The normal modes of the gramicidin-A dimer channel.

The dynamics of the gramicidin-A dimer channel is studied in the harmonic approximation by a vibrational analysis of the atomic motions relative to their equilibrium positions. The system is represented by an empirical potential energy function, and all degrees of freedom (bonds lengths, bond angles, and torsional angles) are allowed to vary. The thermal fluctuations in the backbone dihedral angles phi and psi, atomic root mean square displacements, and the correlations between the different amide planes are computed. It is found that only adjacent dihedral psi i and phi i+1 are strongly correlated, while different hydrogen-bonded amide planes are only weakly correlated. Modes with relatively low vibrational frequencies (75-175 cm-1) make the dominant contributions to the carbonyl librations. The general flexibility of the structure and the role of carbonyl librations in the ion transport mechanism are discussed.     

Structure and dynamics of an amphiphilic peptide in a lipid bilayer: a molecular dynamics study

A molecular dynamics simulation of a simple model membrane system composed of a single amphiphilic helical peptide (ace-K2GL16K2A-amide) in a fully hydrated 1,2-dimyristoyl-sn-glycero-3-phosphocholine bilayer was performed for a total of 1060 ps. The secondary structure of the peptide and its stability were described in terms of average dihedral angles, phi and psi, and the C alpha torsion angles formed by backbone atoms; by the average translation per residue along the helix axis; and by the intramolecular peptide hydrogen bonds. The results indicated that residues 6 through 15 remain in a stable right-handed alpha-helical conformation, whereas both termini exhibit substantial fluctuations. A change in the backbone dihedral angles for residues 16 and 17 is accompanied by the loss of two intramolecular hydrogen bonds, leading to a local but long-lived disruption of the helix. The dynamics of the peptide was characterized in terms of local and global helix motions. The local motions of the N-H bond angles were described in terms of the autocorrelation functions of P2[cos thetaNH(t, t + tau)] and reflected the different degrees of local peptide order as well as a variation in time scale for local motions. The chi1 and chi2 dihedral angles of the leucine side chains underwent frequent transitions between potential minima. No connection between the side-chain positions and their mobility was observed, however. In contrast, the lysine side chains displayed little mobility during the simulation. The global peptide motions were characterized by the tilting and bending motions of the helix. Although the peptide was initially aligned parallel to the bilayer normal, during the simulation it was observed to tilt away from the normal, reaching an angle of approximately 25 degrees by the end of the simulation. In addition, a slight bend of the helix was detected. Finally, the solvation of the peptide backbone and side-chain atoms was also investigated.     

Comparison of normal mode analyses on a small globular protein in dihedral angle space and Cartesian coordinate space

Normal mode analyses on the protein, bovine pancreatic trypsin inhibitor, in dihedral angle space and Cartesian coordinate space are compared. In Cartesian coordinate space it is found that modes of frequencies lower than 30 cm(-1) contribute 80% of the total mean-square fluctuation and are represented almost completely by motions in the dihedral angles. Bond angle and length fluctuations dominate in modes above 200 cm(-1), but contribute less than 2% to the total mean-square fluctuation. In the low-frequency modes a good correspondence between patterns of atomic displacements was found, but on average the root-mean-square fluctuations of the Cartesian coordinate modes are 13% greater than their dihedral angle counterparts. The main effect of fluctuations in the bond angles and lengths, therefore, is to allow the dihedral angles to become more flexible. As the important subspaces determined from the two methods overlap considerably, dihedral angle space analysis can be applied to proteins too large for Cartesian coordinate space analysis.     

Dynamics of transfer RNAs analyzed by normal mode calculation.

Normal mode calculation is applied to tRNAPhe and tRNAAsp, and their structural and vibrational aspects are analyzed. Dihedral angles along the phosphate-ribose backbone (alpha, beta, gamma, epsilon, zeta) and dihedral angles of glycosyl bonds (chi) are selected as movable parameters. The calculated displacement of each atom agrees with experimental data. In modes with frequencies higher than 130 cm-1, the motions are localized around each stem and the elbow region of the L-shape. On the other hand, collective motions such as bending or twisting of arms are seen in modes with lower frequencies. Hinge axes and bend angles are calculated without prior knowledge. Movements in modes with very low frequencies are combinations of hinge bending motions with various hinge axes and bend angles. The thermal fluctuations of dihedral angles well reflect the structural characters of transfer RNAs. There are some dihedral angles of nucleotides located around the elbow region of L-shape, which fluctuate about five to six times more than the average value. Nucleotides in the position seem to be influential in the dynamics of the entire structure. The normal mode calculation seems to provide much information for the study of conformational changes of transfer RNAs induced by aminoacyl-tRNA synthetase or codon during molecular recognition.     

