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.     

Three enhancements to the inference of statistical protein‐DNA potentials

The energetics of protein‐DNA interactions are often modeled using so‐called statistical potentials, that is, energy models derived from the atomic structures of protein‐DNA complexes. Many statistical protein‐DNA potentials based on differing theoretical assumptions have been investigated, but little attention has been paid to the types of data and the parameter estimation process used in deriving the statistical potentials. We describe three enhancements to statistical potential inference that significantly improve the accuracy of predicted protein‐DNA interactions: (i) incorporation of binding energy data of protein‐DNA complexes, in conjunction with their X‐ray crystal structures, (ii) use of spatially‐aware parameter fitting, and (iii) use of ensemble‐based parameter fitting. We apply these enhancements to three widely‐used statistical potentials and use the resulting enhanced potentials in a structure‐based prediction of the DNA binding sites of proteins. These enhancements are directly applicable to all statistical potentials used in protein‐DNA modeling, and we show that they can improve the accuracy of predicted DNA binding sites by up to 21%. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

A new residue-nucleotide propensity potential with structural information considered for discriminating protein-RNA docking decoys

Understanding the key factors that influence the preferences of residue-nucleotide interactions in specific protein-RNA interactions has remained a research focus. We propose an effective approach to derive residue-nucleotide propensity potentials through considering both the types of residues and nucleotides, and secondary structure information of proteins and RNAs from the currently largest nonredundant and nonribosomal protein-RNA interaction database. To test the validity of the potentials, we used them to select near-native structures from protein-RNA docking poses. The results show that considering secondary structure information, especially for RNAs, greatly improves the predictive power of pair potentials. The success rate is raised from 50.7 to 65.5% for the top 2000 structures, and the number of cases in which a near-native structure is ranked in top 50 is increased from 7 to 13 out of 17 cases. Furthermore, the exclusion of ribosomes from the database contributes 8.3% to the success rate. In addition, some very interesting findings follow: (i) the protein secondary structure element π-helix is strongly associated with RNA-binding sites; (ii) the nucleotide uracil occurs frequently in the most preferred pairs in which the unpaired and non-Watson-Crick paired uracils are predominant, which is probably significant in evolution. The new residue-nucleotide potentials can be helpful for the progress of protein-RNA docking methods, and for understanding the mechanisms of protein-RNA interactions.     

Conformation of peptides constructed from achiral amino acid residues Aib and DeltaZPhe: computational study of the effect of L/D- Leu at terminal positions

Conformational studies of the peptides constructed from achiral amino acid residues Aib and Delta(Z)Phe (I) Ac-Aib-Delta(Z)Phe-NHMe (II), and Ac-(Aib-Delta(Z)Phe)(3)-NHMe; peptides III-VI having L-Leu or D-Leu at either the N- or the C-terminal position and of peptides VII-X having Leu residues in different enantiomeric combinations at both the N- and the C-terminal positions in peptide II have been studied to design the peptide with the required helical sense. Peptide II, as expected, adopts degenerate left- and right-handed helical structures. It has been shown that the peptides IV and VI having D-Leu at either the N or the C terminus can be realized in the right-handed helical structure with the phi,psi values of -20 degrees and -60 degrees for the Aib/Delta(Z)Phe residues. L-Leu and D- Leu at both the terminals in peptides VII and VIII, respectively, have hardly any effect as both the left- and the right-handed structures are found to be degenerate. Peptides III and IX can be realized in right- and left-handed helical structures, respectively, in solvents of low polarity whereas peptides V and X are predicted to be in the right-handed helical structures stabilized by carbonyl-carbonyl interactions without the formation of hydrogen bonds. The conformational states with the phi,psi values of 0 degrees and -85 degrees in peptide V are characterized by rise per residue of 2.03 A, rotation per residue of 117.5 degrees , and 3.06 residues per turn. In all peptides having Leu residue at the N terminus, the methyl moiety of the acetyl group is involved in the CH/pi interactions with the Cepsilon--Cdelta edge of the aromatic ring of Delta(Z)Phe (3) and the amino group NH of Delta(Z)Phe is involved in the NH/pi interactions with its own aromatic ring. The CH(3) groups of the Aib residues are also involved in CH/pi interactions with the i + 1th and i + 3th Delta(Z)Phe's aromatic side chains.     

