Predicting protein stability changes upon mutation using a simple orientational potential.

MOTIVATION: Structure-based stability prediction upon mutation is crucial for protein engineering and design, and for understanding genetic diseases or drug resistance events. For this task, we adopted a simple residue-based orientational potential that considers only three backbone atoms, previously applied in protein modeling. Its application to stability prediction only requires parametrizing 12 amino acid-dependent weights using cross-validation strategies on a curated dataset in which we tried to reduce the mutations that belong to protein-protein or protein-ligand interfaces, extreme conditions and the alanine over-representation. RESULTS: Our method, called KORPM, accurately predicts mutational effects on an independent benchmark dataset, whether the wild-type or mutated structure is used as starting point. Compared with state-of-the-art methods on this balanced dataset, our approach obtained the lowest root mean square error (RMSE) and the highest correlation between predicted and experimental ΔΔG measures, as well as better receiver operating characteristics and precision-recall curves. Our method is almost anti-symmetric by construction, and it performs thus similarly for the direct and reverse mutations with the corresponding wild-type and mutated structures. Despite the strong limitations of the available experimental mutation data in terms of size, variability, and heterogeneity, we show competitive results with a simple sum of energy terms, which is more efficient and less prone to overfitting. AVAILABILITY AND IMPLEMENTATION: https://github.com/chaconlab/korpm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Local Normal Mode Analysis for Fast Loop Conformational Sampling.

We propose and validate a novel method to efficiently explore local protein loop conformations based on a new formalism for constrained normal mode analysis (NMA) in internal coordinates. The manifold of possible loop configurations imposed by the position and orientation of the fixed loop ends is reduced to an orthogonal set of motions (or modes) encoding concerted rotations of all the backbone dihedral angles. We validate the sampling power on a set of protein loops with highly variable experimental structures and demonstrate that our approach can efficiently explore the conformational space of closed loops. We also show an acceptable resemblance of the ensembles around equilibrium conformations generated by long molecular simulations and constrained NMA on a set of exposed and diverse loops. In comparison with other methods, the main advantage is the lack of restrictions on the number of dihedrals that can be altered simultaneously. Furthermore, the method is computationally efficient since it only requires the diagonalization of a tiny matrix, and the modes of motions are energetically contextualized by the elastic network model, which includes both the loop and the neighboring residues.

Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm.

Can Conformational Changes of Proteins Be Represented in Torsion Angle Space? A Study with Rescaled Ridge Regression.

Torsion angles are the natural degrees of freedom of protein structures. The ability to determine torsional variations corresponding to observed changes in Cartesian coordinates is highly valuable, notably to investigate the mechanisms of functional conformational changes or to develop computational models of protein dynamics. This issue is far from trivial in practice since the impact of modifying one torsion angle strongly depends on all other angles, and the compounding effects of small variations in bond lengths and valence angles can completely disrupt a protein fold. We demonstrate that naive strategies, such as directly comparing torsion angles between structures without correcting for variations in bond lengths and valence angles or fitting torsional variations without a proper regularization scheme, fail at producing an adequate representation of conformational changes in internal coordinates. In contrast, rescaled ridge regression, a method recently introduced to regularize multidimensional regressions with correlated explanatory variables, is shown to consistently identify a minimal set of torsion angles variations that closely reproduce changes in Cartesian coordinates. This torsional representation of conformational changes is shown to be robust to the choice of experimental structures. It also provides a better agreement with theoretical models of protein dynamics than the Cartesian representation, regarding notably the predominance of low-frequency normal modes in functional motions and the presence, in predicted equilibrium dynamics, of hints of natural selection for specific functional motions. The software is available at https://github.com/ugobas/tnm .

The maximum penalty criterion for ridge regression: application to the calibration of the force constant in elastic network models.

Tikhonov regularization, or ridge regression, is a popular technique to deal with collinearity in multivariate regression. We unveil a formal analogy between ridge regression and statistical mechanics, where the objective function is comparable to a free energy, and the ridge parameter plays the role of temperature. This analogy suggests two novel criteria for selecting a suitable ridge parameter: specific-heat (Cv) and maximum penalty (MP). We apply these fits to evaluate the relative contributions of rigid-body and internal fluctuations, which are typically highly collinear, to crystallographic B-factors. This issue is particularly important for computational models of protein dynamics, such as the elastic network model (ENM), since the amplitude of the predicted internal motion is commonly calibrated using B-factor data. After validation on simulated datasets, our results indicate that rigid-body motions account on average for more than 80% of the amplitude of B-factors. Furthermore, we evaluate the ability of different fits to reproduce the amplitudes of internal fluctuations in X-ray ensembles from the B-factors in the corresponding single X-ray structures. The new ridge criteria are shown to be markedly superior to the commonly used two-parameter fit that neglects rigid-body rotations and to the full fits regularized under generalized cross-validation. In conclusion, the proposed fits ensure a more robust calibration of the ENM force constant and should prove valuable in other applications.

