De novo prediction of polypeptide conformations using dihedral probability grid Monte Carlo methodology.

We tested the dihedral probability grid Monte Carlo (DPG-MC) methodology to determine optimal conformations of polypeptides by applying it to predict the low energy ensemble for two peptides whose solution NMR structures are known: integrin receptor peptide (YGRGDSP, Type II beta-turn) and S3 alpha-helical peptide (YMSEDEL KAAEAAFKRHGPT). DPG-MC involves importance sampling, local random stepping in the vicinity of a current local minima, and Metropolis sampling criteria for acceptance or rejection of new structures. Internal coordinate values are based on side-chain-specific dihedral angle probability distributions (from analysis of high-resolution protein crystal structures). Important features of DPG-MC are: (1) Each DPG-MC step selects the torsion angles (phi, psi, chi) from a discrete grid that are then applied directly to the structure. The torsion angle increments can be taken as S = 60, 30, 15, 10, or 5 degrees, depending on the application. (2) DPG-MC utilizes a temperature-dependent probability function (P) in conjunction with Metropolis sampling to accept or reject new structures. For each peptide, we found close agreement with the known structure for the low energy conformational ensemble located with DPG-MC. This suggests that DPG-MC will be useful for predicting conformations of other polypeptides.     

Reconstruction of protein conformations from estimated positions of the C alpha coordinates.

Protein C alpha coordinates are used to accurately reconstruct complete protein backbones and side-chain directions. This work employs potentials of mean force to align semirigid peptide groups around the axes that connect successive C alpha atoms. The algorithm works well for all residue types and secondary structure classes and is stable for imprecise C alpha coordinates. Tests on known protein structures show that root mean square errors in predicted main-chain and C beta coordinates are usually less than 0.3 A. These results are significantly more accurate than can be obtained from competing approaches, such as modeling of backbone conformations from structurally homologous fragments.     

The solution structure of a B-DNA undecamer comprising a portion of the specific target site for the cAMP receptor protein in the gal operon. Refinement on the basis of interproton distance data.

A restrained least squares refinement of the solution structure of the double-stranded DNA undecamer 5'd(AAGTGT-GACAT).5'd(ATGTCACACTT) comprising a portion of the specific target site of the cAMP receptor protein in the gal operon is presented. The structure is refined on the basis of both distance and planarity restraints, 2331 in all. The distance restraints comprise 150 interproton distances determined from pre-steady state nuclear Overhauser enhancement measurements and 2159 other interatomic distances derived from idealized geometry (i.e., distances between covalently bonded atoms, between atoms defining fixed bond angles, and between atoms defining hydrogen bonding in AT and GC base pairs). Two refinements were carried out and in both cases the final RMS difference between the experimental and calculated interproton distances was 0.2 A. The difference between the two refined structures is small (overall RMS difference of 0.23 A) and represents the error in the refined coordinates. Although the refined structures have an overall B-type conformation there are large variations in many of the local conformational parameters including backbone and glycosidic bond torsion angles, helical twist and propellor twist, base roll and base tilt angles.     

ProVal: a protein-scoring function for the selection of native and near-native folds

A low-resolution scoring function for the selection of native and near-native structures from a set of predicted structures for a given protein sequence has been developed. The scoring function, ProVal (Protein Validate), used several variables that describe an aspect of protein structure for which the proximity to the native structure can be assessed quantitatively. Among the parameters included are a packing estimate, surface areas, and the contact order. A partial least squares for latent variables (PLS) model was built for each candidate set of the 28 decoy sets of structures generated for 22 different proteins using the described parameters as independent variables. The C(alpha) RMS of the candidate structures versus the experimental structure was used as the dependent variable. The final generalized scoring function was an average of all models derived, ensuring that the function was not optimized for specific fold classes or method of structure generation of the candidate folds. The results show that the crystal structure was scored best in 64% of the 28 test sets and was clearly separated from the decoys in many examples. In all the other cases in which the crystal structure did not rank first, it ranked within the top 10%. Thus, although ProVal could not distinguish between predicted structures that were similar overall in fold quality due to its inherently low resolution, it can clearly be used as a primary filter to eliminate approximately 90% of fold candidates generated by current prediction methods from all-atom modeling and further evaluation. The correlation between the predicted and actual C(alpha) RMS values varies considerably between the candidate fold sets.     

