Analysis of protein loop closure. Two types of hinges produce one motion in lactate dehydrogenase

As shown in previous crystallographic investigations, upon binding lactate and NAD, lactate dehydrogenase undergoes a large conformational change that results in a surface loop moving roughly 10 A to cover the active site. In addition, there are appreciable movements (approximately 2 A) of five helices and three other loops. We demonstrate by a new fitting procedure that the loop moves on two hinges separated by a relatively rigid type II turn. The first hinge has few steric constraints on it, and its motion can be well accounted for by large changes in two torsion angles, i.e. as in a classic hinge motion. In contrast, the second hinge, which is part of a helix connected to the end of the loop, has many more constraints on it and distributes its deformation over more torsion angles. This novel motion involves the helix stretching and splitting into alpha-helical and 3(10)-helical components and substantial side-chain repacking in the sense of "cogs hopping between grooves" at its interface with the end of a neighboring helix. The loop is stabilized by five transverse (across loop) hydrogen bonds. These are preserved, through the conformational change and through 17 lactate dehydrogenase sequences, more than the longitudinal hydrogen bonds down the sides of the loop. Through a network of contacts, many of them conserved hydrophobic residues, the motion of the loop is propagated outward to structures that have no direct contact with the ligands. These moving structures are on the surface of the protein, and the whole protein can be subdivided into concentric shells of increasing mobility.     

RNA loop structure prediction via bond scaling and relaxation

We have developed a method for predicting the structure of small RNA loops that can be used to augment already existing RNA modeling techniques. The method requires no input constraints on loop configuration other than end-to-end distance. Initial loop structures are generated by randomizing the torsion angles, beginning at one end of the polynucleotide chain and correlating each successive angle with the previous. The bond lengths of these structures are then scaled to fit within the known end constraints and the equilibrium bond lengths of the potential energy function are scaled accordingly. Through a series of rescaling and minimization steps the structures are allowed to relax to lower energy configurations with standard bond lengths and reduced van der Waals clashes. This algorithm has been tested on the variable loops of yeast tRNA-Asp and yeast tRNA-Phe, as well as the sarcin-ricin tetraloop and the anticodon loop of yeast tRNA-Phe. The results indicate good correlation between potential energy and the loop structure predictions that are closest to the variable loop crystal structures, but poorer correlation for the more isolated stem loops. The number of stacking interactions has proven to be a good objective measure of the best loop predictions. Selecting on the basis of energy and stacking, we obtain two structures with 0.65 and 0.75 Å all-atom rms deviations (RMSD) from the crystal structure for the tRNA-Asp variable loop. The best structure prediction for the tRNA-Phe variable loop has an all-atom RMSD of 2.2 Å and a backbone RMSD of 1.6 Å, with a single base responsible for most of the deviation. For the sarcin-ricin loop from 28S ribosomal RNA, the predicted structure's all-atom RMSD from the nmr structure is 1.0 Å. We obtain a 1.8 Å RMSD structure for the tRNA-Phe anticodon loop. © 1996 John Wiley & Sons, Inc.     

Polynucleotide folding in yeast tRNAPhe: elucidation of short-, medium-, and long-range interactions of sugar-phosphate-sugar backbone and base using a "blocked" nucleotide probe

It has recently been proposed that the repeating backbone nucleotide may be regarded as consisting of two blocks of equal magnitude representable by two virtual bonds. Implicit consideration of the nucleotide (ψ,ψ) and internucleotide (ω′,ω) geometry that generate variety in polynucleotide conformations, and of the constancy of the repeating structural moieties (P-C4′ and C4′-P) independent of the above rotations, has enabled us to utilize this scheme in the study of ordered structures such as di-, oligonucleotides and, most significantly, tRNA. The polynucleotide folding dictated by short-, intermediate-, and long-range interactions in the monoclinic and orthorhombic forms is described and compared through circular plots depicting the virtual bond torsions and distance plots constructed independently for backbone as well as bases. The torsions and the bond angles associated with the virtual bonds afford a clear distinction between ordered helical segments from loops and bends of tRNA. Lower virtual bond torsions (?60° to 60°) concomitant with higher values of virtual bond angles characterize various bend regions, while torsions around 160°–210° typify ordered helical strands. The distance plot elucidates the type of interaction associated with various sub-structures (helix–helix, helix–loop, and loop–loop) that form the constituents of different structural domains. Several other features such as the manifestation of the P₁₀ loop and the approximate twofold symmetry in the tRNA molecule are conspicuous on the distance plot.     

