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.     

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.     

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.     

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.     

Database algorithm for generating protein backbone and side-chain co-ordinates from a C alpha trace application to model building and detection of co-ordinate errors

The problem of constructing all-atom model co-ordinates of a protein from an outline of the polypeptide chain is encountered in protein structure determination by crystallography or nuclear magnetic resonance spectroscopy, in model building by homology and in protein design. Here, we present an automatic procedure for generating full protein co-ordinates (backbone and, optionally, side-chains) given the C alpha trace and amino acid sequence. To construct backbones, a protein structure database is first scanned for fragments that locally fit the chain trace according to distance criteria. A best path algorithm then sifts through these segments and selects an optimal path with minimal mismatch at fragment joints. In blind tests, using fully known protein structures, backbones (C alpha, C, N, O) can be reconstructed with a reliability of 0.4 to 0.6 A root-mean-square position deviation and not more than 0 to 5% peptide flips. This accuracy is sufficient to identify possible errors in protein co-ordinate sets. To construct full co-ordinates, side-chains are added from a library of frequently occurring rotamers using a simple and fast Monte Carlo procedure with simulated annealing. In tests on X-ray structures determined at better than 2.5 A resolution, the positions of side-chain atoms in the protein core (less than 20% relative accessibility) have an accuracy of 1.6 A (r.m.s. deviation) and 70% of chi 1 angles are within 30 degrees of the X-ray structure. The computer program MaxSprout is available on request.     

Building alternate protein structures using the elastic network model

We describe a method for efficiently generating ensembles of alternate, all-atom protein structures that (a) differ significantly from the starting structure, (b) have good stereochemistry (bonded geometry), and (c) have good steric properties (absence of atomic overlap). The method uses reconstruction from a series of backbone framework structures that are obtained from a modified elastic network model (ENM) by perturbation along low-frequency normal modes. To ensure good quality backbone frameworks, the single force parameter ENM is modified by introducing two more force parameters to characterize the interaction between the consecutive carbon alphas and those within the same secondary structure domain. The relative stiffness of the three parameters is parameterized to reproduce B-factors, while maintaining good bonded geometry. After parameterization, violations of experimental Calpha-Calpha distances and Calpha-Calpha-Calpha pseudo angles along the backbone are reduced to less than 1%. Simultaneously, the average B-factor correlation coefficient improves to R = 0.77. Two applications illustrate the potential of the approach. (1) 102,051 protein backbones spanning a conformational space of 15 A root mean square deviation were generated from 148 nonredundant proteins in the PDB database, and all-atom models with minimal bonded and nonbonded violations were produced from this ensemble of backbone structures using the SCWRL side chain building program. (2) Improved backbone templates for homology modeling. Fifteen query sequences were each modeled on two targets. For each of the 30 target frameworks, dozens of improved templates could be produced In all cases, improved full atom homology models resulted, of which 50% could be identified blind using the D-Fire statistical potential.     

Rebuilding flavodoxin from C alpha coordinates: a test study

The tertiary structure of flavodoxin has been model built from only the X-ray crystallographic alpha-carbon coordinates. Main-chain atoms were generated from a dictionary of backbone structures. Side-chain conformations were initially set according to observed statistical distributions, clashes were resolved with reference to other knowledge-based parameters, and finally, energy minimization was applied. The RMSD of the model was 1.7 A across all atoms to the native structure. Regular secondary structural elements were modeled more accurately than other regions. About 40% of the chi 1 torsional angles were modeled correctly. Packing of side chains in the core was energetically stable but diverged significantly from the native structure in some regions. The modeling of protein structures is increasing in popularity but relatively few checks have been applied to determine the accuracy of the approach. In this work a variety of parameters have been examined. It was found that close contacts, and hydrogen-bonding patterns could identify poorly packed residues. These tests, however, did not indicate which residues had a conformation different from the native structure or how to move such residues to bring them into agreement. To assist in the modeling of interacting side chains a database of known interactions has been prepared.     

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.     

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%.     

