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.     

Backrub-like backbone simulation recapitulates natural protein conformational variability and improves mutant side-chain prediction

Incorporation of effective backbone sampling into protein simulation and design is an important step in increasing the accuracy of computational protein modeling. Recent analysis of high-resolution crystal structures has suggested a new model, termed backrub, to describe localized, hinge-like alternative backbone and side-chain conformations observed in the crystal lattice. The model involves internal backbone rotations about axes between C-alpha atoms. Based on this observation, we have implemented a backrub-inspired sampling method in the Rosetta structure prediction and design program. We evaluate this model of backbone flexibility using three different tests. First, we show that Rosetta backrub simulations recapitulate the correlation between backbone and side-chain conformations in the high-resolution crystal structures upon which the model was based. As a second test of backrub sampling, we show that backbone flexibility improves the accuracy of predicting point-mutant side-chain conformations over fixed backbone rotameric sampling alone. Finally, we show that backrub sampling of triosephosphate isomerase loop 6 can capture the millisecond/microsecond oscillation between the open and closed states observed in solution. Our results suggest that backrub sampling captures a sizable fraction of localized conformational changes that occur in natural proteins. Application of this simple model of backbone motions may significantly improve both protein design and atomistic simulations of localized protein flexibility.     

Dead‐end elimination with perturbations (DEEPer): A provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum‐energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (D ead‐E nd E limination with Per turbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*‐based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower‐energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein–ligand interactions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Flexible protein-protein docking

Predicting the structure of protein-protein complexes using docking approaches is a difficult problem whose major challenges include identifying correct solutions, and properly dealing with molecular flexibility and conformational changes. Flexibility can be addressed at several levels: implicitly, by smoothing the protein surfaces or allowing some degree of interpenetration (soft docking) or by performing multiple docking runs from various conformations (cross or ensemble docking); or explicitly, by allowing sidechain and/or backbone flexibility. Although significant improvements have been achieved in the modeling of sidechains, methods for the explicit inclusion of backbone flexibility in docking are still being developed. A few novel approaches have emerged involving collective degrees of motion, multicopy representations and multibody docking, which should allow larger conformational changes to be modeled.     

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.     

RosettaDock in CAPRI rounds 6-12

A challenge in protein-protein docking is to account for the conformational changes in the monomers that occur upon binding. The RosettaDock method, which incorporates sidechain flexibility but keeps the backbone fixed, was found in previous CAPRI rounds (4 and 5) to generate docking models with atomic accuracy, provided that conformational changes were mainly restricted to protein sidechains. In the recent rounds of CAPRI (6-12), large backbone conformational changes occur upon binding for several target complexes. To address these challenges, we explicitly introduced backbone flexibility in our modeling procedures by combining rigid-body docking with protein structure prediction techniques such as modeling variable loops and building homology models. Encouragingly, using this approach we were able to correctly predict a significant backbone conformational change of an interface loop for Target 20 (12 A rmsd between those in the unbound monomer and complex structures), but accounting for backbone flexibility in protein-protein docking is still very challenging because of the significantly larger conformational space, which must be surveyed. Motivated by these CAPRI challenges, we have made progress in reformulating RosettaDock using a "fold-tree" representation, which provides a general framework for treating a wide variety of flexible-backbone docking problems.     

Solution structure and dynamics of a designed hydrophobic core variant of ubiquitin.

BACKGROUND: The recent merger of computation and protein design has resulted in a burst of success in the generation of novel proteins with native-like properties. A critical component of this coupling between theory and experiment is a detailed analysis of the structures and stabilities of designed proteins to assess and improve the accuracy of design algorithms. RESULTS: Here we report the solution structure of a hydrophobic core variant of ubiquitin, referred to as 1D7, which was designed with the core-repacking algorithm ROC. As a measure of conformational specificity, we also present amide exchange protection factors and backbone and sidechain dynamics. The results indicate that 1D7 is similar to wild-type (WT) ubiquitin in backbone structure and degree of conformational specificity. We also observe a good correlation between experimentally determined sidechain structures and those predicted by ROC. However, evaluation of the core sidechain conformations indicates that, in general, 1D7 has more sidechains in less statistically favorable conformations than WT. CONCLUSIONS: Our results provide an explanation for the lower stability of 1D7 compared to WT, and suggest modifications to design algorithms that may improve the accuracy with which structure and stability are predicted. The results also demonstrate that core packing can affect conformational flexibility in subtle ways that are likely to be important for the design of function and protein-ligand interactions.     

