Biophysical and structural considerations for protein sequence evolution

A review of visualisations of protein fold networks and their relationship with sequence and function

Proteins form arguably the most significant link between genotype and phenotype. Understanding the relationship between protein sequence and structure, and applying this knowledge to predict function, is difficult. One way to investigate these relationships is by considering the space of protein folds and how one might move from fold to fold through similarity, or potential evolutionary relationships. The many individual characterisations of fold space presented in the literature can tell us a lot about how well the current Protein Data Bank represents protein fold space, how convergence and divergence may affect protein evolution, how proteins affect the whole of which they are part, and how proteins themselves function. A synthesis of these different approaches and viewpoints seems the most likely way to further our knowledge of protein structure evolution and thus, facilitate improved protein structure design and prediction.

Next-generation development and application of codon model in evolution

To date, numerous nucleotide, amino acid, and codon substitution models have been developed to estimate the evolutionary history of any sequence/organism in a more comprehensive way. Out of these three, the codon substitution model is the most powerful. These models have been utilized extensively to detect selective pressure on a protein, codon usage bias, ancestral reconstruction and phylogenetic reconstruction. However, due to more computational demanding, in comparison to nucleotide and amino acid substitution models, only a few studies have employed the codon substitution model to understand the heterogeneity of the evolutionary process in a genome-scale analysis. Hence, there is always a question of how to develop more robust but less computationally demanding codon substitution models to get more accurate results. In this review article, the authors attempted to understand the basis of the development of different types of codon-substitution models and how this information can be utilized to develop more robust but less computationally demanding codon substitution models. The codon substitution model enables to detect selection regime under which any gene or gene region is evolving, codon usage bias in any organism or tissue-specific region and phylogenetic relationship between different lineages more accurately than nucleotide and amino acid substitution models. Thus, in the near future, these codon models can be utilized in the field of conservation, breeding and medicine.

Characterizing Amino Acid Substitution with Complete Linkage of Sites on a Lineage

Amino acid substitution models are commonly used for phylogenetic inference, for ancestral sequence reconstruction, and for the inference of positive selection. All commonly used models explicitly assume that each site evolves independently, an assumption that is violated by both linkage and protein structural and functional constraints. We introduce two new models for amino acid substitution which incorporate linkage between sites, each based on the (population-genetic) Moran model. The first model is a generalized population process tracking arbitrarily many sites which undergo mutation, with individuals replaced according to their fitnesses. This model provides a reasonably complete framework for simulations but is numerically and analytically intractable. We also introduce a second model which includes several simplifying assumptions but for which some theoretical results can be derived. We analyze the simplified model to determine conditions where linkage is likely to have meaningful effects on sitewise substitution probabilities, as well as conditions under which the effects are likely to be negligible. These findings are an important step in the generation of tractable phylogenetic models that parameterize selective coefficients for amino acid substitution while accounting for linkage of sites leading to both hitchhiking and background selection.

Ancestral Sequence Reconstruction: From Chemical Paleogenetics to Maximum Likelihood Algorithms and Beyond

As both a computational and an experimental endeavor, ancestral sequence reconstruction remains a timely and important technique. Modern approaches to conduct ancestral sequence reconstruction for proteins are built upon a conceptual framework from journal founder Emile Zuckerkandl. On top of this, work on maximum likelihood phylogenetics published in Journal of Molecular Evolution in 1996 was one of the first approaches for generating maximum likelihood ancestral sequences of proteins. From its computational history, future model development needs as well as potential applications in areas as diverse as computational systems biology, molecular community ecology, infectious disease therapeutics and other biomedical applications, and biotechnology are discussed. From its past in this journal, there is a bright future for ancestral sequence reconstruction in the field of evolutionary biology.

