Prediction of protein stability changes for single-site mutations using support vector machines

Accurate prediction of protein stability changes resulting from single amino acid mutations is important for understanding protein structures and designing new proteins. We use support vector machines to predict protein stability changes for single amino acid mutations leveraging both sequence and structural information. We evaluate our approach using cross-validation methods on a large dataset of single amino acid mutations. When only the sign of the stability changes is considered, the predictive method achieves 84% accuracy-a significant improvement over previously published results. Moreover, the experimental results show that the prediction accuracy obtained using sequence alone is close to the accuracy obtained using tertiary structure information. Because our method can accurately predict protein stability changes using primary sequence information only, it is applicable to many situations where the tertiary structure is unknown, overcoming a major limitation of previous methods which require tertiary information. The web server for predictions of protein stability changes upon mutations (MUpro), software, and datasets are available at http://www.igb.uci.edu/servers/servers.html.     

The role of local backrub motions in evolved and designed mutations

Amino acid substitutions in protein structures often require subtle backbone adjustments that are difficult to model in atomic detail. An improved ability to predict realistic backbone changes in response to engineered mutations would be of great utility for the blossoming field of rational protein design. One model that has recently grown in acceptance is the backrub motion, a low-energy dipeptide rotation with single-peptide counter-rotations, that is coupled to dynamic two-state sidechain rotamer jumps, as evidenced by alternate conformations in very high-resolution crystal structures. It has been speculated that backrubs may facilitate sequence changes equally well as rotamer changes. However, backrub-induced shifts and experimental uncertainty are of similar magnitude for backbone atoms in even high-resolution structures, so comparison of wildtype-vs.-mutant crystal structure pairs is not sufficient to directly link backrubs to mutations. In this study, we use two alternative approaches that bypass this limitation. First, we use a quality-filtered structure database to aggregate many examples for precisely defined motifs with single amino acid differences, and find that the effectively amplified backbone differences closely resemble backrubs. Second, we directly apply a provably-accurate, backrub-enabled protein design algorithm to idealized versions of these motifs, and discover that the lowest-energy computed models match the average-coordinate experimental structures. These results support the hypothesis that backrubs participate in natural protein evolution and validate their continued use for design of synthetic proteins.     

Stability Changes upon Mutation of Solvent- accessible Residues in Proteins Evaluated by Database-derived Potentials

The stability changes in peptides and proteins caused by the substitution of a single amino acid, which can be measured experimentally by the change in folding free energy, are evaluated here using effective potentials derived from known protein structures. The analysis is focused on mutations of residues that are accessible to the solvent. These represent in total 106 mutations, introduced at different sites in barnase, bacteriophage T4 lysozyme and chymotrypsin inhibitor 2, and in a synthetic helical peptide. Assuming that the mutations do not modify the backbone structure, the changes in folding free energies are computed using various types of database-derived potentials and are compared with the measured ones. Distance-dependent residue – residue potentials are found to be inadequate for estimating the stability changes caused by these mutations, as they are dominated by hydrophobic interactions, which do not play an essential role at the protein surface. On the contrary, the potentials based on backbone torsion angle propensities yield quite good results. Indeed, for a subset of 96 out of the 106 mutations, the computed and measured changes in folding free energy correlate with a linear correlation coefficient of 0.87. Moreover, the ten mutations that are excluded from the correlation either seem to cause modifications of the backbone structure or to involve strong hydrophobic interactions, which are atypical for solvent-accessible residues. We find furthermore that raising the ionic strength of the solvent used for measuring the changes in folding free energies improves the correlation, as it tends to mask the electrostatic interactions. When adding to these 106 mutations 44 mutations performed in staphylococcal nuclease and chemotactic protein, which were first discarded because some of them were suspected to affect the backbone conformation or the denatured state, the correlation between measured and computed folding free energy changes remains quite good: the correlation coefficient is 0.86 for 135 out of the 150 mutations. The success of the backbone torsion potentials in predicting stability changes indicates that the approximations made for deriving these potentials are adequate. It suggests moreover that the local interactions along the chain dominate at the protein surface.     