Expanded turn conformations: characterization and sequence-structure correspondence in alpha-turns with implications in helix folding

Like the beta-turns, which are characterized by a limiting distance between residues two positions apart (i, i+3), a distance criterion (involving residues at positions i and i+4) is used here to identify alpha-turns from a database of known protein structures. At least 15 classes of alpha-turns have been enumerated based on the location in the phi,psi space of the three central residues (i+1 to i+3)-one of the major being the class AAA, where the residues occupy the conventional helical backbone torsion angles. However, moving towards the C-terminal end of the turn, there is a shift in the phi,psi angles towards more negative phi, such that the electrostatic repulsion between two consecutive carbonyl oxygen atoms is reduced. Except for the last position (i+4), there is not much similarity in residue composition at different positions of hydrogen and non-hydrogen bonded AAA turns. The presence or absence of Pro at i+1 position of alpha- and beta-turns has a bearing on whether the turn is hydrogen-bonded or without a hydrogen bond. In the tertiary structure, alpha-turns are more likely to be found in beta-hairpin loops. The residue composition at the beginning of the hydrogen bonded AAA alpha-turn has similarity with type I beta-turn and N-terminal positions of helices, but the last position matches with the C-terminal capping position of helices, suggesting that the existence of a "helix cap signal" at i+4 position prevents alpha-turns from growing into helices. Our results also provide new insights into alpha-helix nucleation and folding.     

Composites of local structure propensities: Evidence for local encoding of long-range structure

To estimate how extensively the ensemble of denatured-state conformations is constrained by local side-chain–backbone interactions, propensities of each of the 20 amino acids to occur in mono- and dipeptides mapped to discrete regions of the Ramachandran map are computed from proteins of known structure. In addition, propensities are computed for the trans, gauche−, and gauche+ rotamers, with or without consideration of the values of phi and psi. These propensities are used in scoring functions for fragment threading, which estimates the energetic favorability of fragments of protein sequence to adopt the native conformation as opposed to hundreds of thousands of incorrect conformations. As finer subdivisions of the Ramachandran plot, neighboring residue phi/psi angles, and rotamers are incorporated, scoring functions become better at ranking the native conformation as the most favorable. With the best composite propensity function, the native structure can be distinguished from 300,000 incorrect structures for 71% of the 2130 arbitrary protein segments of length 40, 48% of 2247 segments of length 30, and 20% of 2368 segments of length 20. A majority of fragments of length 30–40 are estimated to be folded into the native conformation a substantial fraction of the time. These data suggest that the variations observed in amino acid frequencies in different phi/psi/chi1 environments in folded proteins reflect energetically important local side-chain–backbone interactions, interactions that may severely restrict the ensemble of conformations populated in the denatured state to a relatively small subset with nativelike structure.     

The geometry of alpha-sheet: Implications for its possible function as amyloid precursor in proteins

