A simple model of backbone flexibility improves modeling of side-chain conformational variability

The considerable flexibility of side-chains in folded proteins is important for protein stability and function, and may have a role in mediating allosteric interactions. While sampling side-chain degrees of freedom has been an integral part of several successful computational protein design methods, the predictions of these approaches have not been directly compared to experimental measurements of side-chain motional amplitudes. In addition, protein design methods frequently keep the backbone fixed, an approximation that may substantially limit the ability to accurately model side-chain flexibility. Here, we describe a Monte Carlo approach to modeling side-chain conformational variability and validate our method against a large dataset of methyl relaxation order parameters derived from nuclear magnetic resonance (NMR) experiments (17 proteins and a total of 530 data points). We also evaluate a model of backbone flexibility based on Backrub motions, a type of conformational change frequently observed in ultra-high-resolution X-ray structures that accounts for correlated side-chain backbone movements. The fixed-backbone model performs reasonably well with an overall rmsd between computed and predicted side-chain order parameters of 0.26. Notably, including backbone flexibility leads to significant improvements in modeling side-chain order parameters for ten of the 17 proteins in the set. Greater accuracy of the flexible backbone model results from both increases and decreases in side-chain flexibility relative to the fixed-backbone model. This simple flexible-backbone model should be useful for a variety of protein design applications, including improved modeling of protein-protein interactions, design of proteins with desired flexibility or rigidity, and prediction of correlated motions within proteins.     

Assessment of flexible backbone protein design methods for sequence library prediction in the therapeutic antibody Herceptin-HER2 interface

Computational protein design methods can complement experimental screening and selection techniques by predicting libraries of low-energy sequences compatible with a desired structure and function. Incorporating backbone flexibility in computational design allows conformational adjustments that should broaden the range of predicted low-energy sequences. Here, we evaluate computational predictions of sequence libraries from different protocols for modeling backbone flexibility using the complex between the therapeutic antibody Herceptin and its target human epidermal growth factor receptor 2 (HER2) as a model system. Within the program RosettaDesign, three methods are compared: The first two use ensembles of structures generated by Monte Carlo protocols for near-native conformational sampling: kinematic closure (KIC) and backrub, and the third method uses snapshots from molecular dynamics (MD) simulations. KIC or backrub methods were better able to identify the amino acid residues experimentally observed by phage display in the Herceptin-HER2 interface than MD snapshots, which generated much larger conformational and sequence diversity. KIC and backrub, as well as fixed backbone simulations, captured the key mutation Asp98Trp in Herceptin, which leads to a further threefold affinity improvement of the already subnanomolar parental Herceptin-HER2 interface. Modeling subtle backbone conformational changes may assist in the design of sequence libraries for improving the affinity of antibody-antigen interfaces and could be suitable for other protein complexes for which structural information is available.     

The role of local backrub motions in evolved and designed mutations

Amino acid substitutions in protein structures often require subtle backbone adjustments that are difficult to model in atomic detail. An improved ability to predict realistic backbone changes in response to engineered mutations would be of great utility for the blossoming field of rational protein design. One model that has recently grown in acceptance is the backrub motion, a low-energy dipeptide rotation with single-peptide counter-rotations, that is coupled to dynamic two-state sidechain rotamer jumps, as evidenced by alternate conformations in very high-resolution crystal structures. It has been speculated that backrubs may facilitate sequence changes equally well as rotamer changes. However, backrub-induced shifts and experimental uncertainty are of similar magnitude for backbone atoms in even high-resolution structures, so comparison of wildtype-vs.-mutant crystal structure pairs is not sufficient to directly link backrubs to mutations. In this study, we use two alternative approaches that bypass this limitation. First, we use a quality-filtered structure database to aggregate many examples for precisely defined motifs with single amino acid differences, and find that the effectively amplified backbone differences closely resemble backrubs. Second, we directly apply a provably-accurate, backrub-enabled protein design algorithm to idealized versions of these motifs, and discover that the lowest-energy computed models match the average-coordinate experimental structures. These results support the hypothesis that backrubs participate in natural protein evolution and validate their continued use for design of synthetic proteins.     

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.     

