Evaluation of Protein Dihedral Angle Prediction Methods

Tertiary structure prediction of a protein from its amino acid sequence is one of the major challenges in the field of bioinformatics. Hierarchical approach is one of the persuasive techniques used for predicting protein tertiary structure, especially in the absence of homologous protein structures. In hierarchical approach, intermediate states are predicted like secondary structure, dihedral angles, C^α-C^α distance bounds, etc. These intermediate states are used to restraint the protein backbone and assist its correct folding. In the recent years, several methods have been developed for predicting dihedral angles of a protein, but it is difficult to conclude which method is better than others. In this study, we benchmarked the performance of dihedral prediction methods ANGLOR and SPINE X on various datasets, including independent datasets. TANGLE dihedral prediction method was not benchmarked (due to unavailability of its standalone) and was compared with SPINE X and ANGLOR on only ANGLOR dataset on which TANGLE has reported its results. It was observed that SPINE X performed better than ANGLOR and TANGLE, especially in case of prediction of dihedral angles of glycine and proline residues. The analysis suggested that angle shifting was the foremost reason of better performance of SPINE X. We further evaluated the performance of the methods on independent ccPDB30 dataset and observed that SPINE X performed better than ANGLOR.     

Real-value prediction of backbone torsion angles

The backbone structure of a protein is largely determined by the phi and psi torsion angles. Thus, knowing these angles, even if approximately, will be very useful for protein-structure prediction. However, in a previous work, a sequence-based, real-value prediction of psi angle could only achieve a mean absolute error of 54 degrees (83 degrees, 35 degrees, 33 degrees for coil, strand, and helix residues, respectively) between predicted and actual angles. Moreover, a real-value prediction of phi angle is not yet available. This article employs a neural-network based approach to improve psi prediction by taking advantage of angle periodicity and apply the new method to the prediction to phi angles. The 10-fold-cross-validated mean absolute error for the new method is 38 degrees (58 degrees, 33 degrees, 22 degrees for coil, strand, and helix, respectively) for psi and 25 degrees (35 degrees, 22 degrees, 16 degrees for coil, strand, and helix, respectively) for phi. The accuracy of real-value prediction is comparable to or more accurate than the predictions based on multistate classification of the phi-psi map. More accurate prediction of real-value angles will likely be useful for improving the accuracy of fold recognition and ab initio protein-structure prediction. The Real-SPINE 2.0 server is available on the website http://sparks.informatics.iupui.edu.     

TANGLE: two-level support vector regression approach for protein backbone torsion angle prediction from primary sequences

Protein backbone torsion angles (Phi) and (Psi) involve two rotation angles rotating around the C(α)-N bond (Phi) and the C(α)-C bond (Psi). Due to the planarity of the linked rigid peptide bonds, these two angles can essentially determine the backbone geometry of proteins. Accordingly, the accurate prediction of protein backbone torsion angle from sequence information can assist the prediction of protein structures. In this study, we develop a new approach called TANGLE (Torsion ANGLE predictor) to predict the protein backbone torsion angles from amino acid sequences. TANGLE uses a two-level support vector regression approach to perform real-value torsion angle prediction using a variety of features derived from amino acid sequences, including the evolutionary profiles in the form of position-specific scoring matrices, predicted secondary structure, solvent accessibility and natively disordered region as well as other global sequence features. When evaluated based on a large benchmark dataset of 1,526 non-homologous proteins, the mean absolute errors (MAEs) of the Phi and Psi angle prediction are 27.8° and 44.6°, respectively, which are 1% and 3% respectively lower than that using one of the state-of-the-art prediction tools ANGLOR. Moreover, the prediction of TANGLE is significantly better than a random predictor that was built on the amino acid-specific basis, with the p-value<1.46e-147 and 7.97e-150, respectively by the Wilcoxon signed rank test. As a complementary approach to the current torsion angle prediction algorithms, TANGLE should prove useful in predicting protein structural properties and assisting protein fold recognition by applying the predicted torsion angles as useful restraints. TANGLE is freely accessible at http://sunflower.kuicr.kyoto-u.ac.jp/~sjn/TANGLE/.     

