Maxim V. Shapovalov

Improved prediction of protein side-chain conformations with SCWRL4.

Determination of side‐chain conformations is an important step in protein structure prediction and protein design. Many such methods have been presented, although only a small number are in widespread use. SCWRL is one such method, and the SCWRL3 program (2003) has remained popular because of its speed, accuracy, and ease‐of‐use for the purpose of homology modeling. However, higher accuracy at comparable speed is desirable. This has been achieved in a new program SCWRL4 through: (1) a new backbone‐dependent rotamer library based on kernel density estimates; (2) averaging over samples of conformations about the positions in the rotamer library; (3) a fast anisotropic hydrogen bonding function; (4) a short‐range, soft van der Waals atom–atom interaction potential; (5) fast collision detection using k‐discrete oriented polytopes; (6) a tree decomposition algorithm to solve the combinatorial problem; and (7) optimization of all parameters by determining the interaction graph within the crystal environment using symmetry operators of the crystallographic space group. Accuracies as a function of electron density of the side chains demonstrate that side chains with higher electron density are easier to predict than those with low‐electron density and presumed conformational disorder. For a testing set of 379 proteins, 86% of χ1 angles and 75% of χ1+2 angles are predicted correctly within 40° of the X‐ray positions. Among side chains with higher electron density (25–100th percentile), these numbers rise to 89 and 80%. The new program maintains its simple command‐line interface, designed for homology modeling, and is now available as a dynamic‐linked library for incorporation into other software programs. Proteins 2009.

Neighbor-Dependent Ramachandran Probability Distributions of Amino Acids Developed from a Hierarchical Dirichlet Process Model

Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1) input data size and criteria for structure inclusion (resolution, R-factor, etc.); 2) filtering of suspect conformations and outliers using B-factors or other features; 3) secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included); 4) the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5) whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately) have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp.

Statistical analysis of interface similarity in crystals of homologous proteins

Many proteins function as homo-oligomers and are regulated via their oligomeric state. For some proteins, the stoichiometry of homo-oligomeric states under various conditions has been studied using gel filtration or analytical ultracentrifugation experiments. The interfaces involved in these assemblies may be identified using cross-linking and mass spectrometry, solution-state NMR, and other experiments. However, for most proteins, the actual interfaces that are involved in oligomerization are inferred from X-ray crystallographic structures using assumptions about interface surface areas and physical properties. Examination of interfaces across different Protein Data Bank (PDB) entries in a protein family reveals several important features. First, similarities in space group, asymmetric unit size, and cell dimensions and angles (within 1%) do not guarantee that two crystals are actually the same crystal form, containing similar relative orientations and interactions within the crystal. Conversely, two crystals in different space groups may be quite similar in terms of all the interfaces within each crystal. Second, NMR structures and an existing benchmark of PDB crystallographic entries consisting of 126 dimers as well as larger structures and 132 monomers were used to determine whether the existence or lack of common interfaces across multiple crystal forms can be used to predict whether a protein is an oligomer or not. Monomeric proteins tend to have common interfaces across only a minority of crystal forms, whereas higher-order structures exhibit common interfaces across a majority of available crystal forms. The data can be used to estimate the probability that an interface is biological if two or more crystal forms are available. Finally, the Protein Interfaces, Surfaces, and Assemblies (PISA) database available from the European Bioinformatics Institute is more consistent in identifying interfaces observed in many crystal forms compared with the PDB and the European Bioinformatics Institutes Protein Quaternary Server (PQS). The PDB, in particular, is missing highly likely biological interfaces in its biological unit files for about 10% of PDB entries.

Conformation dependence of backbone geometry in proteins.

