Distribution Of Torsion Angles Research Articles

Change in backbone torsion angle distribution on protein folding

Understanding protein folding requires the determination of the configurational space accessible to the protein at different stages in folding. Here, computer simulation analysis of small angle neutron scattering results is used to probe the change in the distribution of configurations on strong denaturation of a globular protein, phosphoglycerate kinase, in 4 M guanidine hydrochloride solution. To do this atomic-detail ensembles of the unfolded protein chain are modeled and their scattering profiles compared with the experiment. The local conformational statistics are found to strongly influence the experimental intensity at scattering vectors between 0.05 and 0.3 A(-1). Denaturation leads to a reduction in the protein atom-pair distance distribution function over the approximately 3-15 A region that is associated with a quantifiable shift in the backbone torsional angle (phi, psi) distribution toward the beta region of the Ramachandran plot.

Modeling donor/acceptor interactions: Combined roles of theory and computation

An extended superexchange model for electron transfer (ET) matrix elements (HDA) has been formulated as a superposition of McConnell-type pathways and implementated by combined use of configuration interaction wave functions (obtained using the INDO/s model of Zerner and co-workers) and the generalized Mulliken–Hush formulation of charge-localized diabatic states. Applications are made for et (and hole transfer) in several donor/bridge/acceptor radical anion (and cation) systems, (DBA)±, allowing detailed comparison with experimental HDA estimates. For the case of oligo phenylene ethynylene (OPE) bridges, the role of π and σ electronic manifolds for different distributions of phenylene torsion angles is analyzed in detail. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 255–263, 2000

Collapse of diblock copolymer in poor solvent. Molecular dynamics study

AbstractThe modification of unsaturated polyesters (UPE) by poly (ethylene glycol) (PEG) end groups [1] and the computer simulation of the collapse of a single molecule of a diblock copolymer AB consisting of PEG (A) and UPE (B) blocks [2] were reported recently by us. In the present paper the static and dynamic characteristics of the final collapsed structure were investigated by a molecular dynamics simulation. The structure and the local dynamic of collapsed homopolymers (AA and BB) were studied also. The initial conformations in all cases were taken near completely extended ones. The final structures of the diblocks are similar to the structure of a core (UPE) and shell (PEG) model. The differences in torsion angle distributions between diblock and homopolymer are maximal for the CCOC dihedral angles (both in UPE and PEG blocks). The orientational order of the COC vectors (‘chords’ along backbone of polymer chain) inside both blocks is larger in the diblock than in the homopolymer. Local orientational mobility of the COC vector and the translational mobility of the monomers is larger in the diblock than in the homopolymers for both blocks.

Side-chain conformations in an unfolded protein: χ1 distributions in denatured hen lysozyme determined by heteronuclear 13C, 15N NMR spectroscopy

Using a 13C and 15N-labelled sample, multi-dimensional heteronuclear NMR techniques have been carried out to characterise hen lysozyme denatured in 8 M urea at pH 2.0. The measurement of 3J (C′,Cγ) and 3J (N,Cγ) coupling constants has enabled side-chain χ1 torsion angle populations to be probed in the denatured polypeptide chain. Analysis of the coupling constant data has allowed the relative populations of the three staggered rotamers about χ1 to be defined for 51 residues. The amino acids can broadly be divided into five classes that show differing side-chain conformational preferences in the denatured state. These range from a strong preference for the −60 ° χ1 rotamer for methionine and leucine (74–79 % population) to a favouring of the +60 ° χ1 rotamer for threonine (67 % population). The differences in behaviour reflect the steric and electrostatic characteristics of the side-chains concerned. A close agreement is seen between the χ1 populations calculated from the experimental coupling constant data and predictions from the statistical model for a random coil that uses the χ1 torsion angle distributions in a data base of native protein structures. Short-range interactions therefore dominate in determining the local conformational properties of side-chains in a denatured protein. Deviations are, however, observed for many of the aromatic residues involved in hydrophobic clusters within the denatured protein. For these residues the effects of additional non-local interactions in the clusters presumably play a major role in determining the χ1 preferences.

Conformational behaviour of bridging diphenylphosphido ligands.

