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

EvoRator2: Predicting Site-specific Amino Acid Substitutions Based on Protein Structural Information Using Deep Learning

Multiple sequence alignments (MSAs) are the workhorse of molecular evolution and structural biology research. From MSAs, the amino acids that are tolerated at each site during protein evolution can be inferred. However, little is known regarding the repertoire of tolerated amino acids in proteins when only a few or no sequence homologs are available, such as orphan and de novo designed proteins. Here we present EvoRator2, a deep-learning algorithm trained on over 15,000 protein structures that can predict which amino acids are tolerated at any given site, based exclusively on protein structural information mined from atomic coordinate files. We show that EvoRator2 obtained satisfying results for the prediction of position-weighted scoring matrices (PSSM). We further show that EvoRator2 obtained near state-of-the-art performance on proteins with high quality structures in predicting the effect of mutations in deep mutation scanning (DMS) experiments and that for certain DMS targets, EvoRator2 outperformed state-of-the-art methods. We also show that by combining EvoRator2's predictions with those obtained by a state-of-the-art deep-learning method that accounts for the information in the MSA, the prediction of the effect of mutation in DMS experiments was improved in terms of both accuracy and stability. EvoRator2 is designed to predict which amino-acid substitutions are tolerated in such proteins without many homologous sequences, including orphan or de novo designed proteins. We implemented our approach in the EvoRator web server (https://evorator.tau.ac.il).

Gaussian network model revisited: Effects of mutation and ligand binding on protein behavior

The coarse-grained Gaussian Network model, GNM, considers only the alpha carbons of the folded protein. Therefore it is not directly applicable to the study of mutation or ligand binding problems where atomic detail is required. This shortcoming is improved by including all atom pairs within the coordination shell of each other into the Kirchoff Adjacency Matrix. Counting all contacts rather than only alpha carbon contacts diminishes the magnitude of fluctuations in the system. But more importantly, it changes the graph-like connectivity structure, i.e., the Kirchoff Adjacency Matrix of the protein. This change depends on amino acid type which introduces amino acid specific and position specific information into the classical coarse-grained GNM which was originally modelled in analogy with the phantom network model of rubber elasticity. With this modification, it is now possible to explain the consequences of mutation and ligand binding on residue fluctuations, their pair-correlations and mutual information (MI) shared by each pair. We refer to the new model as 'all-atom GNM'. Using examples from published data we show that the all-atom GNM gives B-factors that are in better agreement with experiment, can explain effects of mutation on long range communication in PDZ domains and can predict effects of GDP and GTP binding on the dimerization of KRAS.

Abundance Imparts Evolutionary Constraints of Similar Magnitude on the Buried, Surface, and Disordered Regions of Proteins

An understanding of the forces shaping protein conservation is key, both for the fundamental knowledge it represents and to allow for optimal use of evolutionary information in practical applications. Sequence conservation is typically examined at one of two levels. The first is a residue-level, where intra-protein differences are analyzed and the second is a protein-level, where inter-protein differences are studied. At a residue level, we know that solvent-accessibility is a prime determinant of conservation. By inverting this logic, we inferred that disordered regions are slightly more solvent-accessible on average than the most exposed surface residues in domains. By integrating abundance information with evolutionary data within and across proteins, we confirmed a previously reported strong surface-core association in the evolution of structured regions, but we found a comparatively weak association between disordered and structured regions. The facts that disordered and structured regions experience different structural constraints and evolve independently provide a unique setup to examine an outstanding question: why is a protein’s abundance the main determinant of its sequence conservation? Indeed, any structural or biophysical property linked to the abundance-conservation relationship should increase the relative conservation of regions concerned with that property (e.g., disordered residues with mis-interactions, domain residues with misfolding). Surprisingly, however, we found the conservation of disordered and structured regions to increase in equal proportion with abundance. This observation implies that either abundance-related constraints are structure-independent, or multiple constraints apply to different regions and perfectly balance each other.

