Improved prediction of site-rates from structure with averaging across homologs

Variation in mutation rates at sites in proteins can largely be understood by the constraint that proteins must fold into stable structures. Models that calculate site-specific rates based on protein structure and a thermodynamic stability model have shown a significant but modest ability to predict empirical site-specific rates calculated from sequence. Models that use detailed atomistic models of protein energetics do not outperform simpler approaches using packing density. We demonstrate that a fundamental reason for this is that empirical site-specific rates are the result of the average effect of many different microenvironments in a phylogeny. By analyzing the results of evolutionary dynamics simulations, we show how averaging site-specific rates across many extant protein structures can lead to correct recovery of site-rate prediction. This result is also demonstrated in natural protein sequences and experimental structures. Using predicted structures, we demonstrate that atomistic models can improve upon contact density metrics in predicting site-specific rates from a structure. The results give fundamental insights into the factors governing the distribution of site-specific rates in protein families.

Learning from prepandemic data to forecast viral escape

Effective pandemic preparedness relies on anticipating viral mutations that are able to evade host immune responses to facilitate vaccine and therapeutic design. However, current strategies for viral evolution prediction are not available early in a pandemic-experimental approaches require host polyclonal antibodies to test against1-16, and existing computational methods draw heavily from current strain prevalence to make reliable predictions of variants of concern17-19. To address this, we developed EVEscape, a generalizable modular framework that combines fitness predictions from a deep learning model of historical sequences with biophysical and structural information. EVEscape quantifies the viral escape potential of mutations at scale and has the advantage of being applicable before surveillance sequencing, experimental scans or three-dimensional structures of antibody complexes are available. We demonstrate that EVEscape, trained on sequences available before 2020, is as accurate as high-throughput experimental scans at anticipating pandemic variation for SARS-CoV-2 and is generalizable to other viruses including influenza, HIV and understudied viruses with pandemic potential such as Lassa and Nipah. We provide continually revised escape scores for all current strains of SARS-CoV-2 and predict probable further mutations to forecast emerging strains as a tool for continuing vaccine development ( evescape.org ).

Predicting Anticancer Drug Resistance Mediated by Mutations

Cancer drug resistance presents a challenge for precision medicine. Drug-resistant mutations are always emerging. In this study, we explored the relationship between drug-resistant mutations and drug resistance from the perspective of protein structure. By combining data from previously identified drug-resistant mutations and information of protein structure and function, we used machine learning-based methods to build models to predict cancer drug resistance mutations. The performance of our combined model achieved an accuracy of 86%, a Matthews correlation coefficient score of 0.57, and an F1 score of 0.66. We have constructed a fast, reliable method that predicts and investigates cancer drug resistance in a protein structure. Nonetheless, more information is needed concerning drug resistance and, in particular, clarification is needed about the relationships between the drug and the drug resistance mutations in proteins. Highly accurate predictions regarding drug resistance mutations can be helpful for developing new strategies with personalized cancer treatments. Our novel concept, which combines protein structure information, has the potential to elucidate physiological mechanisms of cancer drug resistance.

Role of juvenile hormone receptor Methoprene-tolerant 1 in silkworm larval brain development and domestication

The insect brain is the central part of the neurosecretory system, which controls morphology, physiology, and behavior during the insect's lifecycle. Lepidoptera are holometabolous insects, and their brains develop during the larval period and metamorphosis into the adult form. As the only fully domesticated insect, the Lepidoptera silkworm Bombyx mori experienced changes in larval brain morphology and certain behaviors during the domestication process. Hormonal regulation in insects is a key factor in multiple processes. However, how juvenile hormone (JH) signals regulate brain development in Lepidoptera species, especially in the larval stage, remains elusive. We recently identified the JH receptor Methoprene tolerant 1 ( Met1) as a putative domestication gene. How artificial selection on Met1 impacts brain and behavioral domestication is another important issue addressing Darwin's theory on domestication. Here, CRISPR/Cas9-mediated knockout of Bombyx Met1 caused developmental retardation in the brain, unlike precocious pupation of the cuticle. At the whole transcriptome level, the ecdysteroid (20-hydroxyecdysone, 20E) signaling and downstream pathways were overactivated in the mutant cuticle but not in the brain. Pathways related to cell proliferation and specialization processes, such as extracellular matrix (ECM)-receptor interaction and tyrosine metabolism pathways, were suppressed in the brain. Molecular evolutionary analysis and in vitro assay identified an amino acid replacement located in a novel motif under positive selection in B. mori, which decreased transcriptional binding activity. The B. mori MET1 protein showed a changed structure and dynamic features, as well as a weakened co-expression gene network, compared with B. mandarina. Based on comparative transcriptomic analyses, we proposed a pathway downstream of JH signaling (i.e., tyrosine metabolism pathway) that likely contributed to silkworm larval brain development and domestication and highlighted the importance of the biogenic amine system in larval evolution during silkworm domestication.