Detecting Signatures of Positive Selection against a Backdrop of Compensatory Processes

There are known limitations in methods of detecting positive selection. Common methods do not enable differentiation between positive selection and compensatory covariation, a major limitation. Further, the traditional method of calculating the ratio of nonsynonymous to synonymous substitutions (dN/dS) does not take into account the 3D structure of biomacromolecules nor differences between amino acids. It also does not account for saturation of synonymous mutations (dS) over long evolutionary time that renders codon-based methods ineffective for older divergences. This work aims to address these shortcomings for detecting positive selection through the development of a statistical model that examines clusters of substitutions in clusters of variable radii. Additionally, it uses a parametric bootstrapping approach to differentiate positive selection from compensatory processes. A previously reported case of positive selection in the leptin protein of primates was reexamined using this methodology.

The search of sequence variants using a constrained protein evolution simulation approach

Protein engineering or candidate therapeutic peptide optimization are processes in which the identification of relevant sequence variants is critical. Starting from one amino-acid sequence, the choice of the substitutions must meet the objective of not disrupting the structure of the protein, not impacting the main functional properties of the starting entity, while also meeting the condition to enhance some expected property such as thermal stability, resistance to degradation, … Here, we introduce a new approach of sequence evolution that focuses on the objective of not disrupting the structure of the initial protein by embedding a point to point control on the preservation of the local structure at each position in the sequence. For 6 mini-proteins, we find that, starting from a single sequence, our simple approach intrinsically contains information about site-specific rate heterogeneity of substitution, and that it is able to reproduce sequence diversity as can be observed in the sequences available in the Uniref repository. We show that our approach is able to provide information about positions not to substitute and about substitutions not to perform at a given position to maintain structure integrity. Overall, our results demonstrate that point to point preservation of the local structure along a sequence is an important determinant of sequence evolution.

Emerging Frontiers in the Study of Molecular Evolution

A collection of the editors of Journal of Molecular Evolution have gotten together to pose a set of key challenges and future directions for the field of molecular evolution. Topics include challenges and new directions in prebiotic chemistry and the RNA world, reconstruction of early cellular genomes and proteins, macromolecular and functional evolution, evolutionary cell biology, genome evolution, molecular evolutionary ecology, viral phylodynamics, theoretical population genomics, somatic cell molecular evolution, and directed evolution. While our effort is not meant to be exhaustive, it reflects research questions and problems in the field of molecular evolution that are exciting to our editors.

Characterizing lineage-specific evolution and the processes driving genomic diversification in chordates

Background

Understanding the origins of genome content has long been a goal of molecular evolution and comparative genomics. By examining genome evolution through the guise of lineage-specific evolution, it is possible to make inferences about the evolutionary events that have given rise to species-specific diversification. Here we characterize the evolutionary trends found in chordate species using The Adaptive Evolution Database (TAED). TAED is a database of phylogenetically indexed gene families designed to detect episodes of directional or diversifying selection across chordates. Gene families within the database have been assessed for lineage-specific estimates of dN/dS and have been reconciled to the chordate species to identify retained duplicates. Gene families have also been mapped to the functional pathways and amino acid changes which occurred on high dN/dS lineages have been mapped to protein structures.

Results

An analysis of this exhaustive database has enabled a characterization of the processes of lineage-specific diversification in chordates. A pathway level enrichment analysis of TAED determined that pathways most commonly found to have elevated rates of evolution included those involved in metabolism, immunity, and cell signaling. An analysis of protein fold presence on proteins, after normalizing for frequency in the database, found common folds such as Rossmann folds, Jelly Roll folds, and TIM barrels were overrepresented on proteins most likely to undergo directional selection. A set of gene families which experience increased numbers of duplications within short evolutionary times are associated with pathways involved in metabolism, olfactory reception, and signaling. An analysis of protein secondary structure indicated more relaxed constraint in β-sheets and stronger constraint on alpha Helices, amidst a general preference for substitutions at exposed sites. Lastly a detailed analysis of the ornithine decarboxylase gene family, a key enzyme in the pathway for polyamine synthesis, revealed lineage-specific evolution along the lineage leading to Cetacea through rapid sequence evolution in a duplicate gene with amino acid substitutions causing active site rearrangement.