Quantifying evolutionary importance of protein sites: A Tale of two measures

A key challenge in evolutionary biology is the accurate quantification of selective pressure on proteins and other biological macromolecules at single-site resolution. The evolutionary importance of a protein site under purifying selection is typically measured by the degree of conservation of the protein site itself. A possible alternative measure is the strength of the site-induced conservation gradient in the rest of the protein structure. However, the quantitative relationship between these two measures remains unknown. Here, we show that despite major differences, there is a strong linear relationship between the two measures such that more conserved protein sites also induce stronger conservation gradient in the rest of the protein. This linear relationship is universal as it holds for different types of proteins and functional sites in proteins. Our results show that the strong selective pressure acting on the functional site in general percolates through the rest of the protein via residue-residue contacts. Surprisingly however, catalytic sites in enzymes are the principal exception to this rule. Catalytic sites induce significantly stronger conservation gradients in the rest of the protein than expected from the degree of conservation of the site alone. The unique requirement for the active site to selectively stabilize the transition state of the catalyzed chemical reaction imposes additional selective constraints on the rest of the enzyme.

Sites within proteins which are important for stability or function are under stronger selective pressure and evolve more slowly than other sites. Catalytic sites in enzymes are such highly conserved sites with relatively low evolutionary rates. Recently, catalytic sites were shown to induce a strong gradient of conservation such that the closer a residue is to the catalytic site, the more conserved it is. Here we show that there is a universal linear relationship between the degree of evolutionary conservation of a protein site and the conservation gradient it induces in the protein tertiary structure, applicable to all types of sites. Our findings suggest that selective pressure acting on a protein site generally percolates through the rest of the protein via residue-residue contacts. Remarkably however, catalytic sites induce significantly stronger conservation gradients than expected from their degree of conservation alone. Our results indicate that the strong conservation gradient induced by catalytic sites is driven by the unique function of enzyme catalysis, which requires the participation of many residues beyond the few key catalytic residues. Our results provide insights into evolutionary conservation patterns of and surrounding proteins functional sites, with implications for functional site prediction and protein design.

Estimating the Influence of Physicochemical and Biochemical Property Indexes on Selection for Amino Acids Usage in Eukaryotic Cells

Proteins can evolve by accumulating changes on amino acid sequences. These changes are mainly caused by missense mutations on its DNA coding sequences. Mutations with neutral or positive effects on fitness can be maintained while deleterious mutations tend to be eliminated by natural selection. Amino acid changes are influenced by the biophysical, chemical, and biological properties of amino acids. There is a multiplicity of amino acid properties that can influence the function and expression of proteins. Amino acid properties can be expressed into numerical indexes, which can help to predict functional and structural aspects of proteins and allow statistical inferences of selection pressure on amino acid usage. The accuracy of these analyses may be compromised by the existence of several numerical indexes that measure the same amino acid property, and the lack of objective parameters to determine the most accurate and biologically relevant index. In the present study, the gradient consistency test was used in order to estimate the magnitude of directional selection imparted by amino acid biochemical and biophysical properties on protein evolution.

Intrinsically Disordered Protein Ensembles Shape Evolutionary Rates Revealing Conformational Patterns

Intrinsically disordered proteins (IDPs) lack stable tertiary structure under physiological conditions. The unique composition and complex dynamical behaviour of IDPs make them a challenge for structural biology and molecular evolution studies. Using NMR ensembles, we found that IDPs evolve under a strong site-specific evolutionary rate heterogeneity, mainly originated by different constraints derived from their inter-residue contacts. Evolutionary rate profiles correlate with the experimentally observed conformational diversity of the protein, allowing the description of different conformational patterns possibly related to their structure-function relationships. The correlation between evolutionary rates and contact information improves when structural information is taken not from any individual conformer or the whole ensemble, but from combining a limited number of conformers. Our results suggest that residue contacts in disordered regions constrain evolutionary rates to conserve the dynamic behaviour of the ensemble and that evolutionary rates can be used as a proxy for the conformational diversity of IDPs.