Improving the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins by guided-learning through a two-layer neural network

This article attempts to increase the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins through improved learning. Most methods developed for improving the backpropagation algorithm of artificial neural networks are limited to small neural networks. Here, we introduce a guided-learning method suitable for networks of any size. The method employs a part of the weights for guiding and the other part for training and optimization. We demonstrate this technique by predicting residue solvent accessibility and real-value backbone torsion angles of proteins. In this application, the guiding factor is designed to satisfy the intuitive condition that for most residues, the contribution of a residue to the structural properties of another residue is smaller for greater separation in the protein-sequence distance between the two residues. We show that the guided-learning method makes a 2-4% reduction in 10-fold cross-validated mean absolute errors (MAE) for predicting residue solvent accessibility and backbone torsion angles, regardless of the size of database, the number of hidden layers and the size of input windows. This together with introduction of two-layer neural network with a bipolar activation function leads to a new method that has a MAE of 0.11 for residue solvent accessibility, 36 degrees for psi, and 22 degrees for phi. The method is available as a Real-SPINE 3.0 server in http://sparks.informatics.iupui.edu.     

Is glycine a surrogate for a d‐amino acid in the collagen triple helix?

Collagen is the most abundant protein in animals. Every third residue in a collagen strand is a glycine with phi, psi = -70 degrees, 175 degrees. A recent computational study suggested that replacing these glycine residues with D-alanine or D-serine would stabilize the collagen triple helix. This hypothesis is of substantial importance, as the glycine residues in collagen constitute nearly 10% of the amino acid residues in humans. To test this hypothesis, we synthesized a series of collagen mimic peptides that contain one or more D-alanine or D-serine residues replacing the canonical glycine residues. Circular dichroism spectroscopy and thermal denaturation experiments indicated clearly that the substitution of glycine with D-alanine or D-serine greatly disfavors the formation of a triple helix. Host-guest studies also revealed that replacing a single glycine residue with D-alanine is more destabilizing than is its replacement with L-alanine, a substitution that results from a common mutation in patients with collagen-related diseases. These data indicate that the glycine residues in collagen are not a surrogate for a D-amino acid and support the notion that the main-chain torsion angles of a glycine residue in the native structure (especially, phi > 0 degrees ) are critical determinants for its beneficial substitution with a D-amino acid in a protein.     

Determination of local conformation of proteins from 1H-NMR spectroscopy data

A method is proposed to determine conformations of amino acid residues of the protein and effective correlation time tau c from cross-peak intensities in two-dimensional nuclear Overhauser enhancement (NOESY) spectra. The method consists in fitting complete relaxation matrix of dipeptide unit protons to experimental cross-peak intensities by varying phi, psi, chi torsional angles and tau c. To verify the method, NOESY spectra of basic pancreatic trypsin inhibitor (BPTI) were theoretically generated at mixing times tau m = 25-300 ms and tau c = 4 ns and used for local structure determination. The method works well with optimum for measurement of NOE intensities tau m 100-200 ms. As a result, the backbone phi, psi torsion angles were unambiguously determined at tau m = 100 ms for all but Gly residues of BPTI, and chi 1 angles were determined for the majority of side chains. The obtained dipeptide unit conformations are very close to the BPTI crystallographic structure: root mean square deviation (RMSD) of interproton distances within dipeptide units, on the average, is 0.08 A (maximal deviation 0.44 A), and RMSD of phi and psi angles are 18 and 9 degrees, respectively (maximal deviations are 44 and 22 degrees).     

Conformational subspace in simulation of early-stage protein folding

A probability calculus was used to simulate the early stages of protein folding in ab initio structure prediction. The probabilities of particular phi and psi angles for each of 20 amino acids as they occur in crystal forms of proteins were used to calculate the amount of information necessary for the occurrence of given phi and psi angles to be predicted. It was found that the amount of information needed to predict phi and psi angles with 5 degrees precision is much higher than the amount of information actually carried by individual amino acids in the polypeptide chain. To handle this problem, a limited conformational space for the preliminary search for optimal polypeptide structure is proposed based on a simplified geometrical model of the polypeptide chain and on the probability calculus. These two models, geometric and probabilistic, based on different sources, yield a common conclusion concerning how a limited conformational space can represent an early stage of polypeptide chain-folding simulation. The ribonuclease molecule was used to test the limited conformational space as a tool for modeling early-stage folding.     

NMR structures of a nonapeptide from DNA binding domain of human polymerase-alpha determined by iterative complete-relaxation-matrix approach.