Conclusion

Episodes of lineage-specific evolution are frequent throughout chordate species. Both duplication and directional selection have played large roles in the evolution of the phylum. TAED is a powerful tool for facilitating this understanding of lineage-specific evolution.

ASPEN, a methodology for reconstructing protein evolution with improved accuracy using ensemble models

Evolutionary reconstruction algorithms produce models of the evolutionary history of proteins or species. Such algorithms are highly sensitive to their inputs: the sequences used and their alignments. Here, we asked whether the variance introduced by selecting different input sequences could be used to better identify accurate evolutionary models. We subsampled from available ortholog sequences and measured the distribution of observed relationships between paralogs produced across hundreds of models inferred from the subsamples. We observed two important phenomena. First, the reproducibility of an all-sequence, single-alignment reconstruction, measured by comparing topologies inferred from 90% subsamples, directly correlates with the accuracy of that single-alignment reconstruction, producing a measurable value for something that has been traditionally unknowable. Second, topologies that are most consistent with the observations made in the ensemble are more accurate and we present a meta algorithm that exploits this property to improve model accuracy.

Using the Mutation-Selection Framework to Characterize Selection on Protein Sequences

When mutational pressure is weak, the generative process of protein evolution involves explicit probabilities of mutations of different types coupled to their conditional probabilities of fixation dependent on selection. Establishing this mechanistic modeling framework for the detection of selection has been a goal in the field of molecular evolution. Building on a mathematical framework proposed more than a decade ago, numerous methods have been introduced in an attempt to detect and measure selection on protein sequences. In this review, we discuss the structure of the original model, subsequent advances, and the series of assumptions that these models operate under.

A new parameter-rich structure-aware mechanistic model for amino acid substitution during evolution

Improvements in the description of amino acid substitution are required to develop better pseudo-energy-based protein structure-aware models for use in phylogenetic studies. These models are used to characterize the probabilities of amino acid substitution and enable better simulation of protein sequences over a phylogeny. A better characterization of amino acid substitution probabilities in turn enables numerous downstream applications, like detecting positive selection, ancestral sequence reconstruction, and evolutionarily-motivated protein engineering. Many existing Markov models for amino acid substitution in molecular evolution disregard molecular structure and describe the amino acid substitution process over longer evolutionary periods poorly. Here, we present a new model upgraded with a site-specific parameterization of pseudo-energy terms in a coarse-grained force field, which describes local heterogeneity in physical constraints on amino acid substitution better than a previous pseudo-energy-based model with minimum cost in runtime. The importance of each weight term parameterization in characterizing underlying features of the site, including contact number, solvent accessibility, and secondary structural elements was evaluated, returning both expected and biologically reasonable relationships between model parameters. This results in the acceptance of proposed amino acid substitutions that more closely resemble those observed site-specific frequencies in gene family alignments. The modular site-specific pseudo-energy function is made available for download through the following website: https://liberles.cst.temple.edu/Software/CASS/index.html.

Relationships between residue Voronoi volume and sequence conservation in proteins

BACKGROUND

Functional and biophysical constraints can cause different levels of sequence conservation in proteins. Previously, structural properties, e.g., relative solvent accessibility (RSA) and packing density of the weighted contact number (WCN), have been found to be related to protein sequence conservation (CS). The Voronoi volume has recently been recognized as a new structural property of the local protein structural environment reflecting CS. However, for surface residues, it is sensitive to water molecules surrounding the protein structure. Herein, we present a simple structural determinant termed the relative space of Voronoi volume (RSV); it uses the Voronoi volume and the van der Waals volume of particular residues to quantify the local structural environment.

METHODS

RSV (range, 0-1) is defined as (Voronoi volume-van der Waals volume)/Voronoi volume of the target residue. The concept of RSV describes the extent of available space for every protein residue.

RESULTS

RSV and Voronoi profiles with and without water molecules (RSVw, RSV, VOw, and VO) were compared for 554 non-homologous proteins. RSV (without water) showed better Pearson's correlations with CS than did RSVw, VO, or VOw values. The mean correlation coefficient between RSV and CS was 0.51, which is comparable to the correlation between RSA and CS (0.49) and that between WCN and CS (0.56).

