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.     

Improved side-chain prediction accuracy using an ab initio potential energy function and a very large rotamer library

Accurate prediction of the placement and comformations of protein side chains given only the backbone trace has a wide range of uses in protein design, structure prediction, and functional analysis. Prediction has most often relied on discrete rotamer libraries so that rapid fitness of side-chain rotamers can be assessed against some scoring function. Scoring functions are generally based on experimental parameters from small-molecule studies or empirical parameters based on determined protein structures. Here, we describe the NCN algorithm for predicting the placement of side chains. A predominantly first-principles approach was taken to develop the potential energy function incorporating van der Waals and electrostatics based on the OPLS parameters, and a hydrogen bonding term. The only empirical knowledge used is the frequency of rotameric states from the PDB. The rotamer library includes nearly 50,000 rotamers, and is the most extensive discrete library used to date. Although the computational time tends to be longer than most other algorithms, the overall accuracy exceeds all algorithms in the literature when placing rotamers on an accurate backbone trace. Considering only the most buried residues, 80% of the total residues tested, the placement accuracy reaches 92% for chi(1), and 83% for chi(1 + 2), and an overall RMS deviation of 1 A. Additionally, we show that if information is available to restrict chi(1) to one rotamer well, then this algorithm can generate structures with an average RMS deviation of 1.0 A for all heavy side-chains atoms and a corresponding overall chi(1 + 2) accuracy of 85.0%.     

Docking and scoring with alternative side-chain conformations

We describe a scoring and modeling procedure for docking ligands into protein models that have either modeled or flexible side-chain conformations. Our methodical contribution comprises a procedure for generating new potentials of mean force for the ROTA scoring function which we have introduced previously for optimizing side-chain conformations with the tool IRECS. The ROTA potentials are specially trained to tolerate small-scale positional errors of atoms that are characteristic of (i) side-chain conformations that are modeled using a sparse rotamer library and (ii) ligand conformations that are generated using a docking program. We generated both rigid and flexible protein models with our side-chain prediction tool IRECS and docked ligands to proteins using the scoring function ROTA and the docking programs FlexX (for rigid side chains) and FlexE (for flexible side chains). We validated our approach on the forty screening targets of the DUD database. The validation shows that the ROTA potentials are especially well suited for estimating the binding affinity of ligands to proteins. The results also show that our procedure can compensate for the performance decrease in screening that occurs when using protein models with side chains modeled with a rotamer library instead of using X-ray structures. The average runtime per ligand of our method is 168 seconds on an Opteron V20z, which is fast enough to allow virtual screening of compound libraries for drug candidates.     

Protein side-chain packing problem: a maximum edge-weight clique algorithmic approach

"Protein Side-chain Packing" has an ever-increasing application in the field of bio-informatics, dating from the early methods of homology modeling to protein design and to the protein docking. However, this problem is computationally known to be NP-hard. In this regard, we have developed a novel approach to solve this problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain packing problem to a graph and then solving the reduced graph to find the maximum clique by applying an efficient clique finding algorithm developed by our co-authors. Since our approach is based on deterministic algorithms in contrast to the various existing algorithms based on heuristic approaches, our algorithm guarantees of finding an optimal solution. We have tested this approach to predict the side-chain conformations of a set of proteins and have compared the results with other existing methods. We have found that our results are favorably comparable or better than the results produced by the existing methods. As our test set contains a protein of 494 residues, we have obtained considerable improvement in terms of size of the proteins and in terms of the efficiency and the accuracy of prediction.     

Configurational-bias sampling technique for predicting side-chain conformations in proteins

Prediction of side-chain conformations is an important component of several biological modeling applications. In this work, we have developed and tested an advanced Monte Carlo sampling strategy for predicting side-chain conformations. Our method is based on a cooperative rearrangement of atoms that belong to a group of neighboring side-chains. This rearrangement is accomplished by deleting groups of atoms from the side-chains in a particular region, and regrowing them with the generation of trial positions that depends on both a rotamer library and a molecular mechanics potential function. This method allows us to incorporate flexibility about the rotamers in the library and explore phase space in a continuous fashion about the primary rotamers. We have tested our algorithm on a set of 76 proteins using the all-atom AMBER99 force field and electrostatics that are governed by a distance-dependent dielectric function. When the tolerance for correct prediction of the dihedral angles is a <20 degrees deviation from the native state, our prediction accuracies for chi1 are 83.3% and for chi1 and chi2 are 65.4%. The accuracies of our predictions are comparable to the best results in the literature that often used Hamiltonians that have been specifically optimized for side-chain packing. We believe that the continuous exploration of phase space enables our method to overcome limitations inherent with using discrete rotamers as trials.     