Efficient Search on Energy Minima for Structure Prediction of Nucleic Acid Motifs

Abstract

Structure prediction of non-canonical motifs such as mismatches, extra unmatched nucleotides or internal and hairpin loop structures in nucleic acids is of great importance for understanding the function and design of nucleic acid structures. Systematic conformational analysis of such motifs typically involves the generation of many possible combinations of backbone dihedral torsion angles for a given motif and subsequent energy minimization (EM) and evaluation. Such approach is limited due to the number of dihedral angle combinations that grows very rapidly with the size of the motif. Two conformational search approaches have been developed that allow both an effective crossing of barriers during con-formational searches and the computational demand grows much less with system size then search methods that explore all combinations of backbone dihedral torsion angles. In the first search protocol single torsion angles are flipped into favorable states using constraint EM and subsequent relaxation without constraints. The approach is repeated in an iterative manner along the backbone of the structural motif until no further energy improvement is obtained. In case of two test systems, a DNA-trinucleotide loop (sequence: GCA) and a RNA tetraloop (sequence: UUCG), the approach successfully identified low energy states close to experiment for two out of five start structures. In the second method randomly selected combinations of up to six backbone torsion angles are simultaneously flipped into preset ranges by a short constraint EM followed by unconstraint EM and acceptance according to a Metropolis acceptance criterion. This combined stochastic/EM search was even more effective than the single torsion flip approach and selected low energy states for the two test cases in between two and four cases out of five start structures.     

Conformational feasibility of a hairpin with two purines in the loop. 5'-d-GGTACIAGTACC-3'

Structural feasibility and conformational requirements for the sequence 5'-d-GGTACIAGTACC-3' to adopt a hairpin loop with I6 and A7 in the loop are studied. It is shown that a hairpin loop containing only two nucleotides can readily be formed without any unusual torsional angles. Stacking is continued on the 5'-side of the loop, with the I6 stacked upon C5. The base A7, on the 3'-side of the loop, can either be partially stacked with I6 or stick outside without stacking. Loop closure can be achieved for both syn and anti conformations of the glycosidic torsions for G8 while maintaining the normal Watson-Crick base pairing with the opposite C5. All torsional angles in the stem fall within the standard B-family of DNA helical structures. The phosphodiesters of the loop have trans,trans conformations. Loop formation might require the torsion about the C4'-C5' bond of G8 to be trans as opposed to the gauche+ observed in B-DNA. These results are discussed in relation to melting temperature studies [Howard et al. (1991) Biochemistry (preceding paper in this issue)] that suggest the formation of very stable hairpin structures for this sequence.     

Efficient search on energy minima for structure prediction of nucleic acid motifs

Structure prediction of non-canonical motifs such as mismatches, extra unmatched nucleotides or internal and hairpin loop structures in nucleic acids is of great importance for understanding the function and design of nucleic acid structures. Systematic conformational analysis of such motifs typically involves the generation of many possible combinations of backbone dihedral torsion angles for a given motif and subsequent energy minimization (EM) and evaluation. Such approach is limited due to the number of dihedral angle combinations that grows very rapidly with the size of the motif. Two conformational search approaches have been developed that allow both an effective crossing of barriers during conformational searches and the computational demand grows much less with system size then search methods that explore all combinations of backbone dihedral torsion angles. In the first search protocol single torsion angles are flipped into favorable states using constraint EM and subsequent relaxation without constraints. The approach is repeated in an iterative manner along the backbone of the structural motif until no further energy improvement is obtained. In case of two test systems, a DNA-trinucleotide loop (sequence: GCA) and a RNA tetraloop (sequence: UUCG), the approach successfully identified low energy states close to experiment for two out of five start structures. In the second method randomly selected combinations of up to six backbone torsion angles are simultaneously flipped into preset ranges by a short constraint EM followed by unconstraint EM and acceptance according to a Metropolis acceptance criterion. This combined stochastic/EM search was even more effective than the single torsion flip approach and selected low energy states for the two test cases in between two and four cases out of five start structures.     

Conformational Studies of Nucleic Acids: III. Empirical Multiple Correlation Functions for Nucleic Acid Torsion Angles

Abstract

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, α (03′-P-05′-C5′), δ (C5′-C4′-C3′-03′) and ε (C4′-C3′-03′-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, α, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.     