Molecular and Functional Bases of Selection against a Mutation Bias in an RNA Virus.

The selective pressures acting on viruses that replicate under enhanced mutation rates are largely unknown. Here, we describe resistance of foot-and-mouth disease virus to the mutagen 5-fluorouracil (FU) through a single polymerase substitution that prevents an excess of A to G and U to C transitions evoked by FU on the wild-type foot-and-mouth disease virus, while maintaining the same level of mutant spectrum complexity. The polymerase substitution inflicts upon the virus a fitness loss during replication in absence of FU but confers a fitness gain in presence of FU. The compensation of mutational bias was documented by in vitro nucleotide incorporation assays, and it was associated with structural modifications at the N-terminal region and motif B of the viral polymerase. Predictions of the effect of mutations that increase the frequency of G and C in the viral genome and encoded polymerase suggest multiple points in the virus life cycle where the mutational bias in favor of G and C may be detrimental. Application of predictive algorithms suggests adverse effects of the FU-directed mutational bias on protein stability. The results reinforce modulation of nucleotide incorporation as a lethal mutagenesis-escape mechanism (that permits eluding virus extinction despite replication in the presence of a mutagenic agent) and suggest that mutational bias can be a target of selection during virus replication.

What evolution tells us about protein physics, and protein physics tells us about evolution.

The integration of molecular evolution and protein biophysics is an emerging theme that steadily gained importance during the last 15 years, significantly advancing both fields. The central integrative concept is the stability of the native state, although non-native conformations are increasingly recognized to play a major role, concerning, for example, aggregation, folding kinetics, or functional dynamics. Besides molecular requirements on fitness, the stability of native and alternative conformations is modulated by a variety of factors, including population size, selective pressure on the replicative system, which determines mutation rates and biases, and epistatic effects. We discuss some of the recent advances, open questions, and integrating views in protein evolution, in light of the many underlying trade-offs, correlations, and dichotomies.

Protein thermostability prediction within homologous families using temperature-dependent statistical potentials.

The ability to rationally modify targeted physical and biological features of a protein of interest holds promise in numerous academic and industrial applications and paves the way towards de novo protein design. In particular, bioprocesses that utilize the remarkable properties of enzymes would often benefit from mutants that remain active at temperatures that are either higher or lower than the physiological temperature, while maintaining the biological activity. Many in silico methods have been developed in recent years for predicting the thermodynamic stability of mutant proteins, but very few have focused on thermostability. To bridge this gap, we developed an algorithm for predicting the best descriptor of thermostability, namely the melting temperature Tm, from the protein's sequence and structure. Our method is applicable when the Tm of proteins homologous to the target protein are known. It is based on the design of several temperature-dependent statistical potentials, derived from datasets consisting of either mesostable or thermostable proteins. Linear combinations of these potentials have been shown to yield an estimation of the protein folding free energies at low and high temperatures, and the difference of these energies, a prediction of the melting temperature. This particular construction, that distinguishes between the interactions that contribute more than others to the stability at high temperatures and those that are more stabilizing at low T, gives better performances compared to the standard approach based on T-independent potentials which predict the thermal resistance from the thermodynamic stability. Our method has been tested on 45 proteins of known Tm that belong to 11 homologous families. The standard deviation between experimental and predicted Tm's is equal to 13.6°C in cross validation, and decreases to 8.3°C if the 6 worst predicted proteins are excluded. Possible extensions of our approach are discussed.

Effective harmonic potentials: insights into the internal cooperativity and sequence-specificity of protein dynamics.

The proper biological functioning of proteins often relies on the occurrence of coordinated fluctuations around their native structure, or on their ability to perform wider and sometimes highly elaborated motions. Hence, there is considerable interest in the definition of accurate coarse-grained descriptions of protein dynamics, as an alternative to more computationally expensive approaches. In particular, the elastic network model, in which residue motions are subjected to pairwise harmonic potentials, is known to capture essential aspects of conformational dynamics in proteins, but has so far remained mostly phenomenological, and unable to account for the chemical specificities of amino acids. We propose, for the first time, a method to derive residue- and distance-specific effective harmonic potentials from the statistical analysis of an extensive dataset of NMR conformational ensembles. These potentials constitute dynamical counterparts to the mean-force statistical potentials commonly used for static analyses of protein structures. In the context of the elastic network model, they yield a strongly improved description of the cooperative aspects of residue motions, and give the opportunity to systematically explore the influence of sequence details on protein dynamics.