Conformational fluctuations versus constraints in amino acid side chains: the evolution of information content from free amino acids to proteins

Like all other complex biological systems, proteins exhibit properties not found in free amino acids (i.e., emergent properties). Here, we explore top-down constraints experienced by the residue side chains in proteins compared to amino acids in increasingly complex molecular environments: free amino acids, end-capped amino acids, and the central residue in an alpha-helical nonapeptide. The crystalline structure of the contractile protein profilin Ib and the enzyme trypsin were chosen as objects of study, and submitted to 10 ns molecular dynamics (MD) simulations. The results revealed increased conformational constraints on the side chains when going from the simpler to the more complex compounds. A Shannon entropy (SE) analysis of the conformational behavior of the side chains showed in most cases a progressive and marked decrease in the SE of the chi1 and chi2 dihedral angles. This is equivalent to stating that conformational constraints on the side chain of residues increase their information content and, hence, recognition specificity compared to free amino acids. In other words, the vastly increased information content of a protein relative to its free monomers is embedded not only in the tertiary structure of the backbone, but also in the conformational behavior of the side chains. The postulated implication is that both backbone and side chains, by virtue of being conformationally constrained, contribute to the protein's recognition specificity toward other macromolecules and ligands.     

Discrete restraint-based protein modeling and the Calpha-trace problem

We present a novel de novo method to generate protein models from sparse, discretized restraints on the conformation of the main chain and side chain atoms. We focus on Calpha-trace generation, the problem of constructing an accurate and complete model from approximate knowledge of the positions of the Calpha atoms and, in some cases, the side chain centroids. Spatial restraints on the Calpha atoms and side chain centroids are supplemented by constraints on main chain geometry, phi/xi angles, rotameric side chain conformations, and inter-atomic separations derived from analyses of known protein structures. A novel conformational search algorithm, combining features of tree-search and genetic algorithms, generates models consistent with these restraints by propensity-weighted dihedral angle sampling. Models with ideal geometry, good phi/xi angles, and no inter-atomic overlaps are produced with 0.8 A main chain and, with side chain centroid restraints, 1.0 A all-atom root-mean-square deviation (RMSD) from the crystal structure over a diverse set of target proteins. The mean model derived from 50 independently generated models is closer to the crystal structure than any individual model, with 0.5 A main chain RMSD under only Calpha restraints and 0.7 A all-atom RMSD under both Calpha and centroid restraints. The method is insensitive to randomly distributed errors of up to 4 A in the Calpha restraints. The conformational search algorithm is efficient, with computational cost increasing linearly with protein size. Issues relating to decoy set generation, experimental structure determination, efficiency of conformational sampling, and homology modeling are discussed.     

Assembly of protein structure from sparse experimental data: An efficient Monte Carlo model

A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Cαs. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 Å from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 Å are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 Å. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints. Proteins 32:475–494, 1998. © 1998 Wiley-Liss, Inc.     

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.     

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.     

Prediction and evaluation of side-chain conformations for protein backbone structures

A common approach to protein modeling is to propose a backbone structure based on homology or threading and then to attempt to build side chains onto this backbone. A fast algorithm using the simple criteria of atomic overlap and overall rotamer probability is proposed for this purpose. The method was first tested in the context of exhaustive searches of side chain configuration space in protein cores and was then applied to all side chains in 49 proteins of known structure, using simulated annealing to sample space. The latter procedure obtains the correct rotamer for 57% and the correct χ₁ value for 74% of the 6751 residues in the sample. When low-temperature Monte-Carlo simulations are initiated from the results of the simulated-annealing processes, consensus configurations are obtained which exhibit slightly more accurate predictions. The Monte-Carlo procedure also allows converged side chain entropies to be calculated for all residues. These prove to be accurate indicators of prediction reliability. For example, the correct rotamer is obtained for 79% and the correct χ₁ value is obtained for 84% of the half of the sample residues exhibiting the lowest entropies. Side chain entropy and predictability are nearly completely uncorrelated with solvent-accessible area. Some precedents for and implications of this observation are discussed. © 1996 Wiley-Liss, Inc.     

