Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.     

Conformational studies on a unique bis-sulfated glycolipid using NMR spectroscopy and molecular dynamics simulations.

The time-averaged solution conformation of a unique bis-sulfated glycolipid (HSO3)2-2,6Manalpha-2Glcalpha-1-sn-2,3-O-alkylglycerol , was studied in terms of the torsional angles of two glycosidic linkages, phi (H1-C1-O-Cx) and psi (C1-O-Cx-Hx), derived from heteronuclear three-bond coupling constants (3JC,H), and inter-residual proton-proton distances from J-HMBC 2D and ROESY experiments, respectively. The dihedral angles of Glcalpha1Gro in glycolipids were determined for the first time. The C1-C4 diagonal line of the alpha-glucose ring makes an angle of approximately 120 degrees with the glycerol backbone, suggesting that the alpha-glucose ring is almost parallel to the membrane surface in contrast with the perpendicular orientation of the beta-isomer. Furthermore, minimum-energy states around the conformation were estimated by Monte Carlo/stochastic dynamics (MCSD) mixed-mode simulations and the energy minimization with assisted model building and energy refinement (AMBER) force field. The Glcalpha1Gro linkage has a single minimum-energy structure. On the other hand, three conformers were observed for the Manalpha2Glc linkage. The flexibility of Manalpha2Glc was further confirmed by the absence of inter-residual hydrogen bonds which were judged from the temperature coefficients of the chemical shifts, ddelta/dT (-10-3 p.p.m. degrees C-1), of hydroxy protons. The conformational flexibility may facilitate interaction of extracellular substances with both sulfate groups.     

Ribosomal subunit orientations determined in the monomeric ribosome by single and by double-labeling immune electron microscopy

The energies of two and three-chain antiparallel and parallel β-sheets have been minimized. The chains were considered to be equivalent. In each case, chains consisting of four and of eight l-alanine residues, respectively, with CH₃CO- and -NHCH₃ end groups were examined. Computations were carried out both for chains constrained to have a regular structure (i.e. the same φ and ψ dihedral angles for each residue) and for chains in which the regularity constraint was relaxed. All computed minimum-energy β-sheets were found to have a right-handed twist, as observed in proteins. As in the case of right-handed α-helices, it is the intrastrand non-bonded interaction energy that plays the key role in forcing β-sheets of l-amino acid residues to adopt a right-handed twist. The non-bonded energy contribution favoring the right-handed twist is the result of many small pairwise interatomic interactions involving the C^βH₃ groups. Polyglycine β-sheets, lacking the C^βH₃ side-chains, are not twisted. The twist of the poly-l-alanine sheet diminishes as the number of residues per chain increases, in agreement with observations. The twist of the four-residue chain increases somewhat (because of interstrand non-bonded interactions, also involving the C^βH₃ groups) in going from a single chain to a two-chain antiparallel structure, but then decreases slightly in going from a two-chain to a three-chain structure. β-Sheets in observed protein structures sometimes have a larger twist than those in the structures computed here. This may be due to irregularities in amino acid sequence and in hydrogenbonding patterns in the observed sheets, or to long-range interactions in proteins. The minimized energies of parallel β-sheets are considerably higher than those of the corresponding antiparallel β-sheets, indicating that parallel β-sheets are intrinsically less stable. This finding about the two kinds of β-sheets agrees with suggestions based on analyses of β-sheets observed in proteins. The energy difference between antiparallel and parallel β-sheets is due to closer packing of the chains and a more favorable alignment of the peptide dipoles in the antiparallel structures. The hydrogen-bond geometry in the computed antiparallel structures is very close to that proposed by Arnott et al. (1967) for the β-form of poly-l-alanine.     