Community-wide evaluation of methods for predicting the effect of mutations on protein-protein interactions.

Community-wide blind prediction experiments such as CAPRI and CASP provide an objective measure of the current state of predictive methodology. Here we describe a community-wide assessment of methods to predict the effects of mutations on protein-protein interactions. Twenty-two groups predicted the effects of comprehensive saturation mutagenesis for two designed influenza hemagglutinin binders and the results were compared with experimental yeast display enrichment data obtained using deep sequencing. The most successful methods explicitly considered the effects of mutation on monomer stability in addition to binding affinity, carried out explicit side-chain sampling and backbone relaxation, evaluated packing, electrostatic, and solvation effects, and correctly identified around a third of the beneficial mutations. Much room for improvement remains for even the best techniques, and large-scale fitness landscapes should continue to provide an excellent test bed for continued evaluation of both existing and new prediction methodologies.

BeAtMuSiC: Prediction of changes in protein-protein binding affinity on mutations.

The ability of proteins to establish highly selective interactions with a variety of (macro)molecular partners is a crucial prerequisite to the realization of their biological functions. The availability of computational tools to evaluate the impact of mutations on protein-protein binding can therefore be valuable in a wide range of industrial and biomedical applications, and help rationalize the consequences of non-synonymous single-nucleotide polymorphisms. BeAtMuSiC (http://babylone.ulb.ac.be/beatmusic) is a coarse-grained predictor of the changes in binding free energy induced by point mutations. It relies on a set of statistical potentials derived from known protein structures, and combines the effect of the mutation on the strength of the interactions at the interface, and on the overall stability of the complex. The BeAtMuSiC server requires as input the structure of the protein-protein complex, and gives the possibility to assess rapidly all possible mutations in a protein chain or at the interface, with predictive performances that are in line with the best current methodologies.

Structure-based mutant stability predictions on proteins of unknown structure.

The ability to rapidly and accurately predict the effects of mutations on the physicochemical properties of proteins holds tremendous importance in the rational design of modified proteins for various types of industrial, environmental or pharmaceutical applications, as well as in elucidating the genetic background of complex diseases. In many cases, the absence of an experimentally resolved structure represents a major obstacle, since most currently available predictive software crucially depend on it. We investigate here the relevance of combining coarse-grained structure-based stability predictions with a simple comparative modeling procedure. Strikingly, our results show that the use of average to high quality structural models leads to virtually no loss in predictive power compared to the use of experimental structures. Even in the case of low quality models, the decrease in performance is quite limited and this combined approach remains markedly superior to other methods based exclusively on the analysis of sequence features.

Detection of perturbation phases and developmental stages in organisms from DNA microarray time series data.

Available DNA microarray time series that record gene expression along the developmental stages of multicellular eukaryotes, or in unicellular organisms subject to external perturbations such as stress and diauxie, are analyzed. By pairwise comparison of the gene expression profiles on the basis of a translation-invariant and scale-invariant distance measure corresponding to least-rectangle regression, it is shown that peaks in the average distance values are noticeable and are localized around specific time points. These points systematically coincide with the transition points between developmental phases or just follow the external perturbations. This approach can thus be used to identify automatically, from microarray time series alone, the presence of external perturbations or the succession of developmental stages in arbitrary cell systems. Moreover, our results show that there is a striking similarity between the gene expression responses to these a priori very different phenomena. In contrast, the cell cycle does not involve a perturbation-like phase, but rather continuous gene expression remodeling. Similar analyses were conducted using three other standard distance measures, showing that the one we introduced was superior. Based on these findings, we set up an adapted clustering method that uses this distance measure and classifies the genes on the basis of their expression profiles within each developmental stage or between perturbation phases.

Protein stability: a single recorded mutation aids in predicting the effects of other mutations in the same amino acid site.