Protein structure determination and predictive modeling have long been guided by the paradigm that the peptide backbone has a single, context-independent ideal geometry. Both quantum-mechanics calculations and empirical analyses have shown this is an incorrect simplification in that backbone covalent geometry actually varies systematically as a function of the phi and Psi backbone dihedral angles. Here, we use a nonredundant set of ultrahigh-resolution protein structures to define these conformation-dependent variations. The trends have a rational, structural basis that can be explained by avoidance of atomic clashes or optimization of favorable electrostatic interactions. To facilitate adoption of this paradigm, we have created a conformation-dependent library of covalent bond lengths and bond angles and shown that it has improved accuracy over existing methods without any additional variables to optimize. Protein structures derived from crystallographic refinement and predictive modeling both stand to benefit from incorporation of the paradigm.

The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design

Over the past decade, the Rosetta biomolecular modeling suite has informed diverse biological questions and engineering challenges ranging from interpretation of low-resolution structural data to design of nanomaterials, protein therapeutics, and vaccines. Central to Rosettas success is the energy function: a model parametrized from small-molecule and X-ray crystal structure data used to approximate the energy associated with each biomolecule conformation. This paper describes the mathematical models and physical concepts that underlie the latest Rosetta energy function, called the Rosetta Energy Function 2015 (REF15). Applying these concepts, we explain how to use Rosetta energies to identify and analyze the features of biomolecular models. Finally, we discuss the latest advances in the energy function that extend its capabilities from soluble proteins to also include membrane proteins, peptides containing noncanonical amino acids, small molecules, carbohydrates, nucleic acids, and other macromolecules.

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 χ1 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 χ1 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. Proteins 2007.

Nonplanar peptide bonds in proteins are common and conserved but not biased toward active sites

The planarity of peptide bonds is an assumption that underlies decades of theoretical modeling of proteins. Peptide bonds strongly deviating from planarity are considered very rare features of protein structure that occur for functional reasons. Here, empirical analyses of atomic-resolution protein structures reveal that trans peptide groups can vary by more than 25° from planarity and that the true extent of nonplanarity is underestimated even in 1.2 Å resolution structures. Analyses as a function of the φ,ψ-backbone dihedral angles show that the expected value deviates by ± 8° from planar as a systematic function of conformation, but that the large majority of variation in planarity depends on tertiary effects. Furthermore, we show that those peptide bonds in proteins that are most nonplanar, deviating by over 20° from planarity, are not strongly associated with active sites. Instead, highly nonplanar peptides are simply integral components of protein structure related to local and tertiary structural features that tend to be conserved among homologs. To account for the systematic φ,ψ-dependent component of nonplanarity, we present a conformation-dependent library that can be used in crystallographic refinement and predictive protein modeling.

Development of a Rotamer Library for Use in β-Peptide Foldamer Computational Design

Foldamers present a particularly difficult challenge for accurate computational design compared to the case for conventional peptide and protein design due to the lack of a large body of structural data to allow parametrization of rotamer libraries and energies. We therefore explored the use of molecular mechanics for constructing rotamer libraries for non-natural foldamer backbones. We first evaluated the accuracy of molecular mechanics (MM) for the prediction of rotamer probability distributions in the crystal structures of proteins is explored. The van der Waals radius, dielectric constant and effective Boltzmann temperature were systematically varied to maximize agreement with experimental data. Boltzmann-weighted probabilities from these molecular mechanics energies compare well with database-derived probabilities for both an idealized alpha-helix (R = 0.95) as well as beta-strand conformations (R = 0.92). Based on these parameters, de novo rotamer probabilities for secondary structures of peptides built from beta-amino acids were determined. To limit computational complexity, it is useful to establish a residue-specific criterion for excluding rare, high-energy rotamers from the library. This is accomplished by including only those rotamers with probability greater than a given threshold (e.g., 10%) of the random value, defined as 1/n where n is the number of potential rotamers for each residue type.