Data retrieved from the Cambridge Structural Database for crystal structures containing (µ-diphenylphosphido) metal complexes, [M(2){µ-PPh(2)}] (where M is a d-block element), have been analysed to evaluate the conformational behaviour of these species. The observed distribution of torsion angles about the P-C bonds has been compared with the potential energy surface (PES) for phenyl rotations in a representative species [(AuBr)(2){µ-PPh(2)}](-) computed using the universal force field. Good agreement was obtained between the low-energy (<8 kJ mol(-1) above the global minimum) regions of the PES and the occupied regions of the two-dimensional P-Ph rotor conformation space. Phenyl ring rotations occur by coupled, geared disrotatory and uncoupled conrotatory motions of the phenyl groups in this and other classes of PPh(2) rotors.

Modeling of continuous random networks: a case study for vitreous GeO 2. II. Topological analysis and refinement

In this paper we present a new method to compare the topological structure of two continuous random network (CRN) models in a quantitative manner. The comparison serves to assess the sampling properties of the molecular modeling program TUMBLEWEED. This program generates spherical CRN clusters and has been introduced in paper I of this series. The structural diversity of the models constructed with this program is found to be satisfactory. Further, the models are very different from the α-cristobalite and α-quartz structures of GeO 2. In addition, we investigate three different techniques for the refinement of the clusters presented in paper I: the conjugate gradient (CG) method, the Monte Carlo (MC) method, and the Reverse Monte Carlo (RMC) method. The former two procedures minimize the potential energy, V, whereas the latter minimizes the deviation, R χ , of the model neutron total correlation function, T( r), from corresponding experimental data. It is found that neither technique gives satisfactory results by itself, since the minimization of R χ leads to an increase of V (including the violation of geometric constraints) and vice versa. By combining the MC and RMC methods, i.e. by simultaneous minimization of V and R χ , we obtain models with realistic geometric properties and an improved fit to the experimental data ( R χ =0.018±0.003 in the range 0–1 nm). This further supports the validity of the CRN approach to the structure of glassy GeO 2. New models with a non-uniform torsion angle distribution have been constructed. It turns out that such models cannot be excluded as possible structures (final R χ =0.020±0.006).

A Molecular Dynamics Study of the First Five Generations of Poly(Propylene Imine) Dendrimers Modified with N-tBoc-L-Phenylalanine

New insights into dendritic boxes: various structural properties for the first five generations of a modified poly(propylene imine) dendrimer are examined. The simulations indicate that cavities, which are partly filled with terminal groups, are present so that guests can be incorporated. It is hypothesised that the low chirality (experimentally observed) could be explained by increasing conformational disorder in the higher generations (the φφ/ψ torsional angle distribution analysis for the fifth generation is shown right).

Characterisation of side-chain conformational preferences in a biologically active but unfolded protein.

A combination of experimental NMR 3J alpha beta coupling constant measurements and theoretical predictions from a statistical model for a random coil have been used to characterise the conformations of amino acid side-chains in an unfolded fibronectin binding protein. The statistical model uses the distribution of torsion angles in a data base of native folded protein structures to provide a description of the torsion angle populations of each residue in a random coil. For all but three of the residues studied a close agreement is observed between the experimental 3J alpha beta data and the model predictions (correlation coefficient 0.90; RMSD 0.70 Hz). In these cases the populations about the chi 1 torsion angles in the conformational ensemble defining the fibronectin binding protein are well described by those present in the protein data base. For Phe 69, Asp 92 and Asp 105 however significant deviations are observed between the predictions and experimental data. Each of these side-chains is found to be involved in persistent non-random structural features arising from clustering of hydrophobic groups or interactions between charged side-chains. The analysis demonstrates the detailed insight that can be provided into conformationally disordered states by combining experimental and theoretical approaches.

Solid-state [formula omitted] NMR investigations of the glycosidic linkage in α-α′ trehalose

The sugar trehalose is known to play a central role in the desiccation tolerance of many organisms. Essential to trehalose's role are its glass forming abilities and ability to directly interact with lipid molecules. Detailed information on the structure and dynamics of glassy trehalose and its interactions with lipids, however, have been elusive. We have used solid-state NMR and ab initio quantum mechanical methods (Gaussian 94) in order to characterize the possible molecular conformations of trehalose. Using a simplified structure (2-(tetrahydropyran-2-yloxy) tetrahydropyran) as a model we have calculated the energy and 13 C magnetic shielding parameters as a function of the two glycosidic torsion angles. Combining ab initio derived maps and using the 13 C lineshape as constraints we were able to construct the torsion angle distribution map for α-α′ trehalose. We believe measurements of 13 C isotropic chemical shift and other solid-state NMR tensor parameter distributions in combination with ab initio methods can prove useful in identifying sources of structural disorder in glassy trehalose. By monitoring these structural distributions new information about the membrane surface associative properties of trehalose and other sugars should be accessible.

