Evolutionary divergence of protein structure: The linearly forced elastic network model

Substitution Models of Protein Evolution with Selection on Enzymatic Activity

Substitution models of evolution are necessary for diverse evolutionary analyses including phylogenetic tree and ancestral sequence reconstructions. At the protein level, empirical substitution models are traditionally used due to their simplicity, but they ignore the variability of substitution patterns among protein sites. Next, in order to improve the realism of the modeling of protein evolution, a series of structurally constrained substitution models were presented, but still they usually ignore constraints on the protein activity. Here, we present a substitution model of protein evolution with selection on both protein structure and enzymatic activity, and that can be applied to phylogenetics. In particular, the model considers the binding affinity of the enzyme-substrate complex as well as structural constraints that include the flexibility of structural flaps, hydrogen bonds, amino acids backbone radius of gyration, and solvent-accessible surface area that are quantified through molecular dynamics simulations. We applied the model to the HIV-1 protease and evaluated it by phylogenetic likelihood in comparison with the best-fitting empirical substitution model and a structurally constrained substitution model that ignores the enzymatic activity. We found that accounting for selection on the protein activity improves the fitting of the modeled functional regions with the real observations, especially in data with high molecular identity, which recommends considering constraints on the protein activity in the development of substitution models of evolution.

Experimental and Bioinformatic Insights into the Effects of Epileptogenic Variants on the Function and Trafficking of the GABA Transporter GAT-1

In this article, we identified a novel epileptogenic variant (G307R) of the gene SLC6A1, which encodes the GABA transporter GAT-1. Our main goal was to investigate the pathogenic mechanisms of this variant, located near the neurotransmitter permeation pathway, and compare it with other variants located either in the permeation pathway or close to the lipid bilayer. The mutants G307R and A334P, close to the gates of the transporter, could be glycosylated with variable efficiency and reached the membrane, albeit inactive. Mutants located in the center of the permeation pathway (G297R) or close to the lipid bilayer (A128V, G550R) were retained in the endoplasmic reticulum. Applying an Elastic Network Model, to these and to other previously characterized variants, we found that G307R and A334P significantly perturb the structure and dynamics of the intracellular gate, which can explain their reduced activity, while for A228V and G362R, the reduced translocation to the membrane quantitatively accounts for the reduced activity. The addition of a chemical chaperone (4-phenylbutyric acid, PBA), which improves protein folding, increased the activity of GAT-1WT, as well as most of the assayed variants, including G307R, suggesting that PBA might also assist the conformational changes occurring during the alternative access transport cycle.

AlphaFold2 models indicate that protein sequence determines both structure and dynamics

AlphaFold 2 (AF2) has placed Molecular Biology in a new era where we can visualize, analyze and interpret the structures and functions of all proteins solely from their primary sequences. We performed AF2 structure predictions for various protein systems, including globular proteins, a multi-domain protein, an intrinsically disordered protein (IDP), a randomized protein, two larger proteins (> 1000 AA), a heterodimer and a homodimer protein complex. Our results show that along with the three dimensional (3D) structures, AF2 also decodes protein sequences into residue flexibilities via both the predicted local distance difference test (pLDDT) scores of the models, and the predicted aligned error (PAE) maps. We show that PAE maps from AF2 are correlated with the distance variation (DV) matrices from molecular dynamics (MD) simulations, which reveals that the PAE maps can predict the dynamical nature of protein residues. Here, we introduce the AF2-scores, which are simply derived from pLDDT scores and are in the range of [0, 1]. We found that for most protein models, including large proteins and protein complexes, the AF2-scores are highly correlated with the root mean square fluctuations (RMSF) calculated from MD simulations. However, for an IDP and a randomized protein, the AF2-scores do not correlate with the RMSF from MD, especially for the IDP. Our results indicate that the protein structures predicted by AF2 also convey information of the residue flexibility, i.e., protein dynamics.

