Calculation of protein conformation by the build-up procedure. Application to bovine pancreatic trypsin inhibitor using limited simulated nuclear magnetic resonance data

Low-energy conformations of a set of tetrapeptides derived from the small protein bovine pancreatic trypsin inhibitor (BPTI) were generated by a build-up procedure from the low-energy conformations of single amino acid residues. At each stage, various-size fragments were built up from all combinations of smaller ones, the total energies were then minimized, and the low-energy conformations were retained for the next stage. The energies of the tetrapeptides were re-ordered by including the effects of hydration. No information other than the amino acid sequence was used to obtain the low-energy conformations of the hydrated tetrapeptides. The latter were then supplemented with a limited set of simulated NMR distance information, derived from the X-ray structure of BPTI, to provide a basis for building the rest of the whole protein molecule by the same procedure. A total of 189 upper bounds, plus 12 pairs of upper and lower bounds pertaining to the location of the three disulfide bonds in this molecule, were used. Four sets of conformations of the entire molecule were generated by utilizing different combinations of smaller fragments. It was possible to obtain low-energy conformations with small rms deviations, 1.1 to 1.4 A for the alpha-carbons, from the structure derived by X-ray diffraction. The average deviations of the backbone dihedral angles were also low, viz. 23 degrees to 26 degrees.     

Three-dimensional structure of the neurotoxin ATX Ia from Anemonia sulcata in aqueous solution determined by nuclear magnetic resonance spectroscopy

With the aid of 1H nuclear magnetic resonance (NMR) spectroscopy, the three-dimensional structure in aqueous solution was determined for ATX Ia, which is a 46 residue polypeptide neurotoxin of the sea anemone Anemonia sulcata. The input for the structure calculations consisted of 263 distance constraints from nuclear Overhauser effects (NOE) and 76 vicinal coupling constants. For the structure calculation several new or ammended programs were used in a revised strategy consisting of five successive computational steps. First, the program HABAS was used for a complete search of all backbone and chi 1 conformations that are compatible with the intraresidual and sequential NMR constraints. Second, using the program DISMAN, we extended this approach to pentapeptides by extensive sampling of all conformations that are consistent with the local and medium-range NMR constraints. Both steps resulted in the definition of additional dihedral angle constraints and in stereospecific assignments for a number of beta-methylene groups. In the next two steps DISMAN was used to obtain a group of eight conformers that contain no significant residual violations of the NMR constraints or van der Waals contacts. Finally, these structures were subjected to restrained energy refinement with a modified version of the molecular mechanics module of AMBER, which in addition to the energy force field includes potentials for the NOE distance constraints and the dihedral angle constraints. The average of the pairwise minimal RMS distances between the resulting refined conformers calculated for the well defined molecular core, which contains the backbone atoms of 35 residues and 20 interior side chains, is 1.5 +/- 0.3 A. This core is formed by a four-stranded beta-sheet connected by two well-defined loops, and there is an additional flexible loop consisting of the eleven residues 8-18. The core of the protein is stabilized by three disulfide bridges, which are surrounded by hydrophobic residues and shielded on one side by hydrophilic residues.     

Conformational study of a peptide epitope shows large preferences for beta-turn conformations.

The conformational preferences of the 7-residue peptide Glu-Val-Val-Pro-His-Lys-Lys was investigated using a global search algorithm, namely the Electrostatically Driven Monte Carlo (EDMC) method, and the ECEPP/2 potential energy function. This particular sequence corresponds to the N-terminal portion of a 19-residue peptide antigen whose three dimensional structure, when complexed to a cognate antibody, was reported recently. As a result of this study a series of low-energy conformations were identified showing a common folding pattern with residues Val-3, Pro-4, His-5 and Lys-6 forming a beta turn. A comparison of the computed conformations with the one determined by X-ray crystallography in the antibody-antigen complex reveals marked similarities. In most of the cases rms deviations smaller than 1.1 A were found for the backbone atoms of the four residues forming the turn. These results suggest that the recognition process is accomplished in this case through the interaction of the antibody with relatively stable conformers of the antigenic peptide.     

