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 reconstruction of side-chain conformations from protein Cα coordinates

A model of nine proteins including side-chain atoms have been built from the known C^α coordinates and amino acid sequences using a Monte Carlo Protein Building Annealing method. The Cartesian coordinates for the side-chain atoms were established with bond lengths and angles selected randomly from within previously determined ranges. A simulated annealing technique is used to generate some 300 structures with differing side-chain conformations. The atomic coordinates of the backbone atoms are fixed during the simulated annealing process. The coordinates of the side-chain atoms of 300 low energy conformations are averaged to obtain a mean structure that is minimized with the C^α atoms constrained to their position in the x-ray structure using the OPLS/AMBER force field with the GB/SA water model. The rms deviation of the main-chain atoms (without C^β) compared with the corresponding crystal structures is in the range 0.20–0.64 Å. The rms deviation of the side-chain atoms is between 1.72 and 2.71 Å and for all atoms is between 1.19 and 1.99 Å. The method is insensitive to random errors in the C^α positions and the computational requirement is modest. © 1997 John Wiley & Sons, Inc.     

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.     

Sampling of the native conformational ensemble of myoglobin via structures in different crystalline environments

Proteins sample multiple conformational substates in their native environment, but the process of crystallization selects the conformers that allow for close packing. The population of conformers can be shifted by varying the environment through a range of crystallization conditions, often resulting in different space groups and changes in the packing arrangements. Three high resolution structures of myoglobin (Mb) in different crystal space groups are presented, including one in a new space group P6(1)22 and two structures in space groups P2(1)2(1)2(1) and P6. We compare coordinates and anisotropic displacement parameters (ADPs) from these three structures plus an existing structure in space group P2(1). While the overall changes are small, there is substantial variation in several external regions with varying patterns of crystal contacts across the space group packing arrangements. The structural ensemble containing four different crystal forms displays greater conformational variance (Calpha rmsd of 0.54-0.79 A) in comparison to a collection of four Mb structures with different ligands and mutations in the same crystal form (Calpha rmsd values of 0.28-0.37 A). The high resolution of the data enables comparison of both the magnitudes and directions of ADPs, which are found to be suppressed by crystal contacts. A composite dynamic profile of Mb structural variation from the four structures was compared with an independent structural ensemble developed from NMR refinement. Despite the limitations and biases of each method, the ADPs of the crystallographic ensemble closely match the positional variance from the solution NMR ensemble with linear correlation of 0.8. This suggests that crystal packing selects conformers representative of the solution ensemble, and several different crystal forms give a more complete view of the plasticity of a protein structure.     

Solution conformation of cytochrome c-551 from Pseudomonas stutzeri ZoBell determined by NMR.

1H NMR spectroscopy and solution structure computations have been used to examine ferrocytochrome c-551 from Pseudomonas stutzeri ZoBell (ATCC 14405). Resonance assignments are proposed for all main-chain and most side-chain protons. Stereospecific assignments were also made for some of the beta-methylene protons and valine methyl protons. Distance constraints were determined based upon nuclear Overhauser enhancements between pairs of protons. Dihedral angle constraints were determined from estimates of scalar coupling constants and intra-residue NOEs. Twenty structures were calculated by distance geometry and refined by energy minimization and simulated annealing on the basis of 1012 interproton distance and 74 torsion angle constraints. Both the main-chain and side-chain atoms are well defined except for two terminal residues, and some side-chain atoms located on the molecular surface. The average root mean squared deviation in the position for equivalent atoms between the 20 individual structures and the mean structure obtained by averaging their coordinates is 0.56 +/- 0.10 A for the main-chain atoms, and 0.95 +/- 0.09 A for all nonhydrogen atoms of residue 3 to 80 plus the heme group. The average structure was compared with an analogous protein, cytochrome c-551 from pseudomonas stutzeri. The main-chain folding patterns are very consistent, but there are some differences, some of which can be attributed to the loss of normally conserved aromatic residues in the ZoBell c-551.     