alpha-sheet has been proposed as the main constituent of the prefibrillar intermediate during amyloid formation. Here the helical parameters of the alpha-sheet strand are calculated from average main-chain dihedral angles reported from molecular dynamics simulations. It is an almost linear polypeptide that forms a right-handed helix of about 100 A diameter, with 100 residues and a rise of 30 A per turn. The strands are curved but untwisted, which implies that neighboring strands need not coil to make interstrand hydrogen bonds. This suggests that compared to beta-sheets in native folded proteins, alpha-sheets can be larger and stack more easily to create extensive 3D blocks. It is shown that alpha-sheet is related to a category of structures termed "mirror" structures. Mirror structures have repetitive pairs of main-chain dihedral angles at residues i and i+1 that satisfy the condition phi(i) (+1) = -psi(i), psi(i) (+1) = -phi(i). They are uniquely identified by the two orientations of their peptide planes, specified by phi(i) and psi(i). Their side chains point alternately in opposite directions. Interestingly, their conformations are insensitive to phi(i) and psi(i) in that the pseudo dihedral angle formed by four consecutive C(alpha) atoms is always close to 180 degrees . There are two types: "beta-mirror" and "alpha-mirror" structure; beta-mirror structures relate to beta-sheet by small peptide plane rotations, of less than 90 degrees , while alpha-mirror structures are close to alpha-sheet and relate to beta-sheet by approximately 180 degrees peptide plane flips. Most mirror structures, and in particular the alpha-mirror, form wide helices with diameters 50-70 A. Their gentle curvature, and therefore that of the alpha-sheet, arises from the orientation of successive peptide units causing the difference in the bond angles at the C and N atoms of the peptide unit to gradually change the direction of the chain.     

Conformational investigation of alpha,beta-dehydropeptides. XVI. Beta-turn tendency in Ac-Pro-DeltaXaa-NHMe: crystallographic and theoretical studies.

The crystal structures of two diastereomeric alpha,beta-dehydrobutyrine peptides Ac-Pro-(Z)-DeltaAbu-NHMe (I) and Ac-Pro-(E)-DeltaAbu-NHMe (II) have been determined. Both dehydropeptides adopt betaI-turn conformation characterized by the pairs of (phi(i+1), psi(i+1)) and (phi(i+2), psi(i+2)) angles as -66, -19, -97, 11 degrees for I and -59, -27, -119, 29 degrees for II. In each peptide, the betaI turn is stabilized by (i + 3) --> i intramolecular hydrogen bonds with N...O distance of 3.12 A for I and 2.93 A for II. These structures have been compared to the crystal structures of homologous peptides Ac-Pro-DeltaVal-NHMe and Ac-Pro-DeltaAla-NHMe. Theoretical analyses by DFT/B3LYP/6-31 + G** method of conformers formed by these four peptides and by the saturated peptide Ac-Pro-Ala-NHMe revealed that peptides with a (Z) substituent at the C(beta) (i+2) atom of dehydroamino acid, i.e. Ac-Pro-DeltaVal-NHMe and Ac-Pro-(Z)-DeltaAbu-NHMe, predominantly form beta turns, both in vacuo and in polar environment. The tendency to adopt beta-turn conformation is much weaker for the peptides lacking the (Z) substituent, Ac-Pro-(E)-DeltaAbu-NHMe and Ac-Pro-DeltaAla-NHMe. The latter adopts a semi-extended or an extended conformation in every polar environment, including a weakly polar solvent. The saturated peptide Ac-Pro-Ala-NHMe in vacuo prefers a beta-turn conformation, but in polar environment the differences between various conformers are small. The role of pi-electron correlation and intramolecular hydrogen bonds interaction in stabilizing the hairpin structures are discussed.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