Parameterizing elastic network models to capture the dynamics of proteins

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

A probabilistic model for indel evolution: differentiating insertions from deletions

Insertions and deletions (indels) are common molecular evolutionary events. However, probabilistic models for indel evolution are under-developed due to their computational complexity. Here, we introduce several improvements to indel modeling: 1) While previous models for indel evolution assumed that the rates and length distributions of insertions and deletions are equal, here we propose a richer model that explicitly distinguishes between the two; 2) we introduce numerous summary statistics that allow approximate Bayesian computation-based parameter estimation; 3) we develop a method to correct for biases introduced by alignment programs, when inferring indel parameters from empirical data sets; and 4) using a model-selection scheme, we test whether the richer model better fits biological data compared with the simpler model. Our analyses suggest that both our inference scheme and the model-selection procedure achieve high accuracy on simulated data. We further demonstrate that our proposed richer model better fits a large number of empirical data sets and that, for the majority of these data sets, the deletion rate is higher than the insertion rate.

The structure-based cancer-related single amino acid variation prediction

Single amino acid variation (SAV) is an amino acid substitution of the protein sequence that can potentially influence the entire protein structure or function, as well as its binding affinity. Protein destabilization is related to diseases, including several cancers, although using traditional experiments to clarify the relationship between SAVs and cancer uses much time and resources. Some SAV prediction methods use computational approaches, with most predicting SAV-induced changes in protein stability. In this investigation, all SAV characteristics generated from protein sequences, structures and the microenvironment were converted into feature vectors and fed into an integrated predicting system using a support vector machine and genetic algorithm. Critical features were used to estimate the relationship between their properties and cancers caused by SAVs. We describe how we developed a prediction system based on protein sequences and structure that is capable of distinguishing if the SAV is related to cancer or not. The five-fold cross-validation performance of our system is 89.73% for the accuracy, 0.74 for the Matthews correlation coefficient, and 0.81 for the F1 score. We have built an online prediction server, CanSavPre ( http://bioinfo.cmu.edu.tw/CanSavPre/ ), which is expected to become a useful, practical tool for cancer research and precision medicine.

Estimating Change in Foldability Due to Multipoint Deletions in Protein Structures

Insertions/deletions of amino acids in the protein backbone potentially result in altered structural/functional specifications. They can either contribute positively to the evolutionary process or can result in disease conditions. Despite being the second most prevalent form of protein modification, there are no databases or computational frameworks that delineate harmful multipoint deletions (MPD) from beneficial ones. We introduce a positive unlabeled learning-based prediction framework (PROFOUND) that utilizes fold-level attributes, environment-specific properties, and deletion site-specific properties to predict the change in foldability arising from such MPDs, both in the non-loop and loop regions of protein structures. In the absence of any protein structure dataset to study MPDs, we introduce a dataset with 153 MPD instances that lead to native-like folded structures and 7650 unlabeled MPD instances whose effect on the foldability of the corresponding proteins is unknown. PROFOUND on 10-fold cross-validation on our newly introduced dataset reports a recall of 82.2% (86.6%) and a fall out rate (FR) of 14.2% (20.6%), corresponding to MPDs in the protein loop (non-loop) region. The low FR suggests that the foldability in proteins subject to MPDs is not random and necessitates unique specifications of the deleted region. In addition, we find that additional evolutionary attributes contribute to higher recall and lower FR. The first of a kind foldability prediction system owing to MPD instances and the newly introduced dataset will potentially aid in novel protein engineering endeavors.