Conformational analysis of a segment in bacterioopsin by two-dimensional (1)H-NMR spectroscopy]

The spatial structure of a synthetic peptide, an analogue of the membrane spanning segment B (residues 34-65) of bacterioopsin from Halobacterium halobium, has been refined. Backbone torsion angles were derived from intensities of short-range interproton NOEs. These, together with a complete set of the NOEs integral intensities formed the basis for the three-dimensional structure refinement by the energy minimization with consideration of NOE penalty functions. Analysis indicates the right-handed alpha-helical conformation of segment B extending from Asp-38 to Tyr-64 with a kink of the helical axis (27 degrees) at Pro-50. The most stable region with an average root-mean-square deviation of 0.43 A between the backbone atoms includes residues 42-60 in six energy refined structures. The N-terminal part of segment B (residues 34-37) has no ordered conformation. The inferred structure is in close agreement with the electron cryomicroscopy structure of bacteriorhodopsin, differing from it in conformations of most of the side chains.     

Spatial structure of Thr-Pro-Ala-Glu-Asp-Phe-Met-Arg-Phe-NH2 molecule

The spatial structure of cardioactive Thr-Pro-Ala-Glu-Asp-Phe-Met-Arg-Phe-NH₂ molecule has been investigated using a theoretical conformational analysis. The low-energy conformations of the molecule were found, the values of the backbone and side T-T chain dihedral angles of amino acid residues constituting the peptide were determined, and the energies of intra- and interresidual interactions were estimated. It is revealed that the spatial structure of this molecule can exist in 11 stable backbone forms.     

Determination of cyclopeptide conformations in solution using NMR data and conformational energy calculations

The three-dimensional structure of the cyclic analogs of bradykinin and substance P C-terminal hexapeptide was studied using conformational energy calculations. Initial conformations for energy minimization were selected with the aid of the measured intensities of local nuclear Overhauser effects (NOEs) and other 1H-NMR data. Expected values of the 1H-NMR parameters for low-energy conformations of the cyclopeptides were calculated and compared with those observed experimentally using semiquantitative gradation of NOE intensities. Several low-energy structures of the cyclic bradykinin analog, possessing similar backbone conformations stabilized by two beta-turns, are in agreement with experimental data. None of the low-energy conformations of the substance P cyclic hexapeptide were in satisfactory agreement with the experimental set of NOEs. The agreement was achieved only by averaging of the calculated 1H-NMR parameters over several combinations of the low-energy conformations.     

Funnel hunting in a rough terrain: learning and discriminating native energy funnels

Protein folding and binding is commonly depicted as a search for the minimum energy conformation. Modeling of protein complex structures by RosettaDock often results in a set of low-energy conformations near the native structure. Ensembles of low-energy conformations can appear, however, in other regions, especially when backbone movements occur upon binding. What then characterizes the energy landscape near the correct orientation? We applied a machine learning algorithm to distinguish ensembles of low-energy conformations around the native conformation from other low-energy ensembles. The resulting classifier, FunHunt, identifies the native orientation in 50/52 protein complexes in a test set. The features used by FunHunt teach us about the nature of native interfaces. Remarkably, the energy decrease of trajectories toward near-native orientations is significantly larger than for other orientations. This provides a possible explanation for the stability of association in the native orientation.     

Spatial structure of the cardioactive octapeptide

The spatial structure of the cardioactive octapeptide Pro1-Gln2-Asp3-Pro4-Phe5-Leu6-Arg7-Ile8-NH2 was investigated using the theoretical conformational analysis. The low-energy conformations of the octapeptide molecule were found, the values of dihedral angles of the backbone and side chains of the amino acid residues constituting the peptide were determined, and the energies of intra-and interresidual interactions were estimated. It was shown that the spatial structure of this molecule represent six stable low-energy forms of the main chain.     