Conformational studies of nucleic acids: III. Empirical multiple correlation functions for nucleic acid torsion angles

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, alpha (O3'-P-O5'-C5'), delta (C5'-C4'-C3'-O3') and epsilon (C4'-C3'-O3'-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, alpha, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.     

Ab initio molecular orbital calculations on furanose sugars: a study with the 6-31G basis set

Ab initio molecular orbital calculations were performed on 2-deoxy-beta-D-glycero-tetrofuranose (1) using the 6-31G* basis set to evaluate the effect of ring conformation on the molecular parameters (bond lengths, angles, and torsions). Geometric optimizations were conducted on the planar and ten envelope conformers of 1, and these data were compared to those obtained from previous calculations using the STO-3G and 3-21G basis sets. Conformational energy profiles derived from 3-21G and 6-31G* data were found to be qualitatively comparable. The effect of furanose ring conformation on key bond lengths (e.g., C-H, C-O), bond angles (e.g., COC), and bond torsions (e.g., the exoanomeric C-1-O-1 torsion) was examined, and a qualitative agreement was observed between the 3-21G and 6-31G* analyses. The results indicate that, for semi-quantitative ab initio studies of intact carbohydrates, the 3-21G basis set is sufficient, and that the STO-3G basis set should not be employed unless crude structural approximations are desired. The observed concerted behavior of C-O bond lengths in the vicinity of the anomeric carbon of the aldofuranose ring has suggested a possible role of C-1-O-1 bond orientation in affecting the mechanism of glycoside bond hydrolysis.     

Analysis of phi and chi 1 torsion angles for hen lysozyme in solution from 1H NMR spin-spin coupling constants

Three-bond 3JHN alpha coupling constants have been determined for 106 residues and 3J alpha beta coupling constants have been measured for 57 residues of the 129-residue protein hen egg white lysozyme. These NMR data have been compared with torsion angles defined in the tetragonal and the triclinic crystal forms of the protein. For most residues the measured 3JHN alpha values were consistent with the phi torsion angles found in both crystal forms; the RMS difference between the coupling constants calculated by using the tetragonal crystal structure phi angles and the experimental 3JHN alpha values is 0.88 Hz. Thus there appears to be no significant averaging of the phi torsion angle either in the interior or at the surface of the protein. For 41 of the residues where 3J alpha beta coupling constants have been determined, the values are consistent with a single staggered conformation about the chi 1 torsion angle and there is complete agreement between the NMR data in solution and the torsion angles defined in the crystalline state. In contrast, for the other 16 residues where 3J alpha beta coupling constant values have been measured, the data indicate extensive motional averaging about the chi 1 torsion angle. These residues occur largely on the surface of the protein and examination of the crystal structures shows that many of these residues adopt a different conformation in the triclinic and tetragonal crystal forms and have high crystallographic temperature factors. It appears, however, that in solution conformational flexibility of the side chains of surface residues is significantly more pronounced than in individual crystal structures.     

Effects of phospholipid unsaturation on the bilayer nonpolar region: a molecular simulation study

Molecular dynamics simulations of two monounsaturated phosphatidylcholine (PC) bilayers made of 1-palmitoyl-2-oleoyl-PC (POPC; cis-unsaturated) and 1-palmitoyl-2-elaidoyl-PC (PEPC; trans-unsaturated) were carried out to investigate the effect of a double bond in the PC beta-chain and its conformation on the bilayer core. Four nanosecond trajectories were used for analyses. A fully saturated 1,2-dimyristoyl-PC (DMPC) bilayer was used as a reference system. In agreement with experimental data, this study shows that properties of the PEPC bilayer are more similar to those of the DMPC than to the POPC bilayer. The differences between POPC and PEPC bilayers may be attributed to the different ranges of angles covered by the torsion angles beta10 and beta12 of the single bonds next to the double bond in the oleoyl (O) and elaidoyl (E) chains. Broader distributions of beta10 and beta12 in the E chain than in the O chain make the E chain more flexible. In effect, the packing of chains in the PEPC bilayer is similar to that in the DMPC bilayer, whereas that in the POPC bilayer is looser than that in the DMPC bilayer. The effect of the cis-double bond on torsions at the beginning of the O chain (beta4 and beta5) is similar to that of cholesterol on these torsions in a myristoyl chain.     

