Modeling protein loops using a phi i + 1, psi i dimer database.

We present an automated method for modeling backbones of protein loops. The method samples a database of phi i + 1 and psi i angles constructed from a nonredundant version of the Protein Data Bank (PDB). The dihedral angles phi i + 1 and psi i completely define the backbone conformation of a dimer when standard bond lengths, bond angles, and a trans planar peptide configuration are used. For the 400 possible dimers resulting from 20 natural amino acids, a list of allowed phi i + 1, psi i pairs for each dimer is created by pooling all such pairs from the loop segments of each protein in the nonredundant version of the PDB. Starting from the N-terminus of the loop sequence, conformations are generated by assigning randomly selected pairs of phi i + 1, psi i for each dimer from the respective pool using standard bond lengths, bond angles, and a trans peptide configuration. We use this database to simulate protein loops of lengths varying from 5 to 11 amino acids in five proteins of known three-dimensional structures. Typically, 10,000-50,000 models are simulated for each protein loop and are evaluated for stereochemical consistency. Depending on the length and sequence of a given loop, 50-80% of the models generated have no stereochemical strain in the backbone atoms. We demonstrate that, when simulated loops are extended to include flanking residues from homologous segments, only very few loops from an ensemble of sterically allowed conformations orient the flanking segments consistent with the protein topology. The presence of near-native backbone conformations for loops from five different proteins suggests the completeness of the dimeric database for use in modeling loops of homologous proteins. Here, we take advantage of this observation to design a method that filters near-native loop conformations from an ensemble of sterically allowed conformations. We demonstrate that our method eliminates the need for a loop-closure algorithm and hence allows for the use of topological constraints of the homologous proteins or disulfide constraints to filter near-native loop conformations.     

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.     

Propensities,probabilities, and the Boltzmann hypothesis

The relative strengths of interactions involving polypeptide chains can be estimated with reasonable accuracy with statistical potentials, free-energy functions derived from the frequency of occurrence of structural arrangements of residues or atoms in collections of protein structures. Recent published work has shown that the energetics of side-chain/backbone interactions can be modeled by the phi/psi propensities of the 20 amino acids. In this report, the more commonly used phi/psi probabilities are demonstrated to fail in evaluating the free energies of protein conformations because of an overriding preference for all helical structures. Comparison of the hypothetical reactions implied by these two different statistics-propensities versus probabilities-leads to the conclusion that the Boltzmann hypothesis may only be applicable for the calculation of statistical potentials after the starting conformation has been specified. This conclusion supports a simple conjecture: The surprising success of the Boltzmann hypothesis in explaining the energetics of protein structures is a direct consequence of a real equilibrium, one extending over evolutionary time that has maintained the stability of each protein within a narrow range of values.     

Structural and dynamic characterization of an unfolded state of poplar apo-plastocyanin formed under nondenaturing conditions

Plastocyanin is a predominantly beta-sheet protein containing a type I copper center. The conformational ensemble of a denatured state of apo-plastocyanin formed in solution under conditions of low salt and neutral pH has been investigated by multidimensional heteronuclear NMR spectroscopy. Chemical shift assignments were obtained by using three-dimensional triple-resonance NMR experiments to trace through-bond heteronuclear connectivities along the backbone and side chains. The (3)J(HN,Halpha) coupling constants, (15)N-edited proton-proton nuclear Overhauser effects (NOEs), and (15)N relaxation parameters were also measured for the purpose of structural and dynamic characterization. Most of the residues corresponding to beta-strands in the folded protein exhibit small upfield shifts of the (13)C(alpha) and (13)CO resonances relative to random coil values, suggesting a slight preference for backbone dihedral angles in the beta region of (phi,psi) space. This is further supported by the presence of strong sequential d(alphaN)(i, i + 1) NOEs throughout the sequence. The few d(NN)(i, i + 1) proton NOEs that are observed are mostly in regions that form loops in the native plastocyanin structure. No medium or long-range NOEs were observed. A short sequence, between residues 59 and 63, was found to populate a nonnative helical conformation in the unfolded state, as indicated by the shift of the (13)C(alpha), (13)CO, and (1)H(alpha) resonances relative to random coil values and by the decreased values of the (3)J(HN,Halpha) coupling constants. The (15)N relaxation parameters indicate restriction of motions on a nanosecond timescale in this region. Intriguingly, this helical conformation is present in a sequence that is close to but not in the same location as the single short helix in the native folded protein. The results are consistent with earlier NMR studies of peptide fragments of plastocyanin and confirm that the regions of the sequence that form beta-strands in the native protein spontaneously populate the beta-region of (phi,psi) space under folding conditions, even in the absence of stabilizing tertiary interactions. We conclude that the state of apo-plastocyanin present under nondenaturing conditions is a noncompact unfolded state with some evidence of nativelike and nonnative local structuring that may be initiation sites for folding of the protein.     