Nuclear magnetic resonance structures of a nonapeptide, ERFKCPCPT, selected from the DNA binding domain of human polymerase-alpha, were determined by complete relaxation matrix analysis of transverse NOE data. The structures exhibit a type III turn with residues KCPC, and the remaining residues exhibit non-ordered structures. The turn was confirmed by alpha, N (i,i+3) connectivity, a low temperature coefficient of NH chemical shift (-3.1 x 10(-3)) of the fourth residue, 3J(NHalpha) coupling constants, and characteristic CD peaks at 228 and 200 nm. Furthermore, phi and psi dihedral angles for the i + 1, and i + 2 residues of the turn are found to be -80 and -41 and -60 and -40 degrees. The first proline residue is trans- while the second exists in both cis- and trans- configurations, with trans- being more than 80% populated. The trans-configuration was established from C5alpha-P6alpha correlation and phi and psi angles of the proline. The five-membered proline ring is in DOWN puckered (C-beta-exo/C-gamma-endo) conformation. The structure of the peptide reveals that the two cysteine thiols are approximately 5 A(o) apart and appropriately positioned to covalently bind cis-diamminedichloroplatinum(II), a widely used anti-cancer drug.     

Empirical torsional potential functions from protein structure data. Phi- and psi-potentials for non-glycyl amino acid residues.

The torsional potential functions Vt(phi) and Vt(psi) around single bonds N--C alpha and C alpha--C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (phi, psi)-plane with the value of Vtot(phi, psi), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in L-configuration, are Vt(phi) = 1.0 cos (phi + 60 degrees); Vt(psi) = 0.5 cos (psi + 60 degrees) - 1.0 cos (2 psi + 30 degrees) - 0.5 cos (3 psi + 30 degrees). The dipeptide energy maps Vtot(phi, psi) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line psi = 0 degrees. These functions derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.     

Conformational study of peptides containing dehydrophenylalanine: helical structures without hydrogen bond

The conformational behaviour of deltaZPhe has been investigated in the model dipeptide Ac-deltaZPhe-NHMe and in the model tripeptides Ac-X-deltaZPhe-NHMe with X=Gly,Ala,Val,Leu,Abu,Aib and Phe and is found to be quite different. In the model tripeptides with X=Ala,Val,Leu,Abu,Phe the most stable structure corresponds to phi1=-30 degrees, psi1=120 degrees and phi2=psi2=30 degrees. This structure is stabilized by the hydrogen bond formation between C=O of acetyl group and the NH of the amide group, resulting in the formation of a 10-membered ring but not a 3(10) helical structure. In the peptides Ac-Aib-deltaZPhe-NHMe and Ac-(Aib-deltaZPhe)3-NHMe, the helical conformers with phi = +/-30 degrees, psi = +/-60 degrees for Aib residue and phi=psi= +/-30 degrees for deltaZPhe are predicted to be most stable. The computational studies for the positional preferences of deltaZPhe residue in the peptide containing one deltaZPhe and nine Ala residues reveal the formation of a 3(10) helical structure in all the cases with terminal preferences for deltaZPhe. The conformational behaviour of Ac-(deltaZPhe)n-NHMe with n< or =4 is predicted to be very labile. With n > 4, degenerate conformational states with phi,psi values of 0 degrees +/- 90 degrees adopt helical structures which are stabilized by carbonyl-carbonyl interactions and the N-H-pi interactions between the amino group of every deltaZPhe residue with one C-C edge of its own phenyl ring. The results are in agreement with the experimental finding that screw sense of helix for peptides containing deltaZPhe residues is ambiguous in solution. The helical structures stabilized by hydrogen bond formation are found to be at least 3kCalmol(-1) less stable. Conformational studies have also been carried out for the peptide Ac-(deltaEPhe)6-NHMe and the peptide Ac-deltaAla-(deltaZPhe)6-NHMe containing deltaAla residue at the N-terminal. The N-H-pi interactions are absent in peptide Ac-(deltaEPhe)6-NHMe.     

