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.     

The J-coupling Restrained Molecular Mechanics (JrMM) Protocol - An Efficient Alternative for Deriving DNA Endocyclic Torsion Angle Constraints Part II: Experimental Application of the JrMM Protocol

Abstract

The J-coupling restrained molecular mechanics (JrMM) protocol, which correlates deoxyribose endocyclic torsion angles and vicinal proton-proton torsion angle φ_{1′ 2′} in Part I of this study, is demonstrated to be a viable alternative to efficiently derive the endocyclic torsion angle constraints for the determination of the solution structures of DNA molecules. Extensive testing demonstrating the validity of the JrMM-derived torsion angle constraints in the restrained molecular dynamics and energy minimization structural refinement processes is performed theoretically using an energy-minimized B-DNA model and experimentally using a DNA hexamer d(CGTACG)₂. The results show that only a 0.2 Å difference exists between the RMSD values of the refined structures using the ideal and the JrMM-derived endocyclic torsion angle constraints. The JrMM-derived torsion angles are also determined to be in good agreement with the torsion angles derived through the use of the vicinal J-derived torsion angles. These results show that through the use of reliably measured J_{1′ 2′} values and computer simulation method, the endocyclic torsion angle constraints can be derived reliably and efficiently. Thus the JrMM method serves as an alternative strategy to generate endocyclic torsion angle constraints for the determination of the solution structures of DNA molecules.     

Structure and Dynamics of Double Helical DNA in Torsion Angle Hyperspace: A Molecular Mechanics Approach

Abstract

Analysis of the conformational space populated by the torsion angles and the correlation between the conformational energy and the sequence of DNA are important for fully understanding DNA structure and function. Presence of seven variable torsion angles about single covalent bonds in DNA main chain puts a big challenge for such analysis. We have carried out restrained energy minimization studies for four representative dinucleosides, namely d(ApA):d(TpT), d(CpG):d(CpG), d(GpC):d(GpC) and d(CpA):d(TpG) to determine the energy hyperspace of DNA in context to the values of the torsion angles and the structural properties of the DNA conformations populating the favorable regions of this energy hyperspace. The torsion angles were manipulated by constraining their values at the reference points and then performing energy minimization. The energy minima obtained on the potential energy contour plots mostly correspond to the conformations populated in crystal structures of DNA. Some novel favorable conformations that are not present in crystal structure data are also found. The plots also suggest few low energy routes for conformational transitions or the associated energy barrier heights. Analyses of base pairing and stacking possibility reveal structural changes accompanying these transitions as well as the flexibility of different base steps towards variations in different torsion angles.     

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.     

Testing an inference of function from structure: Snake vertebrae do the twist

The zygapophyses and zygosphene–zygantrum articulations of snake vertebrae are hypothesized to restrict or eliminate vertebral torsion. This hypothesis is apparently based solely on the inference of function from structure, despite the limitations of such inferences, as well as contradictory observations and measurements. In this study, I observed and measured axial torsion in gopher snakes, Pituophis melanoleucus. To examine the structural basis of axial torsion, I measured the vertebral articulation angles along the body and the insertion angles of five epaxial muscles. To examine torsion in a natural behavior, I digitized video images and measured the degree of apparent axial torsion during terrestrial lateral undulation. Finally, I measured the mechanical capacity of the vertebral joints for actual torsion over intervals of 10 vertebrae in fresh, skinned segments of the trunk. Vertebral articulation angles vary up to 30° and are associated with variation in torsional capacity along the trunk. The freely crawling P. melanoleucus twisted up to 2.19° per vertebra, which produced substantial overall torsion when added over several vertebrae. The vertebral joints are mechanically capable of torsion up to 2.89° per joint. Therefore, despite the mechanical restriction imposed by the complex articulations, vertebral torsion occurs in snakes and appears to be functionally important in several natural behaviors. Even in cases in which mechanical function appears to be narrowly constrained by morphology, specific functions should not be inferred solely from structural analyses. J. Morphol. 241:217–225, 1999. © 1999 Wiley‐Liss, Inc.     

