The evolution and evolutionary consequences of marginal thermostability in proteins

Selection among site-dependent structurally constrained substitution models of protein evolution by approximate Bayesian computation

MOTIVATION

The selection among substitution models of molecular evolution is fundamental for obtaining accurate phylogenetic inferences. At the protein level, evolutionary analyses are traditionally based on empirical substitution models but these models make unrealistic assumptions and are being surpassed by structurally constrained substitution (SCS) models. The SCS models often consider site-dependent evolution, a process that provides realism but complicates their implementation into likelihood functions that are commonly used for substitution model selection.

RESULTS

We present a method to perform selection among site-dependent SCS models, also among empirical and site-dependent SCS models, based on the approximate Bayesian computation (ABC) approach and its implementation into the computational framework ProteinModelerABC. The framework implements ABC with and without regression adjustments and includes diverse empirical and site-dependent SCS models of protein evolution. Using extensive simulated data, we found that it provides selection among SCS and empirical models with acceptable accuracy. As illustrative examples, we applied the framework to analyze a variety of protein families observing that SCS models fit them better than the corresponding best-fitting empirical substitution models.

AVAILABILITY AND IMPLEMENTATION

ProteinModelerABC is freely available from https://github.com/DavidFerreiro/ProteinModelerABC, can run in parallel and includes a graphical user interface. The framework is distributed with detailed documentation and ready-to-use examples.

A computational method for predicting the most likely evolutionary trajectories in the stepwise accumulation of resistance mutations

Pathogen evolution of drug resistance often occurs in a stepwise manner via the accumulation of multiple mutations that in combination have a non-additive impact on fitness, a phenomenon known as epistasis. The evolution of resistance via the accumulation of point mutations in the DHFR genes of Plasmodium falciparum (Pf) and Plasmodium vivax (Pv) has been studied extensively and multiple studies have shown epistatic interactions between these mutations determine the accessible evolutionary trajectories to highly resistant multiple mutations. Here, we simulated these evolutionary trajectories using a model of molecular evolution, parameterised using Rosetta Flex ddG predictions, where selection acts to reduce the target-drug binding affinity. We observe strong agreement with pathways determined using experimentally measured IC50 values of pyrimethamine binding, which suggests binding affinity is strongly predictive of resistance and epistasis in binding affinity strongly influences the order of fixation of resistance mutations. We also infer pathways directly from the frequency of mutations found in isolate data, and observe remarkable agreement with the most likely pathways predicted by our mechanistic model, as well as those determined experimentally. This suggests mutation frequency data can be used to intuitively infer evolutionary pathways, provided sufficient sampling of the population.

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.

Analyses of Mutation Displacements from Homology Models

Evaluation of the structural perturbations introduced by a single amino acid mutation is the main issue for protein structural biology. We propose here to present some recent advances in methods, allowing the splitting of distortion between the actual substitution effect and the contribution of the local flexibility of the position where the mutation occurs. Its main drawback is the need of many structures with a single mutation in each of them. To bypass this difficulty, we propose to use molecular modeling tools, with several software enabling us to build a model from a template, given the sequence. As a proof of concept, we rely on a gold standard, the human lysozyme. Both wild-type and three mutant structures are available in the PDB. Two of these mutations result in amyloid fibril formation, and the last one is neutral. As a conclusion, irrespective of the algorithm used for modeling, side chain conformations at the site of mutation are reliable, although long-range effects are out of reach of these tools.

From oncoproteins to spike proteins: the evaluation of intramolecular stability using hydropathic force field

Evaluation of the intramolecular stability of proteins plays a key role in the comprehension of their biological behavior and mechanism of action. Small structural alterations such as mutations induced by single nucleotide polymorphism can impact biological activity and pharmacological modulation. Covid-19 mutations, that affect viral replication and the susceptibility to antibody neutralization, and the action of antiviral drugs, are just one example. In this work, the intramolecular stability of mutated proteins, like Spike glycoprotein and its complexes with the human target, is evaluated through hydropathic intramolecular energy scoring originally conceived by Abraham and Kellogg based on the “Extension of the fragment method to calculate amino acid zwitterion and side-chain partition coefficients” by Abraham and Leo in Proteins: Struct. Funct. Genet. 1987, 2:130 − 52. HINT is proposed as a fast and reliable tool for the stability evaluation of any mutated system. This work has been written in honor of Prof. Donald J. Abraham (1936–2021).

Stability and expression of SARS-CoV-2 spike-protein mutations

Protein fold stability likely plays a role in SARS-CoV-2 S-protein evolution, together with ACE2 binding and antibody evasion. While few thermodynamic stability data are available for S-protein mutants, many systematic experimental data exist for their expression. In this paper, we explore whether such expression levels relate to the thermodynamic stability of the mutants. We studied mutation-induced SARS-CoV-2 S-protein fold stability, as computed by three very distinct methods and eight different protein structures to account for method- and structure-dependencies. For all methods and structures used (24 comparisons), computed stability changes correlate significantly (99% confidence level) with experimental yeast expression from the literature, such that higher expression is associated with relatively higher fold stability. Also significant, albeit weaker, correlations were seen between stability and ACE2 binding effects. The effect of thermodynamic fold stability may be direct or a correlate of amino acid or site properties, notably the solvent exposure of the site. Correlation between computed stability and experimental expression and ACE2 binding suggests that functional properties of the SARS-CoV-2 S-protein mutant space are largely determined by a few simple features, due to underlying correlations. Our study lends promise to the development of computational tools that may ideally aid in understanding and predicting SARS-CoV-2 S-protein evolution.

Structural heterogeneity and precision of implications drawn from cryo-electron microscopy structures: SARS-CoV-2 spike-protein mutations as a test case

Protein structures may be used to draw functional implications at the residue level, but how sensitive are these implications to the exact structure used? Calculation of the effects of SARS-CoV-2 S-protein mutations based on experimental cryo-electron microscopy structures have been abundant during the pandemic. To understand the precision of such estimates, we studied three distinct methods to estimate stability changes for all possible mutations in 23 different S-protein structures (3.69 million ΔΔG values in total) and explored how random and systematic errors can be remedied by structure-averaged mutation group comparisons. We show that computational estimates have low precision, due to method and structure heterogeneity making results for single mutations uninformative. However, structure-averaged differences in mean effects for groups of substitutions can yield significant results. Illustrating this protocol, functionally important natural mutations, despite individual variations, average to a smaller stability impact compared to other possible mutations, independent of conformational state (open, closed). In summary, we document substantial issues with precision in structure-based protein modeling and recommend sensitivity tests to quantify these effects, but also suggest partial solutions to the problem in the form of structure-averaged “ensemble” estimates for groups of residues when multiple structures are available.