Electronic and vibrational circular dichroism of aromatic amino acids by density functional theory

Structures of model compounds mimicking aromatic amino acid residues in proteins are optimized by density functional theory (DFT), assuming that the main-chain conformation was a random coil. Excitation energies and dipole and rotational strengths for the optimized structures were calculated based on time-dependent DFT (TD-DFT). The electronic circular dichroism (ECD) bands of the models were significantly affected by side-chain conformations. Hydration models of the aromatic residues were also subjected to TD-DFT calculations, and the ECD bands of these models were found to be highly perturbed by the hydration of the main-chain amide groups. In addition to calculating the random-coil conformation, we also performed TD-DFT calculations of the aromatic residue models, assuming that the main-chain conformation was an alpha-helix or beta-strand. As expected, the overall feature of the ECD bands was also perturbed by the main-chain conformations. Moreover, vibrational circular dichroism (VCD) spectra of the hydration models in a random-coil structure were simulated by DFT, which showed that the VCD spectra are more sensitive to the side-chain conformations than the ECD spectra. The present results show that analyses combining ECD and VCD spectroscopy and using DFT calculations can elucidate the main- and side-chain conformations of aromatic residues in proteins.     

The role of carbon-donor hydrogen bonds in stabilizing tryptophan conformations

Although most side-chain torsion angles correspond to low-energy rotameric positions, deviations occur with significant frequency. One striking example arises in Trp residues, which have an important role in stabilizing protein structures because of their size and mixed hydrophobic/hydrophilic character. Ten percent of Trp side-chains have unexplained conformations with chi(2) near 0 degrees instead of the expected 90 degrees. The current work is a structural and energetic analysis of these conformations. It is shown that many Trp residues with these orientations are stabilized by three-center carbon-donor hydrogen bonds of the form C-H...X...H-C, where X is a polar hydrogen-bond acceptor in the environment of the side-chain. The bridging hydrogen bonds occur both within the Trp side-chain and between the side-chain and the local protein backbone. Free energy maps of an isolated Trp residue in an explicit water environment show a minimum corresponding to the off-rotamer peak observed in the crystallographic data. Bridging carbon-donor hydrogen bonds are also shown to stabilize on-rotamer Trp conformations, and similar bridging hydrogen bonds also stabilize some off-rotamer Asp conformations. The present results suggest a previously unrecognized role for three-center carbon-donor hydrogen bonds in protein structures and support the view that the off-rotamer Trp side-chain orientations are real rather than artifacts of crystallographic refinements. Certain of the off-rotamer Trp conformations appear to have a functional role.     

Side-chain entropy and packing in proteins.

What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is a side-chain “freezing” or ordering, i.e., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements (m) have different frequencies, and the frequencies have different dependencies on compactness. mm contacts contribute significantly only at high densities, suggesting that main-chain hydrogen bonding in proteins may be promoted by compactness. The distributions of mm, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.     

Structure determination of symmetric homo-oligomers by a complete search of symmetry configuration space, using NMR restraints and van der Waals packing

Structural studies of symmetric homo-oligomers provide mechanistic insights into their roles in essential biological processes, including cell signaling and cellular regulation. This paper presents a novel algorithm for homo-oligomeric structure determination, given the subunit structure, that is both complete, in that it evaluates all possible conformations, and data-driven, in that it evaluates conformations separately for consistency with experimental data and for quality of packing. Completeness ensures that the algorithm does not miss the native conformation, and being data-driven enables it to assess the structural precision possible from data alone. Our algorithm performs a branch-and-bound search in the symmetry configuration space, the space of symmetry axis parameters (positions and orientations) defining all possible C(n) homo-oligomeric complexes for a given subunit structure. It eliminates those symmetry axes inconsistent with intersubunit nuclear Overhauser effect (NOE) distance restraints and then identifies conformations representing any consistent, well-packed structure to within a user-defined similarity level. For the human phospholamban pentamer in dodecylphosphocholine micelles, using the structure of one subunit determined from a subset of the experimental NMR data, our algorithm identifies a diverse set of complex structures consistent with the nine intersubunit NOE restraints. The distribution of determined structures provides an objective characterization of structural uncertainty: backbone RMSD to the previously determined structure ranges from 1.07 to 8.85 A, and variance in backbone atomic coordinates is an average of 12.32 A(2). Incorporating vdW packing reduces structural diversity to a maximum backbone RMSD of 6.24 A and an average backbone variance of 6.80 A(2). By comparing data consistency and packing quality under different assumptions of oligomeric number, our algorithm identifies the pentamer as the most likely oligomeric state of phospholamban, demonstrating that it is possible to determine the oligomeric number directly from NMR data. Additional tests on a number of homo-oligomers, from dimer to heptamer, similarly demonstrate the power of our method to provide unbiased determination and evaluation of homo-oligomeric complex structures.     

