Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.     

De novo protein design. I. In search of stability and specificity.

We have developed a fully automated protein design strategy that works on the entire sequence of the protein and uses a full atom representation. At each step of the procedure, an all-atom model of the protein is built using the template protein structure and the current designed sequence. The energy of the model is used to drive a Monte Carlo optimization in sequence space: random moves are either accepted or rejected based on the Metropolis criterion. We rely on the physical forces that stabilize native protein structures to choose the optimum sequence. Our energy function includes van der Waals interactions, electrostatics and an environment free energy. Successful protein design should be specific and generate a sequence compatible with the template fold and incompatible with competing folds. We impose specificity by maintaining the amino acid composition constant, based on the random energy model. The specificity of the optimized sequence is tested by fold recognition techniques. Successful sequence designs for the B1 domain of protein G, for the lambda repressor and for sperm whale myoglobin are presented. We show that each additional term of the energy function improves the performance of our design procedure: the van der Waals term ensures correct packing, the electrostatics term increases the specificity for the correct native fold, and the environment solvation term ensures a correct pattern of buried hydrophobic and exposed hydrophilic residues. For the globin family, we show that we can design a protein sequence that is stable in the myoglobin fold, yet incompatible with the very similar hemoglobin fold.     

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.     

Computational protein design with side-chain conformational entropy

Recent advances in modeling protein structures at the atomic level have made it possible to tackle "de novo" computational protein design. Most procedures are based on combinatorial optimization using a scoring function that estimates the folding free energy of a protein sequence on a given main-chain structure. However, the computation of the conformational entropy in the folded state is generally an intractable problem, and its contribution to the free energy is not properly evaluated. In this article, we propose a new automated protein design methodology that incorporates such conformational entropy based on statistical mechanics principles. We define the free energy of a protein sequence by the corresponding partition function over rotamer states. The free energy is written in variational form in a pairwise approximation and minimized using the Belief Propagation algorithm. In this way, a free energy is associated to each amino acid sequence: we use this insight to rescore the results obtained with a standard minimization method, with the energy as the cost function. Then, we set up a design method that directly uses the free energy as a cost function in combination with a stochastic search in the sequence space. We validate the methods on the design of three superficial sites of a small SH3 domain, and then apply them to the complete redesign of 27 proteins. Our results indicate that accounting for entropic contribution in the score function affects the outcome in a highly nontrivial way, and might improve current computational design techniques based on protein stability.     

Direct prediction of profiles of sequences compatible with a protein structure by neural networks with fragment‐based local and energy‐based nonlocal profiles

Locating sequences compatible with a protein structural fold is the well‐known inverse protein‐folding problem. While significant progress has been made, the success rate of protein design remains low. As a result, a library of designed sequences or profile of sequences is currently employed for guiding experimental screening or directed evolution. Sequence profiles can be computationally predicted by iterative mutations of a random sequence to produce energy‐optimized sequences, or by combining sequences of structurally similar fragments in a template library. The latter approach is computationally more efficient but yields less accurate profiles than the former because of lacking tertiary structural information. Here we present a method called SPIN that predicts Sequence Profiles by Integrated Neural network based on fragment‐derived sequence profiles and structure‐derived energy profiles. SPIN improves over the fragment‐derived profile by 6.7% (from 23.6 to 30.3%) in sequence identity between predicted and wild‐type sequences. The method also reduces the number of residues in low complex regions by 15.7% and has a significantly better balance of hydrophilic and hydrophobic residues at protein surface. The accuracy of sequence profiles obtained is comparable to those generated from the protein design program RosettaDesign 3.5. This highly efficient method for predicting sequence profiles from structures will be useful as a single‐body scoring term for improving scoring functions used in protein design and fold recognition. It also complements protein design programs in guiding experimental design of the sequence library for screening and directed evolution of designed sequences. The SPIN server is available at http://sparks‐lab.org . Proteins 2014; 82:2565–2573. © 2014 Wiley Periodicals, Inc.     

Design of an optimal Chebyshev-expanded discrimination function for globular proteins

We describe the construction of a scoring function designed to model the free energy of protein folding. An optimization technique is used to determine the best functional forms of the hydrophobic, residue-residue and hydrogen-bonding components of the potential. The scoring function is expanded by use of Chebyshev polynomials, the coefficients of which are determined by minimizing the score, in units of standard deviation, of native structures in the ensembles of alternate decoy conformations. The derived effective potential is then tested on decoy sets used conventionally in such studies. Using our scoring function, we achieve a high level of discrimination between correct and incorrect folds. In addition, our method is able to represent functions of arbitrary shape with fewer parameters than the usual histogram potentials of similar resolution. Finally, our representation can be combined easily with many optimization methods, because the total energy is a linear function of the parameters. Our results show that the techniques of Z-score optimization and Chebyshev expansion work well.     