Nature of Long-Range Evolutionary Constraint in Enzymes: Insights from Comparison to Pseudoenzymes with Similar Structures

Enzymes are known to fine-tune their sequences to optimize catalytic function, yet quantitative evolutionary design principles of enzymes remain elusive on the proteomic scale. Recently, it was found that the catalytic site in enzymes induces long-range evolutionary constraint, where even sites distant to the catalytic site are more conserved than expected. Given that protein-fold usage is generally different between enzymes and nonenzymes, it remains an open question to what extent this long-range evolutionary constraint in enzymes is dictated, either directly or indirectly, by the special three-dimensional structure of the enzyme. To investigate this question, we have compared evolutionary properties of enzymes with those of counterpart pseudoenzymes that share the same protein fold but are catalytically inactive. We found that the long-range evolutionary constraint observed in enzymes is significantly reduced in pseudoenzyme counterparts, despite very high structural similarity (∼1.5 Å RMSD on average). Furthermore, this significant reduction in long-range evolutionary constraint is observed even in pseudoenzyme counterparts which retain the ligand-binding ability of enzymes. Finally, the distance between the site that induces the highest gradient of sequence conservation and the pseudocatalytic site in pseudoenzymes is significantly larger than the corresponding distance in enzymes. Taken together, our results suggest that the long-range evolutionary constraint in enzymes is induced mainly by the presence of the catalytic site rather than by the special three-dimensional structure of the enzyme, and that such long-range evolutionary constraint in enzymes depends mainly on the catalytic function of the active site rather than on the ligand-binding ability of the enzyme.

Large-Scale Analyses of Site-Specific Evolutionary Rates across Eukaryote Proteomes Reveal Confounding Interactions between Intrinsic Disorder, Secondary Structure, and Functional Domains

Various structural and functional constraints govern the evolution of protein sequences. As a result, the relative rates of amino acid replacement among sites within a protein can vary significantly. Previous large-scale work on Metazoan (Animal) protein sequence alignments indicated that amino acid replacement rates are partially driven by a complex interaction among three factors: intrinsic disorder propensity; secondary structure; and functional domain involvement. Here, we use sequence-based predictors to evaluate the effects of these factors on site-specific sequence evolutionary rates within four eukaryotic lineages: Metazoans; Plants; Saccharomycete Fungi; and Alveolate Protists. Our results show broad, consistent trends across all four Eukaryote groups. In all four lineages, there is a significant increase in amino acid replacement rates when comparing: (i) disordered vs. ordered sites; (ii) random coil sites vs. sites in secondary structures; and (iii) inter-domain linker sites vs. sites in functional domains. Additionally, within Metazoans, Plants, and Saccharomycetes, there is a strong confounding interaction between intrinsic disorder and secondary structure-alignment sites exhibiting both high disorder propensity and involvement in secondary structures have very low average rates of sequence evolution. Analysis of gene ontology (GO) terms revealed that in all four lineages, a high fraction of sequences containing these conserved, disordered-structured sites are involved in nucleic acid binding. We also observe notable differences in the statistical trends of Alveolates, where intrinsically disordered sites are more variable than in other Eukaryotes and the statistical interactions between disorder and other factors are less pronounced.

