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.     

Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.     

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.     

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%.     

A graph-theory algorithm for rapid protein side-chain prediction

Fast and accurate side-chain conformation prediction is important for homology modeling, ab initio protein structure prediction, and protein design applications. Many methods have been presented, although only a few computer programs are publicly available. The SCWRL program is one such method and is widely used because of its speed, accuracy, and ease of use. A new algorithm for SCWRL is presented that uses results from graph theory to solve the combinatorial problem encountered in the side-chain prediction problem. In this method, side chains are represented as vertices in an undirected graph. Any two residues that have rotamers with nonzero interaction energies are considered to have an edge in the graph. The resulting graph can be partitioned into connected subgraphs with no edges between them. These subgraphs can in turn be broken into biconnected components, which are graphs that cannot be disconnected by removal of a single vertex. The combinatorial problem is reduced to finding the minimum energy of these small biconnected components and combining the results to identify the global minimum energy conformation. This algorithm is able to complete predictions on a set of 180 proteins with 34342 side chains in <7 min of computer time. The total chi(1) and chi(1 + 2) dihedral angle accuracies are 82.6% and 73.7% using a simple energy function based on the backbone-dependent rotamer library and a linear repulsive steric energy. The new algorithm will allow for use of SCWRL in more demanding applications such as sequence design and ab initio structure prediction, as well addition of a more complex energy function and conformational flexibility, leading to increased accuracy.     

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.     

GEM: a Gaussian Evolutionary Method for predicting protein side-chain conformations

We have developed an evolutionary approach to predicting protein side-chain conformations. This approach, referred to as the Gaussian Evolutionary Method (GEM), combines both discrete and continuous global search mechanisms. The former helps speed up convergence by reducing the size of rotamer space, whereas the latter, integrating decreasing-based Gaussian mutations and self-adaptive Gaussian mutations, continuously adapts dihedrals to optimal conformations. We tested our approach on 38 proteins ranging in size from 46 to 325 residues and showed that the results were comparable to those using other methods. The average accuracies of our predictions were 80% for chi(1), 66% for chi(1 + 2), and 1.36 A for the root mean square deviation of side-chain positions. We found that if our scoring function was perfect, the prediction accuracy was also essentially perfect. However, perfect prediction could not be achieved if only a discrete search mechanism was applied. These results suggest that GEM is robust and can be used to examine the factors limiting the accuracy of protein side-chain prediction methods. Furthermore, it can be used to systematically evaluate and thus improve scoring functions.     

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.     

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.     

Improved modeling of side-chains in proteins with rotamer-based methods: a flexible rotamer model

Side-chain modeling has a widespread application in many current methods for protein tertiary structure determination, prediction, and design. Of the existing side-chain modeling methods, rotamer-based methods are the fastest and most efficient. Classically, a rotamer is conceived as a single, rigid conformation of an amino acid sidechain. Here, we present a flexible rotamer model in which a rotamer is a continuous ensemble of conformations that cluster around the classic rigid rotamer. We have developed a thermodynamically based method for calculating effective energies for the flexible rotamer. These energies have a one-to-one correspondence with the potential energies of the rigid rotamer. Therefore, the flexible rotamer model is completely general and may be used with any rotamer-based method in substitution of the rigid rotamer model. We have compared the performance of the flexible and rigid rotamer models with one side-chain modeling method in particular (the self-consistent mean field theory method) on a set of 20 high quality crystallographic protein structures. For the flexible rotamer model, we obtained average predictions of 85.8% for chi1, 76.5% for chi1+2 and 1.34 A for root-mean-square deviation (RMSD); the corresponding values for core residues were 93.0%, 87.7% and 0.70 A, respectively. These values represent improvements of 7.3% for chi1, 8.1% for chi1+2 and 0.23 A for RMSD over the predictions obtained with the rigid rotamer model under otherwise identical conditions; the corresponding improvements for core residues were 6.9%, 10.5% and 0.43 A, respectively. We found that the predictions obtained with the flexible rotamer model were also significantly better than those obtained for the same set of proteins with another state-of-the-art side-chain placement method in the literature, especially for core residues. The flexible rotamer model represents a considerable improvement over the classic rigid rotamer model. It can, therefore, be used with considerable advantage in all rotamer-based methods commonly applied to protein tertiary structure determination, prediction, and design and also in predictions of free energies in mutational studies.     

