Conformational Angles Research Articles

Protein structure refinement: Streptomyces griseus serine protease A at 1.8 Å resolution

The crystal structure of the bacterial serine protease from Streptomyces griseus (SGPA) has been refined at 1.8 Å resolution by a restrained parameter least-squares procedure ( Konnert, 1976) to a conventional R factor of 0.139 for 12662 statistically significant reflections [ I > 3 σ( I)]. The number of variable parameters in the final model was 5912 which included positional and individual thermal parameters of the enzyme, and positions, B factors and occupancies of 175 solvent molecules. The algorithm used for this refinement allows for the simultaneous restraint on bond distances and distances related to interbond angles, the coplanarity of atoms in planar groups, the conservation of chirality of asymmetric centres, non-bonded contact distances, conformational torsional angles and individual isotropic temperature factors. The refined structure of SGPA differs from ideal bond lengths by an overall root-mean-square deviation of 0.02 Å; the corresponding value for angle distances is 0.038 Å. Comparison of the phase angles for the shell of data, 8.0 to 2.8 Å, between the multiple isomorphous replacement phases (Brayer et al., 1978 a) and the refined phases, indicates an overall difference (r.m.s.) of 56.6 °. The average conformational angle of the peptide bond (ω) is 179.7 ° (root-mean-square deviation ± 2.5 °) for the 180 peptide bonds of SGPA. Of the 175 solvent molecules included during the course of the refinement, 22 with occupancies ranging from 1.00 to 0.38 are located in the active site and the substrate binding region. It was not until these water molecules were included in the refinement process that the active Ser195 adopted its final conformation ( χ 1 = −77 °). The resulting distance from O γ of Ser195 to N ε 2 of His57 is 3.1 Å, which, when taken with the observed distortion from linearity (50 °), indicates a rather weak interaction.

An incipient 3(10) helix in Piv-Pro-Pro-Ala-NHMe as a model for peptide folding.

The molecular mechanism of helix nucleation in peptides and proteins is not yet understood and the question of whether sharp turns in the polypeptide backbone serve as nuclei for protein folding has evoked controversy. A recent study of the conformation of a tetrapeptide containing the stereochemically constrained residue alpha-aminoisobutyric acid, both in solution and the solid state, yielded a structure consisting of two consecutive beta-turns, leading to an incipient 3(10) helical conformation. :This led us to speculate that specific tri- and tetrapeptide sequences may indeed provide a helical twist to the amino-terminal segment of helical regions in proteins and provide a nucleation site for further propagation. The transformation from a 3(10) helical structure to an alpha-helix should be facile and requires only small changes in the phi and psi conformational angles and a rearrangement of the hydrogen bonding pattern. If such a mechanism is involved then it should be possible to isolate an incipient 3(10) helical conformation in a tripeptide amide or tetrapeptide sequence, based purely on the driving force derived from short-range interactions. We have synthesised and studied the model peptide pivaloyl-Pro-Pro-Ala-NHMe (compound I) and provide here spectroscopic evidence for a 3(10) helical conformation in compound I.

Copper(II)-Nucleic acid interactions—A conformational study

The effect of copper complexation upon the conformational angles in mononucleotides and dinucleotides was studied using classical potential energy expressions. The geometrical parameters were taken from crystallographic reports on the base-metal complexes. It was found that the preferred conformations of the complexes were quite different from the preferred conformations of the corresponding pure nucleotides. Notable among the disallowed conformations in case of Cu(II)-dinucleotide complexes were the regions corresponding to RRNA's, RNA's and the A, B and C forms of DNA. It is proposed that the energetics of a single strand is more important than inter-strand interactions in promoting copper-induced denaturation of DNA.

The chain configurational properties of novolak p‐cresol–formaldehyde resins

AbstractRotational isomeric state chain configurational analysis has been applied to the p‐cresol–form‐aldehyde chain structure. Steric interference allows the chain to be considered by using a twofold potential energy barrier. The bond rotational angles and conformational energies were set empirically to fit existing experimental dipole moment data, and the conformational angles were ±45° with a 132 cal/mole energy barrrier separating the g±g± from the g±g± rotational states. The data predict the existence of a cyclic tetramer in support of other researchers' experimental work. The limiting dipole moment ratio and characteristic ratio were computed to be 5.87 and 21.23, respectively. Support for this structure will have to wait for experimental data from higher‐molecular‐weight materials.