A molecular dynamics approach for the generation of complete protein structures from limited coordinate data

Generation of full protein coordinates from limited information, e.g., the Cα coordinates, is an important step in protein homology modeling and structure determination, and molecular dynamics (MD) simulations may prove to be important in this task. We describe a new method, in which the protein backbone is built quickly in a rather crude way and then refined by minimization techniques. Subsequently, the side chains are positioned using extensive MD calculations. The method is tested on two proteins, and results compared to proteins constructed using two other MD-based methods. In the first method, we supplemented an existing backbone building method with a new procedure to add side chains. The second one largely consists of available methodology. The constructed proteins are compared to the corresponding X-ray structures, which became available during this study, and they are in good agreement (backbone RMS values of 0.5–0.7 Å, and all-atom RMS values of 1.5–1.9 Å). This comparative study indicates that extensive MD simulations are able, to some extent, to generate details of the native protein structure, and may contribute to the development of a standardized methodology to predict reliably (parts of) protein structures when only partial coordinate data are available. © 1994 John Wiley & Sons, Inc.     

Modeling the structure of Pyrococcus furiosus rubredoxin by homology to other X-ray structures.

The three-dimensional structure of rubredoxin from the hyperthermophilic archaebacterium, Pyrococcus furiosus, has been modeled from the X-ray crystal structures of three homologous proteins from Clostridium pasteurianum, Desulfovibrio gigas, and Desulfovibrio vulgaris. All three homology models are similar. When comparing the positions of all heavy atoms and essential hydrogen atoms to the recently solved crystal structure (Day, M. W., et al., 1992, Protein Sci. 1, 1494-1507) of the same protein, the homology model differ from the X-ray structure by 2.09 A root mean square (RMS). The X-ray and the zinc-substituted NMR structures (Blake, P. R., et al., 1992b, Protein Sci. 1, 1508-1521) show a similar level of difference (2.05 A RMS). On average, the homology models are closer to the X-ray structure than to the NMR structures (2.09 vs. 2.42 A RMS).     

Application of a directed conformational search for generating 3-D coordinates for protein structures from alpha-carbon coordinates.

A directed conformational search algorithm using the program CONGEN (ref. 3), which samples backbone conformers, is described. The search technique uses information from the partially built structures to direct the search process and is tested on the problem of generating a full set of backbone Cartesian coordinates given only alpha-carbon coordinates. The method has been tested on six proteins of known structure, varying in size and classification, and was able to generate the original backbone coordinates with RMSs ranging from 0.30-0.87A for the alpha-carbons and 0.5-0.99A RMSs for the backbone atoms. Cis peptide linkages were also correctly identified. The procedure was also applied to two proteins available with only alpha-carbon coordinates in the Brookhaven Protein Data Bank; thioredoxin (SRX) and triacylglycerol acylhydrolase (TGL). All-atom models are proposed for the backbone of both these proteins. In addition, the technique was applied to randomized coordinates of flavodoxin to assess the effects of irregularities in the data on the final RMS. This study represents the first time a deterministic conformational search was used on such a large scale.     

VENUS — a program to display protein structure using raster colour graphics

A Fortran program is described which retrieves the coordinates and connectivities of macromolecular structures and displays them in a variety of styles. These include the wire model, the ball-and-stick model and the space-filling model. The program picks up the coordinates of the α carbon atoms of a protein molecule. They are connected with either lines or platelets to give a wire or pleat model. The coordinates may also be connected by a smooth line, a cubic spline, to give a ribbon model. These models are very helpful in understanding the folding pattern, as well as the secondary structure of a given protein molecule. A user can display a limited sequence of a chain, eg to inspect the active site. Seven colouring schemes are available to differentiate backbone atoms from side-chain atoms, or hydrophilic residues from hydrophobic residues, and so on. Alphanumerics can be displayed to label atoms and residues.     