Protein backbone angle prediction with machine learning approaches

MOTIVATION: Protein backbone torsion angle prediction provides useful local structural information that goes beyond conventional three-state (alpha, beta and coil) secondary structure predictions. Accurate prediction of protein backbone torsion angles will substantially improve modeling procedures for local structures of protein sequence segments, especially in modeling loop conformations that do not form regular structures as in alpha-helices or beta-strands. RESULTS: We have devised two novel automated methods in protein backbone conformational state prediction: one method is based on support vector machines (SVMs); the other method combines a standard feed-forward back-propagation artificial neural network (NN) with a local structure-based sequence profile database (LSBSP1). Extensive benchmark experiments demonstrate that both methods have improved the prediction accuracy rate over the previously published methods for conformation state prediction when using an alphabet of three or four states. AVAILABILITY: LSBSP1 and the NN algorithm have been implemented in PrISM.1, which is available from www.columbia.edu/~ay1/. SUPPLEMENTARY INFORMATION: Supplementary data for the SVM method can be downloaded from the Website www.cs.columbia.edu/compbio/backbone.     

Simulations of the static and dynamic molecular conformations of xyloglucan. The role of the fucosylated sidechain in surface-specific sidechain folding.

The hemicellulosic polysaccharide xyloglucan binds with a strong affinity to cellulosic cell wall microfibrils, the resulting heterogeneous network constituting up to 50% of the dry weight of the cell wall in dicotyledonous plants. To elucidate the molecular details of this interaction, we have performed theoretical potential energy calculations of the static and dynamic equilibrium conformations of xyloglucan using the GEGOP software. In particular, we have evaluated the preferred sidechain conformations of hexa-, octa-, deca- and heptadecasaccharide model fragments of xyloglucan for molecules with a cellulose-like, flat, glucan backbone, and a cellobiose-like, twisted, glucan backbone conformation. For the flat backbone conformation the determination of static equilibrium molecular conformations revealed a tendency for sidechains to fold onto one surface of the backbone, defined here as the H1S face, in the fucosylated region of the polymer. This folding produces a molecule that is sterically accessible on the opposite face of the backbone, the H4S face. Typically, this folding onto the H1S surface is significantly stabilized by favorable interactions between the fucosylated, trisaccharide sidechain and the backbone, with some stabilization from adjacent terminal xylosyl sidechains. In contrast, the trisaccharide sidechain folds onto the H4S face of xyloglucan fragments with a twisted backbone conformation. Preliminary NMR data on nonasaccharide fragments isolated from sycamore suspension-cultured cell walls are consistent with the hypothesis that the twisted conformation of xyloglucan represents the solution form of this molecule. Metropolis Monte Carlo (MMC) simulations were employed to assess sidechain flexibility of the heptadecasaccharide fragments. Simulations performed on the flat, rigid, backbone xyloglucan indicate that the trisaccharide sidechain is less mobile than the terminal xylosyl sidechains. MMC calculations on a fully relaxed molecule revealed a positive correlation between a specific trisaccharide sidechain orientation and the 'flatness' of the backbone glucosyl residues adjacent to this sidechain. These results suggest that the trisaccharide sidechain may play a role in the formation of nucleation sites that initiate the binding of these regions to cellulose. Based on these conformational preferences we suggest the following model for the binding of xyloglucan to cellulose. Nucleation of a binding site is initiated by the fucosylated, trisaccharide sidechain that flattens out an adjacent region of the xyloglucan backbone. Upon contacting a cellulose microfibril this region spreads by step-wise flattening of successive segments of the backbone. Self-association of xyloglucan molecules in solution may be prevented by the low frequency of formation of these nucleation sites and the geometry of the molecules in solution.     