Interactions of molecules with nucleic acids. I. An algorithm to generate nucleic acid structures with an application to the B‐DNA structure and a counterclockwise helix

AbstractAn algorithm is developed that enables the routine determination of backbone conformations of nucleic acids. All atomic positions including hydrogen are specified in accord with experimental bond lengths and angles but with theoretically determined conformational angles. For two Watson‐Crick base pairs at a separation of 3.38 Å, and perpendicular to a common helical axis, minimum energy configurations are found for all 10 combinations at helical angles of α ∼ 36°–38°, corresponding to the B‐DNA structure with C(2′)‐endo sugar puckers. Backbone configurations exist only within the range 35.5° ⩽ α ⩽ 42°, which suggests the origin of the 10‐fold helix. Calculated stacking energies for the B‐DNA structure increases for each of the clustered groups of base pairs: G·C with G·C, G·C with A·T, and A·T with A·T, and they are in approximate agreement with experimental observations. The counter‐clockwise helix is examined, and physically meaningful structures are found only when the helical axes of successive base pairs are disjointed.

Crystal structure and conformation of the cyclic hexapeptide cyclo-(Gly-L-Pro-D-Ala)2

The crystal structure and conformation of cyclo-(Gly-L-Pro-D-Ala)/sub 2/, C/sub 20/H/sub 30/N/sub 6/O/sub 6/, has been determined by single-crystal x-ray diffraction analysis. The crystals have the symmetry of the orthorhombic space group P2/sub l/2/sub l/2/sub l/ with a = 9.389 (6), b = 10.379 (8), and c = 22.006 (16) A. The structure was solved by direct methods and refined to a final R of 0.055 on 1575 unique reflections. The hexapeptide shows significant deviation from internal twofold symmetry. This asymmetric conformer apparently optimized one single 4 ..-->.. l transannular hydrogen bond at the expense of other possible interactions. Conformation angles are compared with those obtained by CD and NMR techniques, and bond distances are discussed. This hexapeptide contains two type II ..beta.. turns. All of the peptide bonds are in the transconformation and the C/sub ..gamma../ atom in one of the proline rings is disordered. 5 tables, 3 figures.

AN ANALYSIS OF SIDE‐CHAIN CONFORMATION IN PROTEINS*

The crystal structures of a number of globular proteins are currently available. An analysis of the distribution of side-chains among different allowed conformations in these proteins has been carried out. The observed conformations of individual residues are discussed on the basis of well-known stereochemical criteria. The population distribution of side-chains in different allowed regions in conformational space can be explained largely on the basis of simple steric considerations. In addition to examining the conformational behaviour of individual residues, some population distributions of conformational angles of general interest involving groups of residues have also been analyzed.

Conformational features of oligocellulose acetates in the solid state and their implications for the structures of cellulose triacetate

AbstractThe crystal data on cellobiose octaacetate and cellotriose undecaacetate are compared in an effort to analyze what information available from crystal structures of oligosaccharides can be used to arrive at the three‐dimensional structure of the related polysaccharides. This comparison points out the remarkable behavior of the reducing end of both molecules. The glycosidic torsion angles (ϕ,ψ) around the reducing and the middle residues in the disaccharide and in the trisaccharide have values around 45° and 14°, while the conformational angles about the nonreducing residues in cellotriose acetate are 24° and −20°. The conformations of the primary acetate groups on the two nonreducing residues are similar, but they differ from those observed for the acetate groups belonging to the reducing residues. The possibility of a 21 symmetry axis between contiguous triacetate residues within the oligosaccharide is examined, along with a comparison of the molecular packing found in the oligomer structures. Conformational energy calculations have been performed on two dimeric entities derived from cellotriose acetate. The isoenergy maps show the drastic influence of the relative orientations of the primary acetate groups. It is proposed that the nonreducing dimer, as found in the crystal structure of cellotriose acetate, most nearly expresses the “polymer averaged” interactions for contiguous residues in cellulose triacetate.