Weighted-persistent-homology-based machine learning for RNA flexibility analysis

With the great significance of biomolecular flexibility in biomolecular dynamics and functional analysis, various experimental and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibility. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models have been proposed for flexibility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model has been proposed. By using the features from persistent homology, this model achieves a remarkable high Pearson correlation coefficient (PCC) in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH) to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a PCC of up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent improvement in performance by at least 10% is achieved in our current model.

Evolutionary couplings detect side-chain interactions

Patterns of amino acid covariation in large protein sequence alignments can inform the prediction of de novo protein structures, binding interfaces, and mutational effects. While algorithms that detect these so-called evolutionary couplings between residues have proven useful for practical applications, less is known about how and why these methods perform so well, and what insights into biological processes can be gained from their application. Evolutionary coupling algorithms are commonly benchmarked by comparison to true structural contacts derived from solved protein structures. However, the methods used to determine true structural contacts are not standardized and different definitions of structural contacts may have important consequences for interpreting the results from evolutionary coupling analyses and understanding their overall utility. Here, we show that evolutionary coupling analyses are significantly more likely to identify structural contacts between side-chain atoms than between backbone atoms. We use both simulations and empirical analyses to highlight that purely backbone-based definitions of true residue–residue contacts (i.e., based on the distance between Cα atoms) may underestimate the accuracy of evolutionary coupling algorithms by as much as 40% and that a commonly used reference point (Cβ atoms) underestimates the accuracy by 10–15%. These findings show that co-evolutionary outcomes differ according to which atoms participate in residue–residue interactions and suggest that accounting for different interaction types may lead to further improvements to contact-prediction methods.

Analyzing Change in Protein Stability Associated with Single Point Deletions in a Newly Defined Protein Structure Database

Protein backbone alternation due to insertion/deletion or mutation operation often results in a change of fundamental biophysical properties of proteins. The proposed work intends to encode the protein stability changes associated with single point deletions (SPDs) of amino acids in proteins. The encoding will help in the primary screening of detrimental backbone modifications before opting for expensive in vitro experimentations. In the absence of any benchmark database documenting SPDs, we curate a data set containing SPDs that lead to both folded conformations and unfolded state. We differentiate these SPD instances with the help of simple structural and physicochemical features and eventually classify the foldability resulting out of SPDs using a Random Forest classifier and an Elliptic Envelope based outlier detector. Adhering to leave one out cross validation, the accuracy of the Random Forest classifier and the Elliptic Envelope is of 99.4% and 98.1%, respectively. The newly defined database and the delineation of SPD instances based on its resulting foldability provide a head start toward finding a solution to the given problem.

CSmetaPred: a consensus method for prediction of catalytic residues

Background

Knowledge of catalytic residues can play an essential role in elucidating mechanistic details of an enzyme. However, experimental identification of catalytic residues is a tedious and time-consuming task, which can be expedited by computational predictions. Despite significant development in active-site prediction methods, one of the remaining issues is ranked positions of putative catalytic residues among all ranked residues. In order to improve ranking of catalytic residues and their prediction accuracy, we have developed a meta-approach based method CSmetaPred. In this approach, residues are ranked based on the mean of normalized residue scores derived from four well-known catalytic residue predictors. The mean residue score of CSmetaPred is combined with predicted pocket information to improve prediction performance in meta-predictor, CSmetaPred_poc.

Results

Both meta-predictors are evaluated on two comprehensive benchmark datasets and three legacy datasets using Receiver Operating Characteristic (ROC) and Precision Recall (PR) curves. The visual and quantitative analysis of ROC and PR curves shows that meta-predictors outperform their constituent methods and CSmetaPred_poc is the best of evaluated methods. For instance, on CSAMAC dataset CSmetaPred_poc (CSmetaPred) achieves highest Mean Average Specificity (MAS), a scalar measure for ROC curve, of 0.97 (0.96). Importantly, median predicted rank of catalytic residues is the lowest (best) for CSmetaPred_poc. Considering residues ranked ≤20 classified as true positive in binary classification, CSmetaPred_poc achieves prediction accuracy of 0.94 on CSAMAC dataset. Moreover, on the same dataset CSmetaPred_poc predicts all catalytic residues within top 20 ranks for ~73% of enzymes. Furthermore, benchmarking of prediction on comparative modelled structures showed that models result in better prediction than only sequence based predictions. These analyses suggest that CSmetaPred_poc is able to rank putative catalytic residues at lower (better) ranked positions, which can facilitate and expedite their experimental characterization.