The influence of helix morphology on co-operative polyamide backbone conformational flexibility in peptide nucleic acid complexes.

A systematic analysis of peptide nucleic acid (PNA) complexes deposited in the Protein Data Bank has been carried out using a set of contiguous atom torsion angle definitions. The analysis is complemented by molecular mechanics adiabatic potential energy calculations on hybrid PNA-nucleic acid model systems. Hitherto unobserved correlations in the values of the (alpha and epsilon) dihedral angles flanking the backbone secondary amide bond are found. This dihedral coupling forms the basis of a PNA backbone conformation classification scheme. Six conformations are thus characterised in experimental structures. Helix morphology is found to exert a significant influence on backbone conformation and flexibility: Watson-Crick PNA strands in complexes with DNA and RNA, that possess A-like base-pair stacking, adopt backbone conformations distinct from those in PNA.DNA-PNA triplex and PNA-PNA duplex P-helix forms. Solvation effects on Watson-Crick PNA backbone conformation in heterotriplexes are discussed and the possible involvement of inter-conformational transitions and dihedral angle uncoupling in asymmetric heteroduplex base-pair breathing is suggested.     

β-Turn conformations in crystal structures of model peptides containing α,α-Di-n-propylglycine and α,α-Di-n-butylglycine

The crystal state conformations of three peptides containing the α,α-dialkylated residues. α,α-di-n-propylglycine (Dpg) and α,α-di-n-butylglycine (Dbg), have been established by x-ray diffraction. Boc-Ala-Dpg-Alu-OMe (I) and Boc-Ala-Dbg-Ala-OMe (III) adopt distorted type II β-turn conformations with Ala (1) and Dpg/Dbg (2) as the corner residues. In both peptides the conformational angles at the Dxg residue (I: ? = 66.2°, ψ = 19.3°; III: ? = 66.5°. ψ = 21.1°) deviate appreciably from ideal values for the i + 2 residue in a type II β-turn. In both peptides the observed (N…O) distances between the Boc CO and Ala (3) NH groups are far too long (1: 3.44 Å: III: 3.63 Å) for an intramolecular 4 → 1 hydrogen bond. Boc-Ala-Dpg-Ata-NHMe (II) crystallizes with two independent molecules in the asymmetric unit. Both molecules HA and HB adopt consecutive β-turn (type III-III in HA and type III-I in IIB) or incipient 3₁₀-helical structures, stabilized by two intramolecular 4 → 1 hydrogen bonds. In all four molecules the bond angle N-C^α-C′ (τ) at the Dxg residues are ≥ 110°. The observation of conformational angles in the helical region of ?,ψ space at these residues is consistent with theoretical predictions. © 1995 John Wiley & Sons, Inc.     

Coarse-grained modeling of the actin filament derived from atomistic-scale simulations

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.     

Polypeptide motions are dominated by peptide group oscillations resulting from dihedral angle correlations between nearest neighbors

To identify basic local backbone motions in unfolded chains, simulations are performed for a variety of peptide systems using three popular force fields and for implicit and explicit solvent models. A dominant "crankshaft-like" motion is found that involves only a localized oscillation of the plane of the peptide group. This motion results in a strong anticorrelated motion of the phi angle of the ith residue (phi(i)) and the psi angle of the residue i - 1 (psi(i-1)) on the 0.1 ps time scale. Only a slight correlation is found between the motions of the two backbone dihedral angles of the same residue. Aside from the special cases of glycine and proline, no correlations are found between backbone dihedral angles that are separated by more than one torsion angle. These short time, correlated motions are found both in equilibrium fluctuations and during the transit process between Ramachandran basins, e.g., from the beta to the alpha region. A residue's complete transit from one Ramachandran basin to another, however, occurs in a manner independent of its neighbors' conformational transitions. These properties appear to be intrinsic because they are robust across different force fields, solvent models, nonbonded interaction routines, and most amino acids.     