Using rigidity analysis to probe mutation-induced structural changes in proteins

Predicting the effect of a single amino acid substitution on the stability of a protein structure is a fundamental task in macromolecular modeling. It has relevance to drug design and understanding of disease-causing protein variants. We present KINARI-Mutagen, a web server for performing in silico mutation experiments on protein structures from the Protein Data Bank. Our rigidity-theoretical approach permits fast evaluation of the effects of mutations that may not be easy to perform in vitro, because it is not always possible to express a protein with a specific amino acid substitution. We use KINARI-Mutagen to identify critical residues, and we show that our predictions correlate with destabilizing mutations to glycine. In two in-depth case studies we show that the mutated residues identified by KINARI-Mutagen as critical correlate with experimental data, and would not have been identified by other methods such as Solvent Accessible Surface Area measurements or residue ranking by contributions to stabilizing interactions. We also generate 48 mutants for 14 proteins, and compare our rigidity-based results against experimental mutation stability data. KINARI-Mutagen is available at http://kinari.cs.umass.edu.     

An optimized FM-index library for nucleotide and amino acid search

In computational structural biology, structure comparison is fundamental for our understanding of proteins. Structure comparison is, e.g., algorithmically the starting point for computational studies of structural evolution and it guides our efforts to predict protein structures from their amino acid sequences. Most methods for structural alignment of protein structures optimize the distances between aligned and superimposed residue pairs, i.e., the distances traveled by the aligned and superimposed residues during linear interpolation. Considering such a linear interpolation, these methods do not differentiate if there is room for the interpolation, if it causes steric clashes, or more severely, if it changes the topology of the compared protein backbone curves. To distinguish such cases, we analyze the linear interpolation between two aligned and superimposed backbones. We quantify the amount of steric clashes and find all self-intersections in a linear backbone interpolation. To determine if the self-intersections alter the protein’s backbone curve significantly or not, we present a path-finding algorithm that checks if there exists a self-avoiding path in a neighborhood of the linear interpolation. A new path is constructed by altering the linear interpolation using a novel interpretation of Reidemeister moves from knot theory working on three-dimensional curves rather than on knot diagrams. Either the algorithm finds a self-avoiding path or it returns a smallest set of essential self-intersections. Each of these indicates a significant difference between the folds of the aligned protein structures. As expected, we find at least one essential self-intersection separating most unknotted structures from a knotted structure, and we find even larger motions in proteins connected by obstruction free linear interpolations. We also find examples of homologous proteins that are differently threaded, and we find many distinct folds connected by longer but simple deformations. TM-align is one of the most restrictive alignment programs. With standard parameters, it only aligns residues superimposed within 5 Ångström distance. We find 42165 topological obstructions between aligned parts in 142068 TM-alignments. Thus, this restrictive alignment procedure still allows topological dissimilarity of the aligned parts. Based on the data we conclude that our program ProteinAlignmentObstruction provides significant additional information to alignment scores based solely on distances between aligned and superimposed residue pairs.     

Can contact potentials reliably predict stability of proteins?

The simplest approximation of interaction potential between amino acid residues in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact potentials to accurately and transferably (across various protein families) predict stability changes of proteins upon mutations. We develop a new methodology to determine the contact potentials in proteins from experimental measurements of changes in protein's thermodynamic stabilities (DeltaDeltaG) upon mutations. We apply our methodology to derive sets of contact interaction parameters for a hierarchy of interaction models including solvation and multi-body contact parameters. We test how well our models reproduce experimental measurements by statistical tests. We evaluate the maximum accuracy of predictions obtained by using contact potentials and the correlation between parameters derived from different data-sets of experimental (DeltaDeltaG) values. We argue that it is impossible to reach experimental accuracy and derive fully transferable contact parameters using the contact models of potentials. However, contact parameters may yield reliable predictions of DeltaDeltaG for datasets of mutations confined to the same amino acid positions in the sequence of a single protein.     

High-resolution structural and thermodynamic analysis of extreme stabilization of human procarboxypeptidase by computational protein design

Recent efforts to design de novo or redesign the sequence and structure of proteins using computational techniques have met with significant success. Most, if not all, of these computational methodologies attempt to model atomic-level interactions, and hence high-resolution structural characterization of the designed proteins is critical for evaluating the atomic-level accuracy of the underlying design force-fields. We previously used our computational protein design protocol RosettaDesign to completely redesign the sequence of the activation domain of human procarboxypeptidase A2. With 68% of the wild-type sequence changed, the designed protein, AYEdesign, is over 10 kcal/mol more stable than the wild-type protein. Here, we describe the high-resolution crystal structure and solution NMR structure of AYEdesign, which show that the experimentally determined backbone and side-chains conformations are effectively superimposable with the computational model at atomic resolution. To isolate the origins of the remarkable stabilization, we have designed and characterized a new series of procarboxypeptidase mutants that gain significant thermodynamic stability with a minimal number of mutations; one mutant gains more than 5 kcal/mol of stability over the wild-type protein with only four amino acid changes. We explore the relationship between force-field smoothing and conformational sampling by comparing the experimentally determined free energies of the overall design and these focused subsets of mutations to those predicted using modified force-fields, and both fixed and flexible backbone sampling protocols.     