Flexibility of the pyranose ring in α- and β-D-glucoses

Conformational energies of α- and β-D -glucopyranoses were computed by varying all the ring bond angles and torsional angles using semiempirical potential functions. Solvent accessibility calculations were also performed to obtain a measure of solvent interaction. The results indicate that the ⁴C₁ (D ) chair is the most favored conformation, both by potential energy and solvent accessibility criteria. The ⁴C₁ (D ) chair conformation is also found to be somewhat flexible, being able to accommodate variations up to 10° in the ring torsional angles without appreciable change in energy. Observed solid-state conformations of these sugars and their derivatives lie in the minimum-energy region, suggesting that the substituents and crystal field forces play a minor role in influencing the pyranose ring conformation. Theory also predicts the variations in the ring torsional angles, i.e., CCCC < CCCO < CCOC, in agreement with the experimental results. The boat and twist-boat conformations are found to be at least 5 kcal mol^?1 higher in energy compared to the ⁴C₁ (D ) chair, suggesting that these forms are unlikely to be present in a polysaccharide chain. The ¹C₄ (D ) chair has energy intermediate between that of the ⁴C₁ (D ) chair and that of the twist-boat conformation. The calculated energy barrier between ⁴C₁ (D ) and ¹C₄ (D ) conformations is high—about 11 kcal mol^?1.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. III. Probable and average conformations of enkephalin

The program SMAPPS (Statistical-Mechanical Algorithm for Predicting Protein Structure) was originally designed to determine the probable and average backbone (?, ψ) conformations of a polypeptide by the application of equilibrium statistical mechanics in conjunction with an adaptive importance sampling Monte Carlo procedure. In the present paper, the algorithm has been extended to include the variation of all side-chain (χ) and peptide-bond (ω) dihedral angles of a polypeptide during the Monte Carlo search of the conformational space. To test the effectiveness of the generalized algorithm, SMAPPS was used to calculate the probable and average conformations of Met-enkephalin for which all dihedral angles of the pentapeptide were allowed to vary. The total conformational energy for each randomly generated structure of Met-enkephalin was obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. The interaction energies were computed by the program ECEPP /2 (Empirical Conformational Energy Program for Peptides). Solvent effects were not included in the computation. The results of the Monte Carlo calculation of the structure of Met-enkephalin indicate that the thermodynamically preferred conformation of the pentapeptide contains a γ-turn involving the three residues Gly²-Gly³-Phe⁴. The γ-turn conformation, however, does not correspond to the structure of lowest conformational energy. Rather, the global minimum-energy conformation, recently determined by a new optimization technique developed in this laboratory, contains a type II′ β-bend that is formed by the interaction of the four residues Gly²-Gly³-Phe⁴-Met⁵. A similar minimum-energy conformation is found by the SMAPPS procedure. The thermodynamically preferred γ-turn structure has a conformational energy of 4.93 kcal/mole higher than the β-bend structure of lowest energy but, because of the inclusion of entropy in the SMAPPS procedure, it is estimated to be ～ 9 kcal/mole lower in free energy. The calculation of the average conformation of Met-enkephalin was repeated until a total of ten independent average conformations were established. As far as the phenylalanine residue of the pentapeptide is concerned, the results of the ten independent average conformations were all found to lie in the region of conformational space corresponding to the γ-turn. These results further support the conclusion that the γturn conformation is thermodynamically favored.     

Dead-End Based Modeling Tools to Explore the Sequence Space That Is Compatible with a Given Scaffold

The dead-end elimination algorithm has proven to be a powerful tool in protein homology modeling since it allows one to determine rapidly the global minimum-energy conformation (GMEC) of an arbitrarily large collection of side chains, given fixed backbone coordinates. After introducing briefly the necessary background, we focus on logic arguments that increase the efficacy of the dead-end elimination process. Second, we present new theoretical considerations on the use of the dead-end elimination method as a tool to identify sequences that are compatible with a given scaffold structure. Third, we initiate a search for properties derived from the computed GMEC structure to predict whether a given sequence can be well packed in the core of a protein. Three properties will be considered: the nonbonded energy, the accessible surface area, and the extent by which the GMEC side-chain conformations deviate from a locally optimal conformation.     