Prestrain-induced contraction in one-dimensional random elastic chains

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. Motivated by this observation, we here consider a minimal model in one dimension to set the stage for understanding the response of such networks as a function of the prestrain. To this end we consider a chain [one-dimensional (1D) network] of elastic springs upon which a random, zero mean, finite variance prestrain is imposed. Numerical simulations and analytical predictions quantify the magnitude of the contraction as a function of the variance of the prestrain, and show that the chain always shrinks. To test these predictions, we vary the topology of the chain, consider more complex connectivity and show that our results are relatively robust to these changes.

Evolutionary coupling range varies widely among enzymes depending on selection pressure

Recent studies proposed that enzyme-active sites induce evolutionary constraints at long distances. The physical origin of such long-range evolutionary coupling is unknown. Here, I use a recent biophysical model of evolution to study the relationship between physical and evolutionary couplings on a diverse data set of monomeric enzymes. I show that evolutionary coupling is not universally long-range. Rather, range varies widely among enzymes, from 2 to 20 Å. Furthermore, the evolutionary coupling range of an enzyme does not inform on the underlying physical coupling, which is short range for all enzymes. Rather, evolutionary coupling range is determined by functional selection pressure.

The variation among sites of protein structure divergence is shaped by mutation and scaled by selection

Protein structures do not evolve uniformly, but the degree of structure divergence varies among sites. The resulting site-dependent structure divergence patterns emerge from a process that involves mutation and selection, which may both, in principle, influence the emergent pattern. In contrast with sequence divergence patterns, which are known to be mainly determined by selection, the relative contributions of mutation and selection to structure divergence patterns is unclear. Here, studying 6 protein families with a mechanistic biophysical model of protein evolution, we untangle the effects of mutation and selection. We found that even in the absence of selection, structure divergence varies from site to site because the mutational sensitivity is not uniform. Selection scales the profile, increasing its amplitude, without changing its shape. This scaling effect follows from the similarity between mutational sensitivity and sequence variability profiles.

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The degree of evolutionary divergence of protein structures varies among sites.

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A Mutation-Selection model (MSM) of protein structure evolution with selection for stability is developed.

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Even in the case of no selection, the sensitivity of the structure to random mutations varies among sites. Selection amplifies this variation but it does not affect its shape.

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This scaling effect of selection follows from the similarity between the selection-independent mutational sensitivity and the selection-dependent sequence divergence, the two contributions that are combined to produce the observed structural divergence profile.

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.

Fast computational mutation-response scanning of proteins

Studying the effect of perturbations on protein structure is a basic approach in protein research. Important problems, such as predicting pathological mutations and understanding patterns of structural evolution, have been addressed by computational simulations that model mutations using forces and predict the resulting deformations. In single mutation-response scanning simulations, a sensitivity matrix is obtained by averaging deformations over point mutations. In double mutation-response scanning simulations, a compensation matrix is obtained by minimizing deformations over pairs of mutations. These very useful simulation-based methods may be too slow to deal with large proteins, protein complexes, or large protein databases. To address this issue, I derived analytical closed formulas to calculate the sensitivity and compensation matrices directly, without simulations. Here, I present these derivations and show that the resulting analytical methods are much faster than their simulation counterparts.

HOPMA: Boosting Protein Functional Dynamics with Colored Contact Maps

In light of the recent very rapid progress in protein structure prediction, accessing the multitude of functional protein states is becoming more central than ever before. Indeed, proteins are flexible macromolecules, and they often perform their function by switching between different conformations. However, high-resolution experimental techniques such as X-ray crystallography and cryogenic electron microscopy can catch relatively few protein functional states. Many others are only accessible under physiological conditions in solution. Therefore, there is a pressing need to fill this gap with computational approaches. We present HOPMA, a novel method to predict protein functional states and transitions by using a modified elastic network model. The method exploits patterns in a protein contact map, taking its 3D structure as input, and excludes some disconnected patches from the elastic network. Combined with nonlinear normal mode analysis, this strategy boosts the protein conformational space exploration, especially when the input structure is highly constrained, as we demonstrate on a set of more than 400 transitions. Our results let us envision the discovery of new functional conformations, which were unreachable previously, starting from the experimentally known protein structures. The method is computationally efficient and available at https://github.com/elolaine/HOPMA and https://team.inria.fr/nano-d/software/nolb-normal-modes.