600 ps Molecular dynamics reveals stable substructures and flexible hinge points in cAMP dependent protein kinase

Molecular dynamics simulations of the catalytic subunit of cAMP dependent protein kinase (cAPK) have been performed in an aqueous environment. The relations among the protein hydrogen‐bonding network, secondary structural elements, and the internal motions of rigid domains were examined. The values of fluctuations of protein dihedral angles during dynamics show quite distinct maxima in the regions of loops and minima in the regions of α‐helices and β‐strands. Analyses of conformation snapshots throughout the run show stable subdomains and indicate that these rigid domains are constrained during the dynamics by a stable network of hydrogen bonds. The most stable subdomain during the dynamics was in the small lobe including part of the carboxy‐terminal tail. The most significant flexible region was the highly conserved glycine‐rich loop between β strands 1 and 2 in the small lobe. Many of the main chain dihedral angle changes measured in a comparison of the crystallographic structures of “open” and “closed” conformations of cAPK correspond to the highly flexible residues found during dynamics. © 1999 John Wiley & Sons, Inc. Biopoly 50: 513–524, 1999     

Shape of the conformational energy surface near the global minimum and low-frequency vibrations in the native conformation of globular proteins

Based on the assumption that the conformational energy surface of a protein molecule can be approximated near the global minimum point by a multidimensional parabola, conformational fluctuations in the native state are discussed. In this approximation the conformational fluctuations can be viewed as excitations of coupled harmonic oscillations of dihedral angles. For the purpose of estimating the range of frequencies vibrations, globular proteins are assumed to made of homogeneous continuous elastic material. The number of vibrational modes in such an elastic body, with the wavelength no less than the characteristic length of an amino acid residue, are estimated roughly to be three times the number of amino acid residues in a protein, which is slightly less than the number of variable dihedral angles in a protein. Their frequencies, when converted to the wavenumber of corresponding light, are found to range from 1.8 × 10 cm^?1 to 2.1 × 10²cm^?1 for a protein with the diameter d = 40 Å, when Young's E = 10¹¹ dyne/cm² is assumed. A significant fraction of the coupled vibrations of dihedral angles in real globular proteins are collective ones, i.e., those involving the whole protein molecules. Based on these results, it concluded that the depth of the global minimum s at least 150 Kcal/mol.     

Influence of the environment in the conformation of alpha-helices studied by protein database search and molecular dynamics simulations

The influence of the solvent on the main-chain conformation (phi and Psi dihedral angles) of alpha-helices has been studied by complementary approaches. A first approach consisted in surveying crystal structures of both soluble and membrane proteins. The residues of analysis were further classified as exposed to either the water (polar solvent) or the lipid (apolar solvent) environment or buried to the core of the protein (intermediate polarity). The statistical results show that the more polar the environment, the lower the value of phi(i) and the higher the value of Psi(i) are. The intrahelical hydrogen bond distance increases in water-exposed residues due to the additional hydrogen bond between the peptide carbonyl oxygen and the aqueous environment. A second approach involved nanosecond molecular dynamics simulations of poly-Ala alpha-helices in environments of different polarity: water to mimic hydrophilic environments that can form hydrogen bonds with the peptide carbonyl oxygen and methane to mimic hydrophobic environments without this hydrogen bond capabilities. These simulations reproduce similar effects in phi and Psi angles and intrahelical hydrogen bond distance and angle as observed in the protein survey analysis. The magnitude of the intrahelical hydrogen bond in the methane environment is stronger than in the water environment, suggesting that alpha-helices in membrane-embedded proteins are less flexible than in soluble proteins. There is a remarkable coincidence between the phi and Psi angles obtained in the analysis of residues exposed to the lipid in membrane proteins and the results from computer simulations in methane, which suggests that this simulation protocol properly mimic the lipidic cell membrane and reproduce several structural characteristics of membrane-embedded proteins. Finally, we have compared the phi and Psi torsional angles of Pro kinks in membrane protein crystal structures and in computer simulations.     

Density functional and Møller–Plesset studies of cyclobutanone⋯HF and ⋯HCl complexes

The molecular structure (hydrogen bonding, bond distances and angles), dipole moment and vibrational spectroscopic data [vibrational frequencies, IR and vibrational circular dichroism (VCD)] of cyclobutanone?HX (X?=?F, Cl) complexes were calculated using density functional theory (DFT) and second order Møller–Plesset perturbation theory (MP2) with basis sets ranging from 6–311G, 6–311G^**, 6–311 + + G^**. The theoretical results are discussed mainly in terms of comparisons with available experimental data. For geometric data, good agreement between theory and experiment is obtained for the MP2 and B3LYP levels with basis sets including diffuse functions. Surface potential energy calculations were carried out with scanning HCl and HF near the oxygen atom. The nonlinear hydrogen bonds of 1.81 Å and 175° for HCl and 1.71 Å and 161° for HF were calculated. In these complexes the C=O and H–X bonds participating in the hydrogen bond are elongated, while others bonds are compressed. The calculated vibrational spectra were interpreted and the band assignments reported are in excellent agreement with experimental IR spectra. The C=O stretching vibrational frequencies of the complexes show red shifts with respect to cyclobutanone.     