CONCLUSIONS

RSV is a robust structural descriptor with and without water molecules and can quantitatively reflect evolutionary information in a single protein structure. Therefore, it may represent a practical structural determinant to study protein sequence, structure, and function relationships.

Chaperone-client interactions: Non-specificity engenders multifunctionality

Here, we provide an overview of the different mechanisms whereby three different chaperones, Spy, Hsp70, and Hsp60, interact with folding proteins, and we discuss how these chaperones may guide the folding process. Available evidence suggests that even a single chaperone can use many mechanisms to aid in protein folding, most likely due to the need for most chaperones to bind clients promiscuously. Chaperone mechanism may be better understood by always considering it in the context of the client's folding pathway and biological function.

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

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

Accelerated simulation of evolutionary trajectories in origin-fixation models

We present an accelerated algorithm to forward-simulate origin-fixation models. Our algorithm requires, on average, only about two fitness evaluations per fixed mutation, whereas traditional algorithms require, per one fixed mutation, a number of fitness evaluations of the order of the effective population size, Ne Our accelerated algorithm yields the exact same steady state as the original algorithm but produces a different order of fixed mutations. By comparing several relevant evolutionary metrics, such as the distribution of fixed selection coefficients and the probability of reversion, we find that the two algorithms behave equivalently in many respects. However, the accelerated algorithm yields less variance in fixed selection coefficients. Notably, we are able to recover the expected amount of variance by rescaling population size, and we find a linear relationship between the rescaled population size and the population size used by the original algorithm. Considering the widespread usage of origin-fixation simulations across many areas of evolutionary biology, we introduce our accelerated algorithm as a useful tool for increasing the computational complexity of fitness functions without sacrificing much in terms of accuracy of the evolutionary simulation.

The utility of protein structure as a predictor of site-wise dN/dS varies widely among HIV-1 proteins

Protein structure acts as a general constraint on the evolution of viral proteins. One widely recognized structural constraint explaining evolutionary variation among sites is the relative solvent accessibility (RSA) of residues in the folded protein. In influenza virus, the distance from functional sites has been found to explain an additional portion of the evolutionary variation in the external antigenic proteins. However, to what extent RSA and distance from a reference site in the protein can be used more generally to explain protein adaptation in other viruses and in the different proteins of any given virus remains an open question. To address this question, we have carried out an analysis of the distribution and structural predictors of site-wise dN/dS in HIV-1. Our results indicate that the distribution of dN/dS in HIV follows a smooth gamma distribution, with no special enrichment or depletion of sites with dN/dS at or above one. The variation in dN/dS can be partially explained by RSA and distance from a reference site in the protein, but these structural constraints do not act uniformly among the different HIV-1 proteins. Structural constraints are highly predictive in just one of the three enzymes and one of three structural proteins in HIV-1. For these two proteins, the protease enzyme and the gp120 structural protein, structure explains between 30 and 40% of the variation in dN/dS. Finally, for the gp120 protein of the receptor-binding complex, we also find that glycosylation sites explain just 2% of the variation in dN/dS and do not explain gp120 evolution independently of either RSA or distance from the apical surface.

Selection on metabolic pathway function in the presence of mutation-selection-drift balance leads to rate-limiting steps that are not evolutionarily stable

Background

While commonly assumed in the biochemistry community that the control of metabolic pathways is thought to be critical to cellular function, it is unclear if metabolic pathways generally have evolutionarily stable rate limiting (flux controlling) steps.

Results

A set of evolutionary simulations using a kinetic model of a metabolic pathway was performed under different conditions to evaluate the evolutionary stability of rate limiting steps. Simulations used combinations of selection for steady state flux, selection against the cost of molecular biosynthesis, and selection against the accumulation of high concentrations of a deleterious intermediate. Two mutational regimes were used, one with mutations that on average were neutral to molecular phenotype and a second with a preponderance of activity-destroying mutations. The evolutionary stability of rate limiting steps was low in all simulations with non-neutral mutational processes. Clustering of parameter co-evolution showed divergent inter-molecular evolutionary patterns under different evolutionary regimes.