Proteins' Evolution upon Point Mutations

As the reader must be already aware, state-of-the-art protein folding prediction methods have reached a smashing success in their goal of accurately determining the three-dimensional structures of proteins. Yet, a solution to simple problems such as the effects of protein point mutations on their (i) native conformation; (ii) marginal stability; (iii) ensemble of high-energy nativelike conformations; and (iv) metamorphism propensity and, hence, their evolvability, remains as an unsolved problem. As a plausible solution to the latter, some properties of the amide hydrogen-deuterium exchange, a highly sensitive probe of the structure, stability, and folding of proteins, are assessed from a new perspective. The preliminary results indicate that the protein marginal stability change upon point mutations provides the necessary and sufficient information to estimate, through a Boltzmann factor, the evolution of the amide hydrogen exchange protection factors and, consequently, that of the ensemble of folded conformations coexisting with the native state. This work contributes to our general understanding of the effects of point mutations on proteins and may spur significant progress in our efforts to develop methods to determine the appearance of new folds and functions accurately.

Evolution of amino acid propensities under stability-mediated epistasis

Site-specific amino acid preferences are influenced by the genetic background of the protein. The preferences for resident amino acids are expected to, on average, increase over time because of replacements at other sites - a nonadaptive phenomenon referred to as the 'evolutionary Stokes shift'. Alternatively, decreases in resident amino acid propensity have recently been viewed as evidence of adaptations to external environmental changes. Using population genetics theory and thermodynamic stability-constraints, we show that nonadaptive evolution can lead to both positive and negative shifts in propensities following the fixation of an amino acid, emphasizing that the detection of negative shifts is not conclusive evidence of adaptation. Considering shifts in propensities over windows between substitutions at a focal site, we find that following ≈ 50% of substitutions the propensity for the new resident amino acid decreases over time, and both positive and negative shifts were comparable in magnitude. Preferences were often conserved via a significant negative autocorrelation in propensity changes-increases in propensities often followed by decreases, and vice versa. Lastly, we explore the underlying mechanisms that lead propensities to fluctuate. We observe that stabilizing replacements increase the mutational tolerance at a site and in doing so decrease the propensity for the resident amino acid. In contrast, destabilizing substitutions result in more rugged fitness landscapes that tend to favor the resident amino acid. In summary, our results characterize propensity trajectories under nonadaptive stability-constrained evolution against which evidence of adaptations should be calibrated.

Data set and fitting dependencies when estimating protein mutant stability: Toward simple, balanced, and interpretable models

Accurate prediction of protein stability changes upon mutation (ΔΔG) is increasingly important to evolution studies, protein engineering, and screening of disease-causing gene variants but is challenged by biases in training data. We investigated 45 linear regression models trained on data sets that account systematically for destabilization bias and mutation-type bias B_M . The models were externally validated on three test data sets probing different pathologies and for internal consistency (symmetry and neutrality). Model structure and performance substantially depended on training data and even fitting method. We developed two final models: SimBa-IB for typical natural mutations and SimBa-SYM for situations where stabilizing and destabilizing mutations occur to a similar extent. SimBa-SYM, despite is simplicity, is essentially non-biased (vs. the S^sym data set) while still performing well for all data sets (R ~ 0.46-0.54, MAE = 1.16-1.24 kcal/mol). The simple models provide advantage in terms of interpretability, use and future improvement, and are freely available on GitHub.

Structure and Mutations of SARS-CoV-2 Spike Protein: A Focused Overview

The spike protein (S-protein) of SARS-CoV-2, the protein that enables the virus to infect human cells, is the basis for many vaccines and a hotspot of concerning virus evolution. Here, we discuss the outstanding progress in structural characterization of the S-protein and how these structures facilitate analysis of virus function and evolution. We emphasize the differences in reported structures and that analysis of structure-function relationships is sensitive to the structure used. We show that the average residue solvent exposure in nearly complete structures is a good descriptor of open vs closed conformation states. Because of structural heterogeneity of functionally important surface-exposed residues, we recommend using averages of a group of high-quality protein structures rather than a single structure before reaching conclusions on specific structure-function relationships. To illustrate these points, we analyze some significant chemical tendencies of prominent S-protein mutations in the context of the available structures. In the discussion of new variants, we emphasize the selectivity of binding to ACE2 vs prominent antibodies rather than simply the antibody escape or ACE2 affinity separately. We note that larger chemical changes, in particular increased electrostatic charge or side-chain volume of exposed surface residues, are recurring in mutations of concern, plausibly related to adaptation to the negative surface potential of human ACE2. We also find indications that the fixated mutations of the S-protein in the main variants are less destabilizing than would be expected on average, possibly pointing toward a selection pressure on the S-protein. The richness of available structures for all of these situations provides an enormously valuable basis for future research into these structure-function relationships.

Methodologies for Microbial Ancestral Sequence Reconstruction

The reconstruction of genetic material of ancestral organisms constitutes a powerful application of evolutionary biology. A fundamental step in this inference is the ancestral sequence reconstruction (ASR), which can be performed with diverse methodologies implemented in computer frameworks. However, most of these methodologies ignore evolutionary properties frequently observed in microbes, such as genetic recombination and complex selection processes, that can bias the traditional ASR. From a practical perspective, here I review methodologies for the reconstruction of ancestral DNA and protein sequences, with particular focus on microbes, and including biases, recommendations, and software implementations. I conclude that microbial ASR is a complex analysis that should be carefully performed and that there is a need for methods to infer more realistic ancestral microbial sequences.

Conformational dynamics promotes disordered regions from function-dispensable to essential in evolved site-specific DNA recombinases

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New functional regions emerging in evolution of DNA site-specific recombinase tails.

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Transient structural nucleation promotes function-dispensable regions to essential.

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Molecular dynamics reveals conformational diversity and its functional implications.

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Evolved disordered molecular mechanisms of N-term tails for protein stability.