ProMode: a database of normal mode analyses on protein molecules with a full-atom model

MOTIVATION: Although information from protein dynamics simulation is important to understand principles of architecture of a protein structure and its function, simulations such as molecular dynamics and Monte Carlo are very CPU-intensive. Although the ability of normal mode analysis (NMA) is limited because of the need for a harmonic approximation on which NMA is based, NMA is adequate to carry out routine analyses on many proteins to compute aspects of the collective motions essential to protein dynamics and function. Furthermore, it is hoped that realistic animations of the protein dynamics can be observed easily without expensive software and hardware, and that the dynamic properties for various proteins can be compared with each other. RESULTS: ProMode, a database collecting NMA results on protein molecules, was constructed. The NMA calculations are performed with a full-atom model, by using dihedral angles as independent variables, faster and more efficiently than the calculations using Cartesian coordinates. In ProMode, an animation of the normal mode vibration is played with a free plug-in, Chime (MDL Information Systems, Inc.). With the full-atom model, the realistic three-dimensional motions at an atomic level are displayed with Chime. The dynamic domains and their mutual screw motions defined from the NMA results are also displayed. Properties for each normal mode vibration and their time averages, e.g. fluctuations of atom positions, fluctuations of dihedral angles and correlations between the atomic motions, are also presented graphically for characterizing the collective motions in more detail. AVAILABILITY: http://promode.socs.waseda.ac.jp     

Calculation of the molecular parameters of the alpha-helix-coil and beta-structure-coil transitions.

Monte-Carlo calculations of geometric and thermodynamic characteristics of the α-helix and the β-structure of polypeptides have been carried out. To describe a hydrogen bond both the Lippincott–Schroeder and Morse potentials were used. The internal rotation angles φ and ψ in the α-helix have been shown to fluctuate in the range of ±7°. The distribution functions on angles φ and ψ and on hydrogen bond lengths and angles in the α-helix have been computed and compared with those in myoglobin and lysozyme. Thermodynamic characteristics of the α-helix calculated in different approximations with the two forms of the hydrogen bond potentials have also been compared. The data obtained are close to the experimental values for polypeptides in neutral solution. Some geometric and thermodynamic characteristics of the regular parallel and antiparallel and irregular antiparallel β-structure have been found. In the β-structure the internal rotation angles vary within the interval ±15–20°. An increase in the cross and longitudinal dimensions of the β-structure only slightly influence both the geometric and thermodynamic characteristics.     

Analyse conformationnelle de la N-méthylamide de l'acide L-pyroglutamique par diffusion Rayleigh depolarisée,spectroscopie de vibration et calcul de l'energie conformationnelle

Conformational analysis of N-methylamide of pyroglutamic acid has been performed by theoretical energy calculations and experimental physical techniques, namely, laser Raman spectroscopy and depolarized Rayleigh scattering. The two theoretically predicted conformations are evidenced in crystalline state (ψ₁ = +169°) and in aqueous solution (ψ₁ ? ?20°). This study confirms the interest of a careful vibrational analysis of peptides and N-deuterated derivatives for providing an estimate of the dihedral angle ψ. The relationship between amide III frequency and ψ values is emphasized.     

