitness landscape model further hints that proteome folding times did not undergo additional major selection pressures – to make proteins fold faster – other than the primary requirement to “sufficiently beat the clock” against its lifetime. Direct comparison between the predicted folding time and experimentally measured halflife further shows 99% of the proteome have a folding time less than their corresponding lifetime. These two findings together suggest that proteome folding kinetics may be bounded by protein halflife.

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.

Interplay between chaperones and protein disorder promotes the evolution of protein networks

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

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.

Loss of quaternary structure is associated with rapid sequence divergence in the OSBS family

The rate of protein evolution is determined by a combination of selective pressure on protein function and biophysical constraints on protein folding and structure. Determining the relative contributions of these properties is an unsolved problem in molecular evolution with broad implications for protein engineering and function prediction. As a case study, we examined the structural divergence of the rapidly evolving o-succinylbenzoate synthase (OSBS) family, which catalyzes a step in menaquinone synthesis in diverse microorganisms and plants. On average, the OSBS family is much more divergent than other protein families from the same set of species, with the most divergent family members sharing <15% sequence identity. Comparing 11 representative structures revealed that loss of quaternary structure and large deletions or insertions are associated with the family's rapid evolution. Neither of these properties has been investigated in previous studies to identify factors that affect the rate of protein evolution. Intriguingly, one subfamily retained a multimeric quaternary structure and has small insertions and deletions compared with related enzymes that catalyze diverse reactions. Many proteins in this subfamily catalyze both OSBS and N-succinylamino acid racemization (NSAR). Retention of ancestral structural characteristics in the NSAR/OSBS subfamily suggests that the rate of protein evolution is not proportional to the capacity to evolve new protein functions. Instead, structural features that are conserved among proteins with diverse functions might contribute to the evolution of new functions.

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.

Depletion of cells and abundant proteins from biological samples by enhanced dielectrophoresis

Platforms that are sensitive and specific enough to assay low-abundance protein biomarkers, in a high throughput multiplex format, within a complex biological fluid specimen, are necessary to enable protein biomarker based diagnostics for diseases such as cancer. The signal from an assay for a low-abundance protein biomarker in a biological fluid sample like blood is typically buried in a background that arises from the presence of blood cells and from high-abundance proteins that make up 90% of the assayed protein mass. We present an automated on-chip platform for the depletion of cells and highly abundant serum proteins in blood. Our platform consists of two components, the first of which is a microfluidic mixer that mixes beads containing antibodies against the highly abundant proteins in the whole blood. This complex mixture (consisting of beads, cells, and serum proteins) is then injected into the second component of our microfluidic platform, which comprises a filter trench to capture all the cells and the beads. The size-based trapping of the cells and beads into the filter trench is significantly enhanced by leveraging additional negative dielectrophoretic forces to push the micron sized particles (cells and beads which have captured the highly abundant proteins) down into the trench, allowing the serum proteins of lower abundance to flow through. In general, dielectrophoresis using bare electrodes is incapable of producing forces beyond the low piconewton range that tend to be insufficient for separation applications. However, by using electrodes passivated with atomic layer deposition, we demonstrate the application of enhanced negative DEP electrodes together with size-based flltration induced by the filter trench, to deplete 100% of the micron sized particles in the mixture.

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.

Comparing protein folding in vitro and in vivo: foldability meets the fitness challenge

In this review, we compare and contrast current knowledge about in vitro and in vivo protein folding. Major advances in understanding fundamental principles underlying protein folding in optimized in vitro conditions have yielded detailed physicochemical principles of folding landscapes for small, single domain proteins. In addition, there has been increased research focusing on the key features of protein folding in the cell that differentiate it from in vitro folding, such as co-translational folding, chaperone-facilitated folding, and folding in crowded conditions with many weak interactions. Yet these two research areas have not been bridged effectively in research carried out to date. This review points to gaps between the two that are ripe for future research. Moreover, we emphasize the biological selection pressures that impact protein folding in vivo and how fitness drives the evolution of protein sequences in ways that may place foldability in tension with other requirements on a given protein. We suggest that viewing the physicochemical process of protein folding through the lens of evolution will unveil new insights and pose novel challenges about in-cell folding landscapes.

Fitness costs of minimal sequence alterations causing protein instability and toxicity

Destabilization of a protein impairs its metabolic efficiency. It is less clear how often destabilization also results in a gain of toxicity. We derived collections of temperature-sensitive, and thus structurally unstable, mutants of the yeast ADE2 and LYS2 genes by introducing single or very few amino acids substitutions. Overexpression of these mutant proteins led to a common, although unequal, fitness decrease. Interestingly, although the mutant proteins were functionally redundant, higher expression levels were associated with higher fitness. This result suggests that growth was hampered not by the accumulation of damaged chains but by the activities needed to remove them or by the damage caused before they were removed. Our results support the idea that any protein can become toxic when destabilized by a point mutation.