Comparison of Rosetta flexible-backbone computational protein design methods on binding interactions

Computational design of binding sites in proteins remains difficult, in part due to limitations in our current ability to sample backbone conformations that enable precise and accurate geometric positioning of side chains during sequence design. Here we present a benchmark framework for comparison between flexible-backbone design methods applied to binding interactions. We quantify the ability of different flexible backbone design methods in the widely used protein design software Rosetta to recapitulate observed protein sequence profiles assumed to represent functional protein/protein and protein/small molecule binding interactions. The CoupledMoves method, which combines backbone flexibility and sequence exploration into a single acceptance step during the sampling trajectory, better recapitulates observed sequence profiles than the BackrubEnsemble and FastDesign methods, which separate backbone flexibility and sequence design into separate acceptance steps during the sampling trajectory. Flexible-backbone design with the CoupledMoves method is a powerful strategy for reducing sequence space to generate targeted libraries for experimental screening and selection.     

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.     

High-resolution structural and thermodynamic analysis of extreme stabilization of human procarboxypeptidase by computational protein design

Recent efforts to design de novo or redesign the sequence and structure of proteins using computational techniques have met with significant success. Most, if not all, of these computational methodologies attempt to model atomic-level interactions, and hence high-resolution structural characterization of the designed proteins is critical for evaluating the atomic-level accuracy of the underlying design force-fields. We previously used our computational protein design protocol RosettaDesign to completely redesign the sequence of the activation domain of human procarboxypeptidase A2. With 68% of the wild-type sequence changed, the designed protein, AYEdesign, is over 10 kcal/mol more stable than the wild-type protein. Here, we describe the high-resolution crystal structure and solution NMR structure of AYEdesign, which show that the experimentally determined backbone and side-chains conformations are effectively superimposable with the computational model at atomic resolution. To isolate the origins of the remarkable stabilization, we have designed and characterized a new series of procarboxypeptidase mutants that gain significant thermodynamic stability with a minimal number of mutations; one mutant gains more than 5 kcal/mol of stability over the wild-type protein with only four amino acid changes. We explore the relationship between force-field smoothing and conformational sampling by comparing the experimentally determined free energies of the overall design and these focused subsets of mutations to those predicted using modified force-fields, and both fixed and flexible backbone sampling protocols.     

The backrub motion: how protein backbone shrugs when a sidechain dances

Surprisingly, the frozen structures from ultra-high-resolution protein crystallography reveal a prevalent, but subtle, mode of local backbone motion coupled to much larger, two-state changes of sidechain conformation. This "backrub" motion provides an influential and common type of local plasticity in protein backbone. Concerted reorientation of two adjacent peptides swings the central sidechain perpendicular to the chain direction, changing accessible sidechain conformations while leaving flanking structure undisturbed. Alternate conformations in sub-1 angstroms crystal structures show backrub motions for two-thirds of the significant Cbeta shifts and 3% of the total residues in these proteins (126/3882), accompanied by two-state changes in sidechain rotamer. The Backrub modeling tool is effective in crystallographic rebuilding. For homology modeling or protein redesign, backrubs can provide realistic, small perturbations to rigid backbones. For large sidechain changes in protein dynamics or for single mutations, backrubs allow backbone accommodation while maintaining H bonds and ideal geometry.     

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.     

Toward better refinement of comparative models: predicting loops in inexact environments

Achieving atomic-level accuracy in comparative protein models is limited by our ability to refine the initial, homolog-derived model closer to the native state. Despite considerable effort, progress in developing a generalized refinement method has been limited. In contrast, methods have been described that can accurately reconstruct loop conformations in native protein structures. We hypothesize that loop refinement in homology models is much more difficult than loop reconstruction in crystal structures, in part, because side-chain, backbone, and other structural inaccuracies surrounding the loop create a challenging sampling problem; the loop cannot be refined without simultaneously refining adjacent portions. In this work, we single out one sampling issue in an artificial but useful test set and examine how loop refinement accuracy is affected by errors in surrounding side-chains. In 80 high-resolution crystal structures, we first perturbed 6-12 residue loops away from the crystal conformation, and placed all protein side chains in non-native but low energy conformations. Even these relatively small perturbations in the surroundings made the loop prediction problem much more challenging. Using a previously published loop prediction method, median backbone (N-Calpha-C-O) RMSD's for groups of 6, 8, 10, and 12 residue loops are 0.3/0.6/0.4/0.6 A, respectively, on native structures and increase to 1.1/2.2/1.5/2.3 A on the perturbed cases. We then augmented our previous loop prediction method to simultaneously optimize the rotamer states of side chains surrounding the loop. Our results show that this augmented loop prediction method can recover the native state in many perturbed structures where the previous method failed; the median RMSD's for the 6, 8, 10, and 12 residue perturbed loops improve to 0.4/0.8/1.1/1.2 A. Finally, we highlight three comparative models from blind tests, in which our new method predicted loops closer to the native conformation than first modeled using the homolog template, a task generally understood to be difficult. Although many challenges remain in refining full comparative models to high accuracy, this work offers a methodical step toward that goal.     