Crystal structure of yeast phenylalanine transfer RNA: II. Structural features and functional implications

The structural features of yeast phenylalanine transfer RNA are analyzed and documented in detail, based on atomic co-ordinates obtained from an extensive crystallographic refinement of the crystal structure of the molecule at 2.7 Å resolution (see preceding paper). We describe here: the relative orientation and the helicity of the base-paired stems; more definitive assignments of tertiary hydrogen bonds involving bases, riboses and phosphates; binding sites for magnesium hydrates, spermine and water; iriter-molecular contacts and base-stacking; flexibility of the molecule; conformational analysis of nucleotides in the structure. Among the more noteworthy features are a considerable irregularity in the helicity of the base-paired stems, a greater flexibility in the anticodon and aminoacyl acceptor arms, and a “coupling” among several conformational angles. The functional implications of these structural features are also discussed.

The conformational wheel—a circular plot for correlating the primary and secondary structure of a linear polymer with the conformational angles of its individual residues

The conformational wheel—a circular plot for correlating the primary and secondary structure of a linear polymer with the conformational angles of its individual residues

Conformational structure of glycerol trivalerate and its relation to phospholipids: Studies by NMR and potential energy calculations

The structure of a model lipid (glycerol trivalerate, GTV) has been investigated by 1H and 13C NMR, and energy calculations based on classical potential functions (CPF). The structure of glycerol-ester pivot in GTV is characterized by a dynamic equilibrium between two dominant conformations. One of the two conformations (SA) is similar to the reported crystal structure of triglycerides β-triaurin and β-tricaprin and has the following conformational angles: θ 1 = 52°, θ 3 = 46°, α 1 = 208°, β 1 = 156° and γ 1 = 186° . The other conformer (SB) is similar to the reported crystal structure of β and γ chains in 1,2- dilauroyl-D,L- phosphatidylethanolamine and has the conformational angles: θ 1 = 287°, θ 3 = 155°, α 1 = 195°, β 1 = 85° and γ 1 = 194° . The ester groups acquire a rigid planar conformation ( α 2, β 2, γ 2 = 180° ), while the potential energy curves for rotation around the chemical bonds OCOCCC( α 3, β 3 and γ 3 ) indicate a high degree of flexibility. The hydrocarbon chains show a distribution of the gauche and trans conformations around CCCC bonds with a preference for the trans arrangement by almost 0.8 kcal/mol. The conformational picture of the hydrocarbon chains and glycerol moiety in GTV is very similar to that in phospholipids. These results indicate caution in using the reported crystal structure of 1,2- dilauroyl-D,L- phosphatidylethanolamine as the only model for the organization of lipid molecules in biological membranes.

Chain‐configurational properties of novolac phenol–formaldehyde resins

AbstractRotational isomeric‐state chain‐configurational calculations have been applied to the novolac phenol–formaldehyde structure. Steric interference allows the chain to be considered with a twofold potential energy barrier model. Computations that fit the observed dipole‐moment data over a range of molecular weights indicate that the conformational angle is near ±80°, with the g±g= states on the average being 155 cal/mole below the g±g± states. The limiting dipole‐moment ratio is computed to be 1.47, compared to the experimental value of 1.48. A negative temperature coefficient agrees in sign with the experimental value, and the characteristic ratio of the end‐to‐end molecular dimensions is calculated to be 3.27, as compared to the experimental value of 4.76.

