Protein side‐chain modeling with a protein‐dependent optimized rotamer library

Despite years of effort, the problem of predicting the conformations of protein side chains remains a subject of inquiry. This problem has three major issues, namely defining the conformations that a side chain may adopt within a protein, developing a sampling procedure for generating possible side‐chain packings, and defining a scoring function that can rank these possible packings. To solve the former of these issues, most procedures rely on a rotamer library derived from databases of known protein structures. We introduce an alternative method that is free of statistics. We begin with a rotamer library that is based only on stereochemical considerations; this rotamer library is then optimized independently for each protein under study. We show that this optimization step restores the diversity of conformations observed in native proteins. We combine this protein‐dependent rotamer library (PDRL) method with the self‐consistent mean field (SCMF) sampling approach and a physics‐based scoring function into a new side‐chain prediction method, SCMF–PDRL. Using two large test sets of 831 and 378 proteins, respectively, we show that this new method compares favorably with competing methods such as SCAP, OPUS‐Rota, and SCWRL4 for energy‐minimized structures. Proteins 2014; 82:2000–2017. © 2014 Wiley Periodicals, Inc.     

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.     

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

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.     

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.     

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.     

Advantages of fine-grained side chain conformer libraries

We compare the modelling accuracy of two common rotamer libraries, the Dunbrack-Cohen and the 'Penultimate' rotamer libraries, with that of a novel library of discrete side chain conformations extracted from the Protein Data Bank. These side chain conformer libraries are extracted automatically from high-quality protein structures using stringent filters and maintain crystallographic bond lengths and angles. This contrasts with traditional rotamer libraries defined in terms of chi angles under the assumption of idealized covalent geometry. We demonstrate that side chain modelling onto native and near-native main chain conformations is significantly more successful with the conformer libraries than with the rotamer libraries when solely considering excluded-volume interactions. The rotamer libraries are inadequate to model side chains without atomic clashes on over 20% of targets if the backbone is held fixed in the native conformation. An algorithm is described for simultaneously modelling both main chain and side chain atoms during discrete ab initio sampling. The resulting models have equivalent root mean square deviations from the experimentally determined protein loops as models from backbone-only ensembles, indicating that all-atom modelling does not detract from the accuracy of conformational sampling.     

Structure refinement of protein model decoys requires accurate side‐chain placement

In this study, the application of temperature‐based replica‐exchange (T‐ReX) simulations for structure refinement of decoys taken from the I‐TASSER dataset was examined. A set of eight nonredundant proteins was investigated using self‐guided Langevin dynamics (SGLD) with a generalized Born implicit solvent model to sample conformational space. For two of the protein test cases, a comparison of the SGLD/T‐ReX method with that of a hybrid explicit/implicit solvent molecular dynamics T‐ReX simulation model is provided. Additionally, the effect of side‐chain placement among the starting decoy structures, using alternative rotamer conformations taken from the SCWRL4 modeling program, was investigated. The simulation results showed that, despite having near‐native backbone conformations among the starting decoys, the determinant of their refinement is side‐chain packing to a level that satisfies a minimum threshold of native contacts to allow efficient excursions toward the downhill refinement regime on the energy landscape. By repacking using SCWRL4 and by applying the RWplus statistical potential for structure identification, the SGLD/T‐ReX simulations achieved refinement to an average of 38% increase in the number of native contacts relative to the original I‐TASSER decoy sets and a 25% reduction in values of C_α root‐mean‐square deviation. The hybrid model succeeded in obtaining a sharper funnel to low‐energy states for a modeled target than the implicit solvent SGLD model; yet, structure identification remained roughly the same. Without meeting a threshold of near‐native packing of side chains, the T‐ReX simulations degrade the accuracy of the decoys, and subsequently, refinement becomes tantamount to the protein folding problem. Proteins 2013. 2012 Published by Wiley Periodicals, Inc.     

Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm

We describe an algorithm which enables us to search the conformational space of the side chains of a protein to identify the global minimum energy combination of side chain conformations as well as all other conformations within a specified energy cutoff of the global energy minimum. The program is used to explore the side chain conformational energy surface of a number of proteins, to investigate how this surface varies with the energy model used to describe the interactions within the system and the rotamer library. Enumeration of the rotamer combinations enables us to directly evaluate the partition function, and thus calculate the side chain contribution to the conformational entropy of the folded protein. An investigation of these conformations and the relationships between them shows that most of the conformations near to the global energy minimum arise from changes in side chain conformations that are essentially independent; very few result from a concerted change in conformation of two or more residues. Some of the limitations of the approach are discussed. Proteins 33:227–239, 1998. © 1998 Wiley-Liss, Inc.     