Experimental Determination and Prediction of the Fitness Effects of Random Point Mutations in the Biosynthetic Enzyme HisA

The distribution of fitness effects of mutations is a factor of fundamental importance in evolutionary biology. We determined the distribution of fitness effects of 510 mutants that each carried between 1 and 10 mutations (synonymous and nonsynonymous) in the hisA gene, encoding an essential enzyme in the l-histidine biosynthesis pathway of Salmonella enterica. For the full set of mutants, the distribution was bimodal with many apparently neutral mutations and many lethal mutations. For a subset of 81 single, nonsynonymous mutants most mutations appeared neutral at high expression levels, whereas at low expression levels only a few mutations were neutral. Furthermore, we examined how the magnitude of the observed fitness effects was correlated to several measures of biophysical properties and phylogenetic conservation.We conclude that for HisA: (i) The effect of mutations can be masked by high expression levels, such that mutations that are deleterious to the function of the protein can still be neutral with regard to organism fitness if the protein is expressed at a sufficiently high level; (ii) the shape of the fitness distribution is dependent on the extent to which the protein is rate-limiting for growth; (iii) negative epistatic interactions, on an average, amplified the combined effect of nonsynonymous mutations; and (iv) no single sequence-based predictor could confidently predict the fitness effects of mutations in HisA, but a combination of multiple predictors could predict the effect with a SD of 0.04 resulting in 80% of the mutations predicted within 12% of their observed selection coefficients.

Beyond Thermodynamic Constraints: Evolutionary Sampling Generates Realistic Protein Sequence Variation

Biological evolution generates a surprising amount of site-specific variability in protein sequences. Yet, attempts at modeling this process have been only moderately successful, and current models based on protein structural metrics explain, at best, 60% of the observed variation. Surprisingly, simple measures of protein structure, such as solvent accessibility, are often better predictors of site-specific variability than more complex models employing all-atom energy functions and detailed structural modeling. We suggest here that these more complex models perform poorly because they lack consideration of the evolutionary process, which is, in part, captured by the simpler metrics. We compare protein sequences that are computationally designed to sequences that are computationally evolved using the same protein-design energy function and to homologous natural sequences. We find that, by a wide variety of metrics, evolved sequences are much more similar to natural sequences than are designed sequences. In particular, designed sequences are too conserved on the protein surface relative to natural sequences, whereas evolved sequences are not. Our results suggest that evolutionary simulation produces a realistic sampling of sequence space. By contrast, protein design-at least as currently implemented-does not. Existing energy functions seem to be sufficiently accurate to correctly describe the key thermodynamic constraints acting on protein sequences, but they need to be paired with realistic sampling schemes to generate realistic sequence alignments.

Measuring evolutionary rates of proteins in a structural context

We describe how to measure site-specific rates of evolution in protein-coding genes and how to correlate these rates with structural features of the expressed protein, such as relative solvent accessibility, secondary structure, or weighted contact number. We present two alternative approaches to rate calculations: One based on relative amino-acid rates, and the other based on site-specific codon rates measured as dN/ dS. We additionally provide a code repository containing scripts to facilitate the specific analysis protocols we recommend.

Measuring evolutionary rates of proteins in a structural context

We describe how to measure site-specific rates of evolution in protein-coding genes and how to correlate these rates with structural features of the expressed protein, such as relative solvent accessibility, secondary structure, or weighted contact number. We present two alternative approaches to rate calculations: One based on relative amino-acid rates, and the other based on site-specific codon rates measured as dN/ dS. We additionally provide a code repository containing scripts to facilitate the specific analysis protocols we recommend.

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.

Calculating site-specific evolutionary rates at the amino-acid or codon level yields similar rate estimates

Site-specific evolutionary rates can be estimated from codon sequences or from amino-acid sequences. For codon sequences, the most popular methods use some variation of the dN∕dS ratio. For amino-acid sequences, one widely-used method is called Rate4Site, and it assigns a relative conservation score to each site in an alignment. How site-wise dN∕dS values relate to Rate4Site scores is not known. Here we elucidate the relationship between these two rate measurements. We simulate sequences with known dN∕dS, using either dN∕dS models or mutation–selection models for simulation. We then infer Rate4Site scores on the simulated alignments, and we compare those scores to either true or inferred dN∕dS values on the same alignments. We find that Rate4Site scores generally correlate well with true dN∕dS, and the correlation strengths increase in alignments with greater sequence divergence and more taxa. Moreover, Rate4Site scores correlate very well with inferred (as opposed to true) dN∕dS values, even for small alignments with little divergence. Finally, we verify this relationship between Rate4Site and dN∕dS in a variety of empirical datasets. We conclude that codon-level and amino-acid-level analysis frameworks are directly comparable and yield very similar inferences.