Molecular and crystal structure of cellulose triacetate I: A parallel chain structure

The crystal structure of cellulose triacetate I (CTA I), obtained by heterogeneous acetylation of ramie cellulose I, has been determined by a combined X-ray diffraction and stereochemical model analysis. The structure packs in a two chain, orthogonal unit cell with dimensions a = 23.63 A ̊ , b = 6.27 A ̊ , c ( fibre repeat) = 10.43 A ̊ , but with P2 1 symmetry. The two chains pack with parallel polarity and the two-fold screw axes coincide with the chain axes. In these respects, the structure of CTA I is similar to that of cellulose I. The conformations of the chain and of the glucose residue are similar to the conformation of the crystalline cellotriose undecaacetate, in that the ф, ψ angles, the 0(6) rotational positions, acetate positions and bond and conformation angles are comparable in both structures. The reliability of the structure determination of CTA I is indicated by the crystallographic R = 0.242.

The atomic structure of crystalline porcine pancreatic elastase at 2.5 Å resolution: Comparisons with the structure of α-chymotrypsin

Three isomorphous heavy-atom derivatives have been used to calculate a 2.5 Å resolution electron density map of tosyl-elastase at pH 5.0, from which an accurate atomic model has been constructed. Atomic co-ordinates measured from this model have been refined using model building, real-space refinement and energy minimization programs. The three-dimensional conformation of the polypeptide chain is described in terms of conformational angles, hydrogen-bonding networks and the environment of different types of amino acid side-chain. Difference Fourier calculation of the high resolution structure of native elastase at pH 5.0 shows it to be virtually identical to that of the tosyl derivative, except near the tosyl group. The conformation of the catalytically important residues in native elastase is very similar to that of native α-chymotrypsin, except for the orientation of the active centre serine oxygen. The significance of important structural similarities and differences between these two enzymes is discussed. Elastase contains 25 internal water molecules which play an important role in stabilizing the active conformation of the enzyme. Many of these water molecules are in identical positions to those found in the interior of α-chymotrypsin

Helical structures of poly(D-L-peptides). A conformational energy analysis.

Conformational energy calculations are reported for a number of possible helical structures of poly(D-L-peptides): the alpha helix, two single-stranded piDL, and five double-stranded pipiDL helices. For a poly(D-alanine-L-alanine) sequence, the energies of the various helices are found to differ by less than 1 kcal/(mol residue). For some helices (especially the piDL ones) two structural variants are predicted. These variants, called "goniomers", are characterized by reversed sequences of conformational angles but have the same screw sense and similar helical parameters. A biological implication of these goniomers is suggested, and their usefulness as a critical test for energy calculations is considered.

Packing analysis of carbohydrates and polysaccharides. V. Crystal structures of two polymorphs of pachyman triacetate.

AbstractThe crystal structures of two polymorphic forms of pachyman triacetate, the fully acetylated derivative of a naturally occuring β‐(1 → 3)‐D‐glucan, were determined by a combination of stereochemical and x‐ray diffraction analysis. The two polymorphs could be obtained depending on the temperature and the degree of stretching of film specimens of the substance: polymorph I resulted from stretching 25–50% at 125°C and polymorph II resulted from further stretching to 300% at 215°C. Both polymorphs had previously been shown to have sixfold helical chain conformations, but of unequal pitch. Subsequent detailed structure refinement performed with bond lengths, bond angles, conformational angles, and helix‐packing parameters as refinement variables, and the simultaneous minimization of packing and conformational energy and the crystallographic R‐factor as refinement criteria, resulted in a complete determination of the two crystal structures. Pachyman triacetate I was found to be a right‐handed helix packing with antiparallel polarity and space group P212121 symmetry (unit‐cell parameters a = 11.0, b = 19.0, c (fiber repeat) = 22.38 Å). The acetate groups were nearly planar and the O(2) and O(4) acetates were oriented in such a fashion that the carbonyl double‐bond nearly eclipsed the corresponding C—H bond of the ring. The O(6) was in the tg position and its acetate was oriented in such a fashion that the bond sequence C(6)—O(6)—C(6C)—C(6M) was nearly trans‐planar, with the carbonyl double‐bond bisecting the tetrahedral angle formed by C(6) and its two hydrogens. The final R = 0.221. Pachyman triacetate II was similarly found to be a right‐handed helix, but packing as a 50:50 mixture of parallel and antiparallel polarities (unit‐cell parameters a = 11.49, b = 20.13, c (fiber repeat) = 18.6 Å). The acetate positions in pachyman triacetate II were substantially the same as in pachyman triacetate I. The final R for the 50:50 mixture was 0.234. Probable reasons for the change in packing polarities are discussed, as are the difficulties encountered in the structure refinement of acetate derivatives.