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.     

Validation of NMR side-chain conformations by packing calculations

The precision and accuracy of protein structures determined by nuclear magnetic resonance (NMR) spectroscopy depend on the completeness of input experimental data set. Typically, rather than a single structure, an ensemble of up to 20 equally representative conformers is generated and routinely deposited in the Protein Database. There are substantially more experimentally derived restraints available to define the main-chain coordinates than those of the side chains. Consequently, the side-chain conformations among the conformers are more variable and less well defined than those of the backbone. Even when a side chain is determined with high precision and is found to adopt very similar orientations among all the conformers in the ensemble, it is possible that its orientation might still be incorrect. Thus, it would be helpful if there were a method to assess independently the side-chain orientations determined by NMR. Recently, homology modeling by side-chain packing algorithms has been shown to be successful in predicting the side-chain conformations of the buried residues for a protein when the main-chain coordinates and sequence information are given. Since the main-chain coordinates determined by NMR are consistently more reliable than those of the side-chains, we have applied the side-chain packing algorithms to predict side-chain conformations that are compatible with the NMR-derived backbone. Using four test cases where the NMR solution structures and the X-ray crystal structure of the same protein are available, we demonstrate that the side-chain packing method can provide independent validation for the side-chain conformations of NMR structures. Comparison of the side-chain conformations derived by side-chain packing prediction and by NMR spectroscopy demonstrates that when there is agreement between the NMR model and the predicted model, on average 78% of the time the X-ray structure also concurs. While the side-chain packing method can confirm the reliable residue conformations in NMR models, more importantly, it can also identify the questionable residue conformations with an accuracy of 60%. This validation method can serve to increase the confidence level for potential users of structural models determined by NMR.     

Statistical and conformational analysis of the electron density of protein side chains

Protein side chains make most of the specific contacts between proteins and other molecules, and their conformational properties have been studied for many years. These properties have been analyzed primarily in the form of rotamer libraries, which cluster the observed conformations into groups and provide frequencies and average dihedral angles for these groups. In recent years, these libraries have improved with higher resolution structures and using various criteria such as high thermal factors to eliminate side chains that may be misplaced within the crystallographic model coordinates. Many of these side chains have highly non-rotameric dihedral angles. The origin of side chains with high B-factors and/or with non-rotameric dihedral angles is of interest in the determination of protein structures and in assessing the prediction of side chain conformations. In this paper, using a statistical analysis of the electron density of a large set of proteins, it is shown that: (1) most non-rotameric side chains have low electron density compared to rotameric side chains; (2) up to 15% of chi1 non-rotameric side chains in PDB models can clearly be fit to density at a single rotameric conformation and in some cases multiple rotameric conformations; (3) a further 47% of non-rotameric side chains have highly dispersed electron density, indicating potentially interconverting rotameric conformations; (4) the entropy of these side chains is close to that of side chains annotated as having more than one chi(1) rotamer in the crystallographic model; (5) many rotameric side chains with high entropy clearly show multiple conformations that are not annotated in the crystallographic model. These results indicate that modeling of side chains alternating between rotamers in the electron density is important and needs further improvement, both in structure determination and in structure prediction.     

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.     