The Study of Possible A and B Conformations of Alternating DNA Using a New Program for Conformational Analysis of Duplexes (CONAN)

Abstract

A new program, CONAN has been designed for CONformational ANalysis of oligonucleotide duplexes with natural and modified bases. It allows to model both regular DNA fragments with different types of symmetry and irregular ones including bends, junctions, mismatched pairs and base lesions. Computations and minimization of the energy are performed in a space of internal structural variables chosen to build start structure easier and conveniently analyze the results obtained. These internal structural variables determine mutual base-base and base-sugar arrangement and sugar puckering. The analytical closure procedure is applied both to sugar rings and to backbone fragments between adjacent sugars. For more effective energy minimization, analytical gradient is calculated. The CONAN was applied to the search for low-energy conformations of poly(dA-dT)·poly(dA-dT) and poly(dG-dC)·poly(dG-dC) duplexes. Extended regions of low-energy A and B conformations are revealed and characterized. These regions contain structures with different relative values of helical twist, τ, for pur-pyr and pyr-pur steps, namely, conformations with τ(pur-pyr)>τ(pyr-pur) and with τ(pur-pyr)<τ(pyr-pur). Two types of sugar puckering were found for B-form low-energy conformations, the first type with all C2′-endo sugar residues and the second one—;with C2′-endo purines and O1′-endo pyrimidines. The calculated conformations are compared with X-ray diffraction data for crystals and fibers and NMR data for solution.     

Conformational analysis of single-base bulges in A-form DNA and RNA using a hierarchical approach and energetic evaluation with a continuum solvent model.

The analysis and prediction of non-canonical structural motifs in RNA is of great importance for an understanding of the function and design of RNA structures. A hierarchical method has been employed to generate a large variety of sterically possible conformations for a single-base adenine bulge structure in A -form DNA and RNA. A systematic conformational search was performed on the isolated bulge motif and neighboring nucleotides under the constraint to fit into a continuous helical structure. These substructures were recombined with double-stranded DNA or RNA. Energy minimization resulted in more than 300 distinct bulge conformations. Energetic evaluation using a solvation model based on the finite-difference Poisson-Boltzmann method identified three basic classes of low-energy structures. The three classes correspond to conformations with the bulge base stacked between flanking nucleotides (I), location of the bulge base in the minor groove (II) and conformations with a continuous stacking of the flanking helices and a looped out bulge base (III). For the looped out class, two subtypes (IIIa and IIIb) with different backbone geometries at the bulge site could be distinguished. The conformation of lowest calculated energy was a class I structure with backbone torsion angles close to those in standard A -form RNA. Conformations very close to the extra-helical looped out bulge structure determined by X-ray crystallography were also among the low-energy structures. In addition, topologies observed in other experimentally determined bulge structures have been found among low-energy conformers. The implicit solvent model was further tested by comparing an uridine and adenine bulge flanked by guanine:cytosine base-pairs, respectively. In agreement with the experimental observation, a looped out form was found as the energetically most favorable form for the uridine bulge and a stacked conformation in case of the adenine bulge. The inclusion of solvation effects especially electrostatic reaction field contributions turned out to be critically important in order to select realistic low-energy bulge structures from a large number of sterically possible conformations. The results indicate that the approach might be useful to model the three-dimensional structure of non-canonical motifs embedded in double-stranded RNA, in particular, to restrict the number of possible conformations to a manageable number of conformers with energies below a certain threshold.     

On the multiple-minima problem in the conformational analysis of polypeptides. IV. Application of the electrostatically driven Monte Carlo method to the 20-residue membrane-bound portion of melittin

The conformational space of the membrane-bound portion of melittin has been searched using the electrostatically driven Monte Carlo (EDMC) method with the ECEPP/2 (empirical conformational energy program for peptides) algorithm. The former methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. The algorithm produces a Monte Carlo search in the conformational hyperspace of the polypeptide using electrostatic predictions and a random sampling technique, combined with local minimization of the energy function, to locate low-energy conformations. As a result of 8 test calculations on the 20-residue membrane-bound portion of melittin, starting from six arbitrary and two completely random conformations, the method was able to locate a very low-energy region of the potential with a well-defined structure for the backbone. In all of the cases under study, the method found a cluster of similar low-energy conformations that agree well with the structure deduced from x-ray diffraction experiments and with one computed earlier by the build-up procedure.     