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.

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.

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.

A Generative Angular Model of Protein Structure Evolution

Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a generative, evolutionary model of protein structure and sequence that is valid on a local length scale. The model concerns the local dependencies between sequence and structure evolution in a pair of homologous proteins. The evolutionary trajectory between the two structures in the protein pair is treated as a random walk in dihedral angle space, which is modeled using a novel angular diffusion process on the two-dimensional torus. Coupling sequence and structure evolution in our model allows for modeling both “smooth” conformational changes and “catastrophic” conformational jumps, conditioned on the amino acid changes. The model has interpretable parameters and is comparatively more realistic than previous stochastic models, providing new insights into the relationship between sequence and structure evolution. For example, using the trained model we were able to identify an apparent sequence–structure evolutionary motif present in a large number of homologous protein pairs. The generative nature of our model enables us to evaluate its validity and its ability to simulate aspects of protein evolution conditioned on an amino acid sequence, a related amino acid sequence, a related structure or any combination thereof.

In silico identification of rescue sites by double force scanning

Motivation

A deleterious amino acid change in a protein can be compensated by a second-site rescue mutation. These compensatory mechanisms can be mimicked by drugs. In particular, the location of rescue mutations can be used to identify protein regions that can be targeted by small molecules to reactivate a damaged mutant.

Results

We present the first general computational method to detect rescue sites. By mimicking the effect of mutations through the application of forces, the double force scanning (DFS) method identifies the second-site residues that make the protein structure most resilient to the effect of pathogenic mutations. We tested DFS predictions against two datasets containing experimentally validated and putative evolutionary-related rescue sites. A remarkably good agreement was found between predictions and experimental data. Indeed, almost half of the rescue sites in p53 was correctly predicted by DFS, with 65% of remaining sites in contact with DFS predictions. Similar results were found for other proteins in the evolutionary dataset.

Availability and implementation

The DFS code is available under GPL at https://fornililab.github.io/dfs/.

Supplementary information

Supplementary data are available at Bioinformatics online.

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

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

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.

Conformational dynamics of nonsynonymous variants at protein interfaces reveals disease association

Recent studies have shown that the protein interface sites between individual monomeric units in biological assemblies are enriched in disease-associated non-synonymous single nucleotide variants (nsSNVs). To elucidate the mechanistic underpinning of this observation, we investigated the conformational dynamic properties of protein interface sites through a site-specific structural dynamic flexibility metric (dfi) for 333 multimeric protein assemblies. dfi measures the dynamic resilience of a single residue to perturbations that occurred in the rest of the protein structure and identifies sites contributing the most to functionally critical dynamics. Analysis of dfi profiles of over a thousand positions harboring variation revealed that amino acid residues at interfaces have lower average dfi (31%) than those present at non-interfaces (50%), which means that protein interfaces have less dynamic flexibility. Interestingly, interface sites with disease-associated nsSNVs have significantly lower average dfi (23%) as compared to those of neutral nsSNVs (42%), which directly relates structural dynamics to functional importance. We found that less conserved interface positions show much lower dfi for disease nsSNVs as compared to neutral nsSNVs. In this case, dfi is better as compared to the accessible surface area metric, which is based on the static protein structure. Overall, our proteome-wide conformational dynamic analysis indicates that certain interface sites play a critical role in functionally related dynamics (i.e., those with low dfi values), therefore mutations at those sites are more likely to be associated with disease.