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Structural disorder-based link between protein evolution, stability and function.

Protein intrinsically disordered regions (IDRs) play pivotal roles in molecular recognition and regulatory processes through structural disorder-to-order transitions. To understand and exploit the distinctive functional implications of IDRs and to unravel the underlying molecular mechanisms, structural disorder-to-function relationships need to be deciphered. The DNA site-specific recombinase system Cre/loxP represents an attractive model to investigate functional molecular mechanisms of IDRs. Cre contains a functionally dispensable disordered N-terminal tail, which becomes indispensable in the evolved Tre/loxLTR recombinase system. The difficulty to experimentally obtain structural information about this tail has so far precluded any mechanistic study on its involvement in DNA recombination. Here, we use in vitro and in silico evolution data, conformational dynamics, AI-based folding simulations, thermodynamic stability calculations, mutagenesis and DNA recombination assays to investigate how evolution and the dynamic behavior of this IDR may determine distinct functional properties. Our studies suggest that partial conformational order in the N-terminal tail of Tre recombinase and its packing to a conserved hydrophobic surface on the protein provide thermodynamic stability. Based on our results, we propose a link between protein stability and function, offering new plausible atom-detailed mechanistic insights into disorder-function relationships. Our work highlights the potential of N-terminal tails to be exploited for regulation of the activity of Cre-like tyrosine-type SSRs, which merits future investigations and could be of relevance in future rational engineering for their use in biotechnology and genomic medicine.

Shifts in amino acid preferences as proteins evolve: A synthesis of experimental and theoretical work

Amino acid preferences vary across sites and time. While variation across sites is widely accepted, the extent and frequency of temporal shifts are contentious. Our understanding of the drivers of amino acid preference change is incomplete: To what extent are temporal shifts driven by adaptive versus nonadaptive evolutionary processes? We review phenomena that cause preferences to vary (e.g., evolutionary Stokes shift, contingency, and entrenchment) and clarify how they differ. To determine the extent and prevalence of shifted preferences, we review experimental and theoretical studies. Analyses of natural sequence alignments often detect decreases in homoplasy (convergence and reversions) rates, and variation in replacement rates with time-signals that are consistent with temporally changing preferences. While approaches inferring shifts in preferences from patterns in natural alignments are valuable, they are indirect since multiple mechanisms (both adaptive and nonadaptive) could lead to the observed signal. Alternatively, site-directed mutagenesis experiments allow for a more direct assessment of shifted preferences. They corroborate evidence from multiple sequence alignments, revealing that the preference for an amino acid at a site varies depending on the background sequence. However, shifts in preferences are usually minor in magnitude and sites with significantly shifted preferences are low in frequency. The small yet consistent perturbations in preferences could, nevertheless, jeopardize the accuracy of inference procedures, which assume constant preferences. We conclude by discussing if and how such shifts in preferences might influence widely used time-homogenous inference procedures and potential ways to mitigate such effects.

Quantifying the impact of changes in effective population size and expression level on the rate of coding sequence evolution

Molecular sequences are shaped by selection, where the strength of selection relative to drift is determined by effective population size (N_e). Populations with high N_e are expected to undergo stronger purifying selection, and consequently to show a lower substitution rate for selected mutations relative to the substitution rate for neutral mutations (ω). However, computational models based on biophysics of protein stability have suggested that ω can also be independent of N_e. Together, the response of ω to changes in N_e depends on the specific mapping from sequence to fitness. Importantly, an increase in protein expression level has been found empirically to result in decrease of ω, an observation predicted by theoretical models assuming selection for protein stability. Here, we derive a theoretical approximation for the response of ω to changes in N_e and expression level, under an explicit genotype-phenotype-fitness map. The method is generally valid for additive traits and log-concave fitness functions. We applied these results to protein undergoing selection for their conformational stability and corroborate out findings with simulations under more complex models. We predict a weak response of ω to changes in either N_e or expression level, which are interchangeable. Based on empirical data, we propose that fitness based on the conformational stability may not be a sufficient mechanism to explain the empirically observed variation in ω across species. Other aspects of protein biophysics might be explored, such as protein-protein interactions, which can lead to a stronger response of ω to changes in N_e.

Evolutionary Processes and Biophysical Mechanisms: Revisiting Why Evolved Proteins Are Marginally Stable

Evolved proteins observed in natural organisms are found to be only marginally stable. Several mechanistic hypotheses have been presented to date to explain this observation. One idea that has been put forward is that active selection prevents proteins from becoming too stable to enable proper function. A second idea is that marginal stability reflects the point of mutation-selection-drift balance, where it is mutational pressure that generates marginal stability. A third idea explored in this issue of Journal of Molecular Evolution is that a physical limit prevents the evolution of more stable proteins rather than an evolutionary process. While the first two notions are based upon specific evolutionary processes, discussion here is aimed at reconciling evolutionary processes with the physics of protein folding, drawing upon the ideas that have been presented.

A thermodynamic model of protein structure evolution explains empirical amino acid substitution matrices

Proteins evolve under a myriad of biophysical selection pressures that collectively control the patterns of amino acid substitutions. These evolutionary pressures are sufficiently consistent over time and across protein families to produce substitution patterns, summarized in global amino acid substitution matrices such as BLOSUM, JTT, WAG, and LG, which can be used to successfully detect homologs, infer phylogenies, and reconstruct ancestral sequences. Although the factors that govern the variation of amino acid substitution rates have received much attention, the influence of thermodynamic stability constraints remains unresolved. Here we develop a simple model to calculate amino acid substitution matrices from evolutionary dynamics controlled by a fitness function that reports on the thermodynamic effects of amino acid mutations in protein structures. This hybrid biophysical and evolutionary model accounts for nucleotide transition/transversion rate bias, multi‐nucleotide codon changes, the number of codons per amino acid, and thermodynamic protein stability. We find that our theoretical model accurately recapitulates the complex yet universal pattern observed in common global amino acid substitution matrices used in phylogenetics. These results suggest that selection for thermodynamically stable proteins, coupled with nucleotide mutation bias filtered by the structure of the genetic code, is the primary driver behind the global amino acid substitution patterns observed in proteins throughout the tree of life.