The conformations and energetics of photodamaged DNA

Energy minimization techniques are used in conjunction with the results of small molecule crystallographic studies on relevant compounds to propose structural models for photodamaged DNAs. Specifically, we present models both for a DNA molecule containing a psoralen photo-crosslink and for a DNA molecule containing a thymine photodimer. In both models, significant distortions of the nucleic acid helix are observed, including kinking and unwinding at the damage site and numerous changes in the backbone torsion angles relative to their standard conformations. Both the torsion angle geometries and the energetics of the models are presented in detail.     

RNA conformational classes

RNA exhibits a large diversity of conformations. Three thousand nucleotides of 23S and 5S ribosomal RNA from a structure of the large ribosomal subunit were analyzed in order to classify their conformations. Fourier averaging of the six 3D distributions of torsion angles and analyses of the resulting pseudo electron maps, followed by clustering of the preferred combinations of torsion angles were performed on this dataset. Eighteen non-A-type conformations and 14 A-RNA related conformations were discovered and their torsion angles were determined; their Cartesian coordinates are available.     

Determination of Femoral Neck Angle and Torsion Angle Utilizing a Novel Three-Dimensional Modeling and Analytical Technology Based on CT Datasets

Introduction

Exact knowledge of femoral neck inclination and torsion angles is important in recognizing, understanding and treating pathologic conditions in the hip joint. However, published results vary widely between different studies, which indicates that there are persistent difficulties in carrying out exact measurements.

Methods

A three dimensional modeling and analytical technology was used for the analysis of 1070 CT datasets of skeletally mature femurs. Individual femoral neck angles and torsion angles were precisely computed, in order to establish whether gender, age, body mass index and ethnicity influence femoral neck angles and torsion angles.

Results

The median femoral neck angle was 122.2° (range 100.1–146.2°, IQR 117.9–125.6°). There are significant gender (female 123.0° vs. male 121.5°; p = 0.007) and ethnic (Asian 123.2° vs. Caucasian 121.9°; p = 0.0009) differences. The median femoral torsion angle was 14.2° (-23.6–48.7°, IQR 7.4–20.4°). There are significant gender differences (female 16.4° vs. male 12.1°; p = 0.0001). Femoral retroversion was found in 7.8% of the subjects.

Conclusion

Precise femoral neck and torsion angles were obtained in over one thousand cases. Systematic deviations in measurement due to human error were eliminated by using automated high accuracy morphometric analysis. Small but significant gender and ethnic differences were found in femoral neck and torsion angles.     

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.     

Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks

A new program, TALOS-N, is introduced for predicting protein backbone torsion angles from NMR chemical shifts. The program relies far more extensively on the use of trained artificial neural networks than its predecessor, TALOS+. Validation on an independent set of proteins indicates that backbone torsion angles can be predicted for a larger, ≥90 % fraction of the residues, with an error rate smaller than ca 3.5 %, using an acceptance criterion that is nearly two-fold tighter than that used previously, and a root mean square difference between predicted and crystallographically observed (?, ψ) torsion angles of ca 12º. TALOS-N also reports sidechain χ¹ rotameric states for about 50 % of the residues, and a consistency with reference structures of 89 %. The program includes a neural network trained to identify secondary structure from residue sequence and chemical shifts.     

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 analysis of protein and nucleic acid fragments with the new grid search algorithm FOUND

The new computer algorithm FOUND, which is implemented as an integrated module of the DYANA structure calculation program, is capable of performing systematic local conformation analyses by exhaustive grid searches for arbitrary contiguous fragments of proteins and nucleic acids. It uses torsion angles as the only degrees of freedom to identify all conformations that fulfill the steric and NMR-derived conformational restraints within a contiguous molecular fragment, as defined either by limits on the maximal restraint violations or by the fragment-based DYANA target function value. Sets of mutually dependent torsion angles, for example in ribose rings, are treated as a single degree of freedom. The results of the local conformation analysis include allowed torsion angle ranges and stereospecific assignments for diastereotopic substituents, which are then included in the input of a subsequent structure calculation. FOUND can be used for grid searches comprising up to 13 torsion angles, such as the backbone of a complete -helical turn or dinucleotide fragments in nucleic acids, and yields a significantly higher number of stereospecific assignments than the precursor grid search algorithm HABAS.     

Derivation of the angle of torsion of the eye.