Spatial structure of isoleucine pentapeptides Glu-Phe-Leu-Arg-Ile-NH2 and Pro-Phe-Tyr-Arg-Ile-NH2

The spatial structure of two cardioactive isoleucine pentapeptides Glu-Phe-Leu-Arg-Ile-NH2 (I) and Pro-Phe-Tyr-Arg-Ile-NH2 (II) have been investigated using the theoretical conformational analysis. The low-energy conformations of these molecules were found, the values of dihedral angles of the backbone and side chains of the amino acid residues constituting these peptides were determined, and the energies of intra- and interresidual interactions were estimated. It was revealed that the spatial structure of molecule I can exist as five and that of molecule II as seven stable backbone forms.     

Predicting the Structure of the Flavodoxin from Eschericia coli by Homology Modeling,Distance Geometry and Molecular Dynamics

Abstract

As part of our on-going development of a method, based upon distance geometry calculations, for predicting the structures of proteins from the known structures of their homologues, we have predicted the structure of the 176 residue Flavodoxin from Escherichia coli. This prediction was based upon the crystal structures of the homologous Flavodoxins from Anacystis nidulans, Chondrus crispus, Desulfovibrio vulgaris and Clostridium beijerinckii, whose sequence identities with Escherichia coli were 44%, 33%, 23% and 16%, respectively. A total of 13,043 distance constraints among the alpha-carbons of the Escherichia coli structure were derived from the sequence alignments with the known structures, together with 8,893 distance constraints among backbone and sidechain atoms of adjacent residues, 978 between the alpha-carbons and selected atoms of the flavin mononucleotide cofactor, 116 constraints to enforce conserved hydrogen bonds, and 452 constraints on the torsion angles in conserved residues. An ensemble of ten random Escherichia coli structures was computed from these constraints, with an average root mean square coordinate deviation (RMSD) among the alpha carbons of 0.85 Ångstroms (excluding the first 1 and last 6 residues, which have no corresponding residues in any of the homologues and hence were unconstrained); the corresponding average heavy-atom RMSD was 1.60 Å.

Since the distance geometry calculations were performed without hydrogen atoms, protons were added to the resulting structures and these structures embedded in a 50 × 50 × 40 Å solvent box with periodic boundary conditions. They were then subjected to a 20 picosecond dynamical simulated annealing procedure, starting at 300 K and gradually reduced to 10K, in which all the distance and torsion angle constraints were maintained by means of harmonic restraint functions. This was followed up by 1000 iterations of unrestrained conjugate gradients minimization. The goal of this energy refinement procedure was not to drastically modify the structures in an attempt at a priori prediction, but merely to improve upon the predictions obtained from the geometric constraints, particularly with regard to their local backbone and sidechain conformations and their hydrogen bonds. The resulting structures differed from the respective starting structures by an average of 1.52 Å in their heavy atom RMSD's, while the average RMSD among the heavy atoms of residues 2-170 increased slightly to 1.66 Å. We hope these structures will be good enough to enable the phase problem to be solved for the crystallographic data that is now being collected on this protein.     

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.     

Tertiary structure of myelopeptides. II. Conformational analysis of Phe-Arg-Pro-Arg-Ile-Met-Thr-Pro, Val-Val-Tyr-Pro-Asp, and Val-Asp-Pro-Pro

Theoretical conformational analysis was used to study the spatial structure and conformational properties of myelopeptides, bone marrow peptide mediators. The low-energy conformations of myelopeptides MP-4 (Phe-Arg-Pro-Arg-Ile-Met-Thr-Pro), MP-5 (Val-Val-Tyr-Pro-Asp), and MP-6 (Val-Asp-Pro-Pro) were found; the values of dihedral angles of backbone and side chains of the amino acid residues were determined; and the energies of intra- and interresidual interactions were estimated.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. II. Average backbone structure of enkephalin