Thoughts on the Protein's Native State

The presence of metamorphism in the protein's native state is not yet fully understood. To shed light on this issue, we present an assessment, in terms of the amide hydrogen exchange protection factor, that aims to determine the possible existence of structural fluctuations in the native-state consistent with both the upper-bound marginal stability of proteins and the presence of metamorphism. The preliminary results enable us to conclude that the native-state metamorphism is, indeed, more probable than previously thought.

Inferring long-term effective population size with Mutation-Selection Models

Mutation–selection phylogenetic codon models are grounded on population genetics first principles and represent a principled approach for investigating the intricate interplay between mutation, selection, and drift. In their current form, mutation–selection codon models are entirely characterized by the collection of site-specific amino-acid fitness profiles. However, thus far, they have relied on the assumption of a constant genetic drift, translating into a unique effective population size (Ne) across the phylogeny, clearly an unrealistic assumption. This assumption can be alleviated by introducing variation in Ne between lineages. In addition to Ne, the mutation rate (μ) is susceptible to vary between lineages, and both should covary with life-history traits (LHTs). This suggests that the model should more globally account for the joint evolutionary process followed by all of these lineage-specific variables (Ne, μ, and LHTs). In this direction, we introduce an extended mutation–selection model jointly reconstructing in a Bayesian Monte Carlo framework the fitness landscape across sites and long-term trends in Ne, μ, and LHTs along the phylogeny, from an alignment of DNA coding sequences and a matrix of observed LHTs in extant species. The model was tested against simulated data and applied to empirical data in mammals, isopods, and primates. The reconstructed history of Ne in these groups appears to correlate with LHTs or ecological variables in a way that suggests that the reconstruction is reasonable, at least in its global trends. On the other hand, the range of variation in Ne inferred across species is surprisingly narrow. This last point suggests that some of the assumptions of the model, in particular concerning the assumed absence of epistatic interactions between sites, are potentially problematic.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Quantifying the Mutational Robustness of Protein-Coding Genes

We use large-scale mutagenesis data and computer simulations to quantify the mutational robustness of protein-coding genes by taking into account constraints arising from protein function and the genetic code. Analyses of the distribution of amino acid substitutions from 18 mutagenesis studies revealed an average of 45% of neutral variants; while mutagenesis data of 12 proteins artificially designed under no other constraints but stability, reach an average of 60%. Simulations using a lattice protein model allow us to contrast these estimates to the expected mutational robustness of protein families by generating unbiased samples of foldable sequences, which we find to have 30% of neutral variants. In agreement with mutagenesis data of designed proteins, the model shows that maximally robust protein families might access up to twice the amount of neutral variants observed in the unbiased samples (i.e. 60%). A biophysical model of protein-ligand binding suggests that constraints associated to molecular function have only a moderate impact on robustness of approximately 5 to 10% of neutral variants; and that the direction of this effect depends on the relation between functional performance and thermodynamic stability. Although the genetic code constraints the access of a gene's nucleotide sequence to only 30% of the full distribution of amino acid mutations, it provides an extra 15 to 20% of neutral variants to the estimations above, such that the expected, observed, and maximal robustness of protein-coding genes are approximately 50, 65, and 75%, respectively. We discuss our results in the light of three main hypothesis put forward to explain the existence of mutationally robust genes.

Three Simple Properties Explain Protein Stability Change upon Mutation

Accurate prediction of protein stability upon mutation enables rational engineering of new proteins and insights into protein evolution and monogenetic diseases caused by single-point amino acid substitutions. Many tools have been developed to this aim, ranging from energy-based models to machine-learning methods that use large amounts of experimental data. However, as the methods become more complex, the interpretation of the chemistry underlying the protein stability effects becomes obscure. It is thus of interest to identify the simplest prediction model that retains complete amino acid specific interpretation; for a given number of input descriptors, we expect such a model to be almost universal. In this study, we identify such a limiting model, SimBa, a simple multilinear regression model trained on a substitution-type-balanced experimental data set. The model accounts only for the solvent accessibility of the site, volume difference, and polarity difference caused by mutation. Our results show that this very simple and directly applicable model performs comparably to other much more complex, widely used protein stability prediction methods. This suggests that a hard limit of ∼1 kcal/mol numerical accuracy and an R ∼ 0.5 trend accuracy exists and that new features, such as account of unfolded states, water colocalization, and amino acid correlations, are required to improve accuracy to, e.g., 1/2 kcal/mol.

A base measure of precision for protein stability predictors: structural sensitivity

BACKGROUND

Prediction of the change in fold stability (ΔΔG) of a protein upon mutation is of major importance to protein engineering and screening of disease-causing variants. Many prediction methods can use 3D structural information to predict ΔΔG. While the performance of these methods has been extensively studied, a new problem has arisen due to the abundance of crystal structures: How precise are these methods in terms of structure input used, which structure should be used, and how much does it matter? Thus, there is a need to quantify the structural sensitivity of protein stability prediction methods.

RESULTS

We computed the structural sensitivity of six widely-used prediction methods by use of saturated computational mutagenesis on a diverse set of 87 structures of 25 proteins. Our results show that structural sensitivity varies massively and surprisingly falls into two very distinct groups, with methods that take detailed account of the local environment showing a sensitivity of ~ 0.6 to 0.8 kcal/mol, whereas machine-learning methods display much lower sensitivity (~ 0.1 kcal/mol). We also observe that the precision correlates with the accuracy for mutation-type-balanced data sets but not generally reported accuracy of the methods, indicating the importance of mutation-type balance in both contexts.

CONCLUSIONS

The structural sensitivity of stability prediction methods varies greatly and is caused mainly by the models and less by the actual protein structural differences. As a new recommended standard, we therefore suggest that ΔΔG values are evaluated on three protein structures when available and the associated standard deviation reported, to emphasize not just the accuracy but also the precision of the method in a specific study. Our observation that machine-learning methods deemphasize structure may indicate that folded wild-type structures alone, without the folded mutant and unfolded structures, only add modest value for assessing protein stability effects, and that side-chain-sensitive methods overstate the significance of the folded wild-type structure.

