A pH-dependent variation in alpha-helix structure of the S-peptide of ribonuclease A studied by Monte Carlo simulated annealing.

Low-energy conformations of the S-peptide fragment (20 amino acid residues long) of ribonuclease A were studied by Monte Carlo simulated annealing. The obtained lowest-energy structures have alpha-helices with different size and location, depending distinctively on the ionizing states of acidic amino acid residues. The simulation started from completely random initial conformation and was performed without any bias toward a particular structure. The most conspicuous alpha-helices arose from the simulation when both Glu 9 and Asp 14 were assumed to be electrically neutral, whereas the resulting conformations became much less helical when Asp 14 rather than Glu 9 was allowed to have a negative charge. Together with experimental evidence that the alpha-helix in the S-peptide is most stable at pH 3.8, we consider the helix formation need the carboxyl group of Asp 14 to be electrically neutral in this weakly acidic condition. In contrast, a negative charge at Asp 14 appears to function in support of a view that this residue is crucial to helix termination owing to its possibility to form a salt bridge with His 12. These results indicate that the conformation of the S-peptide depends considerably on the ionizing state of Asp 14.     

Molecular dynamics simulations of beta-hairpin folding

Molecular dynamics simulations of beta-hairpin folding have been carried out with a solvent-referenced potential at 274 K. The model peptide V4DPGV4 formed stable beta-hairpin conformations and the beta-hairpin ratio calculated by the DSSP algorithm was about 56% in the 50-ns simulation. Folding into beta-hairpin conformations is independent of the initial conformations. The simulations provided insights into the folding mechanism. The hydrogen bond often formed in a beta-turn first, and then propagated by forming more hydrogen bonds along the strands. Unfolding and refolding occurred repeatedly during the simulations. Both the hydrogen bonding and the hydrophobic interaction played important roles in forming the ordered structure. Without the hydrophobic effect, stable beta-hairpin conformations did not form in the simulations. With the same energy functions, the alanine-based peptide (AAQAA)3Y folded into helical conformations, in agreement with experiments. Folding into an alpha-helix or a beta-hairpin is amino acid sequence-dependent.     

Beta-sheet folding of fragment (16-36) of bovine pancreatic trypsin inhibitor as predicted by Monte Carlo simulated annealing.

A tertiary structure prediction is described using Monte Carlo simulated annealing for the peptide fragment corresponding to residues 16-36 of bovine pancreatic trypsin inhibitor (BPTI). The simulation starts with randomly chosen initial conformations and is performed without imposing experimental constraints using energy functions given for generic interatomic interactions. Out of 20 simulation trials, seven conformations show a sheet-like structure--two strands connected by a turn--although this sheet-like structure is not as rigid as that observed in native BPTI. It is also shown that these conformations are mostly looped and exhibit a native-like right-handed twist. Unlike the case with the C-peptide of RNase A, no conspicuous alpha-helical structure is found in any of the final conformations obtained in the simulation. However, the lowest-energy conformation does not resemble exactly the native structure. This indicates that the rigid beta-sheet conformation of native BPTI merely corresponds to a local minimum of the energy function if the fragment with residues 16-36 is isolated from the native protein. A statistical analysis of all 20 final conformations suggests that the tendency for the peptide segments to form extended beta-strands is strong for those with residues 18-24, and moderate for those with residues 30-35. The segment of residues 25-29 does not tend to form any definite structure. In native BPTI, the former segments are involved in the beta-sheet and the latter in the turn. A folding scenario is also speculated from this analysis.     

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.     

Crystal Structure and Molecular Conformation of the Cyclic Hexapeptide cyclo-(Gly-Aib-Gly)2

We have synthesized and crystallized the cyclic peptide (Gly-Aib-Gly) ₂. Its structure has been determined by conventional X-ray diffracti on methods. In the crystal it adopts a conformation with one β-turn (type I) and its mirror image at the other side of the ring. All conformation al angles are similar to those reported for these amino acid residues. In particular the Aib residue has a conformation intermediate between α- and 3₁₀-helical conformations. The ring is an adequate model for the β-turn conformation. A molecule of formic acid is found in the crystal which shows a very short hydrogen bond with one of the glycine carbonyl groups.     