Structure validation by Calpha geometry: phi,psi and Cbeta deviation

Geometrical validation around the Calpha is described, with a new Cbeta measure and updated Ramachandran plot. Deviation of the observed Cbeta atom from ideal position provides a single measure encapsulating the major structure-validation information contained in bond angle distortions. Cbeta deviation is sensitive to incompatibilities between sidechain and backbone caused by misfit conformations or inappropriate refinement restraints. A new phi,psi plot using density-dependent smoothing for 81,234 non-Gly, non-Pro, and non-prePro residues with B < 30 from 500 high-resolution proteins shows sharp boundaries at critical edges and clear delineation between large empty areas and regions that are allowed but disfavored. One such region is the gamma-turn conformation near +75 degrees,-60 degrees, counted as forbidden by common structure-validation programs; however, it occurs in well-ordered parts of good structures, it is overrepresented near functional sites, and strain is partly compensated by the gamma-turn H-bond. Favored and allowed phi,psi regions are also defined for Pro, pre-Pro, and Gly (important because Gly phi,psi angles are more permissive but less accurately determined). Details of these accurate empirical distributions are poorly predicted by previous theoretical calculations, including a region left of alpha-helix, which rates as favorable in energy yet rarely occurs. A proposed factor explaining this discrepancy is that crowding of the two-peptide NHs permits donating only a single H-bond. New calculations by Hu et al. [Proteins 2002 (this issue)] for Ala and Gly dipeptides, using mixed quantum mechanics and molecular mechanics, fit our nonrepetitive data in excellent detail. To run our geometrical evaluations on a user-uploaded file, see MOLPROBITY (http://kinemage.biochem.duke.edu) or RAMPAGE (http://www-cryst.bioc.cam.ac.uk/rampage).     

Influence of N-terminal residue stereochemistry on the prolyl amide geometry and the conformation of 5-tert-butylproline type VI beta-turn mimics.

The effects of N-terminal amino acid stereochemistry on prolyl amide geometry and peptide turn conformation were investigated by coupling both L- and D-amino acids to (2S, 5R)-5-tert-butylproline and L-proline to generate, respectively, N-(acetyl)dipeptide N'-methylamides 1 and 2. Prolyl amide cis- and trans-isomers were, respectively, favored for peptides 1 and 2 as observed by proton NMR spectroscopy in water, DMSO and chloroform. The influence of solvent composition on amide proton chemical shift indicated an intramolecular hydrogen bond between the N'-methylamide proton and the acetamide carbonyl for the major conformer of dipeptides (S)-1, that became less favorable in (R)-1 and 2. The coupling constant (3J(NH,alpha)) values for the cis-isomer of (R)-1 indicated a phi2 dihedral angle value characteristic of a type VIb beta-turn conformation in solution. X-ray crystallographic analysis of N-acetyl-D-leucyl-5-tert-butylproline N'-methylamide (R)-lb showed the prolyl residue in a type VIb beta-turn geometry possessing an amide cis-isomer and psi3-dihedral angle having a value of 157 degrees, which precluded an intramolecular hydrogen bond. Intermolecular hydrogen bonding between the leucyl residues of two turn structures within the unit cell positioned the N-terminal residue in a geometry where their phi2 and psi2 dihedral angle values were not characteristic of an ideal type VIb turn. The circular dichroism spectra of tert-butylprolyl peptides (S)- and (R)-1b were found not to be influenced by changes in solvent composition from water to acetonitrile. The type B spectrum exhibited by (S)-1b has been previously assigned to a type VIa beta-turn conformation [Halab L, Lubell WD. J. Org. Chem. 1999; 64: 3312-3321]. The type C spectrum exhibited by the (R)-lb has previously been associated with type II' beta-turn and alpha-helical conformations in solution and appears now to be also characteristic for a type VIb geometry.     

Structures, basins, and energies: a deconstruction of the Protein Coil Library

Globular proteins adopt complex folds, composed of organized assemblies of alpha-helix and beta-sheet together with irregular regions that interconnect these scaffold elements. Here, we seek to parse the irregular regions into their structural constituents and to rationalize their formative energetics. Toward this end, we dissected the Protein Coil Library, a structural database of protein segments that are neither alpha-helix nor beta-strand, extracted from high-resolution protein structures. The backbone dihedral angles of residues from coil library segments are distributed indiscriminately across the phi,psi map, but when contoured, seven distinct basins emerge clearly. The structures and energetics associated with the two least-studied basins are the primary focus of this article. Specifically, the structural motifs associated with these basins were characterized in detail and then assessed in simple simulations designed to capture their energetic determinants. It is found that conformational constraints imposed by excluded volume and hydrogen bonding are sufficient to reproduce the observed ,psi distributions of these motifs; no additional energy terms are required. These three motifs in conjunction with alpha-helices, strands of beta-sheet, canonical beta-turns, and polyproline II conformers comprise approximately 90% of all protein structure.     