Structural and thermodynamic analyses of Escherichia coli RNase HI variant with quintuple thermostabilizing mutations

A combination of five thermostabilizing mutations, Gly23-->Ala, His62-->Pro, Val74-->Leu, Lys95-->Gly, and Asp134-->His, has been shown to additively enhance the thermostability of Escherichia coli RNase HI [Akasako A, Haruki M, Oobatake M & Kanaya S (1995) Biochemistry34, 8115-8122]. In this study, we determined the crystal structure of the protein with these mutations (5H-RNase HI) to analyze the effects of the mutations on the structure in detail. The structures of the mutation sites were almost identical to those of the mutant proteins to which the mutations were individually introduced, except for G23A, for which the structure of the single mutant protein is not available. Moreover, only slight changes in the backbone conformation of the protein were observed, and the interactions of the side chains were almost conserved. These results indicate that these mutations almost independently affect the protein structure, and are consistent with the fact that the thermostabiling effects of the mutations are cumulative. We also determined the protein stability curve describing the temperature dependence of the free energy of unfolding of 5H-RNase HI to elucidate the thermostabilization mechanism. The maximal stability for 5H-RNase HI was as high as that for the cysteine-free variant of Thermus thermophilus RNase HI. In contrast, the heat capacity of unfolding for 5H-RNase H was similar to that for E. coli RNase HI, which is considerably higher than that for T. thermophilus RNase HI. These results suggest that 5H-RNase HI is stabilized, in part, by the thermostabilization mechanism adopted by T. thermophilus RNase HI.     

Energetics, stability, and prediction of transmembrane helices

We show that the peptide backbone of an alpha-helix places a severe thermodynamic constraint on transmembrane (TM) stability. Neglect of this constraint by commonly used hydrophobicity scales underlies the notorious uncertainty of TM helix prediction by sliding-window hydropathy plots of membrane protein (MP) amino acid sequences. We find that an experiment-based whole-residue hydropathy scale (WW scale), which includes the backbone constraint, identifies TM helices of membrane proteins with an accuracy greater than 99 %. Furthermore, it correctly predicts the minimum hydrophobicity required for stable single-helix TM insertion observed in Escherichia coli. In order to improve membrane protein topology prediction further, we introduce the augmented WW (aWW) scale, which accounts for the energetics of salt-bridge formation. An important issue for genomic analysis is the ability of the hydropathy plot method to distinguish membrane from soluble proteins. We find that the method falsely predicts 17 to 43 % of a set of soluble proteins to be MPs, depending upon the hydropathy scale used.     

The interplay between transient α-helix formation and side chain rotamer distributions in disordered proteins probed by methyl chemical shifts

The peptide backbones of disordered proteins are routinely characterized by NMR with respect to transient structure and dynamics. Little experimental information is, however, available about the side chain conformations and how structure in the backbone affects the side chains. Methyl chemical shifts can in principle report the conformations of aliphatic side chains in disordered proteins and in order to examine this two model systems were chosen: the acid denatured state of acyl-CoA binding protein (ACBP) and the intrinsically disordered activation domain of the activator for thyroid hormone and retinoid receptors (ACTR). We find that small differences in the methyl carbon chemical shifts due to the γ-gauche effect may provide information about the side chain rotamer distributions. However, the effects of neighboring residues on the methyl group chemical shifts obscure the direct observation of γ-gauche effect. To overcome this, we reference the chemical shifts to those in a more disordered state resulting in residue specific random coil chemical shifts. The (13)C secondary chemical shifts of the methyl groups of valine, leucine, and isoleucine show sequence specific effects, which allow a quantitative analysis of the ensemble of χ(2)-angles of especially leucine residues in disordered proteins. The changes in the rotamer distributions upon denaturation correlate to the changes upon helix induction by the co-solvent trifluoroethanol, suggesting that the side chain conformers are directly or indirectly related to formation of transient α-helices.     