Predictions of protein backbone bond distances and angles from first principles

A procedure is described, based on a spline-function representation of ab initio peptide conformational geometry maps, that allows one to predict backbone bond distances and angles of proteins as functions of the peptide ?(N-C^α)/Ψ(C^α-C′) torsions with an accuracy comparable to that of high-resolution protein crystallography. For example, for the more than 40 residues of crambin, the rms deviation between predicted and crystallographic values of N-C^α-C′ is 1.9° for the 1.5 Å resolution structure and 1.9° for the 0.83 Å resolution structure, compared with angle variations of < 10°. Accurate information on protein backbone geometries is important for establishing dictionaries of flexible geometry functions for use in empirical peptide and protein modeling. © 1995 John Wiley & Sons, Inc.     

Torsion and Antero-Posterior Bending in the In Vivo Human Tibia Loading Regimes during Walking and Running

Bending, in addition to compression, is recognized to be a common loading pattern in long bones in animals. However, due to the technical difficulty of measuring bone deformation in humans, our current understanding of bone loading patterns in humans is very limited. In the present study, we hypothesized that bending and torsion are important loading regimes in the human tibia. In vivo tibia segment deformation in humans was assessed during walking and running utilizing a novel optical approach. Results suggest that the proximal tibia primarily bends to the posterior (bending angle: 0.15°–1.30°) and medial aspect (bending angle: 0.38°–0.90°) and that it twists externally (torsion angle: 0.67°–1.66°) in relation to the distal tibia during the stance phase of overground walking at a speed between 2.5 and 6.1 km/h. Peak posterior bending and peak torsion occurred during the first and second half of stance phase, respectively. The peak-to-peak antero-posterior (AP) bending angles increased linearly with vertical ground reaction force and speed. Similarly, peak-to-peak torsion angles increased with the vertical free moment in four of the five test subjects and with the speed in three of the test subjects. There was no correlation between peak-to-peak medio-lateral (ML) bending angles and ground reaction force or speed. On the treadmill, peak-to-peak AP bending angles increased with walking and running speed, but peak-to-peak torsion angles and peak-to-peak ML bending angles remained constant during walking. Peak-to-peak AP bending angle during treadmill running was speed-dependent and larger than that observed during walking. In contrast, peak-to-peak tibia torsion angle was smaller during treadmill running than during walking. To conclude, bending and torsion of substantial magnitude were observed in the human tibia during walking and running. A systematic distribution of peak amplitude was found during the first and second parts of the stance phase.     

Geometry of the five-membered ring mathematical demonstration of the pseudorotation formulae

The geometrical relations between the 15 typical parameters (bond lengths and angles, torsion angles) of a five-membered ring are derived for any ring then for a regular one. It is demonstrated that for the case of the 20 symmetrical C ₂ and C _sconformations, only geometrical considerations are needed to obtain the pseudorotation formulae for the torsion angles. However, the puckering intensity as well as the bond angle values cannot be expressed from geometrical constraints alone but would require energetical considerations.     

TANGLE: two-level support vector regression approach for protein backbone torsion angle prediction from primary sequences

Protein backbone torsion angles (Phi) and (Psi) involve two rotation angles rotating around the C(α)-N bond (Phi) and the C(α)-C bond (Psi). Due to the planarity of the linked rigid peptide bonds, these two angles can essentially determine the backbone geometry of proteins. Accordingly, the accurate prediction of protein backbone torsion angle from sequence information can assist the prediction of protein structures. In this study, we develop a new approach called TANGLE (Torsion ANGLE predictor) to predict the protein backbone torsion angles from amino acid sequences. TANGLE uses a two-level support vector regression approach to perform real-value torsion angle prediction using a variety of features derived from amino acid sequences, including the evolutionary profiles in the form of position-specific scoring matrices, predicted secondary structure, solvent accessibility and natively disordered region as well as other global sequence features. When evaluated based on a large benchmark dataset of 1,526 non-homologous proteins, the mean absolute errors (MAEs) of the Phi and Psi angle prediction are 27.8° and 44.6°, respectively, which are 1% and 3% respectively lower than that using one of the state-of-the-art prediction tools ANGLOR. Moreover, the prediction of TANGLE is significantly better than a random predictor that was built on the amino acid-specific basis, with the p-value<1.46e-147 and 7.97e-150, respectively by the Wilcoxon signed rank test. As a complementary approach to the current torsion angle prediction algorithms, TANGLE should prove useful in predicting protein structural properties and assisting protein fold recognition by applying the predicted torsion angles as useful restraints. TANGLE is freely accessible at http://sunflower.kuicr.kyoto-u.ac.jp/~sjn/TANGLE/.     