PEPstr: a de novo method for tertiary structure prediction of small bioactive peptides

Among secondary structure elements, beta-turns are ubiquitous and major feature of bioactive peptides. We analyzed 77 biologically active peptides with length varying from 9 to 20 residues. Out of 77 peptides, 58 peptides were found to contain at least one beta-turn. Further, at the residue level, 34.9% of total peptide residues were found to be in beta-turns, higher than the number of helical (32.3%) and beta-sheet residues (6.9%). So, we utilized the predicted beta-turns information to develop an improved method for predicting the three-dimensional (3D) structure of small peptides. In principle, we built four different structural models for each peptide. The first 'model I' was built by assigning all the peptide residues an extended conformation (phi = Psi = 180 degrees ). Second 'model II' was built using the information of regular secondary structures (helices, beta-strands and coil) predicted from PSIPRED. In third 'model III', secondary structure information including beta-turn types predicted from BetaTurns method was used. The fourth 'model IV' had main-chain phi, Psi angles of model III and side chain angles assigned using standard Dunbrack backbone dependent rotamer library. These models were further refined using AMBER package and the resultant C(alpha) rmsd values were calculated. It was found that adding the beta-turns to the regular secondary structures greatly reduces the rmsd values both before and after the energy minimization. Hence, the results indicate that regular and irregular secondary structures, particularly beta-turns information can provide valuable and vital information in the tertiary structure prediction of small bioactive peptides. Based on the above study, a web server PEPstr (http://www.imtech.res.in/raghava/pepstr/) was developed for predicting the tertiary structure of small bioactive peptides.     

Facile transition between 3(10)- and alpha-helix: structures of 8-, 9-, and 10-residue peptides containing the -(Leu-Aib-Ala)2-Phe-Aib- fragment.

A structural transition from a 3(10)-helix to an alpha-helix has been characterized at high resolution for an octapeptide segment located in 3 different sequences. Three synthetic peptides, decapeptide (A) Boc-Aib-Trp-(Leu-Aib-Ala)2-Phe-Aib-OMe, nonapeptide (B) Boc-Trp-(Leu-Aib-Ala)2-Phe-Aib-OMe, and octapeptide (C) Boc-(Leu-Aib-Ala)2-Phe-Aib-OMe, are completely helical in their respective crystals. At 0.9 A resolution, R factors for A, B, and C are 8.3%, 5.4%, and 7.3%, respectively. The octapeptide and nonapeptide form ideal 3(10)-helices with average torsional angles phi(N-C alpha) and psi(C alpha-C') of -57 degrees, -26 degrees C and -60 degrees, -27 degrees for B. The 10-residue peptide (A) begins as a 3(10)-helix and abruptly changes to an alpha-helix at carbonyl O(3), which is the acceptor for both a 4-->1 hydrogen bond with N(6)H and a 5-->1 hydrogen with N(7)H, even though the last 8 residues have the same sequence in all 3 peptides. The average phi, psi angles in the decapeptide are -58 degrees, -28 degrees for residues 1-3 and -63 degrees, -41 degrees for residues 4-10. The packing of helices in the crystals does not provide any obvious reason for the transition in helix type. Fourier transform infrared studies in the solid state also provide evidence for a 3(10)- to alpha-helix transition with the amide I band appearing at 1,656-1,657 cm-1 in the 9- and 10-residue peptides, whereas in shorter sequences the band is observed at 1,667 cm-1.     

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.     

Influence of solvent molecules on the stereochemical code of glycyl residues in proteins

The Ramachandran steric map and energy diagrams of the glycyl residue are symmetric. A plot of (phi,psi) angles of glycyl residues in 250 nonhomologous and high-resolution protein structures is also largely symmetric. However, there is a clear aberration in the symmetry. Although there is a cluster of points corresponding to the right-handed alpha-helical region, the "equivalent" cluster is clearly shifted to in and around the (phi,psi) values of (90 degrees, 0 degrees ) instead of being centered at the left-handed alpha-helical region of (60 degrees, 40 degrees ). This lack of symmetry exists even in the (phi,psi) distribution of residues from non-alpha-helical regions in proteins. Here we provide an explanation for this observation. An analysis of glycyl conformations in small peptide structures and in "coil" proteins, which are largely devoid of helical and sheet regions, shows that glycyl residues prefer to adopt conformations around (+/-90 degrees, 0 degrees ) instead of right- and left-handed alpha-helical regions. By using theoretical calculations, such conformations are shown to have highest solvent accessibility in a system of two-linked peptide units with glycyl residue at the central C(alpha) atom. This finding is consistent with the observations from 250 nonhomologous protein structures where glycyl residues with conformations close to (+/-90 degrees, 0 degrees ) are seen to have high solvent accessibility. Analysis of a subset of nonhomologous structures with very high resolution (1.5 A or better) shows that water molecules are indeed present at distances suitable for hydrogen bond interaction with glycyl residues possessing conformations close to (+/-90 degrees, 0 degrees ). It is suggested that water molecules play a key role in determining and stabilizing these conformations of glycyl residues and explain the aberration in the symmetry of glycyl conformations in proteins.     