Characterization of beta-turn and Asx-turns mimicry in a model peptide: stabilization via C--H . . . O interaction

The chemical synthesis and single-crystal X-ray diffraction analysis of a model peptide, Boc-Thr-Thr-NH2 (1) comprised of proteinogenic residues bearing an amphiphilic Cbeta -stereogenic center, has been described. Interestingly, the analysis of its molecular structure revealed the existence of a distinct conformation that mimics a typical beta-turn and Asx-turns, i.e., the two Thr residues occupy the left- and right-corner positions. The main-chain torsion angles of the N- and C-terminal residues i.e., semiextended: phi = -68.9 degrees , psi = 128.6 degrees ; semifolded: phi = -138.1 degrees , psi = 2.5 degrees conformations, respectively, in conjunction with a gauche- disposition of the obligatory C-terminus Thr CgammaH3 group, characterize the occurrence of the newly described beta-turn- and Asx-turns-like topology. The preferred molecular structure is suggested to be stabilized by an effective nonconventional main-chain to side-chain Ci=O . . . H--Cgamma(i+2)-type intraturn hydrogen bond. Noteworthy, the observed topology of the resulting 10-membered hydrogen-bonded ring is essentially similar to the one perceived for a classical beta-turn and the Asx-turns, stabilized by a conventional intraturn hydrogen bond. Considering the signs as well as magnitudes of the backbone torsion angles and the orientation of the central peptide bond, the overall mimicked topology resembles the type II beta-turn or type II Asx-turns. An analysis of Xaa-Thr sequences in high-resolution X-ray elucidated protein structures revealed the novel topology prevalence in functional proteins (unpublished). In view of indubitable structural as well as functional importance of nonconventional interactions in bioorganic and biomacromolecules, we intend to highlight the participation of Thr CgammaH in the creation of a short-range C=O . . . H--Cgamma -type interaction in peptides and proteins.     

Sequence specificity, statistical potentials, and three-dimensional structure prediction with self-correcting distance geometry calculations of beta-sheet formation in proteins

A statistical analysis of a representative data set of 169 known protein structures was used to analyze the specificity of residue interactions between spatial neighboring strands in beta-sheets. Pairwise potentials were derived from the frequency of residue pairs in nearest contact, second nearest and third nearest contacts across neighboring beta-strands compared to the expected frequency of residue pairs in a random model. A pseudo-energy function based on these statistical pairwise potentials recognized native beta-sheets among possible alternative pairings. The native pairing was found within the three lowest energies in 73% of the cases in the training data set and in 63% of beta-sheets in a test data set of 67 proteins, which were not part of the training set. The energy function was also used to detect tripeptides, which occur frequently in beta-sheets of native proteins. The majority of native partners of tripeptides were distributed in a low energy range. Self-correcting distance geometry (SECODG) calculations using distance constraints sets derived from possible low energy pairing of beta-strands uniquely identified the native pairing of the beta-sheet in pancreatic trypsin inhibitor (BPTI). These results will be useful for predicting the structure of proteins from their amino acid sequence as well as for the design of proteins containing beta-sheets.     

A new catalog of protein beta-sheets

Systematic protein folding studies depend on protein three-dimensional structure annotation, the assignment of amino acid structural types from atomic coordinates. Significant stabilizing factors between adjacent beta-sheet peptide chains have recently been characterized and were not considered during the development of previously published annotation methods. To produce an accurate beta-sheet domain catalog and to encompass the full beta-sheet spectacle, we developed a method, beta-Spider, which evaluates a packing energy between adjacent peptide chains in accordance with the newly discovered stabilizing factors. While considering important energetic factors, our approach also minimizes the use of subjective criteria, such as (phi,psi) boundaries and sets of H-bonding motifs that are used in other existing methods. As a result of the application of beta-Spider to a set of available high-resolution X-ray crystal structures, we present here a new beta-sheet catalog that differs considerably from the one produced by the most acclaimed DSSP method. The catalog includes new H-bonding motifs that were never reported.     