OLDERADO: on-line database of ensemble representatives and domains. On Line Database of Ensemble Representatives And DOmains.

In cases where the structure of a single protein is represented by an ensemble of conformations, there is often a need to determine the common features and to choose a "representative" conformation. This occurs, for example, with structures determined by NMR spectroscopy, analysis of the trajectory from a molecular dynamics simulation, or an ensemble of structures produced by comparative modeling. We reported previously automatic methods for (1) defining the atoms with low spatial variance across an ensemble (i.e., the "core" atoms) and the domains in which these atoms lie, and (2) clustering an ensemble into conformationally related subfamilies. To extend the utility of these methods, we have developed a freely available server on the World Wide Web at http:/(/)neon.chem.le.ac.uk/olderado/. This (1) contains an automatically generated database of representative structures, core atoms, and domains determined for 449 ensembles of NMR-derived protein structures in the Protein Data Bank (PDB) in May 1997, and (2) allows the user to upload a PDB-formatted file containing the coordinates of an ensemble of structures. The server returns in real time: (1) information on the residues constituting domains: (2) the structures that constitute each conformational subfamily; and (3) an interactive java-based three-dimensional viewer to visualise the domains and clusters. Such information is useful, for example, when selecting conformations to be used in comparative modeling and when choosing parts of structures to be used in molecular replacement. Here we describe the OLDERADO server.     

Protein-inhibitor flexible docking by a multicanonical sampling: native complex structure with the lowest free energy and a free-energy barrier distinguishing the native complex from the others

Flexible docking between a protein (lysozyme) and an inhibitor (tri-N-acetyl-D-glucosamine, tri-NAG) was carried out by an enhanced conformational sampling method, multicanonical molecular dynamics simulation. We used a flexible all-atom model to express lysozyme, tri-NAG, and water molecules surrounding the two bio-molecules. The advantages of this sampling method are as follows: the conformation of system is widely sampled without trapping at energy minima, a thermally equilibrated conformational ensemble at an arbitrary temperature can be reconstructed from the simulation trajectory, and the thermodynamic weight can be assigned to each sampled conformation. During the simulation, exchanges between the binding and free (i.e., unbinding) states of the protein and the inhibitor were repeatedly observed. The conformational ensemble reconstructed at 300 K involved various conformational clusters. The main outcome of the current study is that the most populated conformational cluster (i.e., the cluster of the lowest free energy) was assigned to the native complex structure (i.e., the X-ray complex structure). The simulation also produced non-native complex structures, where the protein and the inhibitor bound with different modes from that of the native complex structure, as well as the unbinding structures. A free-energy barrier (i.e., activation free energy) was clearly detected between the native complex structures and the other structures. The thermal fluctuations of tri-NAG in the lowest free-energy complex correlated well with the X-ray B-factors of tri-NAG in the X-ray complex structure. The existence of the free-energy barrier ensures that the lowest free-energy structure can be discriminated naturally from the other structures. In other words, the multicanonical molecular dynamics simulation can predict the native complex structure without any empirical objective function. The current study also manifested that the flexible all-atom model and the physico-chemically defined atomic-level force field can reproduce the native complex structure. A drawback of the current method is that it requires a time consuming computation due to the exhaustive conformational sampling. We discussed a possibility for combining the current method with conventional docking methods.     