Minimal ensembles of side chain conformers for modeling protein-protein interactions

The goal of this article is to reduce the complexity of the side chain search within docking problems. We apply six methods of generating side chain conformers to unbound protein structures and determine their ability of obtaining the bound conformation in small ensembles of conformers. Methods are evaluated in terms of the positions of side chain end groups. Results for 68 protein complexes yield two important observations. First, the end‐group positions change less than 1 Å on association for over 60% of interface side chains. Thus, the unbound protein structure carries substantial information about the side chains in the bound state, and the inclusion of the unbound conformation into the ensemble of conformers is very beneficial. Second, considering each surface side chain separately in its protein environment, small ensembles of low‐energy states include the bound conformation for a large fraction of side chains. In particular, the ensemble consisting of the unbound conformation and the two highest probability predicted conformers includes the bound conformer with an accuracy of 1 Å for 78% of interface side chains. As more than 60% of the interface side chains have only one conformer and many others only a few, these ensembles of low‐energy states substantially reduce the complexity of side chain search in docking problems. This approach was already used for finding pockets in protein–protein interfaces that can bind small molecules to potentially disrupt protein–protein interactions. Side‐chain search with the reduced search space will also be incorporated into protein docking algorithms. Proteins 2012.

A forward-looking suggestion for resolving the stereochemical restraints debate: ideal geometry functions

# 2008 International Union of Crystallography Printed in Singapore – all rights reserved Jaskolski et al. (2007a) initiated a very important discussion (Jaskolski et al., 2007b; Stec, 2007; Tickle, 2007) about the accuracy of ideal geometry targets and the appropriate stringency with which they should be obeyed at various resolutions. All of the discussants agree that protein structures determined at ultra-high resolution, which should be closer to the truth, tend to have larger r.m.s. deviations from ideality. This shows that real deviations from ideality do occur in true protein structures. Another point of agreement is that the real deviations from ideality are to some extent context dependent, so that the single target values used in current refinement programs are a simplification: ‘The N–C –C valence angle has a wide spread and may have a bimodal distribution correlated with secondary structure’, Jaskolski et al. (2007a); ‘Recent results suggest that protein stereochemistry is context-dependent’, Stec (2007); ‘As they point out, the [deviations from ideality] will include real variations arising from the chemical environment’, Tickle (2007); ‘In such a situation, a single target, as used in the refinement programs, will not agree with any of the truly preferred values. This again suggests that the geometrical parameters of protein models should not be too tightly restrained to some predefined values’, Jaskolski et al. (2007b). We point out here that much of the context dependence of stereochemistry can be transformed from a frustrating reality that limits the accuracy of protein modeling to a feature that can instead enhance modeling accuracy. This transformation is possible because much of the context-dependent variation is not random but varies systematically with conformation. This systematic dependence was well documented in the mid-1990s, especially for the N—C —C bond angle, for which the expected value was seen to vary over a range of 10 (Jiang et al.; Karplus, 1996; Schafer et al., 1995). We are now updating these analyses using ultra-high resolution protein structures. These structures not only confirm the highly systematic variation of backbone bond angles with conformation (as illustrated for the N— C —C bond angle in Fig. 1), but they also reveal that the standard deviations are very low. For the N—C —C bond angle, the standard deviations in individual ’, regions vary from 1.0 to 1.7 (Fig. 1b), much lower than the standard deviation of near 2.2 derived for the N—C —C bond angle in the population as a whole (see Table 3 of Jaskolski et al., 2007a). Based on this result, it is clear that no single ideal target value can be appropriate for all of these conformations. However, it is also true that because each mean (or expected value) can be empirically discovered, this feature of protein structure can be accounted for by altering our refinement protocols to allow for ideal geometry targets that are dependent on context. In other words, we propose that more accurate refinement of protein structures at all resolution ranges will be obtained by moving beyond the ‘single ideal value’ paradigm to an ‘ideal geometry function’ paradigm (Schafer et al., 1986) in which each restraint target value varies depending on the local conformation. We are now working to develop a set of empirical conformation-dependent ‘ideal geometry functions’ for backbone bond angles and lengths that can be incorporated into crystallographic refinement software (Berkholz & Karplus, unpublished work).