Structure and function of naturally evolved de novo proteins

Comparative evolutionary genomics has revealed that novel protein coding genes can emerge randomly from non-coding DNA. While most of the myriad of transcripts which continuously emerge vanish rapidly, some attain regulatory regions, become translated and survive. More surprisingly, sequence properties of de novo proteins are almost indistinguishable from randomly obtained sequences, yet de novo proteins may gain functions and integrate into eukaryotic cellular networks quite easily. We here discuss current knowledge on de novo proteins, their structures, functions and evolution. Since the existence of de novo proteins seems at odds with decade-long attempts to construct proteins with novel structures and functions from scratch, we suggest that a better understanding of de novo protein evolution may fuel new strategies for protein design.

Elevated temperature increases genome-wide selection on de novo mutations

Adaptation in new environments depends on the amount of genetic variation available for evolution, and the efficacy by which natural selection discriminates among this variation. However, whether some ecological factors reveal more genetic variation, or impose stronger selection pressures than others, is typically not known. Here, we apply the enzyme kinetic theory to show that rising global temperatures are predicted to intensify natural selection throughout the genome by increasing the effects of DNA sequence variation on protein stability. We test this prediction by (i) estimating temperature-dependent fitness effects of induced mutations in seed beetles adapted to ancestral or elevated temperature, and (ii) calculate 100 paired selection estimates on mutations in benign versus stressful environments from unicellular and multicellular organisms. Environmental stress per se did not increase mean selection on de novo mutation, suggesting that the cost of adaptation does not generally increase in new ecological settings to which the organism is maladapted. However, elevated temperature increased the mean strength of selection on genome-wide polymorphism, signified by increases in both mutation load and mutational variance in fitness. These results have important implications for genetic diversity gradients and the rate and repeatability of evolution under climate change.

ADDRESS: A Database of Disease-associated Human Variants Incorporating Protein Structure and Folding Stabilities

Numerous human diseases are caused by mutations in genomic sequences. Since amino acid changes affect protein function through mechanisms often predictable from protein structure, the integration of structural and sequence data enables us to estimate with greater accuracy whether and how a given mutation will lead to disease. Publicly available annotated databases enable hypothesis assessment and benchmarking of prediction tools. However, the results are often presented as summary statistics or black box predictors, without providing full descriptive information. We developed a new semi-manually curated human variant database presenting information on the protein contact-map, sequence-to-structure mapping, amino acid identity change, and stability prediction for the popular UniProt database. We found that the profiles of pathogenic and benign missense polymorphisms can be effectively deduced using decision trees and comparative analyses based on the presented dataset. The database is made publicly available through https://zhanglab.ccmb.med.umich.edu/ADDRESS.

Consequences of Stability-Induced Epistasis for Substitution Rates

Do interactions between residues in a protein (i.e., epistasis) significantly alter evolutionary dynamics? If so, what consequences might they have on inference from traditional codon substitution models which assume site-independence for the sake of computational tractability? To investigate the effects of epistasis on substitution rates, we employed a mechanistic mutation-selection model in conjunction with a fitness framework derived from protein stability. We refer to this as the stability-informed site-dependent (S-SD) model and developed a new stability-informed site-independent (S-SI) model that captures the average effect of stability constraints on individual sites of a protein. Comparison of S-SI and S-SD offers a novel and direct method for investigating the consequences of stability-induced epistasis on protein evolution. We developed S-SI and S-SD models for three natural proteins and showed that they generate sequences consistent with real alignments. Our analyses revealed that epistasis tends to increase substitution rates compared with the rates under site-independent evolution. We then assessed the epistatic sensitivity of individual site and discovered a counterintuitive effect: Highly connected sites were less influenced by epistasis relative to exposed sites. Lastly, we show that, despite the unrealistic assumptions, traditional models perform comparably well in the presence and absence of epistasis and provide reasonable summaries of average selection intensities. We conclude that epistatic models are critical to understanding protein evolutionary dynamics, but epistasis might not be required for reasonable inference of selection pressure when averaging over time and sites.

Survival of the cheapest: how proteome cost minimization drives evolution

Darwin's theory of evolution emphasized that positive selection of functional proficiency provides the fitness that ultimately determines the structure of life, a view that has dominated biochemical thinking of enzymes as perfectly optimized for their specific functions. The 20th-century modern synthesis, structural biology, and the central dogma explained the machinery of evolution, and nearly neutral theory explained how selection competes with random fixation dynamics that produce molecular clocks essential e.g. for dating evolutionary histories. However, quantitative proteomics revealed that selection pressures not relating to optimal function play much larger roles than previously thought, acting perhaps most importantly via protein expression levels. This paper first summarizes recent progress in the 21st century toward recovering this universal selection pressure. Then, the paper argues that proteome cost minimization is the dominant, underlying 'non-function' selection pressure controlling most of the evolution of already functionally adapted living systems. A theory of proteome cost minimization is described and argued to have consequences for understanding evolutionary trade-offs, aging, cancer, and neurodegenerative protein-misfolding diseases.

Common mechanism of thermostability in small α- and β-proteins studied by molecular dynamics

Protein thermostability is important to evolution, diseases, and industrial applications. Proteins use diverse molecular strategies to achieve stability at high temperature, yet reducing the entropy of unfolding seems required. We investigated five small α-proteins and five β-proteins with known, distinct structures and thermostability (T_m ) using multi-seed molecular dynamics simulations at 300, 350, and 400 K. The proteins displayed diverse changes in hydrogen bonding, solvent exposure, and secondary structure with no simple relationship to T_m . Our dynamics were in good agreement with experimental B-factors at 300 K and insensitive to force-field choice. Despite the very distinct structures, the native-state (300 + 350 K) free-energy landscapes (FELs) were significantly broader for the two most thermostable proteins and smallest for the three least stable proteins in both the α- and β-group and with both force fields studied independently (tailed t-test, 95% confidence level). Our results suggest that entropic ensembles stabilize proteins at high temperature due to reduced entropy of unfolding, viz., ΔG = ΔH - TΔS. Supporting this mechanism, the most thermostable proteins were also the least kinetically stable, consistent with broader FELs, typified by villin headpiece and confirmed by specific comparison to a mesophilic ortholog of Thermus thermophilus apo-pyrophosphate phosphohydrolase. We propose that molecular strategies of protein thermostabilization, although diverse, tend to converge toward highest possible entropy in the native state consistent with the functional requirements. We speculate that this tendency may explain why many proteins are not optimally structured and why molten-globule states resemble native proteins so much.