Energy minimization method using automata network for sequence and side-chain conformation prediction from given backbone geometry

Globular proteins have high packing densities as a result of residue side chains in the core achieving a tight, complementary packing. The internal packing is considered the main determinant of native protein structure. From that point of view, we present here a method of energy minimization using an automata network to predict a set of amino acid sequences and their side-chain conformations from a desired backbone geometry for de novo design of proteins. Using discrete side-chain conformations, that is, rotamers, the sequence generation problem from a given backbone geometry becomes one of combinatorial problems. We focused on the residues composing the interior core region and predicted a set of amino acid Sequences and their side-chain conformations only from a given backbone geometry. The kinds of residues were restricted to six hydrophobic amino acids (Ala, Ile, Met, Leu, Phe, and Val) because the core regions are almost always composed of hydrophobic residues. The obtained sequences were well packed as was the native sequence. The method can be used for automated sequence generation in the de novo design of proteins. © 1994 Wiley-Liss, Inc.     

The structure and dynamics of rat apo-cellular retinol-binding protein II in solution: comparison with the X-ray structure

The structure and dynamics of rat apo-cellular retinol binding protein II (apo-CRBP II) in solution has been determined by multidimensional NMR analysis of uniformly enriched recombinant rat 13C, 15N-apo-CRBP II and 15N-apo-CRBP II. The final ensemble of 24 NMR structures has been calculated from 3274 conformational restraints or 24.4 restraints/residue. The average root-mean-square deviation of the backbone atoms for the final 24 structures relative to their mean structure is 1.06 A. Although the average solution structure is very similar to the crystal structure, it differs at the putative entrance to the binding cavity, which is formed by the helix-turn-helix motif, the betaC-betaD turn and the betaE-betaF turn. The mean coordinates of the main-chain atoms of amino acid residues 28-38 are displaced in the solution structure relative to the crystal structure. The side-chain of F58, located on the betaC-betaD turn, is reoriented such that it interacts with L37 and no longer blocks entry into the ligand-binding pocket. Residues 28-35, which form the second helix of the helix-turn-helix motif in the crystal structure, do not exhibit a helical conformation in the solution structure. The solution structure of apo-CRBP II exhibits discrete regions of backbone disorder which are most pronounced at residues 28-32, 37-38 and 73-76 in the betaE-betaF turn as evaluated by the consensus chemical shift index, the root-mean-square deviation, amide 1H exchange rates and 15N relaxation studies. These studies indicate that fluctuations in protein conformation occur on the microseconds to ms time-scale in these regions of the protein. Some of these exchange processes can be directly observed in the three-dimensional 15N-resolved NOESY spectrum. These results suggest that in solution, apo-CRBP II undergoes conformational changes on the microseconds to ms time-scale which result in increased access to the binding cavity.     

The interrelationships of side-chain and main-chain conformations in proteins

The accurate determination of a large number of protein structures by X-ray crystallography makes it possible to conduct a reliable statistical analysis of the distribution of the main-chain and side-chain conformational angles, how these are dependent on residue type, adjacent residue in the sequence, secondary structure, residue-residue interactions and location at the polypeptide chain termini. The interrelationship between the main-chain (phi, psi) and side-chain (chi 1) torsion angles leads to a classification of amino acid residues that simplify the folding alphabet considerably and can be a guide to the design of new proteins or mutational studies. Analyses of residues occurring with disallowed main-chain conformation or with multiple conformations shed some light on why some residues are less favoured in thermophiles.     

Analysis of the relationship between side-chain conformation and secondary structure in globular proteins

The relationship between the preferred side-chain dihedral angles and the secondary structure of a residue was examined. The structures of 61 proteins solved to a resolution of 2.0 A (1 A = 0.1 nm) or better were analysed using a relational database to store the information. The strongest feature observed was that the chi 1 distribution for most side-chains in an alpha-helix showed an absence of the g- conformation and a shift towards the t conformation when compared to the non-alpha/beta structures. The exceptions to this tendency were for short polar side-chains that form hydrogen bonds with the main-chain which prefer g+. Shifts in the chi 1 preferences for residues in the beta-sheet were observed. Other side-chain dihedral angles (chi 2, chi 3, chi 4) were found to be influenced by the main-chain. This paper presents more accurate distributions for the side-chain dihedral angles which were obtained from the increased number of proteins determined to high resolution. The means and standard deviations for chi 1 and chi 2 angles are presented for all residues according to the secondary structure of the main-chain. The means and standard deviations are given for the most popular conformations for side-chains in which chi 3 and chi 4 rotations affect the position of C atoms.     