Alternating torsions in a living '9 + 2' flagellum

Live spermatozoa of the Japanese quail were observed as they swam in highly viscous salines. Under these conditions, torsions of the flagellum were readily seen. The torsions had a characteristic magnitude (nominally 180 degrees) and pattern of incidence. As a cycle of bending propagated over it, each position on the flagellum experienced first a sinistral torsion and, later, a restoring dextral torsion. The two zones of torsion were each associated with bending; between them was a torsion-free zone that tended to be straight. The amount of interdoublet sliding needed to generate the torsions may be as little as 10 nm. These dynamic propagating torsions have been detected by following the angular displacements of individual (swollen) mitochondria lying adjacent to the axoneme. It is suggested that torque generation is a primary outcome when the unconstrained ''9 + 2'' axoneme is activated.     

Some fundamental aspects of building protein structures from fragment libraries

We have investigated some of the basic principles that influence generation of protein structures using a fragment-based, random insertion method. We tested buildup methods and fragment library quality for accuracy in constructing a set of known structures. The parameters most influential in the construction procedure are bond and torsion angles with minor inaccuracies in bond angles alone causing >6 A CalphaRMSD for a 150-residue protein. Idealization to a standard set of values corrects this problem, but changes the torsion angles and does not work for every structure. Alternatively, we found using Cartesian coordinates instead of torsion angles did not reduce performance and can potentially increase speed and accuracy. Under conditions simulating ab initio structure prediction, fragment library quality can be suboptimal and still produce near-native structures. Using various clustering criteria, we created a number of libraries and used them to predict a set of native structures based on nonnative fragments. Local CalphaRMSD fit of fragments, library size, and takeoff/landing angle criteria weakly influence the accuracy of the models. Based on a fragment's minimal perturbation upon insertion into a known structure, a seminative fragment library was created that produced more accurate structures with fragments that were less similar to native fragments than the other sets. These results suggest that fragments need only contain native-like subsections, which when correctly overlapped, can recreate a native-like model. For fragment-based, random insertion methods used in protein structure prediction and design, our findings help to define the parameters this method needs to generate near-native structures.     

Conformational Characteristics of Mixed Sugar Puckered Deoxydinucleoside Triphosphate Units d-pCpGp and d-pGpCp from Energy Minimization Studies

Abstract

The deoxydinucleoside triphosphate units d-pCpGp and d-pGpCp were subjected to a rigorous theoretical investigation with a view to describing their distinctive conformational characteristics. For each unit 216 probable three-dimensional forms defined by the backbone-base dihedral angles and sugar pucker modes were considered for conformational energy minimization process and scrutinized with reference to properties, such as base-stacking, hydrogen-bonding, internal flexibility and base sequence-phosphate influence. The P-O bond torsions and the phosphate groups were treated with special attention. The results reveal a number of preferred conformational states other than the known helical forms, such as, A-, B-, C-, Z-, and Watson-Crick conformation. Many interesting one-step (change in only one of the dihedral angles or sugar puckers) conformational transitions which involve just about a kcal/mol of energy came to light. The two base sequences CG and GC were noted to differ strikingly in many of their conformational characteristics.     

Dynamic stereochemistry of rutin (vitamin P) in solution: theoretical approaches and experimental validation

Rutin, vitamin P, was extracted from Salvia macrosiphon and identified by ¹H, ¹³C, ¹H-¹H COSY, HMQC, and HMBC spectroscopy. In parallel, density functional theory (DFT) using B₃LYP functional and split-valance 6-311G∗∗ basis set has been used to optimize the structures and conformers of rutin. Also experimental and theoretical methods have been used to correlate the dependencies of ¹J, ²J, and ³J involving ¹H and ¹³C on the C5″-C6″ (ω), C6″-O6″ (θ), and C1?-O6″ (φ) torsion angles in the glycosidic moiety. New Karplus equations are proposed to assist in the structural interpretation of these couplings. ³J_HH depends mainly on the C-C (ω) torsion angle, as expected, and ²J_HH values depend on both C-C (ω) and C-O (θ) torsions. ¹J_CH values within hydroxymethyl fragments were also examined and found to depend on r_CH, which is modulated by specific bond orientation and stereoelectronic factors. In all calculations solvent effects were considered using a polarized continuum model (PCM).