Extending the accuracy limits of prediction for side-chain conformations

Current techniques for the prediction of side-chain conformations on a fixed backbone have an accuracy limit of about 1.0-1.5 A rmsd for core residues. We have carried out a detailed and systematic analysis of the factors that influence the prediction of side-chain conformation and, on this basis, have succeeded in extending the limits of side-chain prediction for core residues to about 0.7 A rmsd from native, and 94 % and 89 % of chi(1) and chi(1+2 ) dihedral angles correctly predicted to within 20 degrees of native, respectively. These results are obtained using a force-field that accounts for only van der Waals interactions and torsional potentials. Prediction accuracy is strongly dependent on the rotamer library used. That is, a complete and detailed rotamer library is essential. The greatest accuracy was obtained with an extensive rotamer library, containing over 7560 members, in which bond lengths and bond angles were taken from the database rather than simply assuming idealized values. Perhaps the most surprising finding is that the combinatorial problem normally associated with the prediction of the side-chain conformation does not appear to be important. This conclusion is based on the fact that the prediction of the conformation of a single side-chain with all others fixed in their native conformations is only slightly more accurate than the simultaneous prediction of all side-chain dihedral angles.     

GEMDOCK: a generic evolutionary method for molecular docking

We have developed an evolutionary approach for flexible ligand docking. This approval, GEMDOCK, uses a Generic Evolutionary Method for molecular DOCKing and an empirical scoring function. The former combines both discrete and continuous global search strategies with local search strategies to speed up convergence, whereas the latter results in rapid recognition of potential ligands. GEMDOCK was tested on a diverse data set of 100 protein-ligand complexes from the Protein Data Bank. In 79% of these complexes, the docked lowest energy ligand structures had root-mean-square derivations (RMSDs) below 2.0 A with respect to the corresponding crystal structures. The success rate increased to 85% if the structure water molecules were retained. We evaluated GEMDOCK on two cross-docking experiments in which each ligand of a protein ensemble was docked into each protein of the ensemble. Seventy-six percent of the docked structures had RMSDs below 2.0 A when the ligands were docked into foreign structures. We analyzed and validated GEMDOCK with respect to various search spaces and scoring functions, and found that if the scoring function was perfect, then the predicted accuracy was also essentially perfect. This study suggests that GEMDOCK is a useful tool for molecular recognition and may be used to systematically evaluate and thus improve scoring functions.     

Coupling Protein Side-Chain and Backbone Flexibility Improves the Re-design of Protein-Ligand Specificity

Interactions between small molecules and proteins play critical roles in regulating and facilitating diverse biological functions, yet our ability to accurately re-engineer the specificity of these interactions using computational approaches has been limited. One main difficulty, in addition to inaccuracies in energy functions, is the exquisite sensitivity of protein–ligand interactions to subtle conformational changes, coupled with the computational problem of sampling the large conformational search space of degrees of freedom of ligands, amino acid side chains, and the protein backbone. Here, we describe two benchmarks for evaluating the accuracy of computational approaches for re-engineering protein-ligand interactions: (i) prediction of enzyme specificity altering mutations and (ii) prediction of sequence tolerance in ligand binding sites. After finding that current state-of-the-art “fixed backbone” design methods perform poorly on these tests, we develop a new “coupled moves” design method in the program Rosetta that couples changes to protein sequence with alterations in both protein side-chain and protein backbone conformations, and allows for changes in ligand rigid-body and torsion degrees of freedom. We show significantly increased accuracy in both predicting ligand specificity altering mutations and binding site sequences. These methodological improvements should be useful for many applications of protein – ligand design. The approach also provides insights into the role of subtle conformational adjustments that enable functional changes not only in engineering applications but also in natural protein evolution.     