Simulation of alpha-helix and beta-hairpin formation in water-soluble proteins by the code physics method

One of the possible ways for complete and final solution of the problem of determination of three-dimensional structure of proteins on amino acid sequence is simulation of protein three-dimensional structure formation. The use of the code physics method developed by the author has been suggested to fulfill this task. The simulation of alpha-helix and beta-hairpin formation in water-soluble proteins as a start of realization of the plan is described here. The results of the simulation were compared with the experimental data for 14 proteins of no more than 50 amino acids and therefore with little number of alpha-helices and beta-strands (to meet limits of simulation process) and with secondary structure predictions by the best to data methods of protein secondary structure prediction, PSIpred, PORTER and PROFsec. Secondary structure of the proteins, obtained as a result of the simulation of alpha-helix and beta-hairpin formation using the code physics method, corresponded completely to experimental data while the secondary structure predicted by the PSIpred, PORTER and PROFsec methods differed from these data significantly.     

Approaching a complete classification of protein secondary structure

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

Assembly of polypeptide and protein backbone conformations from low energy ensembles of short fragments: development of strategies and construction of models for myoglobin, lysozyme, and thymosin beta 4.

Recently we developed methods for the construction of knowledge-based mean fields from a data base of known protein structures. As shown previously, this approach can be used to calculate ensembles of probable conformations for short fragments of polypeptide chains. Here we develop procedures for the assembly of short fragments to complete three-dimensional models of polypeptide chains. The amino acid sequence of a given protein is decomposed into all possible overlapping fragments of a given length, and an ensemble of probable conformations is calculated for each fragment. The fragments are assembled to a complete model by choosing appropriate conformations from the individual ensembles and by averaging over equivalent angles. Finally a consistent model is obtained by rebuilding the conformation from the average angles. From the average angles the local variability of the structure can be calculated, which is a useful criterion for the reliability of the model. The procedure is applied to the calculation of the local backbone conformations of myoglobin and lysozyme whose structures have been solved by X-ray analysis and thymosin beta 4, a polypeptide of 43 amino acid residues whose structure was recently investigated by NMR spectroscopy. We demonstrate that substantial fractions of the calculated local backbone conformations are similar to the experimentally determined structures.     

Local deformation studies of chain molecules: differential conditions for changes of dihedral angles

New first and second-order differential equations for changes of dihedral angles characterizing local deformations of chain molecules with fixed bond lengths and bond angles are derived. Two methods for integrating the differential relations are given. The proposed method is used to generate a path of locally deformed conformations around a β-turn region of a small protein, bovine pancreatic trypsin inhibitor. The variable regions change their conformations by more than 3 Å root-mean-square distance value whereas the fixed regions stay within 0.02 Å. Possible applications of this method are in the field of computer graphics, Monte Carlo simulations, and energy minimization calculations of chain molecules.     

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

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

Molecular thermodynamic model to predict the alpha-helical secondary structure of polypeptide chains in solution.

The native state of a protein molecule in aqueous solutions represents one of the lowest states of Gibbs energy [Anfinsen, C.B. (1973) Science 181, 223-230]. Much progress has been made about the rules of protein folding [King, J. (1989) Chem. Eng. News 67, 32-54] and the dominant forces in protein folding [Dill, K.A. (1990) Biochemistry 29, 7133-7155]. However, the quantitative contributions of different Gibbs energy terms to protein stability remains a controversial issue [Moult, J., & Unger, R. (1991) Biochemistry 30, 3816-3824]. A molecular thermodynamic model has been proposed for the Gibbs energy of folding a residue in aqueous homopolypeptides from a random-coiled state to either the alpha-helix state or the beta-sheet state [Chen, C.-C., Zhu, Y., King, J.A., & Evans, L.B. (1992) Biopolymers 32, 1375-1392]. In this work, we present a generalization of the molecular thermodynamic model for the Gibbs energy of folding natural and synthetic heteropolypeptides from random-coiled conformations into alpha-helical conformations. The generalized model incorporates the intrinsic folding potential due to residue-solvent interactions, the cooperative folding effect due to residue-residue interactions, and the location and length of alpha-helices. The utility of the model was demonstrated by examining the stability of alpha-helical conformations of a number of natural polypeptides including C-peptide (residues 1-13) and S-peptide (residues 1-20) of RNase A (bovine pancreatic ribonuclease A), the P alpha fragment in BPTI (bovine pancreatic trypsin inhibitor), and synthetic polypeptides (the copolymers of different amino acid residues) including alanine-based peptides (16 or 17 residues long) in water. The computed Gibbs energies correspond well with the experimental data on helicity. The results also accounted for the effects of amino acid substitution and temperature on the stability of alpha-helical conformations of the test polypeptides.     