Recent advances in the development and application of implicit solvent models in biomolecule simulations

Advances have recently been made in the development of implicit solvent methodologies and their application to the modeling of biomolecules, particularly with regard to generalized Born approaches, dielectric screening function formulations and models based on solvent-accessible surface areas. Interesting new developments include more refined non-polar solvation energy estimators, and implicit methods for modeling low-dielectric and heterogeneous environments such as membrane systems. These have been successfully applied to molecular dynamics simulations, the scoring of protein conformations, and the calculation of binding affinities and folding free energy landscapes.     

Protein structure evaluation using an all-atom energy based empirical scoring function

Arriving at the native conformation of a polypeptide chain characterized by minimum most free energy is a problem of long standing interest in protein structure prediction endeavors. Owing to the computational requirements in developing free energy estimates, scoring functions--energy based or statistical--have received considerable renewed attention in recent years for distinguishing native structures of proteins from non-native like structures. Several cleverly designed decoy sets, CASP (Critical Assessment of Techniques for Protein Structure Prediction) structures and homology based internet accessible three dimensional model builders are now available for validating the scoring functions. We describe here an all-atom energy based empirical scoring function and examine its performance on a wide series of publicly available decoys. Barring two protein sequences where native structure is ranked second and seventh, native is identified as the lowest energy structure in 67 protein sequences from among 61,659 decoys belonging to 12 different decoy sets. We further illustrate a potential application of the scoring function in bracketing native-like structures of two small mixed alpha/beta globular proteins starting from sequence and secondary structural information. The scoring function has been web enabled at www.scfbio-iitd.res.in/utility/proteomics/energy.jsp.     

PROTDES: CHARMM toolbox for computational protein design

We present an open-source software able to automatically mutate any residue positions and find the best aminoacids in an arbitrary protein structure without requiring pairwise approximations. Our software, PROTDES, is based on CHARMM and it searches automatically for mutations optimizing a protein folding free energy. PROTDES allows the integration of molecular dynamics within the protein design. We have implemented an heuristic optimization algorithm that iteratively searches the best aminoacids and their conformations for an arbitrary set of positions within a structure. Our software allows CHARMM users to perform protein design calculations and to create their own procedures for protein design using their own energy functions. We show this by implementing three different energy functions based on different solvent treatments: surface area accessibility, generalized Born using molecular volume and an effective energy function. PROTDES, a tutorial, parameter sets, configuration tools and examples are freely available at http://soft.synth-bio.org/protdes.html.     

Applying Physics-Based Scoring to Calculate Free Energies of Binding for Single Amino Acid Mutations in Protein-Protein Complexes

Predicting changes in protein binding affinity due to single amino acid mutations helps us better understand the driving forces underlying protein-protein interactions and design improved biotherapeutics. Here, we use the MM-GBSA approach with the OPLS2005 force field and the VSGB2.0 solvent model to calculate differences in binding free energy between wild type and mutant proteins. Crucially, we made no changes to the scoring model as part of this work on protein-protein binding affinity—the energy model has been developed for structure prediction and has previously been validated only for calculating the energetics of small molecule binding. Here, we compare predictions to experimental data for a set of 418 single residue mutations in 21 targets and find that the MM-GBSA model, on average, performs well at scoring these single protein residue mutations. Correlation between the predicted and experimental change in binding affinity is statistically significant and the model performs well at picking “hotspots,” or mutations that change binding affinity by more than 1 kcal/mol. The promising performance of this physics-based method with no tuned parameters for predicting binding energies suggests that it can be transferred to other protein engineering problems.     

A novel ensemble-based scoring and search algorithm for protein redesign and its application to modify the substrate specificity of the gramicidin synthetase a phenylalanine adenylation enzyme.