Analysis of side-chain rotamers in transmembrane proteins

We measured the frequency of side-chain rotamers in 14 alpha-helical and 16 beta-barrel membrane protein structures and found that the membrane environment considerably perturbs the rotamer frequencies compared to soluble proteins. Although there are limited experimental data, we found statistically significant changes in rotamer preferences depending on the residue environment. Rotamer distributions were influenced by whether the residues were lipid or protein facing, and whether the residues were found near the N- or C-terminus. Hydrogen-bonding interactions with the helical backbone perturbs the rotamer populations of Ser and His. Trp and Tyr favor side-chain conformations that allow their side chains to extend their polar atoms out of the membrane core, thereby aligning the side-chain polarity gradient with the polarity gradient of the membrane. Our results demonstrate how the membrane environment influences protein structures, providing information that will be useful in the structure prediction and design of transmembrane proteins.     

Analysis of the relationship between side-chain conformation and secondary structure in globular proteins

The relationship between the preferred side-chain dihedral angles and the secondary structure of a residue was examined. The structures of 61 proteins solved to a resolution of 2.0 A (1 A = 0.1 nm) or better were analysed using a relational database to store the information. The strongest feature observed was that the chi 1 distribution for most side-chains in an alpha-helix showed an absence of the g- conformation and a shift towards the t conformation when compared to the non-alpha/beta structures. The exceptions to this tendency were for short polar side-chains that form hydrogen bonds with the main-chain which prefer g+. Shifts in the chi 1 preferences for residues in the beta-sheet were observed. Other side-chain dihedral angles (chi 2, chi 3, chi 4) were found to be influenced by the main-chain. This paper presents more accurate distributions for the side-chain dihedral angles which were obtained from the increased number of proteins determined to high resolution. The means and standard deviations for chi 1 and chi 2 angles are presented for all residues according to the secondary structure of the main-chain. The means and standard deviations are given for the most popular conformations for side-chains in which chi 3 and chi 4 rotations affect the position of C atoms.     

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.     

The role of carbon-donor hydrogen bonds in stabilizing tryptophan conformations

Although most side-chain torsion angles correspond to low-energy rotameric positions, deviations occur with significant frequency. One striking example arises in Trp residues, which have an important role in stabilizing protein structures because of their size and mixed hydrophobic/hydrophilic character. Ten percent of Trp side-chains have unexplained conformations with chi(2) near 0 degrees instead of the expected 90 degrees. The current work is a structural and energetic analysis of these conformations. It is shown that many Trp residues with these orientations are stabilized by three-center carbon-donor hydrogen bonds of the form C-H...X...H-C, where X is a polar hydrogen-bond acceptor in the environment of the side-chain. The bridging hydrogen bonds occur both within the Trp side-chain and between the side-chain and the local protein backbone. Free energy maps of an isolated Trp residue in an explicit water environment show a minimum corresponding to the off-rotamer peak observed in the crystallographic data. Bridging carbon-donor hydrogen bonds are also shown to stabilize on-rotamer Trp conformations, and similar bridging hydrogen bonds also stabilize some off-rotamer Asp conformations. The present results suggest a previously unrecognized role for three-center carbon-donor hydrogen bonds in protein structures and support the view that the off-rotamer Trp side-chain orientations are real rather than artifacts of crystallographic refinements. Certain of the off-rotamer Trp conformations appear to have a functional role.     

Constructing side chains on near-native main chains for ab initio protein structure prediction

Is there value in constructing side chains while searching protein conformational space during an ab initio simulation? If so, what is the most computationally efficient method for constructing these side chains? To answer these questions, four published approaches were used to construct side chain conformations on a range of near-native main chains generated by ab initio protein structure prediction methods. The accuracy of these approaches was compared with a naive approach that selects the most frequently observed rotamer for a given amino acid to construct side chains. An all-atom conditional probability discriminatory function is useful at selecting conformations with overall low all-atom root mean square deviation (r.m.s.d.) and the discrimination improves on sets that are closer to the native conformation. In addition, the naive approach performs as well as more sophisticated methods in terms of the percentage of chi(1) angles built accurately and the all-atom r. m.s.d., between the native and near-native conformations. The results suggest that the naive method would be extremely useful for fast and efficient side chain construction on vast numbers of conformations for ab initio prediction of protein structure.