Solving and analyzing side-chain positioning problems using linear and integer programming

MOTIVATION: Side-chain positioning is a central component of homology modeling and protein design. In a common formulation of the problem, the backbone is fixed, side-chain conformations come from a rotamer library, and a pairwise energy function is optimized. It is NP-complete to find even a reasonable approximate solution to this problem. We seek to put this hardness result into practical context. RESULTS: We present an integer linear programming (ILP) formulation of side-chain positioning that allows us to tackle large problem sizes. We relax the integrality constraint to give a polynomial-time linear programming (LP) heuristic. We apply LP to position side chains on native and homologous backbones and to choose side chains for protein design. Surprisingly, when positioning side chains on native and homologous backbones, optimal solutions using a simple, biologically relevant energy function can usually be found using LP. On the other hand, the design problem often cannot be solved using LP directly; however, optimal solutions for large instances can still be found using the computationally more expensive ILP procedure. While different energy functions also affect the difficulty of the problem, the LP/ILP approach is able to find optimal solutions. Our analysis is the first large-scale demonstration that LP-based approaches are highly effective in finding optimal (and successive near-optimal) solutions for the side-chain positioning problem.     

SIDEpro: a novel machine learning approach for the fast and accurate prediction of side-chain conformations

Accurate protein side-chain conformation prediction is crucial for protein modeling and existing methods for the task are widely used; however, faster and more accurate methods are still required. Here we present a new machine learning approach to the problem where an energy function for each rotamer in a structure is computed additively over pairs of contacting atoms. A family of 156 neural networks indexed by amino acid and contacting atom types is used to compute these rotamer energies as a function of atomic contact distances. Although direct energy targets are not available for training, the neural networks can still be optimized by converting the energies to probabilities and optimizing these probabilities using Markov Chain Monte Carlo methods. The resulting predictor SIDEpro makes predictions by initially setting the rotamer probabilities for each residue from a backbone-dependent rotamer library, then iteratively updating these probabilities using the trained neural networks. After convergences of the probabilities, the side-chains are set to the highest probability rotamer. Finally, a post processing clash reduction step is applied to the models. SIDEpro represents a significant improvement in speed and a modest, but statistically significant, improvement in accuracy when compared with the state-of-the-art for rapid side-chain prediction method SCWRL4 on the following datasets: (1) 379 protein test set of SCWRL4; (2) 94 proteins from CASP9; (3) a set of seven large protein-only complexes; and (4) a ribosome with and without the RNA. Using the SCWRL4 test set, SIDEpro's accuracy (χ(1) 86.14%, χ(1+2) 74.15%) is slightly better than SCWRL4-FRM (χ(1) 85.43%, χ(1+2) 73.47%) and it is 7.0 times faster. On the same test set SIDEpro is clearly more accurate than SCWRL4-rigid rotamer model (RRM) (χ(1) 84.15%, χ(1+2) 71.24%) and 2.4 times faster. Evaluation on the additional test sets yield similar accuracy results with SIDEpro being slightly more accurate than SCWRL4-flexible rotamer model (FRM) and clearly more accurate than SCWRL4-RRM; however, the gap in CPU time is much more significant when the methods are applied to large protein complexes. SIDEpro is part of the SCRATCH suite of predictors and available from: http://scratch.proteomics.ics.uci.edu/.     

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.     

Beyond rotamers: a generative,probabilistic model of side chains in proteins

Background  

Accurately covering the conformational space of amino acid side chains is essential for important applications such as protein design, docking and high resolution structure prediction. Today, the most common way to capture this conformational space is through rotamer libraries - discrete collections of side chain conformations derived from experimentally determined protein structures. The discretization can be exploited to efficiently search the conformational space. However, discretizing this naturally continuous space comes at the cost of losing detailed information that is crucial for certain applications. For example, rigorously combining rotamers with physical force fields is associated with numerous problems.     

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.     

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

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

Structural basis of hierarchical multiple substates of a protein. III: Side chain and main chain local conformations

An analysis is carried out of differences in the minimum energy conformations obtained in the previous paper by energy minimization starting from conformations sampled by a Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. Main conformational differences in each pair of energy minima are found usually localized in several side chains and in a few local main chain segments. Such side chains and local main chain segments are found to take a few distinct local conformations in the minimum energy conformations. Energy minimum conformations can thus be described in terms of combinations of these multiple local conformations.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

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.