Conclusions

This study provides a null model for pathway evolution when compensatory processes dominate with potential applications to predicting pathway functional change. This result also suggests a possible mechanism in which studies in statistical genetics that aim to associate a genotype to a phenotype assuming independent action of variants may be mis-specified through a mis-characterization of the link between individual gene function and pathway function. A better understanding of the genotype-phenotype map has potential applications in differentiating between compensatory changes and directional selection on pathways as well as detecting SNPs and fixed differences that might have phenotypic effects.

Reviewers

This article was reviewed by Arne Elofsson, David Ardell, and Shamil Sunyaev.

Electronic supplementary material

The online version of this article (doi:10.1186/s13062-016-0133-6) contains supplementary material, which is available to authorized users.

Selection on protein structure, interaction, and sequence

Characterizing the probabilities of observing amino acid substitutions at specific sites in a protein over evolutionary time is a major goal in the field of molecular evolution. While purely statistical approaches at different levels of complexity exist, approaches rooted in underlying biological processes are necessary to characterize both the context-dependence of sequence changes (epistasis) and to extrapolate to sequences not observed in biological databases. To develop such approaches, an understanding of the different selective forces that act on amino acid substitution is necessary. Here, an overview of selection on and corresponding modeling of folding stability, folding specificity, binding affinity and specificity for ligands, the evolution of new binding sites on protein surfaces, protein dynamics, intrinsic disorder, and protein aggregation as well as the interplay with protein expression level (concentration) and biased mutational processes are presented.

Functional Sites Induce Long-Range Evolutionary Constraints in Enzymes

Functional residues in proteins tend to be highly conserved over evolutionary time. However, to what extent functional sites impose evolutionary constraints on nearby or even more distant residues is not known. Here, we report pervasive conservation gradients toward catalytic residues in a dataset of 524 distinct enzymes: evolutionary conservation decreases approximately linearly with increasing distance to the nearest catalytic residue in the protein structure. This trend encompasses, on average, 80% of the residues in any enzyme, and it is independent of known structural constraints on protein evolution such as residue packing or solvent accessibility. Further, the trend exists in both monomeric and multimeric enzymes and irrespective of enzyme size and/or location of the active site in the enzyme structure. By contrast, sites in protein-protein interfaces, unlike catalytic residues, are only weakly conserved and induce only minor rate gradients. In aggregate, these observations show that functional sites, and in particular catalytic residues, induce long-range evolutionary constraints in enzymes.

Characterizing selective pressures on the pathway for de novo biosynthesis of pyrimidines in yeast

Background

Selection on proteins is typically measured with the assumption that each protein acts independently. However, selection more likely acts at higher levels of biological organization, requiring an integrative view of protein function. Here, we built a kinetic model for de novo pyrimidine biosynthesis in the yeast Saccharomyces cerevisiae to relate pathway function to selective pressures on individual protein-encoding genes.

Results

Gene families across yeast were constructed for each member of the pathway and the ratio of nonsynonymous to synonymous nucleotide substitution rates (dN/dS) was estimated for each enzyme from S. cerevisiae and closely related species. We found a positive relationship between the influence that each enzyme has on pathway function and its selective constraint.

Conclusions

We expect this trend to be locally present for enzymes that have pathway control, but over longer evolutionary timescales we expect that mutation-selection balance may change the enzymes that have pathway control.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-015-0515-x) contains supplementary material, which is available to authorized users.

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.