Theoretical conformational analysis of tripeptides. N-acetyl-L-alanyl-L-alanyl-L-alanyl methylamide]

The minimization procedure has been used for calculation of the local minimum conformations of threepeptide--Ac-(L-Ala)3-NHMe without intramolecular H-bonds. The significant energy deviations from additivity found, arising with increase backbone length to three links, can be considered as the evidence for mutual dependence of conformational states of the neighbouring and terminal amino acid residues. It have been shown that stability of alpha-helix form for alanine threepeptide in contrary to corresponding dipeptide is noticeably higher due to stabilizing effect of dispersion interactions. The results of calculations are compared with the data on conformational distrubution of the threepeptide fragments in proteins with known three dimensional structure. The important role of the backbone interaction in protein chain have been marked.     

Conformational similarity among amino acid residues: 1. Analysis of protein crystal structure data

The probability distribution in the (?,ψ)-plane obtained for each amino acid residue from cyrstal structure data of globular proteins is compared. This has shown amino acid residues. Pro and Gly to be conformationally unique. Conformational similarity in the (?,ψ)-plane of amino acid reced does not necessarily mean that they will have the same chemical or biochemical properties or similar secondary structures. A set of amino acid residues are given which can adopt the conformations of other amino acid residues without much difficulty either in the whole (?,ψ)-plane or in regions, where the observed conformations are maximum.     

A 175-psec molecular dynamics simulation of camphor-bound cytochrome P-450cam.

The structure and internal motions of cytochrome P-450cam, a monooxygenase heme enzyme with 414 amino acid residues, with camphor bound at the active site have been evaluated on the basis of a 175-psec molecular dynamics simulation carried out at 300 K. All hydrogen atoms were explicitly modeled, and 204 crystallographic waters were included in the simulation. Based on an analysis of the time course of the trajectory versus potential energy, root mean square deviation, radius of gyration, and hydrogen bonding, the simulation was judged to be stable and representative of the average experimental structure. The averaged structural properties of the enzyme were evaluated from the final 135 psec of the simulation. The average atomic displacement from the X-ray structure was 1.39 A for all heavy atoms and 1.17 A for just C-alpha atoms. The average root-mean-square (rms) fluctuations of all heavy atoms and backbone atoms were 0.42 and 0.37 A, respectively. The computed rms fluctuations were in reasonable agreement with the experimentally determined temperature factors. All 13 segments of alpha-helix and 5 segments of beta-sheet were well preserved with the exception of the N-terminal half of helix F which alternated between an alpha-helix and a 310-helix. In addition there were in general only small variations in the relative orientation of adjacent alpha-helices. The rms fluctuations of the backbone dihedral angles in the secondary structure elements were almost uniformly smaller, with the fluctuation in alpha-helices and beta-sheets, 31 and 10% less, respectively, than those in nonsecondary structure regions. The reported crystal structure contains kinks in both helices C and I. In the simulation, both of these regions showed high mobility and large deviations from their starting positions. Since the kink in the I helix is at the oxygen binding site, these motions may have mechanistic implications.     

New stochastic strategy to analyze helix folding

We propose an alternative stochastic strategy to search secondary structures based on the generalized simulated annealing (GSA) algorithm, by using conformational preferences based on the Ramachandran map. We optimize the search for polypeptide conformational space and apply to peptides considered to be good alpha-helix promoters above a critical number of residues. Our strategy to obtain conformational energies consist in coupling a classical force field (THOR package) with the GSA procedure, biasing the Phi x Psi backbone angles to the allowed regions in the Ramachandran map. For polyalanines we obtained stable alpha-helix structures when the number of residues were equal or exceeded 13 amino acids residues. We also observed that the energy gap between the global minimum and the first local minimum tends to increase with the polypeptide size. These conformations were generated by performing 2880 stochastic molecular optimizations with a continuum medium approach. When compared with molecular dynamics or Monte Carlo methods, GSA can be considered the fastest.     

Computational and experimental determination of the alpha-helix unfolding reaction coordinate

We demonstrate a calculated alpha-helix peptide folding energy landscape which accurately simulates the first experimentally measured alpha-helix melting energy landscape. We examine a 21-amino acid, mainly polyalanine peptide and calculate the free energy along the Psi Ramachandran angle secondary folding coordinate. The experimental free energy landscape was determined using UV resonance Raman spectroscopy. The relative free energy values are very close as are the equilibrium peptide conformations. We find 2.3 kcal/mol activation barriers between the alpha-helix-like and PPII-like basins. We also find that the alpha-helix-like conformations are quite defective and the alpha-helix-like structure dynamically samples 310-helix and pi-bulges.     