Evolution of oligomeric state through allosteric pathways that mimic ligand binding

Evolution and design of protein complexes are almost always viewed through the lens of amino acid mutations at protein interfaces. We showed previously that residues not involved in the physical interaction between proteins make important contributions to oligomerization by acting indirectly or allosterically. In this work, we sought to investigate the mechanism by which allosteric mutations act, using the example of the PyrR family of pyrimidine operon attenuators. In this family, a perfectly sequence-conserved helix that forms a tetrameric interface is exposed as solvent-accessible surface in dimeric orthologs. This means that mutations must be acting from a distance to destabilize the interface. We identified 11 key mutations controlling oligomeric state, all distant from the interfaces and outside ligand-binding pockets. Finally, we show that the key mutations introduce conformational changes equivalent to the conformational shift between the free versus nucleotide-bound conformations of the proteins.

Comparing the intrinsic dynamics of multiple protein structures using elastic network models

BACKGROUND

Elastic network models (ENMs) are based on the simple idea that a protein can be described as a set of particles connected by springs, which can then be used to describe its intrinsic flexibility using, for example, normal mode analysis. Since the introduction of the first ENM by Monique Tirion in 1996, several variants using coarser protein models have been proposed and their reliability for the description of protein intrinsic dynamics has been widely demonstrated. Lately an increasing number of studies have focused on the meaning of slow dynamics for protein function and its potential conservation through evolution. This leads naturally to comparisons of the intrinsic dynamics of multiple protein structures with varying levels of similarity.

SCOPE OF REVIEW

We describe computational strategies for calculating and comparing intrinsic dynamics of multiple proteins using elastic network models, as well as a selection of examples from the recent literature.

MAJOR CONCLUSIONS

The increasing interest for comparing dynamics across protein structures with various levels of similarity, has led to the establishment and validation of reliable computational strategies using ENMs. Comparing dynamics has been shown to be a viable way for gaining greater understanding for the mechanisms employed by proteins for their function. Choices of ENM parameters, structure alignment or similarity measures will likely influence the interpretation of the comparative analysis of protein motion.

GENERAL SIGNIFICANCE

Understanding the relation between protein function and dynamics is relevant to the fundamental understanding of protein structure-dynamics-function relationship. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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

Background

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

Results

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

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

Conclusions

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

Characterizing conformation changes in proteins through the torsional elastic response

The relationship between functional conformation changes and thermal dynamics of proteins is investigated with the help of the torsional network model (TNM), an elastic network model in torsion angle space that we recently introduced. We propose and test a null-model of "random" conformation changes that assumes that the contributions of normal modes to conformation changes are proportional to their contributions to thermal fluctuations. Deviations from this null model are generally small. When they are large and significant, they consist in conformation changes that are represented by very few low frequency normal modes and overcome small energy barriers. We interpret these features as the result of natural selection favoring the intrinsic protein dynamics consistent with functional conformation changes. These "selected" conformation changes are more frequently associated to ligand binding, and in particular phosphorylation, than to pairs of conformations with the same ligands. This deep relationship between the thermal dynamics of a protein, represented by its normal modes, and its functional dynamics can reconcile in a unique framework the two models of conformation changes, conformational selection and induced fit. The program TNM that computes torsional normal modes and analyzes conformation changes is available upon request. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Structural dynamics flexibility informs function and evolution at a proteome scale

Protein structures are dynamic entities with a myriad of atomic fluctuations, side-chain rotations, and collective domain movements. Although the importance of these dynamics to proper functioning of proteins is emerging in the studies of many protein families, there is a lack of broad evidence for the critical role of protein dynamics in shaping the biological functions of a substantial fraction of residues for a large number of proteins in the human proteome. Here, we propose a novel dynamic flexibility index (dfi) to quantify the dynamic properties of individual residues in any protein and use it to assess the importance of protein dynamics in 100 human proteins. Our analyses involving functionally critical positions, disease-associated and putatively neutral population variations, and the rate of interspecific substitutions per residue produce concordant patterns at a proteome scale. They establish that the preservation of dynamic properties of residues in a protein structure is critical for maintaining the protein/biological function. Therefore, structural dynamics needs to become a major component of the analysis of protein function and evolution. Such analyses will be facilitated by the dfi, which will also enable the integrative use of structural dynamics with evolutionary conservation in genomic medicine as well as functional genomics investigations.