Computational Assessment of Protein–protein Binding Affinity by Reversely Engineering the Energetics in Protein Complexes

The cellular functions of proteins are maintained by forming diverse complexes. The stability of these complexes is quantified by the measurement of binding affinity, and mutations that alter the binding affinity can cause various diseases such as cancer and diabetes. As a result, accurate estimation of the binding stability and the effects of mutations on changes of binding affinity is a crucial step to understanding the biological functions of proteins and their dysfunctional consequences. It has been hypothesized that the stability of a protein complex is dependent not only on the residues at its binding interface by pairwise interactions but also on all other remaining residues that do not appear at the binding interface. Here, we computationally reconstruct the binding affinity by decomposing it into the contributions of interfacial residues and other non-interfacial residues in a protein complex. We further assume that the contributions of both interfacial and non-interfacial residues to the binding affinity depend on their local structural environments such as solvent-accessible surfaces and secondary structural types. The weights of all corresponding parameters are optimized by Monte-Carlo simulations. After cross-validation against a large-scale dataset, we show that the model not only shows a strong correlation between the absolute values of the experimental and calculated binding affinities, but can also be an effective approach to predict the relative changes of binding affinity from mutations. Moreover, we have found that the optimized weights of many parameters can capture the first-principle chemical and physical features of molecular recognition, therefore reversely engineering the energetics of protein complexes. These results suggest that our method can serve as a useful addition to current computational approaches for predicting binding affinity and understanding the molecular mechanism of protein–protein interactions.     

Dissecting the Critical Factors for Thermodynamic Stability of Modular Proteins Using Molecular Modeling Approach

Repeat proteins have recently attracted much attention as alternative scaffolds to immunoglobulin antibodies due to their unique structural and biophysical features. In particular, repeat proteins show high stability against temperature and chaotic agents. Despite many studies, structural features for the stability of repeat proteins remain poorly understood. Here we present an interesting result from in silico analyses pursuing the factors which affect the stability of repeat proteins. Previously developed repebody structure based on variable lymphocytes receptors (VLRs) which consists of leucine-rich repeat (LRR) modules was used as initial structure for the present study. We constructed extra six repebody structures with varying numbers of repeat modules and those structures were used for molecular dynamics simulations. For the structures, the intramolecular interactions including backbone H-bonds, van der Waals energy, and hydrophobicity were investigated and then the radius of gyration, solvent-accessible surface area, ratio of secondary structure, and hydration free energy were also calculated to find out the relationship between the number of LRR modules and stability of the protein. Our results show that the intramolecular interactions lead to more compact structure and smaller surface area of the repebodies, which are critical for the stability of repeat proteins. The other features were also well compatible with the experimental results. Based on our observations, the repebody-5 was proposed as the best structure from the all repebodies in structure optimization process. The present study successfully demonstrated that our computer-based molecular modeling approach can significantly contribute to the experiment-based protein engineering challenge.     

Dead‐end elimination with perturbations (DEEPer): A provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum‐energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (D ead‐E nd E limination with Per turbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*‐based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower‐energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein–ligand interactions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Thermal Stabilization of Dihydrofolate Reductase Using Monte Carlo Unfolding Simulations and Its Functional Consequences

Design of proteins with desired thermal properties is important for scientific and biotechnological applications. Here we developed a theoretical approach to predict the effect of mutations on protein stability from non-equilibrium unfolding simulations. We establish a relative measure based on apparent simulated melting temperatures that is independent of simulation length and, under certain assumptions, proportional to equilibrium stability, and we justify this theoretical development with extensive simulations and experimental data. Using our new method based on all-atom Monte-Carlo unfolding simulations, we carried out a saturating mutagenesis of Dihydrofolate Reductase (DHFR), a key target of antibiotics and chemotherapeutic drugs. The method predicted more than 500 stabilizing mutations, several of which were selected for detailed computational and experimental analysis. We find a highly significant correlation of r = 0.65–0.68 between predicted and experimentally determined melting temperatures and unfolding denaturant concentrations for WT DHFR and 42 mutants. The correlation between energy of the native state and experimental denaturation temperature was much weaker, indicating the important role of entropy in protein stability. The most stabilizing point mutation was D27F, which is located in the active site of the protein, rendering it inactive. However for the rest of mutations outside of the active site we observed a weak yet statistically significant positive correlation between thermal stability and catalytic activity indicating the lack of a stability-activity tradeoff for DHFR. By combining stabilizing mutations predicted by our method, we created a highly stable catalytically active E. coli DHFR mutant with measured denaturation temperature 7.2°C higher than WT. Prediction results for DHFR and several other proteins indicate that computational approaches based on unfolding simulations are useful as a general technique to discover stabilizing mutations.     