Energy landscape of a peptide consisting of alpha-helix, 3(10)-helix, beta-turn, beta-hairpin, and other disordered conformations

The energy landscape of a peptide [Ace-Lys-Gln-Cys-Arg-Glu-Arg-Ala-Nme] in explicit water was studied with a multicanonical molecular dynamics simulation, and the AMBER parm96 force field was used for the energy calculation. The peptide was taken from the recognition helix of the DNA-binding protein, c-MYB: A rugged energy landscape was obtained, in which the random-coil conformations were dominant at room temperature. The CD spectra of the synthesized peptide revealed that it is in the random state at room temperature. However, the 300 K canonical ensemble, Q(300K), contained alpha-helix, 3(10)-helix, beta-turn, and beta-hairpin structures with small but notable probabilities of existence. The complete alpha-helix, imperfect alpha-helix, and random-coil conformations were separated from one another in the conformational space. This means that the peptide must overcome energy barriers to form the alpha-helix. The overcoming process may correspond to the hydrogen-bond rearrangements from peptide-water to peptide-peptide interactions. The beta-turn, imperfect 3(10)-helix, and beta-hairpin structures, among which there are no energy barriers at 300 K, were embedded in the ensemble of the random-coil conformations. Two types of beta-hairpin with different beta-turn regions were observed in Q(300K). The two beta-hairpin structures may have different mechanisms for the beta-hairpin formation. The current study proposes a scheme that the random state of this peptide consists of both ordered and disordered conformations. In contrast, the energy landscape obtained from the parm94 force field was funnel like, in which the peptide formed the helical conformation at room temperature and random coil at high temperature.     

Analysis of forces that determine helix formation in alpha-proteins

A model for prediction of alpha-helical regions in amino acid sequences has been tested on the mainly-alpha protein structure class. The modeling represents the construction of a continuous hypothetical alpha-helical conformation for the whole protein chain, and was performed using molecular mechanics tools. The positive prediction of alpha-helical and non-alpha-helical pentapeptide fragments of the proteins is 79%. The model considers only local interactions in the polypeptide chain without the influence of the tertiary structure. It was shown that the local interaction defines the alpha-helical conformation for 85% of the native alpha-helical regions. The relative energy contributions to the energy of the model were analyzed with the finding that the van der Waals component determines the formation of alpha-helices. Hydrogen bonds remain at constant energy independently whether alpha-helix or non-alpha-helix occurs in the native protein, and do not determine the location of helical regions. In contrast to existing methods, this approach additionally permits the prediction of conformations of side chains. The model suggests the correct values for ~60% of all chi-angles of alpha-helical residues.     

The sequence TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase displays structural ambivalence and interconverts between alpha-helical and beta-hairpin conformations mediated by collapsed conformational states.

The peptide TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase adopts a helical conformation in the crystal structure and is a site for two hydrated helical segments, which are thought to be helical folding intermediates. Overlapping sequences of four to five residues from the peptide, sample both helical and strand conformations in known protein structures, which are dissimilar to glyceraldehyde-3-phosphate dehydrogenase suggesting that the peptide may have a structural ambivalence. Molecular dynamics simulations of the peptide sequence performed for a total simulation time of 1.2 micros, starting from the various initial conformations using GROMOS96 force field under NVT conditions, show that the peptide samples a large number of conformational forms with transitions from alpha-helix to beta-hairpin and vice versa. The peptide, therefore, displays a structural ambivalence. The mechanism from alpha-helix to beta-hairpin transition and vice versa reveals that the compact bends and turns conformational forms mediate such conformational transitions. These compact structures including helices and hairpins have similar hydrophobic radius of gyration (Rgh) values suggesting that similar hydrophobic interactions govern these conformational forms. The distribution of conformational energies is Gaussian with helix sampling lowest energy followed by the hairpins and coil. The lowest potential energy of the full helix may enable the peptide to take up helical conformation in the crystal structure of the glyceraldehyde-3-phosphate dehydrogenase, even though the peptide has a preference for hairpin too. The relevance of folding and unfolding events observed in our simulations to hydrophobic collapse model of protein folding are discussed.