Dihedral angle preferences of amino acid residues forming various non-local interactions in proteins

In theory, a polypeptide chain can adopt a vast number of conformations, each corresponding to a set of backbone rotation angles. Many of these conformations are excluded due to steric overlaps. Ramachandran and coworkers were the first to look into this problem by plotting backbone dihedral angles in a two-dimensional plot. The conformational space in the Ramachandran map is further refined by considering the energetic contributions of various non-bonded interactions. Alternatively, the conformation adopted by a polypeptide chain may also be examined by investigating interactions between the residues. Since the Ramachandran map essentially focuses on local interactions (residues closer in sequence), out of interest, we have analyzed the dihedral angle preferences of residues that make non-local interactions (residues far away in sequence and closer in space) in the folded structures of proteins. The non-local interactions have been grouped into different types such as hydrogen bond, van der Waals interactions between hydrophobic groups, ion pairs (salt bridges), and ππ-stacking interactions. The results show the propensity of amino acid residues in proteins forming local and non-local interactions. Our results point to the vital role of different types of non-local interactions and their effect on dihedral angles in forming secondary and tertiary structural elements to adopt their native fold.     

Structure of alpha-spiral hairpins with short connections in globular proteins

The analysis of conformations of more than 100 alpha-alpha-hairpins with closely packed helical segments and connections up to four amino acid residues in length was carried out. Five types of the connections were revealed and their phi and psi values on the Ramachandran map were found. Each type of alpha-alpha-hairpins was shown to have a unique sequence pattern for hydrophobic and hydrophilic residues.     

Determination of the local structure of the protein insectotoxin I5A from the scorpion Buthus eupeus from 1H-NMR spectroscopy data

The local structure (torsion angles phi, psi and chi 1 of amino acid residues) of insectotoxin I5A (35 residues) of scorpion Buthus eupeus has been determined from cross-peak integral intensities in two-dimensional nuclear Overhauser enhancement (NOESY) spectra and spin coupling constants of vicinal H--NC alpha--H and H--C alpha C beta--H protons. The local structure determination was carried out by fitting complete relaxation matrix of peptide unit protons (protons of a given residue and NH proton of the next residue in the amino acid sequence) with experimental NOESY cross-peak intensities. The obtained intervals of backbone torsional angles phi and psi consistent with NMR data were determined for all but Gly residues. The predominant C alpha--C beta rotamer of the side chain has been unambiguously determined for 42% of the insectotoxin amino acid residues whereas for another 46% residues experimental data are fitted equally well with two rotamers. Stereospecific assignments were obtained for 38% of beta-methylene groups. The determined torsional angles phi, psi and chi 1 correspond to the sterically allowed conformations of the amino acid residues and agree with the insectotoxin secondary structure established earlier by 1H NMR spectroscopy.     

Approaching a complete classification of protein secondary structure

A complete classification of types of the protein secondary structure is developed on the basis of computer analysis of the crystallographic structural data deposited in the protein Data Bank. The majority of amino acid residues fall into five conformation types. A conclusion is drawn that the number of sequence variants of torsion angles phi, psi in globular proteins is limited and is essentially less than the number of possible amino acid sequences for this chain length. Along with alpha-helix and beta-structure, the distribution analysis assigning every maximum of distribution of amino acid conformations on Ramachandran map to a certain type of the secondary structure exposed a third type of the secondary structure that was previously neglected. This type of the structure is extended left-handed helical conformation, designated as mobile (M-) conformation. A full set of M-conformation fragments that seems to play a major role in protein globule dynamics has been obtained, a small radius of correlation for the polypeptide chain in M-conformation is demonstrated. It explains a prevalence of short segments of mobile conformation revealed in globular proteins. For secondary structure types, the frequency of occurrence of amino acid residues has been computed.     

Conformation of di-n-propylglycine residues (Dpg) in peptides: crystal structures of a type I' beta-turn forming tetrapeptide and an alpha-helical tetradecapeptide.