Side-chains in native and random coil protein conformations. Analysis of NMR coupling constants and χ1 torsion angle preferences

The behaviour of amino acid side-chains in proteins in solution has been characterised by analysing NMR 3JHαHβ coupling constants and crystallographic χ1 torsion angles. Side-chains both in the core of native folded proteins and in situations where there is an absence of close packing including the random coil state have been considered. An analysis of experimental 3JHαHβ coupling constant data for ten proteins shows that in the core of native proteins a very close similarity is observed between the χ1 conformations adopted in solution and in crystals. There is clear evidence, however, for significant motional averaging about the χ1 torsion angles in solution. Using a model of a Gaussian distribution about the average torsion angles the extent of these fluctuations has been quantified; the standard deviation for the motion is 26°, the fluctuations about χ1 in the protein core being similar in size to those found for main-chain φ torsion angles in solution. From the distribution of χ1 torsion angles in a data base of protein crystal structures, torsion angle populations and coupling constants have been predicted for a random coil polypeptide. Significant variations in the χ1 distributions for different amino acids give differences in the predicted coupling constants; for 3JHαHβ, for example, values of 5.1 and 5.7 Hz are predicted for serine compared with 4.9 and 9.9 Hz for leucine. Experimental data for short unstructured peptides show an excellent agreement with the predictions, indicating that the overall χ1 distributions in protein crystals reflect the local preferences of the amino acids. Predictions from the protein data base therefore provide an important framework for interpreting experimental data for non-native protein conformations and for residues on the surface of folded proteins.

A laser speckle sensor to measure the distribution of static torsion angles of twisted targets

A novel method for measuring the distribution of static torsion angles of twisted targets is presented. The method is based on Fourier transforming the scattered field in the direction perpendicular to the twist axis, while performing an imaging operation in the direction parallel to the axis. The Fourier transform serves to map the angular distribution of the scattered light field at the target into a linear displacement on a two-dimensional array image sensor placed in the Fourier plane. Measuring this displacement facilitates the determination of the angular displacement of the target. A cylindrical lens serves to image the closely spaced lateral positions of the target along the twist axis onto corresponding lines of the two dimensional image sensor. Thus, every single line of the image sensor measures the torsion angle of the corresponding surface position along the twist axis of the target. Experimentally, we measure the distribution of torsion angles in both uniform and non-uniform deformation zones. It is demonstrated both theoretically and experimentally that the measurements are insensitive to object shape and target distance if the image sensor is placed in the Fourier plane. A straightforward procedure to position the image sensor in the Fourier plane is presented. Furthermore, any transverse movement of the target will give rise to partial speckle decorrelation, but it will not affect the angular measurement. The method is insensitive to any wavelength change of the illuminating light source. No special surface treatment is required for surfaces giving rise to fully developed speckle.

Objectively judging the quality of a protein structure from a Ramachandran plot.

Statistical methods that compare observed and expected distributions of experimental observables provide powerful tools for the quality control of protein structures. The distribution of backbone dihedral angles ('Ramachandran plot') has often been used for such quality control, but without a firm statistical foundation. A new and-simple method is presented for judging the quality of a protein structure based on the distribution of backbone dihedral angles. Inputs to the method are 60 torsion angle distributions extracted from protein structures solved at high resolution; one for each combination of residue type and tri-state secondary structure. Output for a protein is a Ramachandran Z-score, expressing the quality of the Ramachandran plot relative to current state-of-the-art structures.