Conclusions

The benchmarking studies showed that employing meta-approach in combining residue-level scores derived from well-known catalytic residue predictors can improve prediction accuracy as well as provide improved ranked positions of known catalytic residues. Hence, such predictions can assist experimentalist to prioritize residues for mutational studies in their efforts to characterize catalytic residues. Both meta-predictors are available as webserver at: http://14.139.227.206/csmetapred/.

Electronic supplementary material

The online version of this article (10.1186/s12859-017-1987-z) contains supplementary material, which is available to authorized users.

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.

Gaussian network model can be enhanced by combining solvent accessibility in proteins

Gaussian network model (GNM), regarded as the simplest and most representative coarse-grained model, has been widely adopted to analyze and reveal protein dynamics and functions. Designing a variation of the classical GNM, by defining a new Kirchhoff matrix, is the way to improve the residue flexibility modeling. We combined information arising from local relative solvent accessibility (RSA) between two residues into the Kirchhoff matrix of the parameter-free GNM. The undetermined parameters in the new Kirchhoff matrix were estimated by using particle swarm optimization. The usage of RSA was motivated by the fact that our previous work using RSA based linear regression model resulted out higher prediction quality of the residue flexibility when compared with the classical GNM and the parameter free GNM. Computational experiments, conducted based on one training dataset, two independent datasets and one additional small set derived by molecular dynamics simulations, demonstrated that the average correlation coefficients of the proposed RSA based parameter-free GNM, called RpfGNM, were significantly increased when compared with the parameter-free GNM. Our empirical results indicated that a variation of the classical GNMs by combining other protein structural properties is an attractive way to improve the quality of flexibility modeling.

Improving prediction of helix-helix packing in membrane proteins using predicted contact numbers as restraints

One of the challenging problems in tertiary structure prediction of helical membrane proteins (HMPs) is the determination of rotation of α-helices around the helix normal. Incorrect prediction of helix rotations substantially disrupts native residue-residue contacts while inducing only a relatively small effect on the overall fold. We previously developed a method for predicting residue contact numbers (CNs), which measure the local packing density of residues within the protein tertiary structure. In this study, we tested the idea of incorporating predicted CNs as restraints to guide the sampling of helix rotation. For a benchmark set of 15 HMPs with simple to rather complicated folds, the average contact recovery (CR) of best-sampled models was improved for all targets, the likelihood of sampling models with CR greater than 20% was increased for 13 targets, and the average RMSD100 of best-sampled models was improved for 12 targets. This study demonstrated that explicit incorporation of CNs as restraints improves the prediction of helix-helix packing. Proteins 2017; 85:1212-1221. © 2017 Wiley Periodicals, Inc.

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.

Predicting Real-Valued Protein Residue Fluctuation Using FlexPred

The conventional view of a protein structure as static provides only a limited picture. There is increasing evidence that protein dynamics are often vital to protein function including interaction with partners such as other proteins, nucleic acids, and small molecules. Considering flexibility is also important in applications such as computational protein docking and protein design. While residue flexibility is partially indicated by experimental measures such as the B-factor from X-ray crystallography and ensemble fluctuation from nuclear magnetic resonance (NMR) spectroscopy as well as computational molecular dynamics (MD) simulation, these techniques are resource-intensive. In this chapter, we describe the web server and stand-alone version of FlexPred, which rapidly predicts absolute per-residue fluctuation from a three-dimensional protein structure. On a set of 592 nonredundant structures, comparing the fluctuations predicted by FlexPred to the observed fluctuations in MD simulations showed an average correlation coefficient of 0.669 and an average root mean square error of 1.07 Å. FlexPred is available at http://kiharalab.org/flexPred/ .