The crystal structures of two oligopeptides containing di-n-propylglycine (Dpg) residues, Boc-Gly-Dpg-Gly-Leu-OMe (1) and Boc-Val-Ala-Leu-Dpg-Val-Ala-Leu-Val-Ala-Leu-Dpg-Val-Ala-Leu-OMe (2) are presented. Peptide 1 adopts a type I'beta-turn conformation with Dpg(2)-Gly(3) at the corner positions. The 14-residue peptide 2 crystallizes with two molecules in the asymmetric unit, both of which adopt alpha-helical conformations stabilized by 11 successive 5 --> 1 hydrogen bonds. In addition, a single 4 --> 1 hydrogen bond is also observed at the N-terminus. All five Dpg residues adopt backbone torsion angles (phi, psi) in the helical region of conformational space. Evaluation of the available structural data on Dpg peptides confirm the correlation between backbone bond angle N-C(alpha)-C' (tau) and the observed backbone phi,psi values. For tau > 106 degrees, helices are observed, while fully extended structures are characterized by tau < 106 degrees. The mean tau values for extended and folded conformations for the Dpg residue are 103.6 degrees +/- 1.7 degrees and 109.9 degrees +/- 2.6 degrees, respectively.     

Stress and strain in staphylococcal nuclease.

Protein molecules generally adopt a tertiary structure in which all backbone and side chain conformations are arranged in local energy minima; however, in several well-refined protein structures examples of locally strained geometries, such as cis peptide bonds, have been observed. Staphylococcal nuclease A contains a single cis peptide bond between residues Lys 116 and Pro 117 within a type VIa beta-turn. Alternative native folded forms of nuclease A have been detected by NMR spectroscopy and attributed to a mixture of cis and trans isomers at the Lys 116-Pro 117 peptide bond. Analyses of nuclease variants K116G and K116A by NMR spectroscopy and X-ray crystallography are reported herein. The structure of K116A is indistinguishable from that of nuclease A, including a cis 116-117 peptide bond (92% populated in solution). The overall fold of K116G is also indistinguishable from nuclease A except in the region of the substitution (residues 112-117), which contains a predominantly trans Gly 116-Pro 117 peptide bond (80% populated in solution). Both Lys and Ala would be prohibited from adopting the backbone conformation of Gly 116 due to steric clashes between the beta-carbon and the surrounding residues. One explanation for these results is that the position of the ends of the residue 112-117 loop only allow trans conformations where the local backbone interactions associated with the phi and psi torsion angles are strained. When the 116-117 peptide bond is cis, less strained backbone conformations are available. Thus the relaxation of the backbone strain intrinsic to the trans conformation compensates for the energetically unfavorable cis X-Pro peptide bond. With the removal of the side chain from residue 116 (K116G), the backbone strain of the trans conformation is reduced to the point that the conformation associated with the cis peptide bond is no longer favorable.     

Minimalist representations and the importance of nearest neighbor effects in protein folding simulations

In order to investigate the level of representation required to simulate folding and predict structure, we test the ability of a variety of reduced representations to identify native states in decoy libraries and to recover the native structure given the advanced knowledge of the very broad native Ramachandran basin assignments. Simplifications include the removal of the entire side-chain or the retention of only the Cbeta atoms. Scoring functions are derived from an all-atom statistical potential that distinguishes between atoms and different residue types. Structures are obtained by minimizing the scoring function with a computationally rapid simulated annealing algorithm. Results are compared for simulations in which backbone conformations are sampled from a Protein Data Bank-based backbone rotamer library generated by either ignoring or including a dependence on the identity and conformation of the neighboring residues. Only when the Cbeta atoms and nearest neighbor effects are included do the lowest energy structures generally fall within 4 A of the native backbone root-mean square deviation (RMSD), despite the initial configuration being highly expanded with an average RMSD > or = 10 A. The side-chains are reinserted into the Cbeta models with minimal steric clash. Therefore, the detailed, all-atom information lost in descending to a Cbeta-level representation is recaptured to a large measure using backbone dihedral angle sampling that includes nearest neighbor effects and an appropriate scoring function.     

A Bayesian-probability-based method for assigning protein backbone dihedral angles based on chemical shifts and local sequences

Chemical shifts contain substantial information about protein local conformations. We present a method to assign individual protein backbone dihedral angles into specific regions on the Ramachandran map based on the amino acid sequences and the chemical shifts of backbone atoms of tripeptide segments. The method uses a scoring function derived from the Bayesian probability for the central residue of a query tripeptide segment to have a particular conformation. The Ramachandran map is partitioned into representative regions at two levels of resolution. The lower resolution partitioning is equivalent to the conventional definitions of different secondary structure regions on the map. At the higher resolution level, the α and β regions are further divided into subregions. Predictions are attempted at both levels of resolution. We compared our method with TALOS using the original TALOS database, and obtained comparable results. Although TALOS may produce the best results with currently available databases which are much enlarged, the Bayesian-probability-based approach can provide a quantitative measure for the reliability of predictions.     