Prediction of protein--ligand interactions: the complex of porcine pancreatic elastase with a valine-derived benzoxazinone

Prior to availability of the crystal structure of the complex, we evaluated models of the complex between porcine pancreatic elastase and a t-Boc–Val-derived benzoxazinone inhibitor. Models of the noncovalent and covalent complex were generated using computer graphics and each model was subjected to energy minimization using molecular mechanics. After the crystal structure became available, we found that the model with the lowest energy was in good agreement with the crystal structure, except for the position of the His57 side chain. Permissible conformations of the inhibitor were based on information from x-ray crystal structures and an earlier conformational energy investigation of t-Boc–amino acids. We did not, however, limit ourselves to these conformations. The conformation of the inhibitor in the lowest energy model and crystal structure, was not similar to any of the minimum-energy conformations of t-Boc–amino acids. This suggests that limiting proposed binding modes only to the lowest energy conformations of a ligand (prior to binding) may sometimes unfairly bias the procedure.     

Antibody elbow angles are influenced by their light chain class

We have examined the elbow angles for 365 different Fab fragments, and observe that Fabs with lambda light chains have adopted a wider range of elbow angles than their kappa chain counterparts, and that the lambda light chain Fabs are frequently found with very large (>195 degrees ) elbow angles. This apparent hyperflexibility of lambda chain Fabs may be due to an insertion in their switch region, which is one residue longer than in kappa chains, with glycine occurring most frequently at the insertion position. A new, web-based computer program that was used to calculate the Fab elbow angles is described.     

Conformational behavior of α,α-dialkylated peptides

The preferred conformations of N-acetyl-N′-methyl amides of some dialkylglycines have been determined by empirical conformational-energy calculations; minimum-energy conformations were located by minimizing the energy with respect to all the dihedral angles of the molecules. The conformational space of these compounds is sterically restricted, and low-energy conformations are found only in the regions of fully extended and helical structures. Increasing the bulkiness of the substituents on the C^α, the fully extended conformation becomes gradually more stable than the helical structure preferred in the cases of dimethylglycine. This trend is, however, strongly dependent on the bond angles between the substituents on the C^α atom: In particular, helical structures are favored by standard values (111°) of the N-C^α-C′ angle, while fully extended conformations are favored by smaller values of the same angle, as experimentally observed, for instance, in the case of α,α-di-n-propylglycine.     

Conformational analysis of the exopolysaccharide from Burkholderia caribensis strain MWAP71: impact on the interaction with soils

The strain MWAP71 of Burkholderia caribensis produces a branched charged exopolysaccharide (EPS) that is responsible for soil aggregation. Understanding the conformational properties of the isolated polysaccharide is a prerequisite for proper investigation of the interactions between the polysaccharide and the soil at the atomic level. The aim of this study is first to have an overall view of the flexibility of the backbone and then to ascertain the role played by side groups in the conformational properties of the main chain. Conformational analysis of each oligomeric segment of the polysaccharide has been performed by means of adiabatic mapping of the backbone glycosidic torsion angles using the MM3(92) force field. Substitution by an acetyl group or by a Kdo unit has only a slight effect on the potential energy surfaces of the fragment model compounds. Calculated partition functions, however, indicate that the overall flexibility is slightly larger for the substituted oligomers than for the unsubstituted ones. Prediction of selected average interproton distances from the AB and BC potential energy surfaces allows comparison between modeling results and NMR measurements performed on the ABC fragment. Agreement between the experimental and the predicted data suggests that the established surfaces correctly reflect the observed conformational behavior of such fragments and validate the modeling protocol. The above results have been extended to regular and disordered long polymer chains, differing in Kdo content. It is found that Kdo affects the helical conformations of the polysaccharide. The number of stable helices is considerably larger with Kdo than without Kdo. On the contrary, Kdo has only a moderate effect on unperturbed disordered conformations of the polysaccharide. Predicted persistence length of 70 A suggests that the polymer is semirigid with moderate extension. A further validation of the modeling results is obtained by the good concordance between this predicted value and the experimental one of 95 A, measured from light scattering and viscosity experiments. The results lead to an understanding of the interactions of this polysaccharide with soils.     