MOTIVATION: Accurate prediction of protein stability is important for understanding the molecular underpinnings of diseases and for the design of new proteins. We introduce a novel approach for the prediction of changes in protein stability that arise from a single-site amino acid substitution; the approach uses available data on mutations occurring in the same position and in other positions. Our algorithm, named Pro-Maya (Protein Mutant stAbilitY Analyzer), combines a collaborative filtering baseline model, Random Forests regression and a diverse set of features. Pro-Maya predicts the stability free energy difference of mutant versus wild type, denoted as ΔΔG. RESULTS: We evaluated our algorithm extensively using cross-validation on two previously utilized datasets of single amino acid mutations and a (third) validation set. The results indicate that using known ΔΔG values of mutations at the query position improves the accuracy of ΔΔG predictions for other mutations in that position. The accuracy of our predictions in such cases significantly surpasses that of similar methods, achieving, e.g. a Pearson's correlation coefficient of 0.79 and a root mean square error of 0.96 on the validation set. Because Pro-Maya uses a diverse set of features, including predictions using two other methods, it also performs slightly better than other methods in the absence of additional experimental data on the query positions. AVAILABILITY: Pro-Maya is freely available via web server at http://bental.tau.ac.il/ProMaya. CONTACT: nirb@tauex.tau.ac.il; wolf@cs.tau.ac.il SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Flanking domain stability modulates the aggregation kinetics of a polyglutamine disease protein.

Spinocerebellar Ataxia Type 3 (SCA3) is one of nine polyglutamine (polyQ) diseases that are all characterized by progressive neuronal dysfunction and the presence of neuronal inclusions containing aggregated polyQ protein, suggesting that protein misfolding is a key part of this disease. Ataxin-3, the causative protein of SCA3, contains a globular, structured N-terminal domain (the Josephin domain) and a flexible polyQ-containing C-terminal tail, the repeat-length of which modulates pathogenicity. It has been suggested that the fibrillogenesis pathway of ataxin-3 begins with a non-polyQ-dependent step mediated by Josephin domain interactions, followed by a polyQ-dependent step. To test the involvement of the Josephin domain in ataxin-3 fibrillogenesis, we have created both pathogenic and nonpathogenic length ataxin-3 variants with a stabilized Josephin domain, and have both stabilized and destabilized the isolated Josephin domain. We show that changing the thermodynamic stability of the Josephin domain modulates ataxin-3 fibrillogenesis. These data support the hypothesis that the first stage of ataxin-3 fibrillogenesis is caused by interactions involving the non-polyQ containing Josephin domain and that the thermodynamic stability of this domain is linked to the aggregation propensity of ataxin-3.

PoPMuSiC 2.1: a web server for the estimation of protein stability changes upon mutation and sequence optimality.

BACKGROUND: The rational design of modified proteins with controlled stability is of extreme importance in a whole range of applications, notably in the biotechnological and environmental areas, where proteins are used for their catalytic or other functional activities. Future breakthroughs in medical research may also be expected from an improved understanding of the effect of naturally occurring disease-causing mutations on the molecular level. RESULTS: PoPMuSiC-2.1 is a web server that predicts the thermodynamic stability changes caused by single site mutations in proteins, using a linear combination of statistical potentials whose coefficients depend on the solvent accessibility of the mutated residue. PoPMuSiC presents good prediction performances (correlation coefficient of 0.8 between predicted and measured stability changes, in cross validation, after exclusion of 10% outliers). It is moreover very fast, allowing the prediction of the stability changes resulting from all possible mutations in a medium size protein in less than a minute. This unique functionality is user-friendly implemented in PoPMuSiC and is particularly easy to exploit. Another new functionality of our server concerns the estimation of the optimality of each amino acid in the sequence, with respect to the stability of the structure. It may be used to detect structural weaknesses, i.e. clusters of non-optimal residues, which represent particularly interesting sites for introducing targeted mutations. This sequence optimality data is also expected to have significant implications in the prediction and the analysis of particular structural or functional protein regions. To illustrate the interest of this new functionality, we apply it to a dataset of known catalytic sites, and show that a much larger than average concentration of structural weaknesses is detected, quantifying how these sites have been optimized for function rather than stability. CONCLUSION: The freely available PoPMuSiC-2.1 web server is highly useful for identifying very rapidly a list of possibly relevant mutations with the desired stability properties, on which subsequent experimental studies can be focused. It can also be used to detect sequence regions corresponding to structural weaknesses, which could be functionally important or structurally delicate regions, with obvious applications in rational protein design.

Evidence that interaction between conserved residues in transmembrane helices 2, 3, and 7 are crucial for human VPAC1 receptor activation.