PM3 and AM1 Study on �-N-acetyl-muramic Acid and 3 Murein Related Derivatives

The energetically favoured conformations of β-N-acetyl-Muramic acid, its C6-O-acetylated form, the methylamide and the methyl-glycoside have been investigated using the semiempirical PM3 and AM1 methods. All these compounds are either components or fragmentary structures of the murein network. The atomic coordinates of the starting set of the β-N-acetyl-Muramic acid molecule have been obtained by a PM3 minimization of one saccharide molecule cut out from the murein single strand model proposed by Barnickel at al. [1]. The sidegroups of the derivatives have been introduced by a molecular editor. These conformations served as starting points in conformational space for a grid search by scanning all sidechain torsional angles for non-hydrogen atoms with exception of the N-acetyl group which was held in cisoid position (i.e. N2-H bond is parallel to C1-H and C3-H bond) and only minimized. The PM3 method with an additional amide correction potential and the AM1 method were used. The torsional angle distributions of the lactyl sidechain (free acid and methylamide), the C6-O-acetylated sidechain and the C1-methoxy sidechain have been investigated, showing distinct energetically favoured torsional angle regions. The results are compared to earlier studies on β-N-acetyl-Muramic acid by J.S. Yadav et al. [2,3] who were using the MNDO and PCILO methods and by P.N.S. Yadav et al. [4] who were using the empirical MM2 force-field.

Analysis of Main Chain Torsion Angles in Proteins: Prediction of NMR Coupling Constants for Native and Random Coil Conformations

Using a data base of 85 high resolution protein crystal structures the distributions of main chain torsion angles, both in secondary structure and in coil regions where no secondary structure is present, have been analysed. These torsion angle distributions have been used to predict NMR homonuclear and heteronuclear coupling constants for residues in secondary structure using known Karplus relationships. For α helices, 3 10helices and β strands mean predicted 3 J HNαcoupling constants are 4.8, 5.6 and 8.5 Hz, respectively. These values differ significantly from those expected for the ideal 7φ angles (3.9, 3.0 and 8.9 Hz; φ=−57 °, −49 °, −139 ° for α and 3 10helices and β strands (antiparallel), respectively) in regular secondary structure, but agree well with available experimental NMR data for nine proteins. The crystallographic data set has also been used to provide a basis for interpreting coupling constants measured for peptides and denatured proteins. Using a model for a random coil, in which all residues adopt distributions of φ, ψ angles equivalent to those seen for residues in the coil regions of native folded proteins, predicted 3 J HNαvalues for different residue types have been found to range from 5.9 Hz and 6.1 Hz for glycine and alanine, respectively, to 7.7 Hz for valine. A good correlation has been found between the predicted 3 J HNαcoupling constants for this model and experimental values for a set of peptides that other evidence suggest are highly unstructured. For other peptides, however, deviations from the predictions of the model are clear and provide evidence for additional interactions within otherwise disordered states. The values of homonuclear and heteronuclear coupling constants derived from the protein data base listed here therefore provide a basis not only for analysing the secondary structure of native proteins in solution but for assessing and interpreting the extent of structure present in peptides and non-native states of proteins.

Molecular dynamics simulation of the crystalline phase of poly(ethylene oxide)-sodium iodide, PEO 3NaI.

The polymer-polymer interaction potential used in an earlier reported MD simulation of crystalline PEO [Neyertz, Brown and Thomas, J. Chem. Phys., 101, 10064 (1994)] is here transferred to the crystalline phase of poly(ethylene oxide)-sodium iodide, PEO 3NaI. An appropriate set of ion-ion and ion-polymer interactions are also introduced. Force-field and other computational parameters are optimized to reproduce satisfactorily the behaviour of crystalline PEO 3NaI. From the MD simulations performed at 300 K, results are presented for the pressure tensor, mean-square displacements, distributions of torsion angles and radial distribution functions. These are compared with the X-ray determined PEO 3NaI and pure PEO structures.

Effect of cosolvent on a tripeptide solution using molecular dynamics simulations

We have performed molecular dynamics simulations on tricomponent solutions containing tripeptide, cosolvent and water molecules to investigate the structural and energetic effects of cosolvents on peptide and water molecules at 300 K. We use glycerol or urea molecules as cosolvents and Gly-Ala-Phe (GAF) as the tripeptide in each simulation. The concentration of cosolvent is adjusted to about 6–7 vol% of water. We analyze the structural and dynamic change of the tripeptide by the torsional angle distribution and the root-mean-square (r.m.s.) fluctuation. The interactions between all constituent molecules are analyzed by their H-bonding characteristics. We examine the water structure through H-bonds, the distribution of energies and H-bonded circular networks, rings. Cosolvent-induced conformational changes occur in the Ala residue of the tripeptide in urea solution. The Ala residue interacts with urea molecules substituted for water molecules through H-bonds. The water structure around the peptide is slightly more ordered in glycerol solution where glycerol is excluded in the vicinity of the peptide.