Why are the low-energy protein normal modes evolutionarily conserved?

Proteins fluctuate, and such fluctuations are functionally important. As with any functionally relevant trait, it is interesting to study how fluctuations change during evolution. In contrast with sequence and structure, the study of the evolution of protein motions is much more recent. Yet, it has been shown that the overall fluctuation pattern is evolutionarily conserved. Moreover, the lowest-energy normal modes have been found to be the most conserved. The reasons behind such a differential conservation have not been explicitly studied. There are two limiting explanations. A “biological” explanation is that because such modes are functional, there is natural selection pressure against their variation. An alternative “physical” explanation is that the lowest-energy normal modes may be more conserved because they are just more robust with respect to random mutations. To investigate this issue, I studied a set of globin-like proteins using a perturbed elastic network model (ENM) of the effect of random mutations on normal modes. I show that the conservation predicted by the model is in excellent agreement with observations. These results support the physical explanation: the lowest normal modes are more conserved because they are more robust.

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

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

Automating the search of molecular motor templates by evolutionary methods

Biological molecular motors are nanoscale devices capable of transforming chemical energy into mechanical work, which are being researched in many scientific disciplines. From a computational point of view, the characteristics and dynamics of these motors are studied at multiple time scales, ranging from very detailed and complex molecular dynamics simulations spanning a few microseconds, to extremely simple and coarse-grained theoretical models of their working cycles. However, this research is performed only in the (relatively few) instances known from molecular biology. In this work, results from elastic network analysis and behaviour-finding methods are applied to explore a subset of the configuration space of template molecular structures that are able to transform chemical energy into directed movement, for a fixed instance of working cycle. While using methods based on elastic networks limits the scope of our results, it enables the implementation of computationally lightweight methods, in a way that evolutionary search techniques can be applied to discover novel molecular motor templates. The results show that molecular motion can be attained from a variety of structural configurations, when a functional working cycle is provided. Additionally, these methods enable a new computational way to test hypotheses about molecular motors.

Torsional network model: normal modes in torsion angle space better correlate with conformation changes in proteins

We introduce the torsional network model (TNM), an elastic network model whose degrees of freedom are the torsion angles of the protein backbone. Normal modes of the TNM displace backbone atoms including C(β) maintaining their covalent geometry. For many proteins, low frequency TNM modes are localized in torsion space yet collective in Cartesian space, reminiscent of hinge motions. A smaller number of TNM modes than anisotropic network model modes are enough to represent experimentally observed conformation changes. We observed significant correlation between the contribution of each normal mode to equilibrium fluctuations and to conformation changes, and defined the excess correlation with respect to a simple neutral model. The stronger this excess correlation, the lower the predicted free energy barrier of the conformation change and the fewer modes contribute to the change.

A perturbative view of protein structural variation

It was recently found that the lowest-energy collective normal modes dominate the evolutionary divergence of protein structures. This was attributed to a presumed functional importance of such motions, i.e., to natural selection. In contrast to this selectionist explanation, we proposed that the observed behavior could be just the expected physical response of proteins to random mutations. This proposal was based on the success of a linearly forced elastic network model (LFENM) of mutational effects on structure to account for the observed pattern of structural divergence. Here, to further test the mutational explanation and the LFENM, we analyze the structural differences observed not only in homologous (globin-like) proteins but also in unselected experimentally engineered myoglobin mutants and in wild-type variants subject to other perturbations such as ligand-binding and pH changes. We show that the lowest normal modes dominate structural change in all the cases considered and that the LFENM reproduces this behavior quantitatively. The collective nature of the lowest normal modes results in global conformational changes that depend little on the exact nature or location of the perturbation. Significantly, the evolutionarily conserved structural core matches the regions observed to be more robust with respect to mutations, so that the core would be more conserved even under unselected random mutations. In a word, the observed patterns of structural variation can be seen as the natural response of proteins to perturbations and can be adequately modeled using the LFENM, which serves as a common framework to relate a priori different phenomena.