Biophysics and population size constrains speciation in an evolutionary model of developmental system drift

Developmental system drift is a likely mechanism for the origin of hybrid incompatibilities between closely related species. We examine here the detailed mechanistic basis of hybrid incompatibilities between two allopatric lineages, for a genotype-phenotype map of developmental system drift under stabilising selection, where an organismal phenotype is conserved, but the underlying molecular phenotypes and genotype can drift. This leads to number of emergent phenomenon not obtainable by modelling genotype or phenotype alone. Our results show that: 1) speciation is more rapid at smaller population sizes with a characteristic, Orr-like, power law, but at large population sizes slow, characterised by a sub-diffusive growth law; 2) the molecular phenotypes under weakest selection contribute to the earliest incompatibilities; and 3) pair-wise incompatibilities dominate over higher order, contrary to previous predictions that the latter should dominate. The population size effect we find is consistent with previous results on allopatric divergence of transcription factor-DNA binding, where smaller populations have common ancestors with a larger drift load because genetic drift favours phenotypes which have a larger number of genotypes (higher sequence entropy) over more fit phenotypes which have far fewer genotypes; this means less substitutions are required in either lineage before incompatibilities arise. Overall, our results indicate that biophysics and population size provide a much stronger constraint to speciation than suggested by previous models, and point to a general mechanistic principle of how incompatibilities arise the under stabilising selection for an organismal phenotype.

The process of speciation is of fundamental importance to the field of evolution as it is intimately connected to understanding the immense bio-diversity of life. There is still relatively little understanding of the underlying genetic mechanisms that give rise to hybrid incompatibilities with results suggesting that divergence in transcription factor DNA binding and gene expression play an important role. A key finding from the field of evo-devo is that organismal phenotypes show developmental system drift, where species maintain the same phenotype, but diverge in developmental pathways; this is an important potential source of hybrid incompatibilities. Here, we explore a theoretical framework to understand how incompatibilities arise due to developmental system drift, using a tractable biophysically inspired genotype-phenotype for spatial gene expression. Modelling the evolution of phenotypes in this way has the key advantage that it mirrors how selection works in nature, i.e. that selection acts on phenotypes, but variation (mutation) arise at the level of genotypes. This results, as we demonstrate, in a number of non-trivial and testable predictions concerning speciation due to developmental system drift, which would not be obtainable by modelling evolution of genotypes or phenotypes alone.

Survival of the simplest in microbial evolution

The evolution of microbial and viral organisms often generates clonal interference, a mode of competition between genetic clades within a population. Here we show how interference impacts systems biology by constraining genetic and phenotypic complexity. Our analysis uses biophysically grounded evolutionary models for molecular phenotypes, such as fold stability and enzymatic activity of genes. We find a generic mode of phenotypic interference that couples the function of individual genes and the population’s global evolutionary dynamics. Biological implications of phenotypic interference include rapid collateral system degradation in adaptation experiments and long-term selection against genome complexity: each additional gene carries a cost proportional to the total number of genes. Recombination above a threshold rate can eliminate this cost, which establishes a universal, biophysically grounded scenario for the evolution of sex. In a broader context, our analysis suggests that the systems biology of microbes is strongly intertwined with their mode of evolution.

In asexual populations selection at different genomic loci can interfere with each other. Here, using a biophysical model of molecular evolution the authors show that interference results in long-term degradation of molecular function, an effect that strongly depends on genome size.

Substrate inhibition imposes fitness penalty at high protein stability

Proteins are only moderately stable. It has long been debated whether this narrow range of stabilities is solely a result of neutral drift toward lower stability or purifying selection against excess stability-for which no experimental evidence was found so far-is also at work. Here, we show that mutations outside the active site in the essential Escherichia coli enzyme adenylate kinase (Adk) result in a stability-dependent increase in substrate inhibition by AMP, thereby impairing overall enzyme activity at high stability. Such inhibition caused substantial fitness defects not only in the presence of excess substrate but also under physiological conditions. In the latter case, substrate inhibition caused differential accumulation of AMP in the stationary phase for the inhibition-prone mutants. Furthermore, we show that changes in flux through Adk could accurately describe the variation in fitness effects. Taken together, these data suggest that selection against substrate inhibition and hence excess stability may be an important factor determining stability observed for modern-day Adk.

Massively Parallel Assays and Quantitative Sequence-Function Relationships

Over the last decade, a rich variety of massively parallel assays have revolutionized our understanding of how biological sequences encode quantitative molecular phenotypes. These assays include deep mutational scanning, high-throughput SELEX, and massively parallel reporter assays. Here, we review these experimental methods and how the data they produce can be used to quantitatively model sequence-function relationships. In doing so, we touch on a diverse range of topics, including the identification of clinically relevant genomic variants, the modeling of transcription factor binding to DNA, the functional and evolutionary landscapes of proteins, and cis-regulatory mechanisms in both transcription and mRNA splicing. We further describe a unified conceptual framework and a core set of mathematical modeling strategies that studies in these diverse areas can make use of. Finally, we highlight key aspects of experimental design and mathematical modeling that are important for the results of such studies to be interpretable and reproducible.

The Molecular Clock in the Evolution of Protein Structures

The molecular clock hypothesis, which states that substitutions accumulate in protein sequences at a constant rate, plays a fundamental role in molecular evolution but it is violated when selective or mutational processes vary with time. Such violations of the molecular clock have been widely investigated for protein sequences, but not yet for protein structures. Here, we introduce a novel statistical test (Significant Clock Violations) and perform a large scale assessment of the molecular clock in the evolution of both protein sequences and structures in three large superfamilies. After validating our method with computer simulations, we find that clock violations are generally consistent in sequence and structure evolution, but they tend to be larger and more significant in structure evolution. Moreover, changes of function assessed through Gene Ontology and InterPro terms are associated with large and significant clock violations in structure evolution. We found that almost one third of significant clock violations are significant in structure evolution but not in sequence evolution, highlighting the advantage to use structure information for assessing accelerated evolution and gathering hints of positive selection. Clock violations between closely related pairs are frequently significant in sequence evolution, consistent with the observed time dependence of the substitution rate attributed to segregation of neutral and slightly deleterious polymorphisms, but not in structure evolution, suggesting that these substitutions do not affect protein structure although they may affect stability. These results are consistent with the view that natural selection, both negative and positive, constrains more strongly protein structures than protein sequences. Our code for computing clock violations is freely available at https://github.com/ugobas/Molecular_clock.