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

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

Side-chain and backbone flexibility in protein core design.

We have developed a computational approach for the design and prediction of hydrophobic cores that includes explicit backbone flexibility. The program consists of a two-stage combination of a genetic algorithm and monte carlo sampling using a torsional model of the protein. Backbone structures are evaluated either by a canonical force-field or a constraining potential that emphasizes the preservation of local geometry. The utility of the method for protein design and engineering is explored by designing three novel hydrophobic core variants of the protein 434 cro. We use the new method to evaluate these and previously designed 434 cro variants, as well as a series of phage T4 lysozyme variants. In order to properly evaluate the influence of backbone flexibility, we have also analyzed the effects of varying amounts of side-chain flexibility on the performance of fixed backbone methods. Comparison of results using a fixed versus flexible backbone reveals that, surprisingly, the two methods are almost equivalent in their abilities to predict relative experimental stabilities, but only when full side-chain flexibility is allowed. The prediction of core side-chain structure can vary dramatically between methods. In some, but not all, cases the flexible backbone method is a better predictor of structure. The development of a flexible backbone approach to core design is particularly important for attempts at de novo protein design, where there is no prior knowledge of a precise backbone structure.     

Rosetta FlexPepDock ab-initio: simultaneous folding, docking and refinement of peptides onto their receptors

Flexible peptides that fold upon binding to another protein molecule mediate a large number of regulatory interactions in the living cell and may provide highly specific recognition modules. We present Rosetta FlexPepDock ab-initio, a protocol for simultaneous docking and de-novo folding of peptides, starting from an approximate specification of the peptide binding site. Using the Rosetta fragments library and a coarse-grained structural representation of the peptide and the receptor, FlexPepDock ab-initio samples efficiently and simultaneously the space of possible peptide backbone conformations and rigid-body orientations over the receptor surface of a given binding site. The subsequent all-atom refinement of the coarse-grained models includes full side-chain modeling of both the receptor and the peptide, resulting in high-resolution models in which key side-chain interactions are recapitulated. The protocol was applied to a benchmark in which peptides were modeled over receptors in either their bound backbone conformations or in their free, unbound form. Near-native peptide conformations were identified in 18/26 of the bound cases and 7/14 of the unbound cases. The protocol performs well on peptides from various classes of secondary structures, including coiled peptides with unusual turns and kinks. The results presented here significantly extend the scope of state-of-the-art methods for high-resolution peptide modeling, which can now be applied to a wide variety of peptide-protein interactions where no prior information about the peptide backbone conformation is available, enabling detailed structure-based studies and manipulation of those interactions.     

Intrinsic α‐helical and β‐sheet conformational preferences: A computational case study of alanine

A fundamental question in protein science is what is the intrinsic propensity for an amino acid to be in an α-helix, β-sheet, or other backbone dihedral angle (-ψ) conformation. This question has been hotly debated for many years because including all protein crystal structures from the protein database, increases the probabilities for α-helical structures, while experiments on small peptides observe that β-sheet-like conformations predominate. We perform molecular dynamics (MD) simulations of a hard-sphere model for Ala dipeptide mimetics that includes steric interactions between nonbonded atoms and bond length and angle constraints with the goal of evaluating the role of steric interactions in determining protein backbone conformational preferences. We find four key results. For the hard-sphere MD simulations, we show that (1) β-sheet structures are roughly three and half times more probable than α-helical structures, (2) transitions between α-helix and β-sheet structures only occur when the backbone bond angle τ (N–C_α–C) is greater than 110°, and (3) the probability distribution of τ for Ala conformations in the “bridge” region of-ψ space is shifted to larger angles compared to other regions. In contrast, (4) the distributions obtained from Amber and CHARMM MD simulations in the bridge regions are broader and have increased τ compared to those for hard sphere simulations and from high-resolution protein crystal structures. Our results emphasize the importance of hard-sphere interactions and local stereochemical constraints that yield strong correlations between -ψ conformations and τ.     