A simple probabilistic model of multibody interactions in proteins

Protein structure prediction methods typically use statistical potentials, which rely on statistics derived from a database of know protein structures. In the vast majority of cases, these potentials involve pairwise distances or contacts between amino acids or atoms. Although some potentials beyond pairwise interactions have been described, the formulation of a general multibody potential is seen as intractable due to the perceived limited amount of data. In this article, we show that it is possible to formulate a probabilistic model of higher order interactions in proteins, without arbitrarily limiting the number of contacts. The success of this approach is based on replacing a naive table‐based approach with a simple hierarchical model involving suitable probability distributions and conditional independence assumptions. The model captures the joint probability distribution of an amino acid and its neighbors, local structure and solvent exposure. We show that this model can be used to approximate the conditional probability distribution of an amino acid sequence given a structure using a pseudo‐likelihood approach. We verify the model by decoy recognition and site‐specific amino acid predictions. Our coarse‐grained model is compared to state‐of‐art methods that use full atomic detail. This article illustrates how the use of simple probabilistic models can lead to new opportunities in the treatment of nonlocal interactions in knowledge‐based protein structure prediction and design. Proteins 2013; 81:1340–1350. © 2013 Wiley Periodicals, Inc.     

Geometric cooperativity and anticooperativity of three-body interactions in native proteins

Characterizing multibody interactions of hydrophobic, polar, and ionizable residues in protein is important for understanding the stability of protein structures. We introduce a geometric model for quantifying 3-body interactions in native proteins. With this model, empirical propensity values for many types of 3-body interactions can be reliably estimated from a database of native protein structures, despite the overwhelming presence of pairwise contacts. In addition, we define a nonadditive coefficient that characterizes cooperativity and anticooperativity of residue interactions in native proteins by measuring the deviation of 3-body interactions from 3 independent pairwise interactions. It compares the 3-body propensity value from what would be expected if only pairwise interactions were considered, and highlights the distinction of propensity and cooperativity of 3-body interaction. Based on the geometric model, and what can be inferred from statistical analysis of such a model, we find that hydrophobic interactions and hydrogen-bonding interactions make nonadditive contributions to protein stability, but the nonadditive nature depends on whether such interactions are located in the protein interior or on the protein surface. When located in the interior, many hydrophobic interactions such as those involving alkyl residues are anticooperative. Salt-bridge and regular hydrogen-bonding interactions, such as those involving ionizable residues and polar residues, are cooperative. When located on the protein surface, these salt-bridge and regular hydrogen-bonding interactions are anticooperative, and hydrophobic interactions involving alkyl residues become cooperative. We show with examples that incorporating 3-body interactions improves discrimination of protein native structures against decoy conformations. In addition, analysis of cooperative 3-body interaction may reveal spatial motifs that can suggest specific protein functions.     

Design of peptides with branched beta-carbon dehydro-residues: syntheses, crystal structures and molecular conformations of two peptides, (I) N-Carbobenzoxy-DeltaVal-Ala-Leu-OCH3 and (II) N-Carbobenzoxy-DeltaIle-Ala-Leu-OCH3.