The limit of accuracy of protein modeling: influence of crystal packing on protein structure

The size of the protein database (PDB) makes it now feasible to arrive at statistical conclusions regarding structural effects of crystal packing. These effects are relevant for setting upper practical limits of accuracy on protein modeling. Proteins whose crystals have more than one molecule in the asymmetric unit or whose structures were determined at least twice by X-ray crystallography were paired and their differences analyzed. We demonstrate a clear influence of crystal environment on protein structure, including backbone conformations, hinge-like motions and side-chain conformations. The positions of surface water molecules tend to be variable in different crystal environments while those of ligands are not. Structures determined by independent groups vary more than structures determined by the same authors. The use of different refinement methods is a major source for this effect. Our pair-wise analysis derives a practical limit to the accuracy of protein modeling. For different crystal forms, the limit of accuracy (C(alpha), root-mean-square deviation (RMSD)) is approximately 0.8A for the entire protein, which includes approximately 0.3A due to crystal packing. For organized secondary elements, the upper limit of C(alpha) RMSD is 0.5-0.6A while for loops or protein surface it reaches 1.0A. Twenty percent of exposed side- chains exhibit different chi(1+2) conformations with approximately half of the effect also resulting from crystal packing. A web based tool for analysis and graphic presentation of surface areas of crystal contacts is available (http://ligin.weizmann.ac.il/cryco).     

ATTRACT: protein-protein docking in CAPRI using a reduced protein model

Protein-protein complex structures have been predicted for CAPRI Rounds 3 and 5 using a reduced protein model. Proteins are represented by up to 3 pseudoatoms per amino acid. The docking approach termed ATTRACT is based on energy minimization in translational and rotational degrees of freedom of one protein with respect to another protein. The reduced protein model allows one to perform systematic docking minimization of many thousand start structures in reasonable computer time. Flexibility of critical surface side-chains can be accounted for by a multiple conformational copy approach. The multicopy approach allows simultaneous adjustment of side-chain conformations and optimization of translational and rotational degrees of freedom of one protein with respect to the partner during docking. For 3 (Targets 8, 14, and 19) out of 5 CAPRI targets, the approach resulted in predictions in close agreement with experiment [root-mean-square deviation (RMSD) of backbone atoms within 10 A of the protein-protein interface < 1.8 A]. The comparison of predicted and experimental structures of the CAPRI targets indicates that besides local conformational changes (e.g., changes in side-chain conformations), global conformational changes of the protein backbone can be critical for complex formation. These conformational changes not accounted for during docking are a likely reason for the unrealistic predictions in 2 cases (Targets 9 and 18).     

基于结构比较的蛋白质同源模建系统及其评估Ⅱ侧链的安装

至今,有关蛋白质侧链的同源模建,除了在本体模板上安装侧链和少数限制条件下在同源模板上安装侧链的报道外,系统的研究和实施似乎还未见报道。本软件系统ＰＭＯＤＥＬＩＮＧ采用同源移植和“死端排除“相结合的侧链安装策略,对与模板蛋白相应践基具有相似大小和形状的目标残基采用直接移植的方法。其余铡链则用广义“死端排除定则”安装。经众多蛋白的测试,达到了较好的模建品质。     

Complete protein structure determination using backbone residual dipolar couplings and sidechain rotamer prediction

Residual dipolar couplings provide significant structural information for proteins in the solution state, which makes them attractive for the rapid determination of protein structures. While dipolar couplings contain inherent structural ambiguities, these can be reduced via an overlap similarity measure that insists that protein fragments assigned to overlapping regions of the sequence must have self-consistent structures. This allows us to determine a backbone fold (including the correct C–C bond orientations) using only residual dipolar coupling data from one ordering medium. The resulting backbone structures are of sufficient quality to allow for modeling of sidechain rotamer states using a rotamer prediction algorithm and a force field employing the Surface Generalized Born continuum solvation model. We demonstrate the applicability of the method using experimental data for ubiquitin. These results illustrate the synergies that are possible between protein structural database and molecular modeling methods and NMR spectroscopy, and we expect that the further development of these methods will lead to the extraction of high resolution structural information from minimal NMR data.     