Structure of a hydroxyproline (Hyp)-arabinogalactan polysaccharide from repetitive Ala-Hyp expressed in transgenic Nicotiana tabacum

A synthetic gene encoding the fusion protein (Ala-Hyp)(51)-enhanced green fluorescent protein expressed in Nicotiana tabacum cells produced a fusion glycoprotein with all proline residues hydroxylated and substituted with an arabinogalactan polysaccharide. Alkaline hydrolysis of the fusion glycoprotein yielded a population of hydroxyproline (Hyp)-arabinogalactan polysaccharides ranging in size from 13 to 26 saccharide residues/Hyp, with a median size of 15-17 residues. We isolated a 15-residue Hyp-arabinogalactan for structure determination by sugar analyses and one- and two-dimensional nuclear magnetic resonance techniques that provided the assignment of proton and carbon signals of a small polysaccharide O-linked to the hydroxyl group of Hyp. The polysaccharide consisted of a 1,3-linked beta-D-Galp backbone with a single 1,6-linked beta-D-Galp "kink." The backbone had two side chains of Galp substituted at position 3 with an arabinose di- or trisaccharide and at position 6 with glucuronic acid or rhamnosyl glucuronic acid. Energy-minimized space-filling molecular models showed hydrogen bonding within polysaccharides attached to repetitive Ala-Hyp and also between polysaccharides and the peptide backbone. Polysaccharides distorted the peptide Ramachandran angles consistent with the circular dichroic spectra of isolated (Ala-Hyp)(51) and its reversion to a polyproline II-like helix after deglycosylation. This first complete structure of a Hyp-arabinogalactan polysaccharide shows that computer-based molecular modeling of Hyp-rich glycoproteins is now feasible and supports the suggestion that small repetitive subunits comprise larger arabinogalactan polysaccharides.     

Simulation of conformational possibilities of DNA via calculation of nonbonded interactions of complementary dinucleoside phosphate complexes

Using classical potential functions, we carried out potential-energy calculations on the complementary deoxydinucleoside phosphate complexes dApdA:dUpdU, dUpdA:dUpdA, and dApdU:dApdU. All dihedral and bond angles, except those of the nitrogen bases, were varied. The resulting minimum-energy conformations of the complexes are close to DNA A- and B-family conformations, with a typical arrangement of the nitrogen bases. The dihedral and bond angles of one of the molecules forming the complex can thereby differ by several degrees from those of the other molecule. For different base sequences, some dihedral and bond angles may vary over a range of several degrees without appreciably changing the total energy of the complex. Some low-energy conformations of the complexes corresponding to other regions of the conformational space are also found. The biological consequences of possible changes in dihedral and bond angles, occurring on interaction with other molecules, are discussed.     

Translocation mechanism of long sugar chains across the maltoporin membrane channel

Maltoporin allows permeation of long maltodextrin chains. It tightly binds the amphiphilic sugar, offering both hydrophobic interactions with a helical lane of aromatic residues and H bonds with ionic side chains. The minimum-energy path of maltohexaose translocation is obtained by the conjugate peak refinement method, which optimizes a continuous string of conformers without applying constraints. This reveals that the protein is passive while the sugar glides screw-like along the aromatic lane. Near instant switching of sugar hydroxyl H bond partners results in two small energy barriers (of approximately 4 kcal/mol each) during register shift by one glucosyl unit, in agreement with a kinetic analysis of experimental dissociation rates for varying sugar chain lengths. Thus, maltoporin functions like an efficient translocation "enzyme," and the slow rate of the register shift (approximately 1/ms) is due to high collisional friction.     