Gaussian-weighted RMSD superposition of proteins: a structural comparison for flexible proteins and predicted protein structures

Many proteins contain flexible structures such as loops and hinged domains. A simple root mean square deviation (RMSD) alignment of two different conformations of the same protein can be skewed by the difference between the mobile regions. To overcome this problem, we have developed a novel method to overlay two protein conformations by their atomic coordinates using a Gaussian-weighted RMSD (wRMSD) fit. The algorithm is based on the Kabsch least-squares method and determines an optimal transformation between two molecules by calculating the minimal weighted deviation between the two coordinate sets. Unlike other techniques that choose subsets of residues to overlay, all atoms are included in the wRMSD overlay. Atoms that barely move between the two conformations will have a greater weighting than those that have a large displacement. Our superposition tool has produced successful alignments when applied to proteins for which two conformations are known. The transformation calculation is heavily weighted by the coordinates of the static region of the two conformations, highlighting the range of flexibility in the overlaid structures. Lastly, we show how wRMSD fits can be used to evaluate predicted protein structures. Comparing a predicted fold to its experimentally determined target structure is another case of comparing two protein conformations of the same sequence, and the degree of alignment directly reflects the quality of the prediction.     

Exploratory studies of ab initio protein structure prediction: multiple copy simulated annealing, AMBER energy functions, and a generalized born/solvent accessibility solvation model.

A theoretical and computational approach to ab initio structure prediction for polypeptides in water is described and applied to selected amino acid sequences for testing and preliminary validation. The method builds systematically on the extensive efforts applied to parameterization of molecular dynamics (MD) force fields, employs an empirically well-validated continuum dielectric model for solvation, and an eminently parallelizable approach to conformational search. The effective free energy of polypeptide chains is estimated from AMBER united atom potential functions, with internal degrees of freedom for both backbone and amino acid side chains explicitly treated. The hydration free energy of each structure is determined using the Generalized Born/Solvent Accessibility (GBSA) method, modified and reparameterized to include atom types consistent with the AMBER force field. The conformational search procedure employs a multiple copy, Monte Carlo simulated annealing (MCSA) protocol in full torsion angle space, applied iteratively on sets of structures of progressively lower free energy until a prediction of a structure with lowest effective free energy is obtained. Calibration tests for the effective energy function and search algorithm are performed on the alanine dipeptide, selected protein crystal structures, and united atom decoys on barnase, crambin, and six examples from the Rosetta set. Specific demonstration cases of the method are provided for the 8-mer sequence of Ala residues, a 12-residue peptide with longer side chains QLLKKLLQQLKQ, a de novo designed 16 residue peptide of sequence (AAQAA)3Y, a 15-residue sequence with a beta sheet motif, GEWTWDATKTFTVTE, and a 36 residue small protein, Villin headpiece. The Ala 8-mer readily formed an alpha-helix. An alpha-helix structure was predicted for the 16-mer, consistent with observed results from IR and CD spectroscopy and with the pattern in psi/straight phi angles of known protein structures. The predicted structure for the 12-mer, composed of a mix of helix and less regular elements of secondary structure, lies 2.65 A RMS from the observed crystal structure. Structure prediction for the 8-mer beta-motif resulted in form 4.50 A RMS from the crystal geometry. For Villin, the predicted native form is very close to the crystal structure, RMS values of 3.5 A (including sidechains), and 1.01 A (main chain only). The methodology permits a detailed analysis of the molecular forces which dominate various segments of the predicted folding trajectory. Analysis of the results in terms of internal torsional, electrostatic and van der Waals and the electrostatic and non-electrostatic contributions to hydration, including the hydrophobic effect, is presented.     

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.     