Computational prediction of the tolerance to amino-acid deletion in green-fluorescent protein

Proteins evolve through two primary mechanisms: substitution, where mutations alter a protein's amino-acid sequence, and insertions and deletions (indels), where amino acids are either added to or removed from the sequence. Protein structure has been shown to influence the rate at which substitutions accumulate across sites in proteins, but whether structure similarly constrains the occurrence of indels has not been rigorously studied. Here, we investigate the extent to which structural properties known to covary with protein evolutionary rates might also predict protein tolerance to indels. Specifically, we analyze a publicly available dataset of single-amino-acid deletion mutations in enhanced green fluorescent protein (eGFP) to assess how well the functional effect of deletions can be predicted from protein structure. We find that weighted contact number (WCN), which measures how densely packed a residue is within the protein's three-dimensional structure, provides the best single predictor for whether eGFP will tolerate a given deletion. We additionally find that using protein design to explicitly model deletions results in improved predictions of functional status when combined with other structural predictors. Our work suggests that structure plays fundamental role in constraining deletions at sites in proteins, and further that similar biophysical constraints influence both substitutions and deletions. This study therefore provides a solid foundation for future work to examine how protein structure influences tolerance of more complex indel events, such as insertions or large deletions.

Evolutionary interplay between structure, energy and epistasis in the coat protein of the ϕX174 phage family

Viral capsids are structurally constrained by interactions among the amino acids (AAs) of their constituent proteins. Therefore, epistasis is expected to evolve among physically interacting sites and to influence the rates of substitution. To study the evolution of epistasis, we focused on the major structural protein of the ϕX174 phage family by first reconstructing the ancestral protein sequences of 18 species using a Bayesian statistical framework. The inferred ancestral reconstruction differed at eight AAs, for a total of 256 possible ancestral haplotypes. For each ancestral haplotype and the extant species, we estimated, in silico, the distribution of free energies and epistasis of the capsid structure. We found that free energy has not significantly increased but epistasis has. We decomposed epistasis up to fifth order and found that higher-order epistasis sometimes compensates pairwise interactions making the free energy seem additive. The dN/dS ratio is low, suggesting strong purifying selection, and that structure is under stabilizing selection. We synthesized phages carrying ancestral haplotypes of the coat protein gene and measured their fitness experimentally. Our findings indicate that stabilizing mutations can have higher fitness, and that fitness optima do not necessarily coincide with energy minima.

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

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

Dissecting the roles of local packing density and longer-range effects in protein sequence evolution

What are the structural determinants of protein sequence evolution? A number of site-specific structural characteristics have been proposed, most of which are broadly related to either the density of contacts or the solvent accessibility of individual residues. Most importantly, there has been disagreement in the literature over the relative importance of solvent accessibility and local packing density for explaining site-specific sequence variability in proteins. We show that this discussion has been confounded by the definition of local packing density. The most commonly used measures of local packing, such as contact number and the weighted contact number, represent the combined effects of local packing density and longer-range effects. As an alternative, we propose a truly local measure of packing density around a single residue, based on the Voronoi cell volume. We show that the Voronoi cell volume, when calculated relative to the geometric center of amino-acid side chains, behaves nearly identically to the relative solvent accessibility, and each individually can explain, on average, approximately 34% of the site-specific variation in evolutionary rate in a data set of 209 enzymes. An additional 10% of variation can be explained by nonlocal effects that are captured in the weighted contact number. Consequently, evolutionary variation at a site is determined by the combined effects of the immediate amino-acid neighbors of that site and effects mediated by more distant amino acids. We conclude that instead of contrasting solvent accessibility and local packing density, future research should emphasize on the relative importance of immediate contacts and longer-range effects on evolutionary variation. Proteins 2016; 84:841-854. © 2016 Wiley Periodicals, Inc.