Combining evolutionary and structural information for local protein structure prediction

We study the effects of various factors in representing and combining evolutionary and structural information for local protein structural prediction based on fragment selection. We prepare databases of fragments from a set of non-redundant protein domains. For each fragment, evolutionary information is derived from homologous sequences and represented as estimated effective counts and frequencies of amino acids (evolutionary frequencies) at each position. Position-specific amino acid preferences called structural frequencies are derived from statistical analysis of discrete local structural environments in database structures. Our method for local structure prediction is based on ranking and selecting database fragments that are most similar to a target fragment. Using secondary structure type as a local structural property, we test our method in a number of settings. The major findings are: (1) the COMPASS-type scoring function for fragment similarity comparison gives better prediction accuracy than three other tested scoring functions for profile-profile comparison. We show that the COMPASS-type scoring function can be derived both in the probabilistic framework and in the framework of statistical potentials. (2) Using the evolutionary frequencies of database fragments gives better prediction accuracy than using structural frequencies. (3) Finer definition of local environments, such as including more side-chain solvent accessibility classes and considering the backbone conformations of neighboring residues, gives increasingly better prediction accuracy using structural frequencies. (4) Combining evolutionary and structural frequencies of database fragments, either in a linear fashion or using a pseudocount mixture formula, results in improvement of prediction accuracy. Combination at the log-odds score level is not as effective as combination at the frequency level. This suggests that there might be better ways of combining sequence and structural information than the commonly used linear combination of log-odds scores. Our method of fragment selection and frequency combination gives reasonable results of secondary structure prediction tested on 56 CASP5 targets (average SOV score 0.77), suggesting that it is a valid method for local protein structure prediction. Mixture of predicted structural frequencies and evolutionary frequencies improve the quality of local profile-to-profile alignment by COMPASS.     

Improved side-chain modeling for protein-protein docking

Success in high-resolution protein-protein docking requires accurate modeling of side-chain conformations at the interface. Most current methods either leave side chains fixed in the conformations observed in the unbound protein structures or allow the side chains to sample a set of discrete rotamer conformations. Here we describe a rapid and efficient method for sampling off-rotamer side-chain conformations by torsion space minimization during protein-protein docking starting from discrete rotamer libraries supplemented with side-chain conformations taken from the unbound structures, and show that the new method improves side-chain modeling and increases the energetic discrimination between good and bad models. Analysis of the distribution of side-chain interaction energies within and between the two protein partners shows that the new method leads to more native-like distributions of interaction energies and that the neglect of side-chain entropy produces a small but measurable increase in the number of residues whose interaction energy cannot compensate for the entropic cost of side-chain freezing at the interface. The power of the method is highlighted by a number of predictions of unprecedented accuracy in the recent CAPRI (Critical Assessment of PRedicted Interactions) blind test of protein-protein docking methods.     

Excluded volume in protein side-chain packing

The excluded volume occupied by protein side-chains and the requirement of high packing density in the protein interior should severely limit the number of side-chain conformations compatible with a given native backbone. To examine the relationship between side-chain geometry and side-chain packing, we use an all-atom Monte Carlo simulation to sample the large space of side-chain conformations. We study three models of excluded volume and use umbrella sampling to effectively explore the entire space. We find that while excluded volume constraints reduce the size of conformational space by many orders of magnitude, the number of allowed conformations is still large. An average repacked conformation has 20 % of its chi angles in a non-native state, a marked reduction from the expected 67 % in the absence of excluded volume. Interestingly, well-packed conformations with up to 50 % non-native chi angles exist. The repacked conformations have native packing density as measured by a standard Voronoi procedure. Entropy is distributed non-uniformly over positions, and we partially explain the observed distribution using rotamer probabilities derived from the Protein Data Bank database. In several cases, native rotamers that occur infrequently in the database are seen with high probability in our simulation, indicating that sequence-specific excluded volume interactions can stabilize rotamers that are rare for a given backbone. In spite of our finding that 65 % of the native rotamers and 85 % of chi(1) angles can be predicted correctly on the basis of excluded volume only, 95 % of positions can accommodate more than one rotamer in simulation. We estimate that, in order to quench the side-chain entropy observed in the presence of excluded volume interactions, other interactions (hydrophobic, polar, electrostatic) must provide an additional stabilization of at least 0.6 kT per residue in order to single out the native state.     