Kinetic study of racemization of aspartyl residues in recombinant human alphaA-crystallin

Asp58 and Asp151 in human lens alphaA-crystallin invert and isomerize to d-beta-aspartyl residues with age. Here, we report that the racemization rate constants (k) of Asp58 and Asp151 residues in human recombinant alphaA-crystallin at 37 degrees C are 3.72 +/- 0.8 x 10(-4) and 10.7 +/- 0.7 x 10(-4)/day, respectively. The activation energy of racemization of Asp58 and Asp151 in the protein was 27.0 +/- 0.5 kcal/mol and 21.0 +/- 0.5 kcal/mol, respectively. The time required for the D/L ratio of Asp58 and Asp151 to approximate to 1.0 (D/L ratio of Asp = 0.99) at 37 degrees C was estimated as 20.9 +/- 3.7 and 6.80 +/- 0.4 years, respectively. Thus, Asp151 is more susceptible to racemization than Asp58, consistent with data from short model peptides. However, the racemization rates of both Asp58 and Asp151 residues in the protein were twice as rapid as in model peptides. These results indicate that the racemization of Asp residues in alphaA-crystallin may be influenced not only by the primary structure but also by the higher order structure around Asp residues in the protein.     

Binding of the recombinant proteinase inhibitor eglin c from leech Hirudo medicinalis to human leukocyte elastase, bovine alpha-chymotrypsin and subtilisin Carlsberg: thermodynamic study

The effect of pH and temperature on the apparent association equilibrium constant (Ka) for the binding of the recombinant proteinase inhibitor eglin c from leech Hirudo medicinalis to human leukocyte elastase (EC 3.4.21.37), bovine alpha-chymotrypsin (EC 3.4.21.1) and subtilisin Carlsberg (EC 3.4.21.14) has been investigated. On lowering the pH from 9.5 to 4.5, values of Ka for eglin c binding to the serine proteinases considered decrease thus reflecting the acid-pK shift of the invariant histidyl catalytic residue (His57 in human leukocyte elastase and bovine alpha-chymotrypsin, and His64 in subtilisin Carlsberg) from congruent to 6.9, in the free enzymes, to congruent to 5.1, in the enzyme:inhibitor adducts. At pH 8.0, values of the apparent thermodynamic parameters for eglin c binding are: human leukocyte elastase - Ka = 1.0 x 10(10) M-1, delta G phi = -13.4 kcal/mol, delta H phi = +1.8 kcal/mol, and delta S phi = +52 entropy units; bovine alpha-chymotrypsin -Ka = 5.0 x 10(9) M-1, delta G phi = -13.0 kcal/mol, delta H phi = +2.0 kcal/mol, and delta S phi = +51 entropy units; and subtilisin Carlsberg - Ka = 6.6 x 10(9) M-1, delta G phi = -13.1 kcal/mol, delta H phi = +2.0 kcal/mol, and delta S phi = +51 entropy units (values of Ka, delta G phi and delta S phi were obtained at 21 degrees C; values of delta H phi were temperature independent over the range explored, i.e. between 10 degrees C and 40 degrees C; 1 kcal = 4184J).(ABSTRACT TRUNCATED AT 250 WORDS)     

Contributions of left-handed helical residues to the structure and stability of bacteriophage T4 lysozyme