Flexibility observed in high resolution structures of <Emphasis Type="Italic">Streptomyces aureofaciens</Emphasis> ribonucleases determined by diffraction methods

It has been widely accepted to distinguish between static structures determined by diffraction methods and dynamic structures determined by nuclear magnetic resonance (NMR). The dynamics of NMR structures is demonstrated by an ensemble of a number of overlaid structures. This cannot be seen in one structure determined by diffraction methods. However, it is possible to see the flexibility of a protein molecule in a number of structures of the same protein determined by X-ray techniques which is manifested by different conformations of main-chain. Multiple protein structure determination does not provide identical structures as a result of various factors including flexibility. Overlap of structures of a protein determined at atomic resolution with high accuracy shows that the root-mean-square deviations (rmsd) of main-chain atoms exceed several fold the accuracy of the positional parameters of each structure. Overlap of a number of structures of a protein determined by diffraction methods shows a similar distribution as that determined by NMR. These observations are demonstrated using high resolution structures of Streptomyces aureofaciens ribonucleases, their mutants and complexes with ligands.     

Excluded volume in protein side-chain packing

The excluded volume occupied by protein side-chains and the requirement of high packing density in the protein interior should severely limit the number of side-chain conformations compatible with a given native backbone. To examine the relationship between side-chain geometry and side-chain packing, we use an all-atom Monte Carlo simulation to sample the large space of side-chain conformations. We study three models of excluded volume and use umbrella sampling to effectively explore the entire space. We find that while excluded volume constraints reduce the size of conformational space by many orders of magnitude, the number of allowed conformations is still large. An average repacked conformation has 20 % of its chi angles in a non-native state, a marked reduction from the expected 67 % in the absence of excluded volume. Interestingly, well-packed conformations with up to 50 % non-native chi angles exist. The repacked conformations have native packing density as measured by a standard Voronoi procedure. Entropy is distributed non-uniformly over positions, and we partially explain the observed distribution using rotamer probabilities derived from the Protein Data Bank database. In several cases, native rotamers that occur infrequently in the database are seen with high probability in our simulation, indicating that sequence-specific excluded volume interactions can stabilize rotamers that are rare for a given backbone. In spite of our finding that 65 % of the native rotamers and 85 % of chi(1) angles can be predicted correctly on the basis of excluded volume only, 95 % of positions can accommodate more than one rotamer in simulation. We estimate that, in order to quench the side-chain entropy observed in the presence of excluded volume interactions, other interactions (hydrophobic, polar, electrostatic) must provide an additional stabilization of at least 0.6 kT per residue in order to single out the native state.     

Structure-fluorescence correlations in a single tryptophan mutant of carp parvalbumin: solution structure, backbone and side-chain dynamics

Heterogeneous fluorescence intensity decays of tryptophan in proteins are often rationalized using a model which proposes that different rotameric states of the indole alanyl side-chain are responsible for the observed fluorescence lifetime heterogeneity. We present here the study of a mutant of carp parvalbumin bearing a single tryptophan residue at position 102 (F102W) whose fluorescence intensity decay is heterogeneous and assess the applicability of a rotamer model to describe the fluorescence decay data. We have determined the solution structure of F102W in the calcium ligated state using multi-dimensional nuclear magnetic resonance (NMR) and have used the minimum perturbation mapping technique to explore the possible existence of multiple conformations of the indole moiety of Trp102 of F102W and, for comparison, Trp48 of holo-azurin. The maps for parvalbumin suggest two potential conformations of the indole side-chain. The high energy barrier for rotational isomerization between these conformers implies that interwell rotation would occur on time-scales of milliseconds or greater and suggests a rotamer basis for the heterogeneous fluorescence. However, the absence of alternate Trp102 conformers in the NMR data (to within 3 % of the dominant species) suggests that the heterogeneous fluorescence of Trp102 may arise from mechanisms independent of rotameric states of the Trp side-chain. The map for holo-azurin has only one conformation, and suggests a rotamer model may not be required to explain its heterogeneous fluorescence intensity decay. The backbone and Trp102 side-chain dynamics at 30 degrees C of F102W has been characterized based on an analysis of (15)N NMR relaxation data which we have interpreted using the Lipari-Szabo formalism. High order parameter (S(2)) values were obtained for both the helical and loop regions. Additionally, the S(2) values imply that the calcium binding CD and EF loops are not strictly equivalent. The S(2) value for the indole side-chain of Trp102 obtained from the fluorescence, NMR relaxation and minimum perturbation data are consistent with a Trp moiety whose motion is restricted.     

Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.