Determinants of protein side-chain packing.

The problem of protein side-chain packing for a given backbone trace is investigated using 3 different prediction models. The first requires an exhaustive search of all possible combinations of side-chain conformers, using the dead-end elimination theorem. The second considers only side-chain-backbone interactions, whereas the third neglects side-chain-backbone interactions and instead keeps side-chain-side-chain interactions. Predictions of side-chain conformations for 11 proteins using all 3 models show that removal of side-chain-side-chain interactions does not cause a large decrease in the prediction accuracy, whereas the model having only side-chain-side-chain interactions still retains a significant level of accuracy. These results suggest that the 2 classes of interactions, side-chain-backbone and side-chain-side-chain, are consistent with each other and work concurrently to stabilize the native conformations. This is confirmed by analyses of energy spectra of the side-chain conformations derived from the fourth prediction model, the Independent model, which gives almost the same quality of the prediction as the dead-end elimination. The analyses indicate that the 2 classes of interactions simultaneously increase the energy difference between the native and nonnative conformations.     

IRECS: a new algorithm for the selection of most probable ensembles of side-chain conformations in protein models

We introduce a new algorithm, IRECS (Iterative REduction of Conformational Space), for identifying ensembles of most probable side-chain conformations for homology modeling. On the basis of a given rotamer library, IRECS ranks all side-chain rotamers of a protein according to the probability with which each side chain adopts the respective rotamer conformation. This ranking enables the user to select small rotamer sets that are most likely to contain a near-native rotamer for each side chain. IRECS can therefore act as a fast heuristic alternative to the Dead-End-Elimination algorithm (DEE). In contrast to DEE, IRECS allows for the selection of rotamer subsets of arbitrary size, thus being able to define structure ensembles for a protein. We show that the selection of more than one rotamer per side chain is generally meaningful, since the selected rotamers represent the conformational space of flexible side chains. A knowledge-based statistical potential ROTA was constructed for the IRECS algorithm. The potential was optimized to discriminate between side-chain conformations of native and rotameric decoys of protein structures. By restricting the number of rotamers per side chain to one, IRECS can optimize side chains for a single conformation model. The average accuracy of IRECS for the chi1 and chi1+2 dihedral angles amounts to 84.7% and 71.6%, respectively, using a 40 degrees cutoff. When we compared IRECS with SCWRL and SCAP, the performance of IRECS was comparable to that of both methods. IRECS and the ROTA potential are available for download from the URL http://irecs.bioinf.mpi-inf.mpg.de.     

Analysis of a data set of paired uncomplexed protein structures: new metrics for side-chain flexibility and model evaluation

We compiled and analyzed a data set of paired protein structures containing proteins for which multiple high-quality uncomplexed atomic structures were available in the Protein Data Bank. Side-chain flexibility was quantified, yielding a set of residue- and environment-specific confidence levels describing the range of motion around chi1 and chi2 angles. As expected, buried residues were inflexible, adopting similar conformations in different crystal structure analyses. Ile, Thr, Asn, Asp, and the large aromatics also showed limited flexibility when exposed on the protein surface, whereas exposed Ser, Lys, Arg, Met, Gln, and Glu residues were very flexible. This information is different from and complementary to the information available from rotamer surveys. The confidence levels are useful for assessing the significance of observed side-chain motion and estimating the extent of side-chain motion in protein structure prediction. We compare the performance of a simple 40 degrees threshold with these quantitative confidence levels in a critical evaluation of side-chain prediction with the program SCWRL.     