A novel exhaustive search algorithm for predicting the conformation of polypeptide segments in proteins

We present a fast ab initio method for the prediction of local conformations in proteins. The program, PETRA, selects polypeptide fragments from a computer-generated database (APD) encoding all possible peptide fragments up to twelve amino acids long. Each fragment is defined by a representative set of eight straight phi/psi pairs, obtained iteratively from a trial set by calculating how fragments generated from them represent the protein databank (PDB). Ninety-six percent (96%) of length five fragments in crystal structures, with a resolution better than 1.5 A and less than 25% identity, have a conformer in the database with less than 1 A root-mean-square deviation (rmsd). In order to select segments from APD, PETRA uses a set of simple rule-based filters, thus reducing the number of potential conformations to a manageable total. This reduced set is scored and sorted using rmsd fit to the anchor regions and a knowledge-based energy function dependent on the sequence to be modelled. The best scoring fragments can then be optimized by minimization of contact potentials and rmsd fit to the core model. The quality of the prediction made by PETRA is evaluated by calculating both the differences in rmsd and backbone torsion angles between the final model and the native fragment. The average rmsd ranges from 1.4 A for three residue loops to 3.9 A for eight residue loops.     

Assessing side-chain perturbations of the protein backbone: a knowledge-based classification of residue Ramachandran space

Grouping the 20 residues is a classic strategy to discover ordered patterns and insights about the fundamental nature of proteins, their structure, and how they fold. Usually, this categorization is based on the biophysical and/or structural properties of a residue's side-chain group. We extend this approach to understand the effects of side chains on backbone conformation and to perform a knowledge-based classification of amino acids by comparing their backbone phi, psi distributions in different types of secondary structure. At this finer, more specific resolution, torsion angle data are often sparse and discontinuous (especially for nonhelical classes) even though a comprehensive set of protein structures is used. To ensure the precision of Ramachandran plot comparisons, we applied a rigorous Bayesian density estimation method that produces continuous estimates of the backbone phi, psi distributions. Based on this statistical modeling, a robust hierarchical clustering was performed using a divergence score to measure the similarity between plots. There were seven general groups based on the clusters from the complete Ramachandran data: nonpolar/beta-branched (Ile and Val), AsX (Asn and Asp), long (Met, Gln, Arg, Glu, Lys, and Leu), aromatic (Phe, Tyr, His, and Cys), small (Ala and Ser), bulky (Thr and Trp), and, lastly, the singletons of Gly and Pro. At the level of secondary structure (helix, sheet, turn, and coil), these groups remain somewhat consistent, although there are a few significant variations. Besides the expected uniqueness of the Gly and Pro distributions, the nonpolar/beta-branched and AsX clusters were very consistent across all types of secondary structure. Effectively, this consistency across the secondary structure classes implies that side-chain steric effects strongly influence a residue's backbone torsion angle conformation. These results help to explain the plasticity of amino acid substitutions on protein structure and should help in protein design and structure evaluation.     

The conformations of polypeptide chains where the main-chain parts of successive residues are enantiomeric. Their occurrence in cation and anion-binding regions of proteins.

We have investigated the shapes of polypeptides where successive residues have main-chain phi,psi conformations of opposite hand. A graph not unlike a Ramachandran plot is presented illustrating the various possible conformations. All are ring-shaped or extended. Some of these conformations occur in native proteins, the commonest approximating to a feature we propose calling a nest, described in the accompanying paper, where the main-chain NH groups point inwards relative to the ring and give rise to an anion-binding site. Another conformation is related but more extended and is found uniquely in the four stretches of polypeptide that line the tetrameric K(+) channel; their CO groups bind the K ions in the channel. In a different ring-shaped conformation that we propose calling a catgrip, the main-chain CO groups point into the ring; this is employed for specific Ca ion binding in the annexin, phospholipase A2 and subtilisin loops, and the regularly arranged beta-roll loops of the serralysin protease family.     