Flexibility of the pyrrolidine ring in proline peptides

A survey of over 50 crystal structures indicates that both imino acid and peptide derivatives of proline populate ring conformers consistent with the torsional potentials about single bonds. In both cases, lower barriers for rotation about C? N bonds relative to those about C? C bonds favor smaller values for dihedral angles about the former bonds. In peptides a minimum in the torsional potential about C? N bonds occurs at zero dihedral angle, further favoring small angles. The pyrrolidine-ring dihedral angles of the proline compounds in the solid state obey a cyclopentane-type pseudorotation function. Thus the puckering of the five-membered ring can be quantitatively described by two parameters. Consistent with small dihedral angles about C? N bonds, C^β and/or C^γ are puckered out of the mean plane of the ring in nearly all of the nonstrained compounds. Utilizing the consistent force-field method of Lifson and coworkers [see A. Warshel, M. Levitt, and S. Lifson (1970) J. Mol. Spectrosc. 33 , 84] the intramolecular energy of five proline peptides was minimized with respect to all internal coordinates. In addition, the energy surface near minima was explored by constraining a particular dihedral angle and reminimizing the energy with respect to all remaining variables. In linear peptides two types of pyrrolidine-ring conformers have identical predicted energies. In the cyclic dipeptide cyclo (Pro-Gly) one of the ring conformers is favored by about 3 kcal/mol, while the cyclic tripeptide cyclo(Pro-Gly-Gly) favors the other conformer by a comparable margin. In agreement with observations in the solid state and in solution, C^β and/or C^γ are puckered in the predicted conformers. A correlation between proline Φ and the details of the puckered conformation was predicted and found to match precisely conformers observed in crystals. For the diamides N-acetyl-L -proline-N′-methyl-amide and N-acetyl-L -proline-N′,N′-dimethylamide (AcProMe₂A) 30% and 60% cis acetyl peptide bonds were predicted in good agreement with observations in nonpolar solvents for the respective compounds. The conformational distributions with respect to proline Ψ are also in accord with experimental observations. For AcProMe₂A, a model for a -Pro-Pro-sequence in a peptide chain, this study is the first to predict stable conformers for proline Ψ either ca. ?50° or 140° for both cis and trans peptides.     

Peptide--water association in peptide crystals.

The structures of 37 peptide crystals, containing 78 water-peptide hydrogen bonds and 77 other hydrogen bonds involving water, were surveyed to identify the geometry of peptide backbone hydration. In the sample, hydration of peptide carbonyl occurred more frequently than hydration of peptide N--H. The most probable value of the C'=O ... O water angle was near 138 degrees, considerably greater than the 120 degrees to the axis of a lone electron pair on the carbonyl oxygen. Associated water oxygens tended to be in the plane of the peptide bond, bui--H and Ci+1=O atoms, was common in glycine-containing cyclic hexapeptides. The distribution of angles between two hydrogen bonds at a single water molecule, as defined by the three nonhydrogen atoms involved, was centered near the tetrahedral angle.     

Refined solution structure and backbone dynamics of the archaeal MC1 protein

The 3D structure of methanogen chromosomal protein 1 (MC1), determined with heteronuclear NMR methods, agrees with its function in terms of the shape and nature of the binding surface, whereas the 3D structure determined with homonuclear NMR does not. The structure features five loops, which show a large distribution in the ensemble of 3D structures. Evidence for the fact that this distribution signifies internal mobility on the nanosecond time scale was provided by using (15)N-relaxation and molecular dynamics simulations. Structural variations of the arm (11 residues) induced large shape anisotropy variations on the nanosecond time scale that ruled out the use of the model-free formalism to analyze the relaxation data. The backbone dynamics analysis of MC1 was achieved by comparison with 20 ns molecular dynamics trajectories. Two β-bulges showed that hydrogen bond formation correlated with ? and ψ dihedral angle transitions. These jumps were observed on the nanosecond time scale, in agreement with a large decrease in (15)N-NOE for Gly17 and Ile89. One water molecule bridging NH(Glu87) and CO(Val57) through hydrogen bonding contributed to these dynamics. Nanosecond slow motions observed in loops LP3 (35-42) and LP5 (67-77) reflected the lack of stable hydrogen bonds, whereas the other loops, LP1 (10-14), LP2 (22-24), and LP4 (50-53), were stabilized by several hydrogen bonds. Dynamics are often directly related to function. Our data strongly suggest that residues belonging to the flexible regions of MC1 could be involved in the interaction with DNA.     

Calculation of the minimum energy conformation of biomolecules using a global optimization technique I. Methodology and application to a model molecular fragment (Normal pentane)

The conformational energy of a molecule is minimized with respect to interatomic distances using Bremermann's method of unconstrained global optimization (1970). The optimal set of distances is then used for calculating the preferred conformation of the molecule. A simultaneous optimization of all the dihedral angles is achieved. The classical potential function is used in this study. An illustration of the method is given by applying it to normal pentane, which is a commonly occurring fragment of biomolecules. Results show that, for the standard geometry (bond lengths and bond angles), the all-trans) conformation is the preferred one. However, fluctuations of the geometry within the limits of the vibrational spectra can lead to preferred conformations that are not necessarily all-trans.