Realization of novel molecular function requires the ability to alter molecular complex formation. Enzymatic function can be altered by changing enzyme-substrate interactions via modification of an enzyme's active site. A redesigned enzyme may either perform a novel reaction on its native substrates or its native reaction on novel substrates. A number of computational approaches have been developed to address the combinatorial nature of the protein redesign problem. These approaches typically search for the global minimum energy conformation among an exponential number of protein conformations. We present a novel algorithm for protein redesign, which combines a statistical mechanics-derived ensemble-based approach to computing the binding constant with the speed and completeness of a branch-and-bound pruning algorithm. In addition, we developed an efficient deterministic approximation algorithm, capable of approximating our scoring function to arbitrary precision. In practice, the approximation algorithm decreases the execution time of the mutation search by a factor of ten. To test our method, we examined the Phe-specific adenylation domain of the nonribosomal peptide synthetase gramicidin synthetase A (GrsA-PheA). Ensemble scoring, using a rotameric approximation to the partition functions of the bound and unbound states for GrsA-PheA, is first used to predict binding of the wildtype protein and a previously described mutant (selective for leucine), and second, to switch the enzyme specificity toward leucine, using two novel active site sequences computationally predicted by searching through the space of possible active site mutations. The top scoring in silico mutants were created in the wetlab and dissociation/binding constants were determined by fluorescence quenching. These tested mutations exhibit the desired change in specificity from Phe to Leu. Our ensemble-based algorithm, which flexibly models both protein and ligand using rotamer-based partition functions, has application in enzyme redesign, the prediction of protein-ligand binding, and computer-aided drug design.     

Incorporating replacement free energy of binding‐site waters in molecular docking

Binding‐site water molecules play a crucial role in protein‐ligand recognition, either being displaced upon ligand binding or forming water bridges to stabilize the complex. However, rigorously treating explicit binding‐site waters is challenging in molecular docking, which requires to fully sample ensembles of waters and to consider the free energy cost of replacing waters. Here, we describe a method to incorporate structural and energetic properties of binding‐site waters into molecular docking. We first developed a solvent property analysis (SPA) program to compute the replacement free energies of binding‐site water molecules by post‐processing molecular dynamics trajectories obtained from ligand‐free protein structure simulation in explicit water. Next, we implemented a distance‐dependent scoring term into DOCK scoring function to take account of the water replacement free energy cost upon ligand binding. We assessed this approach in protein targets containing important binding‐site waters, and we demonstrated that our approach is reliable in reproducing the crystal binding geometries of protein‐ligand‐water complexes, as well as moderately improving the ligand docking enrichment performance. In addition, SPA program (free available to academic users upon request) may be applied in identifying hot‐spot binding‐site residues and structure‐based lead optimization. Proteins 2014; 82:1765–1776. © 2014 Wiley Periodicals, Inc.     

Energy functions for protein design: adjustment with protein-protein complex affinities, models for the unfolded state, and negative design of solubility and specificity

The development of the EGAD program and energy function for protein design is described. In contrast to most protein design methods, which require several empirical parameters or heuristics such as patterning of residues or rotamers, EGAD has a minimalist philosophy; it uses very few empirical factors to account for inaccuracies resulting from the use of fixed backbones and discrete rotamers in protein design calculations, and describes the unfolded state, aggregates, and alternative conformers explicitly with physical models instead of fitted parameters. This approach unveils important issues in protein design that are often camouflaged by heuristic-emphasizing methods. Inter-atom energies are modeled with the OPLS-AA all-atom forcefield, electrostatics with the generalized Born continuum model, and the hydrophobic effect with a solvent-accessible surface area-dependent term. Experimental characterization of proteins designed with an unmodified version of the energy function revealed problems with under-packing, stability, aggregation, and structural specificity. Under-packing was addressed by modifying the van der Waals function. By optimizing only three parameters, the effects of >400 mutations on protein-protein complex formation were predicted to within 1.0 kcal mol(-1). As an independent test, this modified energy function was used to predict the stabilities of >1500 mutants to within 1.0 kcal mol(-1); this required a physical model of the unfolded state that includes more interactions than traditional tripeptide-based models. Solubility and structural specificity were addressed with simple physical approximations of aggregation and conformational equilibria. The complete energy function can design protein sequences that have high levels of identity with their natural counterparts, and have predicted structural properties more consistent with soluble and uniquely folded proteins than the initial designs.     