Organo group VB chemistry: Part VII. On the electric dipole moments of some substituted triarylphosphine derivatives R 3PY, with Y = free electron pair, O and S

The dipole moments of a series of quadruply-coordinated phosphorus derivatives of the general formula R 3PY where R = C 6H 5, 4-XC 6H 4, 3-XC 6H 4 (X = F, Cl) and Y = O, S, are reported. This consistent set of data is used to discuss the suitable values for the whole of group moments μ(C 6H 5-P), bond moments μ(X-C 6H 5), coordination bond moments μ(P → Y), valence angle β and conformation angles Φ.

The influence of molecular orientation on the vapor pressure isotope effect in liquid methanes

The medium cluster model has been used to study the influence of mutual molecular orientation in the liquid state on the vapor pressure isotope effect (vpie) of 13C, 14C, D, and T-substituted methanes. Both the first quantum correction to the classical translational and rotational effect and the isotopic differences in zero-point energy shifts on condensation are cyclic functions of conformational angles. The cyclic behavior for a 3-cluster of spherical top methanes can be attributed, in light of the finite orthogonal polynomial approximation of the reduced partition function ratio, to the interaction of rotation with internal bending and stretching motions. The effects of changing molecular orientation on the predicted vpie decrease with increasing cluster size, until the variations become negligibly small compared to experimental uncertainties in isotopic vapor pressure ratio measurements.

Intramolecular changes during polymorphic transformations of amylose

A survey of small saccharide crystal structures indicates that there is substantial variability in the shape of the α-D-glucose residue and in the conformation angles at the glycosidic linkage. Both factors appear to be altered primarily by hydrogen bonding and crystal packing forces. For the purposes of building computer models of cyclodextrins and amyloses, the residues from different crystals may be characterized in terms of the virtual angles, O(1)-C(1)-C(4) and C(1)-C(4)-O(4). Computer models of six-, seven-, and eight-residue cyclodextrins require residues having different such angular values because of the role played by the parameter n (number of residues per cycle). In computer models of amyloses, a similar role is also played by the helical parameter h (rise per residue). It is therefore concluded that polymorphic transformations often involve alterations in monomeric geometry as well as rotations about valence bonds to the linkage oxygen atoms. Finally, it is proposed that the entire space of accessible conformations be represented on a grid of h vs. n with consideration given to the full range of residue geometries at each grid point.

Macromolecular marionettes

Computer graphics can provide useful tools for molecular biology because pictorial displays are the most efficient way for computers to communicate the details of a complex molecular structure to human beings. The development of suitable hardware has led to the establishment of a number of computer graphics installations devoted to the investigation of molecular structure. We describe here the Evans and Sutherland LDS-1 PDP-10 system of the Princeton University Computer Graphics Laboratory, and the program systems that we have developed for applications to the study of protein and nucleic acid structure and interaction. The hardware can generate displays of complicated three-dimensional line drawings. It allows interactive analysis and modification of a display by a human observer, as well as computational analysis of structural data by a powerful general-purpose digital computer, the PDP-10. We have developed programs for the study and analysis of proteins and nucleic acids of known structure, and for construction and experimentation with models of general polypeptides and polynucleotides. These model-building programs permit the generation of displays of polypeptides and polynucleotides of arbitrary sequence and conformation. It is possible to adjust all conformational angles interactively, or with the assistance of supportive software that can carry out a variety of structural manipulations, such as the folding of a selected region into a helical conformation. Although the purely computational problems encountered in this work are relatively straight-forward—a tribute to the power of the equipment—subtle problems arise in defining the role of a human being as a partner in the execution of an interactive program. Our attempts to achieve the most effective combination of human and computers depend on the recognition of the strengths and limitations of each, and of the efficiencies of the channels of communication between them.