Highly specific structures can be designed by inserting dehydro-residues into peptide sequences. The conformational preferences of branched beta-carbon residues are known to be different from other residues. As an implication it was expected that the branched beta-carbon dehydro-residues would also induce different conformations when substituted in peptides. So far, the design of peptides with branched beta-carbon dehydro-residues at (i + 1) position has not been reported. It may be recalled that the nonbranched beta-carbon residues induced beta-turn II conformation when placed at (i + 2) position while branched beta-carbon residues induced beta-turn III conformation. However, the conformation of a peptide with a nonbranched beta-carbon residue when placed at (i + 1) position was not found to be unique as it depended on the stereochemical nature of its neighbouring residues. Therefore, in order to induce predictably unique structures with dehydro-residues at (i + 1) position, we have introduced branched beta-carbon dehydro-residues instead of nonbranched beta-carbon residues and synthesized two peptides: (I) N-Carbobenzoxy-DeltaVal-Ala-Leu-OCH3 and (II) N-Carbobenzoxy-DeltaIle-Ala-Leu-OCH3 with DeltaVal and DeltaIle, respectively. The crystal structures of peptides (I) and (II) have been determined and refined to R-factors of 0.065 and 0.063, respectively. The structures of both peptides were essentially similar. Both peptides adopted type II beta-turn conformations with torsion angles; (I): phi1 = -38.7 (4) degrees, psi1 = 126.0 (3) degrees; phi2 = 91.6 (3) degrees, psi2 = -9.5 (4) degrees and (II): phi1 = -37.0 (6) degrees, psi1 = 123.6 (4) degrees, phi2 = 93.4 (4), psi2 = -11.0(4) degrees respectively. Both peptide structures were stabilized by intramolecular 4-->1 hydrogen bonds. The molecular packing in both crystal structures were stabilized in each by two identical hydrogen bonds N1...O1' (-x, y + 1/2, -z) and N2...O2' (-x + 1, y + 1/2, -z) and van der Waals interactions.     

Long- and short-range interactions in native protein structures are consistent/minimally frustrated in sequence space

We show that long- and short-range interactions in almost all protein native structures are actually consistent with each other for coarse-grained energy scales; specifically we mean the long-range inter-residue contact energies and the short-range secondary structure energies based on peptide dihedral angles, which are potentials of mean force evaluated from residue distributions observed in protein native structures. This consistency is observed at equilibrium in sequence space rather than in conformational space. Statistical ensembles of sequences are generated by exchanging residues for each of 797 protein native structures with the Metropolis method. It is shown that adding the other category of interaction to either the short- or long-range interactions decreases the means and variances of those energies for essentially all protein native structures, indicating that both interactions consistently work by more-or-less restricting sequence spaces available to one of the interactions. In addition to this consistency, independence by these interaction classes is also indicated by the fact that there are almost no correlations between them when equilibrated using both interactions and significant but small, positive correlations at equilibrium using only one of the interactions. Evidence is provided that protein native sequences can be regarded approximately as samples from the statistical ensembles of sequences with these energy scales and that all proteins have the same effective conformational temperature. Designing protein structures and sequences to be consistent and minimally frustrated among the various interactions is a most effective way to increase protein stability and foldability.     

Stereochemical quality of protein structure coordinates.

Methods have been developed to assess the stereochemical quality of any protein structure both globally and locally using various criteria. Several parameters can be derived from the coordinates of a given structure. Global parameters include the distribution of phi, psi and chi 1 torsion angles, and hydrogen bond energies. There are clear correlations between these parameters and resolution; as the resolution improves, the distribution of the parameters becomes more clustered. These features show a broad distribution about ideal values derived from high-resolution structures. Some structures have tightly clustered distributions even at relatively low resolutions, while others show abnormal scatter though the data go to high resolution. Additional indicators of local irregularity include proline phi angles, peptide bond planarities, disulfide bond lengths, and their chi 3 torsion angles. These stereochemical parameters have been used to generate measures of stereochemical quality which provide a simple guide as to the reliability of a structure, in addition to the most important measures, resolution and R-factor. The parameters used in this evaluation are not novel, and are easily calculated from structure coordinates. A program suite is currently being developed which will quickly check a given structure, highlighting unusual stereochemistry and possible errors.