The Nuanced Interplay of Intrinsic Disorder and Other Structural Properties Driving Protein Evolution

Protein evolution often occurs at unequal rates in different sites along an amino acid chain. Site-specific evolutionary rates have been linked to several structural and functional properties of proteins. Previous analyses of this phenomenon have involved relatively small datasets and, in some cases, the interaction among multiple structural factors is not evaluated. Here, we present the results of a large-scale phylogenetic and statistical analysis, testing the effects and interactions of three structural properties on amino acid replacement rates. We used sequence-based computational methods to predict (i) intrinsic disorder propensity, (ii) secondary structure, and (iii) functional domain involvement across millions of amino acid sites in thousands of sequence alignments of metazoan proteins. Our results somewhat corroborate earlier findings that intrinsically disordered sites tend to be more variable than ordered sites, but there is considerable overlap among their rate distributions, and a significant confounding interaction exists between intrinsic disorder and secondary structure. Notably, protein sites that are consistently predicted to be both intrinsically disordered and involved in secondary structures tend to be the most conserved at the amino acid level, suggesting that they are highly constrained and functionally important. In addition, a significant interaction exists between functional domain involvement and secondary structure. These findings suggest that multiple structural drivers of protein evolution should be evaluated simultaneously in order to get a clear picture of their individual effects as well as any confounding interactions among them.

Causes of evolutionary rate variation among protein sites

It has long been recognized that certain sites within a protein, such as sites in the protein core or catalytic residues in enzymes, are evolutionarily more conserved than other sites. However, our understanding of rate variation among sites remains surprisingly limited. Recent progress to address this includes the development of a wide array of reliable methods to estimate site-specific substitution rates from sequence alignments. In addition, several molecular traits have been identified that correlate with site-specific mutation rates, and novel mechanistic biophysical models have been proposed to explain the observed correlations. Nonetheless, current models explain, at best, approximately 60% of the observed variance, highlighting the limitations of current methods and models and the need for new research directions.

Sequence Conservation, Radial Distance and Packing Density in Spherical Viral Capsids

The conservation level of a residue is a useful measure about the importance of that residue in protein structure and function. Much information about sequence conservation comes from aligning homologous sequences. Profiles showing the variation of the conservation level along the sequence are usually interpreted in evolutionary terms and dictated by site similarities of a proper set of homologous sequences. Here, we report that, of the viral icosahedral capsids, the sequence conservation profile can be determined by variations in the distances between residues and the centroid of the capsid – with a direct inverse proportionality between the conservation level and the centroid distance – as well as by the spatial variations in local packing density. Examining both the centroid and the packing density models against a dataset of 51 crystal structures of nonhomologous icosahedral capsids, we found that many global patterns and minor features derived from the viral structures are consistent with those present in the sequence conservation profiles. The quantitative link between the level of conservation and structural features like centroid-distance or packing density allows us to look at residue conservation from a structural viewpoint as well as from an evolutionary viewpoint.

Structure-Encoded Global Motions and Their Role in Mediating Protein-Substrate Interactions

Recent structure-based computational studies suggest that, in contrast to the classical description of equilibrium fluctuations as wigglings and jigglings, proteins have access to well-defined spectra of collective motions, called intrinsic dynamics, encoded by their structure under native state conditions. In particular, the global modes of motions (at the low frequency end of the spectrum) are shown by multiple studies to be highly robust to minor differences in the structure or to detailed interactions at the atomic level. These modes, encoded by the overall fold, usually define the mechanisms of interactions with substrates. They can be estimated by low-resolution models such as the elastic network models (ENMs) exclusively based on interresidue contact topology. The ability of ENMs to efficiently assess the global motions intrinsically favored by the overall fold as well as the relevance of these predictions to the dominant changes in structure experimentally observed for a given protein in the presence of different substrates suggest that the intrinsic dynamics plays a role in mediating protein-substrate interactions. These observations underscore the functional significance of structure-encoded dynamics, or the importance of the predisposition to favor functional global modes in the evolutionary selection of structures.