Non-glycine residues in proteins are rarely observed to have "left-handed helical" conformations. For glycine, however, this conformation is common. To determine the contributions of left-handed helical residues to the stability of a protein, two such residues in phage T4 lysozyme, Asn55 and Lys124, were replaced with glycine. The mutant proteins fold normally and are fully active, showing that left-handed non-glycine residues, although rare, do not have an indispensable role in the folding of the protein or in its activity. The thermodynamic stability of the Lys124 to Gly variant is essentially identical with that of wild-type lysozyme. The Asn55 to Gly mutant protein is marginally less stable (0.5 kcal/mol). These results indicate that the conformational energy of a glycine and a non-glycine residue in the left-handed helical conformation are very similar. This is consistent with some theoretical energy distributions, but is inconsistent with others, which suggest that replacements of the sort described here might increase the stability of the protein by up to 5 kcal/mol. Crystallographic analysis of the mutant proteins shows that the backbone conformation of the Lys124 to Gly variant is essentially identical with that of the wild-type structure. In the case of the Asn55 to Gly replacement, however, the (phi, psi) values of residue 55 change by about 20 degrees. This suggests that the energy minimum for left-handed glycine residues is not the same as that for non-glycine residues. This is strongly indicated also by a survey of accurately determined protein crystal structures, which suggests that the energy minimum for left-handed glycine residues is near (phi = 90 degrees, psi = 0 degrees), whereas that for non-glycine residues is close to (phi = 60 degrees, psi = 30 degrees). This apparent energy minimum for glycine is not clearly predicted by any of the theoretical (phi, psi) energy contour maps.     

Flexibility of bovine pancreatic trypsin inhibitor

The native conformation of a protein may be expressed in terms of the dihedral angles, phi's and psi's for the backbone, and kappa's for the side chains, for a given geometry (bond lengths and bond angles). We have developed a method to obtain the dihedral angles for a low-energy structure of a protein, starting with the X-ray structure; it is applied here to examine the degree of flexibility of bovine pancreatic trypsin inhibitor. Minimization of the total energy of the inhibitor (including nonbonded, electrostatic, torsional, hydrogen bonding, and disulfide loop energies) yields a conformation having a total energy of -221 kcal/mol and a root mean square deviation between all atoms of the computed and experimental structures of 0.63 A. The optimal conformation is not unique, however, there being at least two other conformations of low-energy (-222 and -220 kcal/mol), which resemble the experimental one (root mean square deviations of 0.66 and 0.64 A, respectively). These three conformations are located in different positions in phi, psi space, i.e., with a total deviation of 81 degrees, 100 degrees and 55 degrees from each other (with a root mean square deviation of several degrees per dihedral angle from each other). The nonbonded energies of the backbones, calculated along lines in phi, psi space connecting these three conformations, are all negative, without any intervening energy barriers (on an energy contour map in the phi, psi plane). Side chains were attached at several representative positions in this plane, and the total energy was minimized by varying the kappa's. The energies were of approximately the same magnitude as the previous ones, indicating that the conformation of low energy is flexible to some extent in a restricted region of phi, psi space. Interestingly, the difference delta phi i+1 in phi i+1 for the (i + 1)th residue from one conformation to another is approximately the same as -delta psi i for the ith residue; i.e., the plane of the peptide group between the ith and (i + 1)th residues re-orient without significant changes in the positions of the other atoms. The flexibility of the orientations of the planes of the peptide groups is probably coupled in a cooperative manner to the flexibility of the positions of the backbone and side-chain atoms.     

Extending the accuracy limits of prediction for side-chain conformations

Current techniques for the prediction of side-chain conformations on a fixed backbone have an accuracy limit of about 1.0-1.5 A rmsd for core residues. We have carried out a detailed and systematic analysis of the factors that influence the prediction of side-chain conformation and, on this basis, have succeeded in extending the limits of side-chain prediction for core residues to about 0.7 A rmsd from native, and 94 % and 89 % of chi(1) and chi(1+2 ) dihedral angles correctly predicted to within 20 degrees of native, respectively. These results are obtained using a force-field that accounts for only van der Waals interactions and torsional potentials. Prediction accuracy is strongly dependent on the rotamer library used. That is, a complete and detailed rotamer library is essential. The greatest accuracy was obtained with an extensive rotamer library, containing over 7560 members, in which bond lengths and bond angles were taken from the database rather than simply assuming idealized values. Perhaps the most surprising finding is that the combinatorial problem normally associated with the prediction of the side-chain conformation does not appear to be important. This conclusion is based on the fact that the prediction of the conformation of a single side-chain with all others fixed in their native conformations is only slightly more accurate than the simultaneous prediction of all side-chain dihedral angles.