How Often Do Protein Genes Navigate Valleys of Low Fitness?

To escape from local fitness peaks, a population must navigate across valleys of low fitness. How these transitions occur, and what role they play in adaptation, have been subjects of active interest in evolutionary genetics for almost a century. However, to our knowledge, this problem has never been addressed directly by considering the evolution of a gene, or group of genes, as a whole, including the complex effects of fitness interactions among multiple loci. Here, we use a precise model of protein fitness to compute the probability P ( s , Δ t ) that an allele, randomly sampled from a population at time t, has crossed a fitness valley of depth s during an interval t - Δ t , t in the immediate past. We study populations of model genes evolving under equilibrium conditions consistent with those in mammalian mitochondria. From this data, we estimate that genes encoding small protein motifs navigate fitness valleys of depth 2 N s ≳ 30 with probability P ≳ 0 . 1 on a time scale of human evolution, where N is the (mitochondrial) effective population size. The results are consistent with recent findings for Watson⁻Crick switching in mammalian mitochondrial tRNA molecules.

SodaPop: a forward simulation suite for the evolutionary dynamics of asexual populations on protein fitness landscapes

Motivation

Protein evolution is determined by forces at multiple levels of biological organization. Random mutations have an immediate effect on the biophysical properties, structure and function of proteins. These same mutations also affect the fitness of the organism. However, the evolutionary fate of mutations, whether they succeed to fixation or are purged, also depends on population size and dynamics. There is an emerging interest, both theoretically and experimentally, to integrate these two factors in protein evolution. Although there are several tools available for simulating protein evolution, most of them focus on either the biophysical or the population-level determinants, but not both. Hence, there is a need for a publicly available computational tool to explore both the effects of protein biophysics and population dynamics on protein evolution.

Results

To address this need, we developed SodaPop, a computational suite to simulate protein evolution in the context of the population dynamics of asexual populations. SodaPop accepts as input several fitness landscapes based on protein biochemistry or other user-defined fitness functions. The user can also provide as input experimental fitness landscapes derived from deep mutational scanning approaches or theoretical landscapes derived from physical force field estimates. Here, we demonstrate the broad utility of SodaPop with different applications describing the interplay of selection for protein properties and population dynamics. SodaPop is designed such that population geneticists can explore the influence of protein biochemistry on patterns of genetic variation, and that biochemists and biophysicists can explore the role of population size and demography on protein evolution.

Availability and implementation

Source code and binaries are freely available at https://github.com/louisgt/SodaPop under the GNU GPLv3 license. The software is implemented in C++ and supported on Linux, Mac OS/X and Windows.

Supplementary information

Supplementary data are available at Bioinformatics online.

The Influence of Protein Stability on Sequence Evolution: Applications to Phylogenetic Inference

Phylogenetic inference from protein data is traditionally based on empirical substitution models of evolution that assume that protein sites evolve independently of each other and under the same substitution process. However, it is well known that the structural properties of a protein site in the native state affect its evolution, in particular the sequence entropy and the substitution rate. Starting from the seminal proposal by Halpern and Bruno, where structural properties are incorporated in the evolutionary model through site-specific amino acid frequencies, several models have been developed to tackle the influence of protein structure on sequence evolution. Here we describe stability-constrained substitution (SCS) models that explicitly consider the stability of the native state against both unfolded and misfolded states. One of them, the mean-field model, provides an independent sites approximation that can be readily incorporated in maximum likelihood methods of phylogenetic inference, including ancestral sequence reconstruction. Next, we describe its validation with simulated and real proteins and its limitations and advantages with respect to empirical models that lack site specificity. We finally provide guidelines and recommendations to analyze protein data accounting for stability constraints, including computer simulations and inferences of protein evolution based on maximum likelihood. Some practical examples are included to illustrate these procedures.

The Site-Specific Amino Acid Preferences of Homologous Proteins Depend on Sequence Divergence

The propensity of protein sites to be occupied by any of the 20 amino acids is known as site-specific amino acid preferences (SSAP). Under the assumption that SSAP are conserved among homologs, they can be used to parameterize evolutionary models for the reconstruction of accurate phylogenetic trees. However, simulations and experimental studies have not been able to fully assess the relative conservation of SSAP as a function of sequence divergence between protein homologs. Here, we implement a computational procedure to predict the SSAP of proteins based on the effect of changes in thermodynamic stability upon mutation. An advantage of this computational approach is that it allows us to interrogate a large and unbiased sample of homologous proteins, over the entire spectrum of sequence divergence, and under selection for the same molecular trait. We show that computational predictions have reproducibilities that resemble those obtained in experimental replicates, and can largely recapitulate the SSAP observed in a large-scale mutagenesis experiment. Our results support recent experimental reports on the conservation of SSAP of related homologs, with a slowly increasing fraction of up to 15% of different sites at sequence distances lower than 40%. However, even under the sole contribution of thermodynamic stability, our conservative approach identifies up to 30% of significant different sites between divergent homologs. We show that this relation holds for homologs of diverse sizes and structural classes. Analyses of residue contact networks suggest that an important determinant of these differences is the increasing accumulation of structural deviations that results from sequence divergence.

Reconstructing the evolutionary history of F420-dependent dehydrogenases

During the last decade the number of characterized F₄₂₀-dependent enzymes has significantly increased. Many of these deazaflavoproteins share a TIM-barrel fold and are structurally related to FMN-dependent luciferases and monooxygenases. In this work, we traced the origin and evolutionary history of the F₄₂₀-dependent enzymes within the luciferase-like superfamily. By a thorough phylogenetic analysis we inferred that the F₄₂₀-dependent enzymes emerged from a FMN-dependent common ancestor. Furthermore, the data show that during evolution, the family of deazaflavoproteins split into two well-defined groups of enzymes: the F₄₂₀-dependent dehydrogenases and the F₄₂₀-dependent reductases. By such event, the dehydrogenases specialized in generating the reduced deazaflavin cofactor, while the reductases employ the reduced F₄₂₀ for catalysis. Particularly, we focused on investigating the dehydrogenase subfamily and demonstrated that this group diversified into three types of dehydrogenases: the already known F₄₂₀-dependent glucose-6-phosphate dehydrogenases, the F₄₂₀-dependent alcohol dehydrogenases, and the sugar-6-phosphate dehydrogenases that were identified in this study. By reconstructing and experimentally characterizing ancestral and extant representatives of F₄₂₀-dependent dehydrogenases, their biochemical properties were investigated and compared. We propose an evolutionary path for the emergence and diversification of the TIM-barrel fold F₄₂₀-dependent dehydrogenases subfamily.