The VPAC(1) receptor belongs to family B of G protein-coupled receptors (GPCR-B) and is activated upon binding of the vasoactive intestinal peptide (VIP). Despite the recent determination of the structure of the N terminus of several members of this receptor family, little is known about the structure of the transmembrane (TM) region and about the molecular mechanisms leading to activation. In the present study, we designed a new structural model of the TM domain and combined it with experimental mutagenesis experiments to investigate the interaction network that governs ligand binding and receptor activation. Our results suggest that this network involves the cluster of residues Arg(188) in TM2, Gln(380) in TM7, and Asn(229) in TM3. This cluster is expected to be altered upon VIP binding, because Arg(188) has been shown previously to interact with Asp(3) of VIP. Several point mutations at positions 188, 229, and 380 were experimentally characterized and were shown to severely affect VIP binding and/or VIP-mediated cAMP production. Double mutants built from reciprocal residue exchanges exhibit strong cooperative or anticooperative effects, thereby indicating the spatial proximity of residues Arg(188), Gln(380), and Asn(229). Because these residues are highly conserved in the GPCR-B family, they can moreover be expected to have a general role in mediating function.

Thermo- and mesostabilizing protein interactions identified by temperature-dependent statistical potentials.

The goal of controlling protein thermostability is tackled here through establishing, by in silico analyses, the relative weight of residue-residue interactions in proteins as a function of temperature. We have designed for that purpose a (melting-) temperature-dependent, statistical distance potential, where the interresidue distances are computed between the side-chain geometric centers or their functional centers. Their separate derivation from proteins of either high or low thermal resistance reveals the interactions that contribute most to stability in different temperature ranges. Thermostabilizing interactions include salt bridges and cation-pi interactions (especially those involving arginine), aromatic interactions, and H-bonds between negatively charged and some aromatic residues. In contrast, H-bonds between two polar noncharged residues or between a polar noncharged residue and a negatively charged residue are relatively less stabilizing at high temperatures. An important observation is that it is necessary to consider both repulsive and attractive interactions in overall thermostabilization, as the degree of repulsion may also vary with temperature. These temperature-dependent potentials are not only useful for the identification of meso- and thermostabilizing pair interactions, but also exhibit predictive power, as illustrated by their ability to predict the melting temperature of a protein based on the melting temperature of homologous proteins.

Fast and accurate predictions of protein stability changes upon mutations using statistical potentials and neural networks: PoPMuSiC-2.0.

MOTIVATION: The rational design of proteins with modified properties, through amino acid substitutions, is of crucial importance in a large variety of applications. Given the huge number of possible substitutions, every protein engineering project would benefit strongly from the guidance of in silico methods able to predict rapidly, and with reasonable accuracy, the stability changes resulting from all possible mutations in a protein. RESULTS: We exploit newly developed statistical potentials, based on a formalism that highlights the coupling between four protein sequence and structure descriptors, and take into account the amino acid volume variation upon mutation. The stability change is expressed as a linear combination of these energy functions, whose proportionality coefficients vary with the solvent accessibility of the mutated residue and are identified with the help of a neural network. A correlation coefficient of R = 0.63 and a root mean square error of sigma(c) = 1.15 kcal/mol between measured and predicted stability changes are obtained upon cross-validation. These scores reach R = 0.79, and sigma(c) = 0.86 kcal/mol after exclusion of 10% outliers. The predictive power of our method is shown to be significantly higher than that of other programs described in the literature. AVAILABILITY: http://babylone.ulb.ac.be/popmusic

Modeling the temporal evolution of the Drosophila gene expression from DNA microarray time series.

The time evolution of gene expression across the developmental stages of the host organism can be inferred from appropriate DNA microarray time series. Modeling this evolution aims eventually at improving the understanding and prediction of the complex phenomena that are the basis of life. We focus on the embryonic-to-adult development phases of Drosophila melanogaster, and chose to model the expression network with the help of a system of differential equations with constant coefficients, which are nonlinear in the transcript concentrations but linear in their logarithms. To reduce the dimensionality of the problem, genes having similar expression profiles are grouped into 17 clusters. We show that a simple linear model is able to reproduce the experimental data with very good precision, owing to the large number of parameters that represent the connections between the clusters. Remarkably, the parameter reduction allowed elimination of up to 80-85% of these connections while keeping fairly good precision. This result supports the low-connectivity hypothesis of gene expression networks, with about three connections per cluster, without introducing a priori hypotheses. The core of the network shows a few gene clusters with negative self-regulation, and some highly connected clusters involving proteins with crucial functions.