Catalysis of protein folding by chaperones accelerates evolutionary dynamics in adapting cell populations

Although molecular chaperones are essential components of protein homeostatic machinery, their mechanism of action and impact on adaptation and evolutionary dynamics remain controversial. Here we developed a physics-based ab initio multi-scale model of a living cell for population dynamics simulations to elucidate the effect of chaperones on adaptive evolution. The 6-loci genomes of model cells encode model proteins, whose folding and interactions in cellular milieu can be evaluated exactly from their genome sequences. A genotype-phenotype relationship that is based on a simple yet non-trivially postulated protein-protein interaction (PPI) network determines the cell division rate. Model proteins can exist in native and molten globule states and participate in functional and all possible promiscuous non-functional PPIs. We find that an active chaperone mechanism, whereby chaperones directly catalyze protein folding, has a significant impact on the cellular fitness and the rate of evolutionary dynamics, while passive chaperones, which just maintain misfolded proteins in soluble complexes have a negligible effect on the fitness. We find that by partially releasing the constraint on protein stability, active chaperones promote a deeper exploration of sequence space to strengthen functional PPIs, and diminish the non-functional PPIs. A key experimentally testable prediction emerging from our analysis is that down-regulation of chaperones that catalyze protein folding significantly slows down the adaptation dynamics.

Molecular chaperones or heat-shock proteins are essential components of protein homeostatic machinery in all three domains of life, whose role is not only to prevent protein aggregation but also catalyze the protein folding process by decreasing the energetic barrier for folding. Importantly, chaperones have often been implicated as phenotypic capacitors since they buffer the deleterious effects of mutations, promote genetic diversity, and thus speed up adaptive evolution. Here we explore computationally the consequences of chaperone activity in cytoplasm via long-time evolutionary dynamics simulations. We use a 6-loci multi scale model of cell populations, where the fitness of each cell is determined from its genome, based on statistical mechanical principles of protein folding and protein-protein interactions. We find that by catalyzing protein folding chaperones buffer the deleterious effect of mutations on folding stability and thus open up a sequence space for efficient and simultaneous optimization of multiple molecular traits determining the cellular fitness. As a result, chaperones dramatically accelerate adaptation dynamics.

Conserved proteins are fragile

Levels of selective constraint vary among proteins. Although strong constraint on a protein is often attributed to its functional importance, evolutionary rate may also be limited if a protein is fragile, such that a large proportion of amino acid replacements reduce its fitness. To determine the relative contributions of essentiality and fragility to selective constraint, we compared relationships of selection against nonsense mutations (snon) and selection against missense mutations (smis) to protein sequence conservation (Ka). As expected, snon is greater than smis; however, the correlation between smis and Ka is nearly three times stronger than the correlation between snon and Ka. Moreover, examination of relationships to gene expression level, tissue specificity, and number of protein-protein interactions shows that smis is more strongly correlated than snon to all three measures of biological function. Thus, our analysis reveals that slowly evolving proteins are under strong selective constraint primarily because they are fragile, and that this association likely exists because allowing a protein to function improperly, rather than removing it from a biological network, can negatively affect the functions of other molecules it interacts with and their downstream products.

Evolutionary biochemistry: revealing the historical and physical causes of protein properties

The repertoire of proteins and nucleic acids in the living world is determined by evolution; their properties are determined by the laws of physics and chemistry. Explanations of these two kinds of causality - the purviews of evolutionary biology and biochemistry, respectively - are typically pursued in isolation, but many fundamental questions fall squarely at the interface of fields. Here we articulate the paradigm of evolutionary biochemistry, which aims to dissect the physical mechanisms and evolutionary processes by which biological molecules diversified and to reveal how their physical architecture facilitates and constrains their evolution. We show how an integration of evolution with biochemistry moves us towards a more complete understanding of why biological molecules have the properties that they do.

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.

Highly abundant proteins favor more stable 3D structures in yeast

To understand the variation of protein sequences in nature, we need to reckon with evolutionary constraints that are biophysical, cellular, and ecological. Here, we show that under the global selection against protein misfolding, there exists a scaling among protein folding stability, protein cellular abundance, and effective population size. The specific scaling implies that the several-orders-of-magnitude range of protein abundances in the cell should leave imprints on extant protein structures, a prediction that is supported by our structural analysis of the yeast proteome.

Positively selected sites in cetacean myoglobins contribute to protein stability

Since divergence ∼50 Ma ago from their terrestrial ancestors, cetaceans underwent a series of adaptations such as a ∼10-20 fold increase in myoglobin (Mb) concentration in skeletal muscle, critical for increasing oxygen storage capacity and prolonging dive time. Whereas the O2-binding affinity of Mbs is not significantly different among mammals (with typical oxygenation constants of ∼0.8-1.2 µM(-1)), folding stabilities of cetacean Mbs are ∼2-4 kcal/mol higher than for terrestrial Mbs. Using ancestral sequence reconstruction, maximum likelihood and bayesian tests to describe the evolution of cetacean Mbs, and experimentally calibrated computation of stability effects of mutations, we observe accelerated evolution in cetaceans and identify seven positively selected sites in Mb. Overall, these sites contribute to Mb stabilization with a conditional probability of 0.8. We observe a correlation between Mb folding stability and protein abundance, suggesting that a selection pressure for stability acts proportionally to higher expression. We also identify a major divergence event leading to the common ancestor of whales, during which major stabilization occurred. Most of the positively selected sites that occur later act against other destabilizing mutations to maintain stability across the clade, except for the shallow divers, where late stability relaxation occurs, probably due to the shorter aerobic dive limits of these species. The three main positively selected sites 66, 5, and 35 undergo changes that favor hydrophobic folding, structural integrity, and intra-helical hydrogen bonds.