Flexibility of aromatic residues in the active-site gorge of acetylcholinesterase: X-ray versus molecular dynamics

The high aromatic content of the deep and narrow active-site gorge of acetylcholinesterase (AChE) is a remarkable feature of this enzyme. Here, we analyze conformational flexibility of the side chains of the 14 conserved aromatic residues in the active-site gorge of Torpedo californica AChE based on the 47 three-dimensional crystal structures available for the native enzyme, and for its complexes and conjugates, and on a 20-ns molecular dynamics (MD) trajectory of the native enzyme. The degree of flexibility of these 14 aromatic side chains is diverse. Although the side-chain conformations of F330 and W279 are both very flexible, the side-chain conformations of F120, W233, W432, Y70, Y121, F288, F290 and F331 appear to be fixed. Residues located on, or adjacent to, the Ω-loop (C67-C94), namely W84, Y130, Y442, and Y334, display different flexibilities in the MD simulations and in the crystal structures. An important outcome of our study is that the majority of the side-chain conformations observed in the 47 Torpedo californica AChE crystal structures are faithfully reproduced by the MD simulation on the native enzyme. Thus, the protein can assume these conformations even in the absence of the ligand that permitted their experimental detection. These observations are pertinent to structure-based drug design.     

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

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

A consistent set of statistical potentials for quantifying local side-chain and backbone interactions

The frequencies of occurrence of atom arrangements in high-resolution protein structures provide some of the most accurate quantitative measures of interaction energies in proteins. In this report we extend our development of a consistent set of statistical potentials for quantifying local interactions between side-chains and the polypeptide backbone, as well as nearby side-chains. Starting with phi/psi/chi1 propensities that select for optimal interactions of the 20 amino acid side-chains with the 2 flanking peptide bonds, the following 3 new terms are added: (1) a distance-dependent interaction between the side-chain at i and the carbonyl oxygens and amide protons of the peptide units at i +/- 2, i +/- 3, and i +/- 4; (2) a distance-dependent interaction between the side-chain at position i and side-chains at positions i + 1 through i + 4; and (3) an orientation-dependent interaction between the side-chain at position i and side-chains at i + 1 through i + 4. The relative strengths of these 4 pseudo free energy terms are estimated by the average information content of each scoring matrix and by assessing their performance in a simple fragment threading test. They vary from -0.4 - -0.5 kcal/mole per residue for phi/psi/chi1 propensities to a range of -0.15 - -0.6 kcal/mole per residue for each of the other 3 terms. The combined energy function, containing no interactions between atoms more than 4 residues apart, identifies the correct structural fragment for randomly selected 15 mers over 40% of the time, after searching through 232,000 alternative conformations. For 14 out of 20 sets of all-atom Rosetta decoys analyzed, the native structure has a combined score lower than any of the 1700-1900 decoy conformations. The ability of this energy function to detect energetically important details of local structure is demonstrated by its power to distinguish high-resolution crystal structures from NMR solution structures.     

Ig-VAE: Generative modeling of protein structure by direct 3D coordinate generation

While deep learning models have seen increasing applications in protein science, few have been implemented for protein backbone generation—an important task in structure-based problems such as active site and interface design. We present a new approach to building class-specific backbones, using a variational auto-encoder to directly generate the 3D coordinates of immunoglobulins. Our model is torsion- and distance-aware, learns a high-resolution embedding of the dataset, and generates novel, high-quality structures compatible with existing design tools. We show that the Ig-VAE can be used with Rosetta to create a computational model of a SARS-CoV2-RBD binder via latent space sampling. We further demonstrate that the model’s generative prior is a powerful tool for guiding computational protein design, motivating a new paradigm under which backbone design is solved as constrained optimization problem in the latent space of a generative model.     

Structure and internal mobility of proteins: a molecular dynamics study of hen egg white lysozyme

The structure and internal motions of the protein hen egg white lysozyme are studied by analysis of simulation and experimental data. A molecular dynamics simulation and an energy minimization of the protein in vacuum have been made and the results compared with high-resolution structures and temperature factors of hen egg white lysozyme in two different crystal forms and of the homologous protein human lysozyme. The structures obtained from molecular dynamics and energy minimization have root-mean-square deviations for backbone atoms of 2.3 Å and 1.1–1.3 Å, respectively, relative to the crystal structures; the different crystal structures have root-mean-square deviations of 0.73–0.81 Å for the backbone atoms. In comparing the backbone dihedral angles, the difference between the dynamics and the crystal structure on which it is based is the same as that between any two crystal structures. The internal fluctuations of atomic positions calculated from the molecular dynamics trajectory agree well with the temperature factors from the three structures. Simulation and crystal results both show that there are large motions for residues involved in exposed turns of the backbone chain, relatively smaller motions for residues involved in the middle of helices or β-sheet structures, and relatively small motions of residues near disulfide bridges. Also, both the simulation and crystal data show that side-chain atoms have larger fluctuations than main-chain atoms. Moreover, the regions that have large deviations among the x-ray crystal structures, which indicates flexibility, are found to have large fluctuations in the simulation.