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)

Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions.

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.

Flexibility-rigidity index for protein-nucleic acid flexibility and fluctuation analysis

Protein-nucleic acid complexes are important for many cellular processes including the most essential functions such as transcription and translation. For many protein-nucleic acid complexes, flexibility of both macromolecules has been shown to be critical for specificity and/or function. The flexibility-rigidity index (FRI) has been proposed as an accurate and efficient approach for protein flexibility analysis. In this article, we introduce FRI for the flexibility analysis of protein-nucleic acid complexes. We demonstrate that a multiscale strategy, which incorporates multiple kernels to capture various length scales in biomolecular collective motions, is able to significantly improve the state of art in the flexibility analysis of protein-nucleic acid complexes. We take the advantage of the high accuracy and O(N) computational complexity of our multiscale FRI method to investigate the flexibility of ribosomal subunits, which are difficult to analyze by alternative approaches. An anisotropic FRI approach, which involves localized Hessian matrices, is utilized to study the translocation dynamics in an RNA polymerase.

Functional Sites Induce Long-Range Evolutionary Constraints in Enzymes

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

Adaptive BP-Dock: An Induced Fit Docking Approach for Full Receptor Flexibility

We present an induced fit docking approach called Adaptive BP-Dock that integrates perturbation response scanning (PRS) with the flexible docking protocol of RosettaLigand in an adaptive manner. We first perturb the binding pocket residues of a receptor and obtain a new conformation based on the residue response fluctuation profile using PRS. Next, we dock a ligand to this new conformation by RosettaLigand, where we repeat these steps for several iterations. We test this approach on several protein test sets including difficult unbound docking cases such as HIV-1 reverse transcriptase and HIV-1 protease. Adaptive BP-Dock results show better correlation with experimental binding affinities compared to other docking protocols. Overall, the results imply that Adaptive BP-Dock can easily capture binding induced conformational changes by simultaneous sampling of protein and ligand conformations. This can provide faster and efficient docking of novel targets for rational drug design.

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.

The conservation profile of a protein bears the imprint of the molecule that is evolutionarily coupled to the protein

The conservation profile of a protein is a curve of the conservation levels of amino acids along the sequence. Biologists are usually more interested in individual points on the curve (namely, the conserved amino acids) than the overall shape of the curve. Here, we show that the conservation curves of proteins bear the imprints of molecules that are evolutionarily coupled to the proteins. Our method is based on recent studies that a sequence conservation profile is quantitatively linked to its structural packing profile. We find that the conservation profiles of nucleic acid (NA) binding proteins are better correlated with the packing profiles of the protein-NA complexes than those of the proteins alone. This indicates that a nucleic acid binding protein evolves to accommodate the nucleic acid in such a way that the residues involved in binding have their conservation levels closely coupled with the specific nucleotides.

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.

(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.

Synthetic biology for the directed evolution of protein biocatalysts: navigating sequence space intelligently

The amino acid sequence of a protein affects both its structure and its function. Thus, the ability to modify the sequence, and hence the structure and activity, of individual proteins in a systematic way, opens up many opportunities, both scientifically and (as we focus on here) for exploitation in biocatalysis. Modern methods of synthetic biology, whereby increasingly large sequences of DNA can be synthesised de novo, allow an unprecedented ability to engineer proteins with novel functions. However, the number of possible proteins is far too large to test individually, so we need means for navigating the 'search space' of possible protein sequences efficiently and reliably in order to find desirable activities and other properties. Enzymologists distinguish binding (Kd) and catalytic (kcat) steps. In a similar way, judicious strategies have blended design (for binding, specificity and active site modelling) with the more empirical methods of classical directed evolution (DE) for improving kcat (where natural evolution rarely seeks the highest values), especially with regard to residues distant from the active site and where the functional linkages underpinning enzyme dynamics are both unknown and hard to predict. Epistasis (where the 'best' amino acid at one site depends on that or those at others) is a notable feature of directed evolution. The aim of this review is to highlight some of the approaches that are being developed to allow us to use directed evolution to improve enzyme properties, often dramatically. We note that directed evolution differs in a number of ways from natural evolution, including in particular the available mechanisms and the likely selection pressures. Thus, we stress the opportunities afforded by techniques that enable one to map sequence to (structure and) activity in silico, as an effective means of modelling and exploring protein landscapes. Because known landscapes may be assessed and reasoned about as a whole, simultaneously, this offers opportunities for protein improvement not readily available to natural evolution on rapid timescales. Intelligent landscape navigation, informed by sequence-activity relationships and coupled to the emerging methods of synthetic biology, offers scope for the development of novel biocatalysts that are both highly active and robust.