Homology modeling by the ICM method

Five models have been built by the ICM method for the Comparative Modeling section of the Meeting on the Critical Assessment of Techniques for Protein Structure Prediction. The targets have homologous proteins with known three-dimensional structure with sequence identity ranging from 25 to 77%. After alignment of the target sequence with the related three-dimensional structure, the modeling procedure consists of two subproblems: side-chain prediction and loop prediction. The ICM method approaches these problems with the following steps: (1) a starting model is created based on the homologous structure with the conserved portion fixed and the noncon-served portion having standard covalent geometry and free torsion angles; (2) the Biased Probability Monte Carlo (BPMC) procedure is applied to search the subspaces of either all the nonconservative side-chain torsion angles or torsion angles in a loop backbone and surrounding side chains. A special algorithm was designed to generate low-energy loop deformations. The BPMC procedure globally optimizes the energy function consisting of ECEPP/3 and solvation energy terms. Comparison of the predictions with the NMR or crystallographic solutions reveals a high proportion of correctly predicted side chains. The loops were not correctly predicted because imprinted distortions of the backbone increased the energy of the near-native conformation and thus made the solution unrecognizable. Interestingly, the energy terms were found to be reliable and the sampling of conformational space sufficient. The implications of this finding for the strategies of future comparative modeling are discussed. © 1995 Wiley-Liss, Inc.     

A procedure for refining a coiled coil protein structure using x-ray fiber diffraction and modeling

We describe a combined use of experimental and simulation techniques to configure side chains in a coiled coil structure. As already demonstrated in a previous work, x-ray diffraction patterns from hard alpha-keratin fibers in the 5.15 A meridian zone reflect the global configuration of the chi(1) dihedral angle of the coiled coil side chains. Molecular simulations, such as energy minimization and molecular dynamics, and rotameric representation in the PDB, are used here on a heterodimeric coiled coil to investigate the dihedral angle distribution along the sequence. Different procedures have been used to build the structure, the quality assessment was based on the agreement between the simulated diffraction patterns and the experimental ones in the fingerprint region of coiled coils (5.15 A). The best one for building a realistic coiled coil structure consists of placing the side chains using molecular dynamics (MD) simulations, followed by side chain positioning using SMD or SCWRL procedures. The side chains and the backbone are equilibrated during the MD until they reach an equilibrium state for the t/g(+) ratio. Positioning the side chains on the resulting backbone, using the above procedures, gives rise to a well-defined 5.15 A meridian reflection.     

Angular variances for internal bond rotations of side chains in GXG-based tripeptides derived from (13)C-NMR relaxation measurements: Implications to protein folding

The study of backbone and side-chain internal motions in proteins and peptides is crucial to having a better understanding of protein/peptide "structure" and to characterizing unfolded and partially folded states of proteins and peptides. To achieve this, however, requires establishing a baseline for internal motions and motional restrictions for all residues in the fully, solvent-exposed "unfolded state." GXG-based tripeptides are the simpliest peptides where residue X is fully solvent exposed in the context of an actual peptide. In this study, a series of GXG-based tripeptides has been synthesized with X being varied to include all twenty common amino acid residues. Proton-coupled and -decoupled (13)C-nmr relaxation measurements have been performed on these twenty tripeptides and various motional models (Lipari-Szabo model free approach, rotational anisotropic diffusion, rotational fluctuations within a potential well, rotational jump model) have been used to analyze relaxation data for derivation of angular variances and motional correlation times for backbone and side-chain chi(1) and chi(2) bonds and methyl group rotations. At 298 K, backbone motional correlation times range from about 50 to 85 ps, whereas side-chain motional correlation times show a much broader spread from about 18 to 80 ps. Angular variances for backbone phi,psi bond rotations range from 11 degrees to 23 degrees and those for side chains vary from 5 degrees to 24 degrees for chi(1) bond rotations and from 5 degrees to 27 degrees for chi(2) bond rotations. Even in these peptide models of the "unfolded state," side-chain angular variances can be as restricted as those for backbone and beta-branched (valine, threonine, and isoleucine) and aromatic side chains display the most restricted motions probably due to steric hinderence with backbone atoms. Comparison with motional data on residues in partially folded, beta-sheet-forming peptides indicates that side-chain motions of at least hydrophobic residues are less restricted in the partially folded state, suggesting that an increase in side-chain conformational entropy may help drive early-stage protein folding. Copyright 1999 John Wiley & Sons, Inc.