Homology modeling by the ICM method

Five models have been built by the ICM method for the Comparative Modeling section of the Meeting on the Critical Assessment of Techniques for Protein Structure Prediction. The targets have homologous proteins with known three-dimensional structure with sequence identity ranging from 25 to 77%. After alignment of the target sequence with the related three-dimensional structure, the modeling procedure consists of two subproblems: side-chain prediction and loop prediction. The ICM method approaches these problems with the following steps: (1) a starting model is created based on the homologous structure with the conserved portion fixed and the noncon-served portion having standard covalent geometry and free torsion angles; (2) the Biased Probability Monte Carlo (BPMC) procedure is applied to search the subspaces of either all the nonconservative side-chain torsion angles or torsion angles in a loop backbone and surrounding side chains. A special algorithm was designed to generate low-energy loop deformations. The BPMC procedure globally optimizes the energy function consisting of ECEPP/3 and solvation energy terms. Comparison of the predictions with the NMR or crystallographic solutions reveals a high proportion of correctly predicted side chains. The loops were not correctly predicted because imprinted distortions of the backbone increased the energy of the near-native conformation and thus made the solution unrecognizable. Interestingly, the energy terms were found to be reliable and the sampling of conformational space sufficient. The implications of this finding for the strategies of future comparative modeling are discussed. © 1995 Wiley-Liss, Inc.     

Energy-optimal controls in the mammalian neuromuscular system

The hypothesis is advanced that the specific patterns of motor unit recruitment and stimulation frequencies observed in mammalian skeletal muscle under static isometric contractions are determined by a minimum-energy principle. By performing a constrained energy optimization based on a control model of skeletal muscle comprising three different fibre types, and appropriate expressions for the energy rates, it is indeed possible to obtain detailed predictions of recruitment and stimulation frequency patterns which agree well with the experimentally observed functions, thereby providing strong support for the minimum-energy hypothesis. Since the orderly recruitment sequence determined by the size principle is also, independently, predicted by the minimum-energy principle, it is concluded that there exists a relationship between motor unit size and the myoenergetic properties of the recruited unit. It is suggested that this relationship, together with the possibility of adjusting the relative proportions of the fibre types present in a muscle, constitutes an optimal adaptation of the neuromuscular system for practically all types of muscular performances normally encountered. For various types of muscles, the energy rates as functions of the force output are also discussed.     

A new proposal for the primary and secondary structure of the glycan moiety of pseudomurein. Conformational energy calculations on the glycan strands with talosaminuronic acid in 1C conformation and comparison with murein

Using the method of conformational energy calculations, favoured conformations of a pseudomurein sugar strand built up from beta 1,3-linked N-acetyl-D-glucosamine and N-acetyl-L-talosaminuronic acid were obtained. Such a completely beta 1,3-linked polysaccharide primary structure, although contrasting with the originally proposed alternating beta 1,3-alpha 1,3-linked structure [K?nig, H., Kandler, O., Jensen, M. and Rietschel, E. Th. (1983) Hoppe-Seyler's Z. Physiol. Chem. 364, 627-636] would be in agreement with all experimental data hitherto known. Starting from an analysis of favoured conformations of the monosaccharide building blocks and those obtained for disaccharide parts, the favoured helical conformations of the complete polysaccharide chains could be explored. Our completely beta 1,3-linked chain could adopt two types of conformation: extended and hollow; the latter was discarded as unsuitable for cell wall assembly. The extended conformation type was shown to exhibit a remarkable similarity if compared to the secondary structures accessible to murein-type polysaccharide chains. In contrast to the conformations accessible for the beta 1,3-alpha 1,3-linked primary structure, the new hypothetical pseudomurein structure was found to be more extended, possessed a flexible peptide attachment site at every second sugar residue and led to an orientation of consecutive peptide attachment sites analogous to the data known for murein-type chains. From the two possibilities compatible with the experimental data available, the completely beta 1,3-linked sugar strand structure could well be realized in the native pseudomurein network of methanobacteria. In this case the hypothesis for a similar three-dimensional architecture for murein and pseudomurein would be supported.     