On the packing density of the unbound protein-protein interaction interface and its implications in dynamics

Background

Characterizing the interface residues will help shed light on protein-protein interactions, which are involved in many important biological processes. Many studies focus on characterizing sequence or structure features of protein interfaces, but there are few studies characterizing the dynamics of interfaces. Therefore, we would like to know whether there is any specific dynamics pattern in the protein-protein interaction interfaces. Thermal fluctuation is an important dynamical property for a residue, and could be quickly estimated by local packing density without large computation since studies have showen closely relationship between these two properties. Therefore, we divided surface of an unbound subunit (free protein subunits before they are involved in forming the protein complexes) into several separate regions, and compared their average thermal fluctuations of different regions in order to characterize the dynamics pattern in unbound protein-protein interaction interfaces.

Results

We used weighted contact numbers (WCN), a parameter-free method to quantify packing density, to estimate the thermal fluctuations of residues in the interfaces. By analyzing the WCN distributions of interfaces in unbound subunits from 1394 non-homologous protein complexes, we show that the residues in the central regions of interfaces have higher packing density (i.e. more rigid); on the other hand, residues surrounding the central regions have smaller packing density (i.e. more flexible). The distinct distributions of packing density, suggesting distinct thermal fluctuation, reveals specific dynamics pattern in the interface of unbound protein subunits.

Conclusions

We found general trend that the unbound protein-protein interaction interfaces consist of rigid residues in the central regions, which are surrounded by flexible residues. This finding suggests that the dynamics might be one of the important features for the formation of protein complexes.

Protein thermal stability enhancement by designing salt bridges: a combined computational and experimental study

Protein thermal stability is an important factor considered in medical and industrial applications. Many structural characteristics related to protein thermal stability have been elucidated, and increasing salt bridges is considered as one of the most efficient strategies to increase protein thermal stability. However, the accurate simulation of salt bridges remains difficult. In this study, a novel method for salt-bridge design was proposed based on the statistical analysis of 10,556 surface salt bridges on 6,493 X-ray protein structures. These salt bridges were first categorized based on pairing residues, secondary structure locations, and Cα–Cα distances. Pairing preferences generalized from statistical analysis were used to construct a salt-bridge pair index and utilized in a weighted electrostatic attraction model to find the effective pairings for designing salt bridges. The model was also coupled with B-factor, weighted contact number, relative solvent accessibility, and conservation prescreening to determine the residues appropriate for the thermal adaptive design of salt bridges. According to our method, eight putative salt-bridges were designed on a mesophilic β-glucosidase and 24 variants were constructed to verify the predictions. Six putative salt-bridges leaded to the increase of the enzyme thermal stability. A significant increase in melting temperature of 8.8, 4.8, 3.7, 1.3, 1.2, and 0.7°C of the putative salt-bridges N437K–D49, E96R–D28, E96K–D28, S440K–E70, T231K–D388, and Q277E–D282 was detected, respectively. Reversing the polarity of T231K–D388 to T231D–D388K resulted in a further increase in melting temperatures by 3.6°C, which may be caused by the transformation of an intra-subunit electrostatic interaction into an inter-subunit one depending on the local environment. The combination of the thermostable variants (N437K, E96R, T231D and D388K) generated a melting temperature increase of 15.7°C. Thus, this study demonstrated a novel method for the thermal adaptive design of salt bridges through inference of suitable positions and substitutions.