Developing hybrid approaches to predict pKa values of ionizable groups

Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure and the subtle structural changes be accounted by using dielectric constant larger than two. On another hand, if the change of the charge state is accompanied by a large structural reorganization of the target protein, then the relevant conformational changes have to be explicitly taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups whose ionization is expected to cause large conformational changes, termed "problematic" residues, and then applies a special protocol on them, while the rest of the pK(a)s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for "problematic" groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the titration curves of the "problematic" residues and then the results are averaged to obtain the corresponding pKa.     

基于结构比较的蛋白质同源模建系统及其评估Ⅱ侧链的安装

至今,有关蛋白质侧链的同源模建,除了在本体模板上安装侧链和少数限制条件下在同源模板上安装侧链的报道外,系统的研究和实施似乎还未见报道。本软件系统ＰＭＯＤＥＬＩＮＧ采用同源移植和“死端排除“相结合的侧链安装策略,对与模板蛋白相应践基具有相似大小和形状的目标残基采用直接移植的方法。其余铡链则用广义“死端排除定则”安装。经众多蛋白的测试,达到了较好的模建品质。     

Conformation of MeAla6-cyclosporin A by NMR. Relationship of sidechain orientation of the MeBmt-1, MeLeu-9, and MeLeu-10 residues to immunosuppressive activity

MeAla6-cyclosporin A (MeAla6-CsA) is a unique CsA analog that shows weak immunosuppressive activity and yet binds strongly to the proposed cytosolic protein receptor, cyclophilin (CyP). Preliminary 1H NMR data showed significant chemical shift differences between spectra of MeAla6-CsA and CsA, suggesting different preferred conformations. A more detailed study, however, revealed that the backbone conformations of the two molecules are essentially identical, and that the differences can be accounted for, principally, by the sidechain motions of the MeBmt-1, MeLeu-9, and -10 residues. ROE and coupling constant data show that in MeAla6-CsA, the preferred chi 1 rotamers for MeLeu-9 and -10 are + 180 degrees (T), whereas in CsA there is a more even distribution of rotamer populations for MeLeu-10, and a preferred -60 degrees (G-) chi 1 rotamer for MeLeu-9. Similar data argue that the sidechain of MeBmt-1 is more restricted in its motion in MeAla-CsA than in CsA. Temperature studies suggest that these preferred rotamers for MeAla6-CsA may increase the stability of the hydrogen bond between NH(7) and CO(11), but prevent particular residues, especially the essential MeBmt-1 sidechain, from adopting orientations required to elicit immunosuppressive activity. The significant changes observed in the preferred orientations for the sidechains of the MeBmt-1, MeLeu-9, and MeLeu-10 residues in MeAla6-CsA argue that the particular orientations which they assume in CsA are not essential for cyclophilin binding.     

Effects of phosphorylation on the intrinsic propensity of backbone conformations of serine/threonine

Each amino acid has its intrinsic propensity for certain local backbone conformations, which can be further modulated by the physicochemical environment and post-translational modifications. In this work, we study the effects of phosphorylation on the intrinsic propensity for different local backbone conformations of serine/threonine by molecular dynamics simulations. We showed that phosphorylation has very different effects on the intrinsic propensity for certain local backbone conformations for the serine and threonine. The phosphorylation of serine increases the propensity of forming polyproline II, whereas that of threonine has the opposite effect. Detailed analysis showed that such different responses to phosphorylation mainly arise from their different perturbations to the backbone hydration and the geometrical constraints by forming side-chain–backbone hydrogen bonds due to phosphorylation. Such an effect of phosphorylation on backbone conformations can be crucial for understanding the molecular mechanism of phosphorylation-regulated protein structures/dynamics and functions.     

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.