The average conformation of Met-enkephalin was determined by using an adaptive, importance-sampling Monte Carlo algorithm (SMAPPS—Statistical Mechanical Algorithm for Predicting Protein Structure). In the calculation, only the backbone dihedral angles (? and ψ) were allowed to vary; i.e., all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to a low-energy structure of the pentapeptide. The total conformational energy for each randomly generated structure of the polypeptide 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 calculation was repeated until a total of 10 independent average conformations were established. The regions of conformational space occupied by the average structures were compared with the regions of low conditional free energy obtained by SMAPPS in the first paper of this series. Such a comparison provides an analysis of the capacity of SMAPPS to adjust the Monte Carlo search to regions of highest probability. The results demonstrate that the ability of SMAPPS to focus the Monte Carlo search is excellent. Finally, the 10 independent average conformations and the mean of the 10 average structures were utilized as the initial conformations for a direct energy minimization of the pentapeptide. Of the 11 final energy-minimized structures, three of the conformations were found to be equivalent to the conformation of lowest energy determined previously. In addition, all but two of the remaining energy-minimized structures were found to correspond to one of the two other conformations of high probability obtained in the first paper of this series. These results indicate that a set of independent average conformations can provide a rational, unbiased choice for the initial conformation, to be used in a direct energy minimization of a polypeptide. The final energy-minimized structures consequently constitute a set of low-energy conformations, which include the global energy minimum.     

Energy-conformation studies of frequency of beta-turns in tetrapeptide sequences

The optimized energies of seven beta-bends, repeating C5 and C7, and right- and left-handed alpha-helical conformations for each of eight tetrapeptides have been computed using empirical methods. Eight tetramers were selected: four helix-forming sequences with hydrophobic residues such as Val, Leu, Ile and Trp, and four helix-breaking sequences with hydrophilic residues such as Asp, Asn and Ser, as determined by their frequency of occurrence in beta turns in proteins. Analysis of the optimized conformations with energies less than or equal to 2.1 kcal/mol from the absolute minimum energy conformer for each tetramer reveals a correlation between low-energy conformations and those predicted from observed protein structures. These results show that energy calculations on small peptide fragments may be usefulin predicting protein structure.     

Spatial structure of myelopeptides: I. Conformational analysis of MP-1, MP-2, and MP-3

Theoretical conformational analysis was used to study the spatial structure and conformational properties of myelopeptides, bone-marrow peptide mediators. The low-energy conformations of three hexapeptides MP-1 (Phe-Leu-Gly-Phe-Pro-Thr), MP-2 (Leu-Val-Val-Tyr-Pro-Trp), and MP-3 (Leu-Val-Cys-Tyr-Pro-Gln) were found, the values of dihedral angles of the backbone and side chains of the amino acid residues constituting these peptides were determined, and the energies of intra- and interresidual interactions were estimated.     

Benchmarking of structure refinement methods for protein complex models

Protein structure docking is the process in which the quaternary structure of a protein complex is predicted from individual tertiary structures of the protein subunits. Protein docking is typically performed in two main steps. The subunits are first docked while keeping them rigid to form the complex, which is then followed by structure refinement. Structure refinement is crucial for a practical use of computational protein docking models, as it is aimed for correcting conformations of interacting residues and atoms at the interface. Here, we benchmarked the performance of eight existing protein structure refinement methods in refinement of protein complex models. We show that the fraction of native contacts between subunits is by far the most straightforward metric to improve. However, backbone dependent metrics, based on the Root Mean Square Deviation proved more difficult to improve via refinement.     

Survey of conformational role of ester bonds in a cyclic depsipeptide. Study on cyclo(-L-Ala-L-Hmb-)2 by energy calculation and NMR spectroscopy.

The effect of ester bond on the conformation of peptide molecule was studied by designing and synthesizing a model tetradepsipeptide cyclo(-L-Ala-L-Hmb-)2 and by analyzing the conformation both theoretically and experimentally. Theoretical analysis showed that both ester and peptide bonds in the calculated low-energy conformations within 3 kcal/mol of the global minimum take a trans but distorted configuration. The distortion is larger in ester bonds than in peptide bonds. Further, the four carbonyls project from one side of the plane of the cyclic backbone, whereas the side chains project from the other side. These results are consistent with the experimental results obtained by NMR measurement; first, the coupling constant deduced from 1H-NMR species in DMSO-d6 is consistent with the dihedral angles of the calculated low-energy conformations; second, results of NOE measurement can reproduce the calculated configuration of the carbonyls and side chains. From the consistency between theoretical and experimental results, it is concluded that this model tetradepsipeptide takes an all-trans backbone conformation in solution and this backbone conformation is stabilized by large distortion in the ester bond, which compensates the strain resulted from the 12-membered cyclic backbone structure consisting only of L-residues.