Wavelet transformed Gaussian network model

Accurate prediction of the Debye–Waller temperature factor of proteins is of significant importance in the study of protein dynamics and function. This work explores the utility of wavelets for improving the performance of Gaussian network model (GNM). We propose two wavelet transformed Gaussian network models (wtGNM), namely a scale-one wtGNM and a scale-two wtGNM. Based on a set of 113 protein structures, it shows that the mean correlation with experimental results for the scale-one wtGNM is 0.714 and that for the scale-two wtGNM is 0.738. In contrast, the mean correlation for the original GNM is 0.594. Therefore, the wtGNM is a potential algorithm for improving the GNM prediction of protein B-factors.

EXIA2: web server of accurate and rapid protein catalytic residue prediction

We propose a method (EXIA2) of catalytic residue prediction based on protein structure without needing homology information. The method is based on the special side chain orientation of catalytic residues. We found that the side chain of catalytic residues usually points to the center of the catalytic site. The special orientation is usually observed in catalytic residues but not in noncatalytic residues, which usually have random side chain orientation. The method is shown to be the most accurate catalytic residue prediction method currently when combined with PSI-Blast sequence conservation. It performs better than other competing methods on several benchmark datasets that include over 1,200 enzyme structures. The areas under the ROC curve (AUC) on these benchmark datasets are in the range from 0.934 to 0.968.

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

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

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

Background

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

Results

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

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

Conclusions

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

Sequence-based Gaussian network model for protein dynamics

Motivation: Gaussian network model (GNM) is widely adopted to analyze and understand protein dynamics, function and conformational changes. The existing GNM-based approaches require atomic coordinates of the corresponding protein and cannot be used when only the sequence is known.

Results: We report, first of its kind, GNM model that allows modeling using the sequence. Our linear regression-based, parameter-free, sequence-derived GNM (L-pfSeqGNM) uses contact maps predicted from the sequence and models local, in the sequence, contact neighborhoods with the linear regression. Empirical benchmarking shows relatively high correlations between the native and the predicted with L-pfSeqGNM B-factors and between the cross-correlations of residue fluctuations derived from the structure- and the sequence-based GNM models. Our results demonstrate that L-pfSeqGNM is an attractive platform to explore protein dynamics. In contrast to the highly used GNMs that require protein structures that number in thousands, our model can be used to study motions for the millions of the readily available sequences, which finds applications in modeling conformational changes, protein–protein interactions and protein functions.

Contact:zerozhua@126.com

Supplementary information:Supplementary data are available at Bioinformatics online.

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

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

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.

On the structural context and identification of enzyme catalytic residues

Enzymes play important roles in most of the biological processes. Although only a small fraction of residues are directly involved in catalytic reactions, these catalytic residues are the most crucial parts in enzymes. The study of the fundamental and unique features of catalytic residues benefits the understanding of enzyme functions and catalytic mechanisms. In this work, we analyze the structural context of catalytic residues based on theoretical and experimental structure flexibility. The results show that catalytic residues have distinct structural features and context. Their neighboring residues, whether sequence or structure neighbors within specific range, are usually structurally more rigid than those of noncatalytic residues. The structural context feature is combined with support vector machine to identify catalytic residues from enzyme structure. The prediction results are better or comparable to those of recent structure-based prediction methods.

Accurate prediction of protein catalytic residues by side chain orientation and residue contact density

Prediction of protein catalytic residues provides useful information for the studies of protein functions. Most of the existing methods combine both structure and sequence information but heavily rely on sequence conservation from multiple sequence alignments. The contribution of structure information is usually less than that of sequence conservation in existing methods. We found a novel structure feature, residue side chain orientation, which is the first structure-based feature that achieves prediction results comparable to that of evolutionary sequence conservation. We developed a structure-based method, Enzyme Catalytic residue SIde-chain Arrangement (EXIA), which is based on residue side chain orientations and backbone flexibility of protein structure. The prediction that uses EXIA outperforms existing structure-based features. The prediction quality of combing EXIA and sequence conservation exceeds that of the state-of-the-art prediction methods. EXIA is designed to predict catalytic residues from single protein structure without needing sequence or structure alignments. It provides invaluable information when there is no sufficient or reliable homology information for target protein. We found that catalytic residues have very special side chain orientation and designed the EXIA method based on the newly discovered feature. It was also found that EXIA performs well for a dataset of enzymes without any bounded ligand in their crystallographic structures.