Modeling of the structure in aqueous solution of the exopolysaccharide produced by Lactobacillus helveticus 766.

A method is described for constructing a conformational model in water of a heteropolysaccharide built up from repeating units, and is applied to the exopolysaccharide produced by Lactobacillus helveticus 766. The molecular modeling method is based on energy minima, obtained from molecular mechanics calculations of each of the constituting disaccharide fragments of the repeating unit in vacuo, as starting points. Subsequently, adaptive umbrella sampling of the potential of mean force is applied to extract rotamer populations of glycosidic dihedral angles of oligosaccharide fragments in solution. From these analyses, the most probable conformations are constructed for the hexasaccharide-repeating unit of the polysaccharide. After exploring the conformational space of each of the individual structures by molecular dynamics simulations, the different repeating unit conformations are used as building blocks for the generation of oligo- and polysaccharide models, by using a polysaccharide building program. The created models of the exopolysaccharide produced by L. helveticus 766 exhibit a flexible twisted secondary structure and tend to adopt a random coil conformation as tertiary structure.     

Conformational analysis of molecular chains using nano-kinematics

We present algorithms for 3–D manipulation and conforma–tionalanalysis of molecular chains, when bond lengths, bond anglesand related dihedral angles remain fixed. These algorithms areuseful for local deformations of linear molecules, exact ringclosure in cyclic molecules and molecular embedding for shortchains. Other possible applications include structure prediction,protein folding, conformation energy analysis and 3D molecularmatching and docking. The algorithms are applicable to all serialmolecular chains and make no asssumptions about their geometry.We make use of results on direct and inverse kinematics fromrobotics and mechanics literature and show the correspondencebetween kinematics and conformational analysis of molecules.In particular, we pose these problems algebraically and computeall the solutions making use of the structure of these equationsand matrix computations. The algorithms have been implementedand perform well in practice. In particular, they take tensof milliseconds on current workstations for local deformationsand chain closures on molecular chains consisting of six orfewer rotatable dihedral angles     

Structural organization of [met]enkephalin and endorphin molecules. III. Theoretical conformation analysis of beta-endorphin

Conformational energy calculations were carried out for beta-endorphin. Its spatial structure can be described by nine low-energy conformations. The calculations yielded the values of all dihedral angles of the backbone and side chains of these forms as well as intra- and inter-residue interaction energies.     

New strategy for the conformational analysis of carbohydrates based on NOE and 13C NMR coupling constants. Application to the flexible polysaccharide of Streptococcus mitis J22.

For complex oligosaccharides, which are relatively rigid with modest excursions from a single minimum energy conformation, it is straightforward to build conformational models from NOE data. Other oligosaccharides are more flexible with transitions between distinct minima separated by substantial energy barriers. We show that modeling based on scalar coupling data is superior to NOE-based modeling for the latter case. Long range 13C-13C and 13C-1H coupling constants measured for the heptasaccharide repeating subunit of the cell wall polysaccharide from Streptococcus mitis J22 are correlated with individual glycosidic dihedral angles, effectively uncoupling the degrees of freedom of the oligosaccharide and allowing a search for combinations of dihedral angles which are energetically reasonable, i.e., with no bad van der Waals contacts, and which can be combined to satisfy all the measured J values. Allowed values of the individual angles can then be combined to search for overall oligosaccharide conformations which contribute to the ensemble. We show that while the polysaccharide from S. mitis J22 is flexible, requiring multiple conformations, most of the flexibility is localized to a few bonds and only a rather small number of conformations is required to reproduce the experimental NOE and scalar coupling data.