Physical scoring function based on AMBER force field and Poisson-Boltzmann implicit solvent for protein structure prediction

A well-behaved physics-based all-atom scoring function for protein structure prediction is analyzed with several widely used all-atom decoy sets. The scoring function, termed AMBER/Poisson-Boltzmann (PB), is based on a refined AMBER force field for intramolecular interactions and an efficient PB model for solvation interactions. Testing on the chosen decoy sets shows that the scoring function, which is designed to consider detailed chemical environments, is able to consistently discriminate all 62 native crystal structures after considering the heteroatom groups, disulfide bonds, and crystal packing effects that are not included in the decoy structures. When NMR structures are considered in the testing, the scoring function is able to discriminate 8 out of 10 targets. In the more challenging test of selecting near-native structures, the scoring function also performs very well: for the majority of the targets studied, the scoring function is able to select decoys that are close to the corresponding native structures as evaluated by ranking numbers and backbone Calpha root mean square deviations. Various important components of the scoring function are also studied to understand their discriminative contributions toward the rankings of native and near-native structures. It is found that neither the nonpolar solvation energy as modeled by the surface area model nor a higher protein dielectric constant improves its discriminative power. The terms remaining to be improved are related to 1-4 interactions. The most troublesome term is found to be the large and highly fluctuating 1-4 electrostatics term, not the dihedral-angle term. These data support ongoing efforts in the community to develop protein structure prediction methods with physics-based potentials that are competitive with knowledge-based potentials.     

An all atom energy based computational protocol for predicting binding affinities of protein-ligand complexes

We report here a computationally fast protocol for predicting binding affinities of non-metallo protein-ligand complexes. The protocol builds in an all atom energy based empirical scoring function comprising electrostatics, van der Waals, hydrophobicity and loss of conformational entropy of protein side chains upon ligand binding. The method is designed to ensure transferability across diverse systems and has been validated on a heterogenous dataset of 161 complexes consisting of 55 unique protein targets. The scoring function trained on a dataset of 61 complexes yielded a correlation of r=0.92 for the predicted binding free energies against the experimental binding affinities. Model validation and parameter analysis studies ensure the predictive ability of the scoring function. When tested on the remaining 100 protein-ligand complexes a correlation of r=0.92 was recovered. The high correlation obtained underscores the potential applicability of the methodology in drug design endeavors. The scoring function has been web enabled at as binding affinity prediction of protein-ligand (BAPPL) server.     

Protein Structure Evaluation using an All-Atom Energy Based Empirical Scoring Function

Abstract

Arriving at the native conformation of a polypeptide chain characterized by minimum most free energy is a problem of long standing interest in protein structure prediction endeavors. Owing to the computational requirements in developing free energy estimates, scoring functions—energy based or statistical—have received considerable renewed attention in recent years for distinguishing native structures of proteins from non-native like structures. Several cleverly designed decoy sets, CASP (Critical Assessment of Techniques for Protein Structure Prediction) structures and homology based internet accessible three dimensional model builders are now available for validating the scoring functions. We describe here an all-atom energy based empirical scoring function and examine its performance on a wide series of publicly available decoys. Barring two protein sequences where native structure is ranked second and seventh, native is identified as the lowest energy structure in 67 protein sequences from among 61,659 decoys belonging to 12 different decoy sets. We further illustrate a potential application of the scoring function in bracketing native-like structures of two small mixed alpha/beta globular proteins starting from sequence and secondary structural information. The scoring function has been web enabled at www.scfbio-iitd.res.in/utility/proteomics/energy.jsp     

PSI-DOCK: towards highly efficient and accurate flexible ligand docking

We have developed a new docking method, Pose-Sensitive Inclined (PSI)-DOCK, for flexible ligand docking. An improved SCORE function has been developed and used in PSI-DOCK for binding free energy evaluation. The improved SCORE function was able to reproduce the absolute binding free energies of a training set of 200 protein-ligand complexes with a correlation coefficient of 0.788 and a standard error of 8.13 kJ/mol. For ligand binding pose exploration, a unique searching strategy was designed in PSI-DOCK. In the first step, a tabu-enhanced genetic algorithm with a rapid shape-complementary scoring function is used to roughly explore and store potential binding poses of the ligand. Then, these predicted binding poses are optimized and compete against each other by using a genetic algorithm with the accurate SCORE function to determine the binding pose with the lowest docking energy. The PSI-DOCK 1.0 program is highly efficient in identifying the experimental binding pose. For a test dataset of 194 complexes, PSI-DOCK 1.0 achieved a 67% success rate (RMSD < 2.0 A) for only one run and a 74% success rate for 10 runs. PSI-DOCK can also predict the docking binding free energy with high accuracy. For a test set of 64 complexes, the correlation between the experimentally observed binding free energies and the docking binding free energies for 64 complexes is r = 0.777 with a standard deviation of 7.96 kJ/mol. Moreover, compared with other docking methods, PSI-DOCK 1.0 is extremely easy to use and requires minimum docking preparations. There is no requirement for the users to add hydrogen atoms to proteins because all protein hydrogen atoms and the flexibility of the terminal protein atoms are intrinsically taken into account in PSI-DOCK. There is also no requirement for the users to calculate partial atomic charges because PSI-DOCK does not calculate an electrostatic energy term. These features are not only convenient for the users but also help to avoid the influence of different preparation methods.     