Structure-Based Prediction of the Peptide Sequence Space Recognized by Natural and Synthetic PDZ Domains

Protein-protein recognition, frequently mediated by members of large families of interaction domains, is one of the cornerstones of biological function. Here, we present a computational, structure-based method to predict the sequence space of peptides recognized by PDZ domains, one of the largest families of recognition proteins. As a test set, we use a considerable amount of recent phage display data that describe the peptide recognition preferences for 169 naturally occurring and engineered PDZ domains. For both wild-type PDZ domains and single point mutants, we find that 70-80% of the most frequently observed amino acids by phage display are predicted within the top five ranked amino acids. Phage display frequently identified recognition preferences for amino acids different from those present in the original crystal structure. Notably, in about half of these cases, our algorithm correctly captures these preferences, indicating that it can predict mutations that increase binding affinity relative to the starting structure. We also find that we can computationally recapitulate specificity changes upon mutation, a key test for successful forward design of protein-protein interface specificity. Across all evaluated data sets, we find that incorporation backbone sampling improves accuracy substantially, irrespective of using a crystal or NMR structure as the starting conformation. Finally, we report successful prediction of several amino acid specificity changes from blind tests in the DREAM4 peptide recognition domain specificity prediction challenge. Because the foundational methods developed here are structure based, these results suggest that the approach can be more generally applied to specificity prediction and redesign of other protein-protein interfaces that have structural information but lack phage display data.     

Computational sidechain placement and protein mutagenesis with implicit solvent models

Structure prediction and computational protein design should benefit from accurate solvent models. We have applied implicit solvent models to two problems that are central to this area. First, we performed sidechain placement for 29 proteins, using a solvent model that combines a screened Coulomb term with an Accessible Surface Area term (CASA model). With optimized parameters, the prediction quality is comparable with earlier work that omitted electrostatics and solvation altogether. Second, we computed the stability changes associated with point mutations involving ionized sidechains. For over 1000 mutations, including many fully or partly buried positions, we compared CASA and two generalized Born models (GB) with a more accurate model, which solves the Poisson equation of continuum electrostatics numerically. CASA predicts the correct sign and order of magnitude of the stability change for 81% of the mutations, compared to 97% with the best GB. We also considered 140 mutations for which experimental data are available. Comparing to experiment requires additional assumptions about the unfolded protein structure, protein relaxation in response to the mutations, and contributions from the hydrophobic effect. With a simple, commonly-used unfolded state model, the mean unsigned error is 2.1 kcal/mol with both CASA and the best GB. Overall, the electrostatic model is not important for sidechain placement; CASA and GB are equivalent for surface mutations, while GB is far superior for fully or partly buried positions. Thus, for problems like protein design that involve all these aspects, the most recent GB models represent an important step forward. Along with the recent discovery of efficient, pairwise implementations of GB, this will open new possibilities for the computational engineering of proteins.     

Effective scoring function for protein sequence design

We have developed an effective scoring function for protein design. The atomic solvation parameters, together with the weights of energy terms, were optimized so that residues corresponding to the native sequence were predicted with low energy in the training set of 28 protein structures. The solvation energy of non-hydrogen-bonded hydrophilic atoms was considered separately and expressed in a nonlinear way. As a result, our scoring function predicted native residues as the most favorable in 59% of the total positions in 28 proteins. We then tested the scoring function by comparing the predicted stability changes for 103 T4 lysozyme mutants with the experimental values. The correlation coefficients were 0.77 for surface mutations and 0.71 for all mutations. Finally, the scoring function combined with Monte Carlo simulation was used to predict favorable sequences on a fixed backbone. The designed sequences were similar to the natural sequences of the family to which the template structure belonged. The profile of the designed sequences was helpful for identification of remote homologues of the native sequence.     

Rescuing a destabilized protein fold through backbone cyclization

We describe the physicochemical characterization of various circular and linear forms of the approximately 60 residue N-terminal Src homology 3 (SH3) domain from the murine c-Crk adapter protein. Structural, dynamic, thermodynamic, kinetic and biochemical studies reveal that backbone circularization does not prevent the adoption of the natural folded structure in any of the circular proteins. Both the folding and unfolding rate of the protein increased slightly upon circularization. Circularization did not lead to a significant thermodynamic stabilization of the full-length protein, suggesting that destabilizing enthalpic effects (e.g. strain) negate the expected favorable entropic contribution to overall stability. In contrast, we find circularization results in a dramatic stabilization of a truncated version of the SH3 domain lacking a key glutamate residue. The ability to rescue the destabilized mutant indicates that circularization may be a useful tool in protein engineering programs geared towards generating minimized proteins.