Binding of retinol induces changes in rat cellular retinol-binding protein II conformation and backbone dynamics

The structure and backbone dynamics of rat holo cellular retinol-binding protein II (holo-CRBP II) in solution has been determined by multidimensional NMR. The final structure ensemble was based on 3980 distance and 30 dihedral angle restraints, and was calculated using metric matrix distance geometry with pairwise Gaussian metrization followed by simulated annealing. The average RMS deviation of the backbone atoms for the final 25 structures relative to their mean coordinates is 0.85(+/-0.09) A. Comparison of the solution structure of holo-CRBP II with apo-CRBP II indicates that the protein undergoes conformational changes not previously observed in crystalline CRBP II, affecting residues 28-35 of the helix-turn-helix, residues 37-38 of the subsequent linker, as well as the beta-hairpin C-D, E-F and G-H loops. The bound retinol is completely buried inside the binding cavity and oriented as in the crystal structure. The order parameters derived from the (15)N T(1), T(2) and steady-state NOE parameters show that the backbone dynamics of holo-CRBP II is restricted throughout the polypeptide. The T(2) derived apparent backbone exchange rate and amide (1)H exchange rate both indicate that the microsecond to second timescale conformational exchange occurring in the portal region of the apo form has been suppressed in the holo form.     

X-ray crystal structures of a severely desiccated protein.

Unlike most protein crystals, form IX of bovine pancreatic ribonuclease A diffracts well when severely dehydrated. Crystal structures have been solved after 2.5 and 4 days of desiccation with CaSO4, at 1.9 and 2.0 A resolution, respectively. The two desiccated structures are very similar. An RMS displacement of 1.6 A is observed for main-chain atoms in each structure when compared to the hydrated crystal structure with some large rearrangements observed in loop regions. The structural changes are the result of intermolecular contacts formed by strong electrostatic interactions in the absence of a high dielectric medium. The electron density is very diffuse for some surface loops, consistent with a very disordered structure. This disorder is related to the conformational changes. These results help explain conformational changes during the lyophilization of protein and the associated phenomena of denaturation and molecular memory.     

Conformational energy refinement of horse-heart ferricytochrome c.

The reported X-ray structure of horse-heart ferricytochrome c has been refined by conformational energy calculations, using a three-stage computational procedure. In stage I, the atomic positions are adjusted to conform to idealized bond lengths and bond angles characteristic of small amino acid derivatives, while yet remaining as close as possible to the X-ray coordinates. In stage II, atomic overlaps are eliminated by adjusting the backbone and side-chain dihedral angles to minimize the nonbonded energy, hydrogen-bonded energy, and rotational energy contributions. In the final stage of refinement, the electrostatic energy and a more accurate hydrogen-bonded energy treatment are considered, in addition to the energy contributions of stage II. A "fitting potential" of gradually decreasing strength is imposed in both stages II and III, in order to keep the computed structure as similar to the x-ray structure as is consistent with a low-energy conformation. The final computed structure of cytochrome c exhibits a very low conformational energy (-504 kcal/mol) and also closely resembles the X-ray structure (RMS deviation = 0.77 A for all atoms). However, a special treatment was required in order to alter the location of the phenyl ring of phenylalanine-82. In contrast to the originally published X-ray structure, which shows the phenyl ring pointing away from the heme, the phenyl ring in the computed structure is tucked into the heme crevice, in a position similar to that observed in the reduced form of tuna cytochrome c, in the oxidized form of Rhodospirillum rubrum cytochrome c2, and also in the recently determined structure of oxidized tuna cytochrome c.     

4D prediction of protein <Superscript>1</Superscript>H chemical shifts

A 4D approach for protein ¹H chemical shift prediction was explored. The 4th dimension is the molecular flexibility, mapped using molecular dynamics simulations. The chemical shifts were predicted with a principal component model based on atom coordinates from a database of 40 protein structures. When compared to the corresponding non-dynamic (3D) model, the 4th dimension improved prediction by 6–7%. The prediction method achieved RMS errors of 0.29 and 0.50 ppm for Hα and HN shifts, respectively. However, for individual proteins the RMS errors were 0.17–0.34 and 0.34–0.65 ppm for the Hα and HN shifts, respectively. X-ray structures gave better predictions than the corresponding NMR structures, indicating that chemical shifts contain invaluable information about local structures. The ¹H chemical shift prediction tool 4DSPOT is available from .     

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.