Contingency and entrenchment in protein evolution under purifying selection

The phenotypic effect of an allele at one genetic site may depend on alleles at other sites, a phenomenon known as epistasis. Epistasis can profoundly influence the process of evolution in populations and shape the patterns of protein divergence across species. Whereas epistasis between adaptive substitutions has been studied extensively, relatively little is known about epistasis under purifying selection. Here we use computational models of thermodynamic stability in a ligand-binding protein to explore the structure of epistasis in simulations of protein sequence evolution. Even though the predicted effects on stability of random mutations are almost completely additive, the mutations that fix under purifying selection are enriched for epistasis. In particular, the mutations that fix are contingent on previous substitutions: Although nearly neutral at their time of fixation, these mutations would be deleterious in the absence of preceding substitutions. Conversely, substitutions under purifying selection are subsequently entrenched by epistasis with later substitutions: They become increasingly deleterious to revert over time. Our results imply that, even under purifying selection, protein sequence evolution is often contingent on history and so it cannot be predicted by the phenotypic effects of mutations assayed in the ancestral background.

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.

A formal perturbation equation between genotype and phenotype determines the Evolutionary Action of protein-coding variations on fitness

The relationship between genotype mutations and phenotype variations determines health in the short term and evolution over the long term, and it hinges on the action of mutations on fitness. A fundamental difficulty in determining this action, however, is that it depends on the unique context of each mutation, which is complex and often cryptic. As a result, the effect of most genome variations on molecular function and overall fitness remains unknown and stands apart from population genetics theories linking fitness effect to polymorphism frequency. Here, we hypothesize that evolution is a continuous and differentiable physical process coupling genotype to phenotype. This leads to a formal equation for the action of coding mutations on fitness that can be interpreted as a product of the evolutionary importance of the mutated site with the difference in amino acid similarity. Approximations for these terms are readily computable from phylogenetic sequence analysis, and we show mutational, clinical, and population genetic evidence that this action equation predicts the effect of point mutations in vivo and in vitro in diverse proteins, correlates disease-causing gene mutations with morbidity, and determines the frequency of human coding polymorphisms, respectively. Thus, elementary calculus and phylogenetics can be integrated into a perturbation analysis of the evolutionary relationship between genotype and phenotype that quantitatively links point mutations to function and fitness and that opens a new analytic framework for equations of biology. In practice, this work explicitly bridges molecular evolution with population genetics with applications from protein redesign to the clinical assessment of human genetic variations.

Neighbor preferences of amino acids and context-dependent effects of amino acid substitutions in human, mouse, and dog

Amino acids show apparent propensities toward their neighbors. In addition to preferences of amino acids for their neighborhood context, amino acid substitutions are also considered to be context-dependent. However, context-dependence patterns of amino acid substitutions still remain poorly understood. Using relative entropy, we investigated the neighbor preferences of 20 amino acids and the context-dependent effects of amino acid substitutions with protein sequences in human, mouse, and dog. For 20 amino acids, the highest relative entropy was mostly observed at the nearest adjacent site of either N- or C-terminus except C and G. C showed the highest relative entropy at the third flanking site and periodic pattern was detected at G flanking sites. Furthermore, neighbor preference patterns of amino acids varied greatly in different secondary structures. We then comprehensively investigated the context-dependent effects of amino acid substitutions. Our results showed that nearly half of 380 substitution types were evidently context dependent, and the context-dependent patterns relied on protein secondary structures. Among 20 amino acids, P elicited the greatest effect on amino acid substitutions. The underlying mechanisms of context-dependent effects of amino acid substitutions were possibly mutation bias at a DNA level and natural selection. Our findings may improve secondary structure prediction algorithms and protein design; moreover, this study provided useful information to develop empirical models of protein evolution that consider dependence between residues.