Side-chain modeling with an optimized scoring function

Modeling side-chain conformations on a fixed protein backbone has a wide application in structure prediction and molecular design. Each effort in this field requires decisions about a rotamer set, scoring function, and search strategy. We have developed a new and simple scoring function, which operates on side-chain rotamers and consists of the following energy terms: contact surface, volume overlap, backbone dependency, electrostatic interactions, and desolvation energy. The weights of these energy terms were optimized to achieve the minimal average root mean square (rms) deviation between the lowest energy rotamer and real side-chain conformation on a training set of high-resolution protein structures. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. We obtained prediction accuracy of 90.4% for chi(1), 78.3% for chi(1 + 2), and 1.18 A overall rms deviation. Furthermore, the derived scoring function combined with a Monte Carlo search algorithm was used to place all side chains onto a protein backbone simultaneously. The average prediction accuracy was 87.9% for chi(1), 73.2% for chi(1 + 2), and 1.34 A rms deviation for 30 protein structures. Our approach was compared with available side-chain construction methods and showed improvement over the best among them: 4.4% for chi(1), 4.7% for chi(1 + 2), and 0.21 A for rms deviation. We hypothesize that the scoring function instead of the search strategy is the main obstacle in side-chain modeling. Additionally, we show that a more detailed rotamer library is expected to increase chi(1 + 2) prediction accuracy but may have little effect on chi(1) prediction accuracy.     

Equilibrium denaturation of human growth hormone and its cysteine-modified forms

The equilibrium denaturation of human growth hormone (hGH) derived from heterologous gene expression in Escherichia coli was studied. Denaturation was measured by ultraviolet absorbance, intrinsic fluorescence, far ultraviolet circular dichroism, and size exclusion chromatography. The denaturation transitions obtained from each method of detection were coincident, indicating a two-state denaturation mechanism. The denaturation transitions were independent of the concentration of protein. The Gibbs free energy of unfolding is 14.5 +/- 1 kcal/mol. Human growth hormone contains two disulfide bridges between residues 53-165 (large loop) and 182-189 (small loop). The small loop was selectively reduced and cysteines alkylated with iodoacetic acid or iodoacetamide. The tetra-S-carbamidomethylated and tetra-S-carboxymethylated derivatives were also prepared. All S-alkylated hGH forms were indistinguishable from the native conformations in the absence of denaturant by far ultraviolet circular dichroism. The circular dichroism-detected equilibrium denaturation of each derivative was determined and the Gibbs free energy of unfolding of the tetra-S-modified forms was 5.3 +/- 0.5 kcal/mol and of the di-S-alkylated derivatives was 11.2 +/- 0.8 kcal/mol. These results for hGH are different than previously obtained results for bovine, ovine, and rat growth hormones. Stable equilibrium intermediates have been identified for these non-human species of growth hormone. The stable intermediates observed in the denaturation of reduced, alkylated hGH or nonhunam growth hormones are similar and characterized as compact, helical, lacking native-like tertiary structure, and having a tendency to aggregate. The apparent absence of intermediates in the folding of oxidized hGH is due to the relative instability of intermediates compared with their native structures. The hGH conformation is at least 5 kcal/mol more stable than the growth hormones from other species. Reduction and alkylation of the disulfide bridges of hGH diminish the stability differences between the native and intermediate states, such that the denaturation behavior is similar to the nonhuman growth hormones with well-populated intermediates. Most proteins do not demonstrate equilibrium folding intermediates presumably because intermediates are only marginally stable in conditions that disrupt the native state. The folding results with hGH and alkylated hGH substantiate this.     

PoPMuSiC,rationally designing point mutations in protein structures

PoPMuSiC is an efficient tool for rational computer-aided design of single-site mutations in proteins and peptides. Two types of queries can be submitted. The first option allows to estimate the changes in folding free energy for specific point mutations given by the user. In the second option, all possible point mutations in a given protein or protein region are performed and the most stabilizing or destabilizing mutations, or the neutral mutations with respect to thermodynamic stability, are selected. For each sequence position or secondary structure the deviation from the most stable sequence is moreover evaluated, which helps to identify the most suitable sites for the introduction of mutations.