Accuracy of side-chain prediction upon near-native protein backbones generated by ab initio folding methods

The ab initio folding problem can be divided into two sequential tasks of approximately equal computational complexity: the generation of native-like backbone folds and the positioning of side chains upon these backbones. The prediction of side-chain conformation in this context is challenging, because at best only the near-native global fold of the protein is known. To test the effect of displacements in the protein backbones on side-chain prediction for folds generated ab initio, sets of near-native backbones (≤ 4 Å Cα RMS error) for four small proteins were generated by two methods. The steric environment surrounding each residue was probed by placing the side chains in the native conformation on each of these decoys, followed by torsion-space optimization to remove steric clashes on a rigid backbone. We observe that on average 40% of the χ1 angles were displaced by 40° or more, effectively setting the limits in accuracy for side-chain modeling under these conditions. Three different algorithms were subsequently used for prediction of side-chain conformation. The average prediction accuracy for the three methods was remarkably similar: 49% to 51% of the χ1 angles were predicted correctly overall (33% to 36% of the χ1+2 angles). Interestingly, when the inter-side-chain interactions were disregarded, the mean accuracy increased. A consensus approach is described, in which side-chain conformations are defined based on the most frequently predicted χ angles for a given method upon each set of near-native backbones. We find that consensus modeling, which de facto includes backbone flexibility, improves side-chain prediction: χ1 accuracy improved to 51–54% (36–42% of χ1+2). Implications of a consensus method for ab initio protein structure prediction are discussed. Proteins 33:204–217, 1998. © 1998 Wiley-Liss, Inc.     

Beyond the rotamer library: genetic algorithm combined with the disturbing mutation process for upbuilding protein side-chains

The disturbing genetic algorithm, incorporating the disturbing mutation process into the genetic algorithm flow, has been developed to extend the searching space of side-chain conformations and to improve the quality of the rotamer library. Moreover, the growing generation amount idea, simulating the real situation of the natural evolution, is introduced to improve the searching speed. In the calculations using the pseudo energy scoring function of the root mean squared deviation, the disturbing genetic algorithm method has been shown to be highly efficient. With the real energy function based on AMBER force field, the program has been applied to rebuilding side-chain conformations of 25 high-quality crystallographic structures of single-protein and protein-protein complexes. The averaged root mean standard deviation of atom coordinates in side-chains and veracities of the torsion angles of chi(1) and chi(1) + chi(2) are 1.165 A, 88.2 and 72.9% for the buried residues, respectively, and 1.493 A, 79.2 and 64.7% for all residues, showing that the method has equal precision to the program SCWRL, whereas it performs better in the prediction of buried residues and protein-protein interfaces. This method has been successfully used in redesigning the interface of the Basnase-Barstar complex, indicating that it will have extensive application in protein design, protein sequence and structure relationship studies, and research on protein-protein interaction.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.     

The use of side-chain packing methods in modeling bacteriophage repressor and cro proteins.

In recent years, it has been repeatedly demonstrated that the coordinates of the main-chain atoms alone are sufficient to determine the side-chain conformations of buried residues of compact proteins. Given a perfect backbone, the side-chain packing method can predict the side-chain conformations to an accuracy as high as 1.2 Å RMS deviation (RMSD) with greater than 80% of the χ angles correct. However, similarly rigorous studies have not been conducted to determine how well these apply, if at all, to the more important problem of homology modeling per se. Specifically, if the available backbone is imperfect, as expected for practical application of homology modeling, can packing constraints alone achieve sufficiently accurate predictions to be useful? Here, by systematically applying such methods to the pairwise modeling of two repressor and two cro proteins from the closely related bacteriophages 434 and P22, we find that when the backbone RMSD is 0.8 Å, the prediction on buried side chain is accurate with an RMS error of 1.8 Å and approximately 70% of the χ angles correctly predicted. When the backbone RMSD is larger, in the range of 1.6–1.8 Å, the prediction quality is still significantly better than random, with RMS error at 2.2 Å on the buried side chains and 60% accuracy on χ angles. Together these results suggest the following rules-of-thumb for homology modeling of buried side chains. When the sequence identity between the modeled sequence and the template sequence is >50% (or, equivalently, the expected backbone RMSD is <1 Å), side-chain packing methods work well. When sequence identity is between 30–50%, reflecting a backbone RMS error of 1–2 Å, it is still valid to use side-chain packing methods to predict the buried residues, albeit with care. When sequence identity is below 30% (or backbone RMS error greater than 2 Å), the backbone constraint alone is unlikely to produce useful models. Other methods, such as those involving the use of database fragments to reconstruct a template backbone, may be necessary as a complementary guide for modeling.