The trifluoroacetato (CF3COO–) and trifluoroacetate (CF3COO–) groups, their conformation from a database survey of crystal structures and ab initio MO calculations

Data for structures involving either of these groups have been drawn from the Cambridge Structural Database and divided into bidentate and monodentate categories. Statistical distributions of bond distances, selected bond and torsion angles from 414 groups contained in 194 structures yield the following mean values (with e.s.d.'s) : C-F = 1.29 (6), C-C = 1.53 (4), C-O (bidentate)= 1.24 (5), C-O- (monodentate) = 1.25 (4), C=O (monodentate)= 1.21(4) A. Angles in the CF group vary widely from the expected threefold symmetry (e.s.d. of distribution 8.8°). Torsion angles F-C-C-O for the bidentate groups range fairly evenly over all possible values, suggesting free internal rotation. Among monodentate groups all values of the torsional angles are possible but with a marked preference for a C-F to eclipse the carbonyl C=O bond. These observations show good agreement with the results of ab initio calculations using GAUSSIAN90. The calculated barrier to rotation for the bidentate (ion) form of the group is only 310 Jmol- 1 and for the monodentate form (as in the acid) 2.55 kJmol- 1 .

Even-odd effects in liquid crystal dimers with flexible spacers: a test of the rotational isomeric state approximation?

In this work we analyse the consequences of relaxing the rotational isomeric state (RIS) approximation in predicting the transitional properties of nematogenic systems formed by two mesogenic moieties linked by a flexible spacer, as in the homologous series of α,ω-bis(4′-cyanobiphenyl-4-yl)alkanes and α,ω-bis(4′-cyanobiphenyl-4-yloxy)alkanes, generically referred to as CB dimers. Comparison is made therefore between predictions of the nematic-isotropic transition temperatures, entropy changes, and order parameters obtained from the RIS model, and those by taking into account the full distribution of torsional angles. The continuous model predicts a damping of the even-odd effects for long chain systems, with entropy changes and order parameters at the nematic-isotropic transition tending to those of the corresponding monomers.

Molecular Dynamics Simulation of Atactic Polystyrene. 3. Short Range Order

A molecular dynamics simulation of bulk atactic polystyrene was performed, and the result was analyzed in detail to evaluate the intramolecular and intermolecular short range orders present. In this work the analysis was performed only on the results obtained from the united atom model, since, as was shown in the previous two publications, it gives much better agreement with experiment than the all atom model. Most of the study was performed with a system containing a single 80-monomer molecule, but some study was also made with a system containing two 40-monomer molecules. The short range order was examined by evaluating the radial distribution functions and orientational order parameters of pairs of aliphatic backbone segments and of phenyl group centers. In the case of intramolecular phenyl pairs, these quantities were evaluated individually according to the monomeric distance along the chain by which the two phenyls are separated. The conformation of the molecule was examined by evaluating the population distribution of backbone bond torsional angles in meso and racemic diads. The result resembles the conformational energy maps previously prepared by others, but some differences were also noted. The most prominent feature in the intermolecular correlation is the strong tendency for the phenyl groups to have a separation distance of about 6. A detailed analysis was given to define the relative orientation that the pair of phenyls adopt at this separation. Intermolecular pairs of backbone segments were found to be oriented mostly randomly at separation distances larger than 6 A

Conformational analysis of highly extended poly(ethylene terephthalate) chains by Monte Carlo calculations

AbstractThe conformational disorder compatible with the highly extended chains found in mesomorphic poly(ethylene terephthalate) has been studied by Monte Carlo calculations on model oligomers confined inside cylindrical tubes. The distribution of torsional angles for such extended chains is characterized by OCCO bonds being always in the trans domain, while the COCC bonds show an approximately similar probability of being found in trans and gauche states, the probability maxima being centered at 90° and −90° in the latter cases. At variance with the torsional angles of the OCCO and the ester bonds, always very close to 180°, the distributions for all other torsional angles show flat and broad probability maxima, indicating the possibility of substantial deviations from the average value inside each domain. This is also true for the fictitious OC˙˙˙CO bonds across the phenylene rings, for which a nearly trans geometry is preferred in extended conformations.