Local packing density is the main structural determinant of the rate of protein sequence evolution at site level

Functional and biophysical constraints result in site-dependent patterns of protein sequence variability. It is commonly assumed that the key structural determinant of site-specific rates of evolution is the Relative Solvent Accessibility (RSA). However, a recent study found that amino acid substitution rates correlate better with two Local Packing Density (LPD) measures, the Weighted Contact Number (WCN) and the Contact Number (CN), than with RSA. This work aims at a more thorough assessment. To this end, in addition to substitution rates, we considered four other sequence variability scores, four measures of solvent accessibility (SA), and other CN measures. We compared all properties for each protein of a structurally and functionally diverse representative dataset of monomeric enzymes. We show that the best sequence variability measures take into account phylogenetic tree topology. More importantly, we show that both LPD measures (WCN and CN) correlate better than all of the SA measures, regardless of the sequence variability score used. Moreover, the independent contribution of the best LPD measure is approximately four times larger than that of the best SA measure. This study strongly supports the conclusion that a site's packing density rather than its solvent accessibility is the main structural determinant of its rate of evolution.

A mechanistic stress model of protein evolution accounts for site-specific evolutionary rates and their relationship with packing density and flexibility

Background

Protein sites evolve at different rates due to functional and biophysical constraints. It is usually considered that the main structural determinant of a site’s rate of evolution is its Relative Solvent Accessibility (RSA). However, a recent comparative study has shown that the main structural determinant is the site’s Local Packing Density (LPD). LPD is related with dynamical flexibility, which has also been shown to correlate with sequence variability. Our purpose is to investigate the mechanism that connects a site’s LPD with its rate of evolution.

Results

We consider two models: an empirical Flexibility Model and a mechanistic Stress Model. The Flexibility Model postulates a linear increase of site-specific rate of evolution with dynamical flexibility. The Stress Model, introduced here, models mutations as random perturbations of the protein’s potential energy landscape, for which we use simple Elastic Network Models (ENMs). To account for natural selection we assume a single active conformation and use basic statistical physics to derive a linear relationship between site-specific evolutionary rates and the local stress of the mutant’s active conformation.

We compare both models on a large and diverse dataset of enzymes. In a protein-by-protein study we found that the Stress Model outperforms the Flexibility Model for most proteins. Pooling all proteins together we show that the Stress Model is strongly supported by the total weight of evidence. Moreover, it accounts for the observed nonlinear dependence of sequence variability on flexibility. Finally, when mutational stress is controlled for, there is very little remaining correlation between sequence variability and dynamical flexibility.

Conclusions

We developed a mechanistic Stress Model of evolution according to which the rate of evolution of a site is predicted to depend linearly on the local mutational stress of the active conformation. Such local stress is proportional to LPD, so that this model explains the relationship between LPD and evolutionary rate. Moreover, the model also accounts for the nonlinear dependence between evolutionary rate and dynamical flexibility.

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.

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.

Site-specific structural constraints on protein sequence evolutionary divergence: local packing density versus solvent exposure

Protein sequences evolve under selection pressures imposed by functional and biophysical requirements, resulting in site-dependent rates of amino acid substitution. Relative solvent accessibility (RSA) and local packing density (LPD) have emerged as the best candidates to quantify structural constraint. Recent research assumes that RSA is the main determinant of sequence divergence. However, it is not yet clear which is the best predictor of substitution rates. To address this issue, we compared RSA and LPD with site-specific rates of evolution for a diverse data set of enzymes. In contrast with recent studies, we found that LPD measures correlate better than RSA with evolutionary rate. Moreover, the independent contribution of RSA is minor. Taking into account that LPD is related to backbone flexibility, we put forward the possibility that the rate of evolution of a site is determined by the ease with which the backbone deforms to accommodate 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.

Hydrophobic core in domains of immunoglobulin-like fold

This work analyzes proteins which contain an immunoglobulin fold, focusing on their hydrophobic core structure. The "fuzzy oil drop" model was used to measure the regularity of hydrophobicity distribution in globular domains belonging to proteins which exhibit the above-mentioned fold. Light-chain IgG domains are found to frequently contain regular hydrophobic cores, unlike the corresponding heavy-chain domains. Enzymes and DNA binding proteins present in the data-set are found to exhibit poor accordance with the hydrophobic core model.