(PS)2: protein structure prediction server version 3.0

Protein complexes are involved in many biological processes. Examining coupling between subunits of a complex would be useful to understand the molecular basis of protein function. Here, our updated (PS)² web server predicts the three-dimensional structures of protein complexes based on comparative modeling; furthermore, this server examines the coupling between subunits of the predicted complex by combining structural and evolutionary considerations. The predicted complex structure could be indicated and visualized by Java-based 3D graphics viewers and the structural and evolutionary profiles are shown and compared chain-by-chain. For each subunit, considerations with or without the packing contribution of other subunits cause the differences in similarities between structural and evolutionary profiles, and these differences imply which form, complex or monomeric, is preferred in the biological condition for the subunit. We believe that the (PS)² server would be a useful tool for biologists who are interested not only in the structures of protein complexes but also in the coupling between subunits of the complexes. The (PS)² is freely available at http://ps2v3.life.nctu.edu.tw/.

Too packed to change: side-chain packing and site-specific substitution rates in protein evolution

In protein evolution, due to functional and biophysical constraints, the rates of amino acid substitution differ from site to site. Among the best predictors of site-specific rates are solvent accessibility and packing density. The packing density measure that best correlates with rates is the weighted contact number (WCN), the sum of inverse square distances between a site’s C_α and the C_α of the other sites. According to a mechanistic stress model proposed recently, rates are determined by packing because mutating packed sites stresses and destabilizes the protein’s active conformation. While WCN is a measure of C_α packing, mutations replace side chains. Here, we consider whether a site’s evolutionary divergence is constrained by main-chain packing or side-chain packing. To address this issue, we extended the stress theory to model side chains explicitly. The theory predicts that rates should depend solely on side-chain contact density. We tested this prediction on a data set of structurally and functionally diverse monomeric enzymes. We compared side-chain contact density with main-chain contact density measures and with relative solvent accessibility (RSA). We found that side-chain contact density is the best predictor of rate variation among sites (it explains 39.2% of the variation). Moreover, the independent contribution of main-chain contact density measures and RSA are negligible. Thus, as predicted by the stress theory, site-specific evolutionary rates are determined by side-chain packing.

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.

Predicting evolutionary site variability from structure in viral proteins: buriedness, packing, flexibility, and design

Several recent works have shown that protein structure can predict site-specific evolutionary sequence variation. In particular, sites that are buried and/or have many contacts with other sites in a structure have been shown to evolve more slowly, on average, than surface sites with few contacts. Here, we present a comprehensive study of the extent to which numerous structural properties can predict sequence variation. The quantities we considered include buriedness (as measured by relative solvent accessibility), packing density (as measured by contact number), structural flexibility (as measured by B factors, root-mean-square fluctuations, and variation in dihedral angles), and variability in designed structures. We obtained structural flexibility measures both from molecular dynamics simulations performed on nine non-homologous viral protein structures and from variation in homologous variants of those proteins, where they were available. We obtained measures of variability in designed structures from flexible-backbone design in the Rosetta software. We found that most of the structural properties correlate with site variation in the majority of structures, though the correlations are generally weak (correlation coefficients of 0.1-0.4). Moreover, we found that buriedness and packing density were better predictors of evolutionary variation than structural flexibility. Finally, variability in designed structures was a weaker predictor of evolutionary variability than buriedness or packing density, but it was comparable in its predictive power to the best structural flexibility measures. We conclude that simple measures of buriedness and packing density are better predictors of evolutionary variation than the more complicated predictors obtained from dynamic simulations, ensembles of homologous structures, or computational protein design.