The task of determining the local structure of proteins by Overhauser effect nuclear spectroscopy addressed once more]

The testing of the earlier developed theoretical method for determining the backbone protein conformations (the local structure) on the basis of the two-dimensional nuclear Overhauser effect (NOE) spectroscopy has been fulfilled. The method approval has been carried out by the calculation (based upon spectral NOE parameters) of the local plastocyanin and bovine pancreatic trypsin inhibitor structures followed by the comparison of the received conformational parameters with the X-ray data. The comparison of the molecular conformations in solution and crystal has been implemented for different fragments of the polypeptide chain (beta-structures, alpha-helices, irregular segments) using the mathematical statistics methods. The verification of the "zero" hypothesis about the similarity of phi and psi variation rows which was carried out at the reliability level of 0.99 showed that in both cases there were no systematic deviations of dihedral angles of the compared conformations and that their dispersion differences were statistically indiscernible. It has been concluded that the approved method permits to determine the local structure of the conformationally rigid proteins (or their fragments) at the level close to that which provides the high resolution X-ray analysis.     

An observation of non-superimposable stereogeometrical features in a non-chiral one-component beta-Ala model peptide

This paper describes the chemical synthesis and crystal molecular conformation of a non-chiral beta-Ala containing model peptide Boc-beta-Ala-Acc5-OCH3. The analysis revealed the existence of two crystallographically independent molecules A and B, in the asymmetric unit. Unexpectedly, while the magnitudes of the backbone torsion angles in both molecules are remarkably similar, the signs of the corresponding torsion angles are reverse therefore, inclining us to suggest the existence of non-superimposable stereogeometrical features in a non-chiral one-component beta-Ala model system. The critical mu torsion angle around CbetaH2-CalphaH2 bond of the beta-Ala residue represents a typical gauche orientation i.e., mu = 67.7 degrees in A and mu = -61.2 degrees in B, providing the molecule an overall crescent shaped topology. The observed conformation contrasts markedly to those determined for the correlated non-chiral model peptides: Boc-beta-Ala-Acc6-OCH3 and Boc-beta-Ala-Aib-OCH3 signifying the role of stereocontrolling elements since the stereochemically constrained Calpha, alpha-disubstituted glycyl residues (e.g., Acc5, Acc6, and the prototype Aib) are known to strongly restrict the peptide backbone conformations in the 3(10)/alpha-helical-regions ( phi approximately +/-60+/-20 degrees, psi approximately +/-30+/-20 degrees) of the Ramachandran map. Unpredictably, the preferred, phi, psi torsion angles of the Acc5 residue fall outside the helical regions of the Ramachandran map and exhibit opposite-handed twists for A and B. The implications of the semi-extended conformation of the Acc5 residue in the construction of backbone-modified novel scaffolds and peptides of biological relevance are highlighted. Taken together, the results indicate that in short linear beta-Ala containing peptides specific structural changes can be induced by selective substitution of non-coded linear- or cyclic symmetrically Calpha,alpha-disubstituted glycines, reinstating the hypothesis that in addition to conformational restrictions, the chemical nature of the neighboring side-chain substituents and local environments collectively influences the stabilization of folding-unfolding behavior of the two methylene units of a beta-Ala residue.     

Folding of peptide fragments comprising the complete sequence of proteins. Models for initiation of protein folding. II. Plastocyanin.

In an attempt to understand the earliest events in the protein folding pathway, the complete sequence of French bean plastocyanin has been synthesized as a series of short peptide fragments, and the conformational preferences of each peptide examined in aqueous solution using proton n.m.r. methods. Plastocyanin consists largely of beta-sheet, with reverse turns and loops between the strands of the sheet, and one short helix. The n.m.r. experiments indicate that most of the peptides derived from the plastocyanin sequence have remarkably little propensity to adopt folded conformations in aqueous solution, in marked contrast to the peptides derived from the helical protein, myohemerythrin (accompanying paper). For most plastocyanin peptides, the backbone dihedral angles are predominantly in the beta-region of conformational space. Some of the peptides show weak NOE connectivities between adjacent amide protons, indicative of small local populations of backbone conformations in the a region of (phi,psi) space. A conformational preference for a reverse turn is seen in the sequence Ala65-Pro-Gly-Glu68, where a turn structure is found in the folded protein. Significantly, the peptide sequences that populate the alpha-region of (phi,psi) space are mostly derived from turn and loop regions in the protein. The addition of trifluoroethanol does not drive the peptides into helical conformations. In one region of the sequence, the n.m.r. spectra provide evidence of the formation of a hydrophobic cluster involving aromatic and aliphatic side-chains. These results have significance for understanding the initiation of protein folding. From these studies of the fragments of plastocyanin (this paper) and myohemerythrin (accompanying paper), it appears that there is a pre-partitioning of the conformational space sampled by the polypeptide backbone that is related to the secondary structure in the final folded state.