Cross-species comparison of site-specific evolutionary-rate variation in influenza haemagglutinin

We investigate the causes of site-specific evolutionary-rate variation in influenza haemagglutinin (HA) between human and avian influenza, for subtypes H1, H3, and H5. By calculating the evolutionary-rate ratio, ω = dN/dS as a function of a residue's solvent accessibility in the three-dimensional protein structure, we show that solvent accessibility has a significant but relatively modest effect on site-specific rate variation. By comparing rates within HA subtypes among host species, we derive an upper limit to the amount of variation that can be explained by structural constraints of any kind. Protein structure explains only 20-40% of the variation in ω. Finally, by comparing ω at sites near the sialic-acid-binding region to ω at other sites, we show that ω near the sialic-acid-binding region is significantly elevated in both human and avian influenza, with the exception of avian H5. We conclude that protein structure, HA subtype, and host biology all impose distinct selection pressures on sites in influenza HA.

Computer programs and methodologies for the simulation of DNA sequence data with recombination

Computer simulations are useful in evolutionary biology for hypothesis testing, to verify analytical methods, to analyze interactions among evolutionary processes, and to estimate evolutionary parameters. In particular, the simulation of DNA sequences with recombination may help in understanding the role of recombination in diverse evolutionary questions, such as the genome structure. Consequently, plenty of computer simulators have been developed to simulate DNA sequence data with recombination. However, the choice of an appropriate tool, among all currently available simulators, is critical if recombination simulations are to be biologically meaningful. This review provides a practical survival guide to commonly used computer programs and methodologies for the simulation of coding and non-coding DNA sequences with recombination. It may help in the correct design of computer simulation experiments of recombination. In addition, the study includes a review of simulation studies investigating the impact of ignoring recombination when performing various evolutionary analyses, such as phylogenetic tree and ancestral sequence reconstructions. Alternative analytical methodologies accounting for recombination are also reviewed.

Bringing molecules back into molecular evolution

Much molecular-evolution research is concerned with sequence analysis. Yet these sequences represent real, three-dimensional molecules with complex structure and function. Here I highlight a growing trend in the field to incorporate molecular structure and function into computational molecular-evolution work. I consider three focus areas: reconstruction and analysis of past evolutionary events, such as phylogenetic inference or methods to infer selection pressures; development of toy models and simulations to identify fundamental principles of molecular evolution; and atom-level, highly realistic computational modeling of molecular structure and function aimed at making predictions about possible future evolutionary events.

The interface of protein structure, protein biophysics, and molecular evolution

Abstract The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.

REvolver: modeling sequence evolution under domain constraints

Simulating the change of protein sequences over time in a biologically realistic way is fundamental for a broad range of studies with a focus on evolution. It is, thus, problematic that typically simulators evolve individual sites of a sequence identically and independently. More realistic simulations are possible; however, they are often prohibited by limited knowledge concerning site-specific evolutionary constraints or functional dependencies between amino acids. As a consequence, a protein's functional and structural characteristics are rapidly lost in the course of simulated evolution. Here, we present REvolver (www.cibiv.at/software/revolver), a program that simulates protein sequence alteration such that evolutionarily stable sequence characteristics, like functional domains, are maintained. For this purpose, REvolver recruits profile hidden Markov models (pHMMs) for parameterizing site-specific models of sequence evolution in an automated fashion. pHMMs derived from alignments of homologous proteins or protein domains capture information regarding which sequence sites remained conserved over time and where in a sequence insertions or deletions are more likely to occur. Thus, they describe constraints on the evolutionary process acting on these sequences. To demonstrate the performance of REvolver as well as its applicability in large-scale simulation studies, we evolved the entire human proteome up to 1.5 expected substitutions per site. Simultaneously, we analyzed the preservation of Pfam and SMART domains in the simulated sequences over time. REvolver preserved 92% of the Pfam domains originally present in the human sequences. This value drops to 15% when traditional models of amino acid sequence evolution are used. Thus, REvolver represents a significant advance toward a realistic simulation of protein sequence evolution on a proteome-wide scale. Further, REvolver facilitates the simulation of a protein family with a user-defined domain architecture at the root.

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.