Influence of mutation bias and hydrophobicity on the substitution rates and sequence entropies of protein evolution

The number of amino acids that occupy a given protein site during evolution reflects the selective constraints operating on the site. This evolutionary variability is strongly influenced by the structural properties of the site in the native structure, and it is quantified either through sequence entropy or through substitution rates. However, while the sequence entropy only depends on the equilibrium frequencies of the amino acids, the substitution rate also depends on the exchangeability matrix that describes mutations in the mathematical model of the substitution process. Here we apply two variants of a mathematical model of protein evolution with selection for protein stability, both against unfolding and against misfolding. Exploiting the approximation of independent sites, these models allow computing site-specific substitution processes that satisfy global constraints on folding stability. We find that site-specific substitution rates do not depend only on the selective constraints acting on the site, quantified through its sequence entropy. In fact, polar sites evolve faster than hydrophobic sites even for equal sequence entropy, as a consequence of the fact that polar amino acids are characterized by higher mutational exchangeability than hydrophobic ones. Accordingly, the model predicts that more polar proteins tend to evolve faster. Nevertheless, these results change if we compare proteins that evolve under different mutation biases, such as orthologous proteins in different bacterial genomes. In this case, the substitution rates are faster in genomes that evolve under mutational bias that favor hydrophobic amino acids by preferentially incorporating the nucleotide Thymine that is more frequent in hydrophobic codons. This appearingly contradictory result arises because buried sites occupied by hydrophobic amino acids are characterized by larger selective factors that largely amplify the substitution rate between hydrophobic amino acids, while the selective factors of exposed sites have a weaker effect. Thus, changes in the mutational bias produce deep effects on the biophysical properties of the protein (hydrophobicity) and on its evolutionary properties (sequence entropy and substitution rate) at the same time. The program Prot_evol that implements the two site-specific substitution processes is freely available at https://ub.cbm.uam.es/prot_fold_evol/prot_fold_evol_soft_main.php#Prot_Evol.

Selection for Protein Stability Enriches for Epistatic Interactions

A now classical argument for the marginal thermodynamic stability of proteins explains the distribution of observed protein stabilities as a consequence of an entropic pull in protein sequence space. In particular, most sequences that are sufficiently stable to fold will have stabilities near the folding threshold. Here, we extend this argument to consider its predictions for epistatic interactions for the effects of mutations on the free energy of folding. Although there is abundant evidence to indicate that the effects of mutations on the free energy of folding are nearly additive and conserved over evolutionary time, we show that these observations are compatible with the hypothesis that a non-additive contribution to the folding free energy is essential for observed proteins to maintain their native structure. In particular, through both simulations and analytical results, we show that even very small departures from additivity are sufficient to drive this effect.

Direct examination of the relevance for folding, binding and electron transfer of a conserved protein folding intermediate

Near the minimum free energy basin of proteins where the native ensemble resides, partly unfolded conformations of slightly higher energy can be significantly populated under native conditions. It has been speculated that they play roles in molecular recognition and catalysis, but they might represent contemporary features of the evolutionary process without functional relevance. Obtaining conclusive evidence on these alternatives is difficult because it requires comparing the performance of a given protein when populating and when not populating one such intermediate, in otherwise identical conditions. Wild type apoflavodoxin populates under native conditions a partly unfolded conformation (10% of molecules) whose unstructured region includes the binding sites for the FMN cofactor and for redox partner proteins. We recently engineered a thermostable variant where the intermediate is no longer detectable. Using the wild type and variant, we assess the relevance of the intermediate comparing folding kinetics, cofactor binding kinetics, cofactor affinity, X-ray structure, intrinsic dynamics, redox potential of the apoflavodoxin-cofactor complex (Fld), its affinity for partner protein FNR, and electron transfer rate within the Fld/FNR physiological complex. Our data strongly suggest the intermediate state, conserved in long-chain apoflavodoxins, is not required for the correct assembly of flavodoxin nor does it contribute to shape its electron transfer properties. This analysis can be applied to evaluate other native basin intermediates.

Protein evolution depends on multiple distinct population size parameters

That population size affects the fate of new mutations arising in genomes, modulating both how frequently they arise and how efficiently natural selection is able to filter them, is well established. It is therefore clear that these distinct roles for population size that characterize different processes should affect the evolution of proteins and need to be carefully defined. Empirical evidence is consistent with a role for demography in influencing protein evolution, supporting the idea that functional constraints alone do not determine the composition of coding sequences.

Given that the relationship between population size, mutant fitness and fixation probability has been well characterized, estimating fitness from observed substitutions is well within reach with well-formulated models. Molecular evolution research has, therefore, increasingly begun to leverage concepts from population genetics to quantify the selective effects associated with different classes of mutation. However, in order for this type of analysis to provide meaningful information about the intra- and inter-specific evolution of coding sequences, a clear definition of concepts of population size, what they influence, and how they are best parameterized is essential.

Here, we present an overview of the many distinct concepts that “population size” and “effective population size” may refer to, what they represent for studying proteins, and how this knowledge can be harnessed to produce better specified models of protein evolution.

Principles of Protein Stability and Their Application in Computational Design

Proteins are increasingly used in basic and applied biomedical research. Many proteins, however, are only marginally stable and can be expressed in limited amounts, thus hampering research and applications. Research has revealed the thermodynamic, cellular, and evolutionary principles and mechanisms that underlie marginal stability. With this growing understanding, computational stability design methods have advanced over the past two decades starting from methods that selectively addressed only some aspects of marginal stability. Current methods are more general and, by combining phylogenetic analysis with atomistic design, have shown drastic improvements in solubility, thermal stability, and aggregation resistance while maintaining the protein's primary molecular activity. Stability design is opening the way to rational engineering of improved enzymes, therapeutics, and vaccines and to the application of protein design methodology to large proteins and molecular activities that have proven challenging in the past.