The angle of torsion of the eye, that is the amount by which the eye rotates about its anterio-posterior axis, changes with the direction of the line of fixation. If the eye can be considered as a rigid body under an elaborate system for constraints its motion can be described by the laws of kinematics. The techniques of linear algebra can then be used to derive an explicit relationship between the angles defining the direction of fixation and the angle of torsion of the eye. The angle of torsion can then be expressed as a function of the angle of rotation of the eye and the direction cosines of the axis of rotation. However, under conditions in which Listing's Law holds these angles, are well defined functions of the angles defining the direction of fixation, and so the angle of torsion, in this case, can be expressed as an explicit function of this direction.     

Conformational study of asialo-GM1 (GA1) ganglioside

In order to investigate the significance of preferred conformations of the saccharide for the steric orientation and recognition of glycosphingolipids at the membrane surface, the conformational free energy calculations were carried out on the asialo-GM1 [GA1; β-D -Gal(1 → 3) β-D -GalNAc(1 → 4) β-D -Gal(1 → 4) β-D -Glc-O-ceramide] using a new program CONCARB (CONformational study program for CARBohydrate) in the unhydrated and hydrated states. The overall backbone conformation of GA1 appears nearly to be extended with a little bent at the glycosidic II–III linkage, in which two pyranose rings of Gal(IV)-GalNAc-(III) moiety orient approximately perpendicular to those of Gal(II)-Glc(I) moiety. This is consistent with the structures deduced from high-sensitivity differential scanning calorimetry experiments and the nmr study on GA1. The calculated glycosidic torsion angles of the lowest free energy conformation of GA1 in the hydrated state are in accord with the structures of relevant oligosaccharides deduced from nmr experiments and hard sphere exoanomeric calculations. A comparison of the values of glycosidic torsion angles ϕ and π of GA1 and its constituent oligosaccharides indicates that the overall backbone conformation of each oligosaccharide is retained when the oligosaccharide chain becomes longer. This implies that the short-range interactions between the nearest-neighbored saccharides are of significant importance in stabilizing the overall backbone conformation of GA1 in both the unhydrated and hydrated states. The different orientation and hydrogen bonds of hydroxymethyl and hydroxyl groups from one oligosaccharide to another suggest that the medium- and long-range interactions are also of consequence. Hydration seems to affect significantly the conformation of these groups, but not to perturb remarkably the overall backbone conformation of GA1. © 1997 John Wiley & Sons, Inc. Biopoly 42: 19–35, 1997     

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.     

Solid-state NMR analysis of a peptide (Gly-Pro-Gly-Gly-Ala)6-Gly derived from a flagelliform silk sequence of Nephila clavipes

Solid-state NMR is especially useful when the structures of peptides and proteins should be analyzed by taking into account the structural distribution, that is, the distribution of the torsion angle of the individual residue. In this study, two-dimensional spin-diffusion solid-state NMR spectra of 13C-double-labeled model peptides (GPGGA)6G of flagelliform silk were observed for studying the local structure in the solid state. The spin-diffusion NMR spectra calculated by assuming the torsion angles of the beta-spiral structure exclusively could not reproduce the observed spectra. In contrast, the spectra calculated by taking into account the statistical distribution of the torsion angles of the individual central residues in the sequences Ala-Gly-Pro, Gly-Pro-Gly, Pro-Gly-Gly, Gly-Gly-Ala, and Gly-Ala-Gly from PDB data could reproduce the observed spectra well. This indicates that the statistical distribution of the torsion angles should be considered for the structural model of (GPGGA)6G similar to the case of the model peptide of elastin.     

Tanford-Kirkwood theory for concentric dielectric continua: application to dimethylphosphate

The Tanford–Kirkwood theory for evaluating the electrostatic free energy of a discrete charge distribution in the presence of ion atmosphere is extended to concentric dielectric continua. The theory is applied to study the conformational preferences with respect to phosphodiester torsion angles in the dimethylphosphate anion (DMP^?) and the sodium dimethylphosphate ion pair (Na⁺DMP^?), in the absence and presence of ion atmosphere and at varying local dielectric constants. Results indicate that phosphodiester torsion angles in DMP^? prefer the gauche-gauche conformation in aqueous solutions.     

Handedness of duplex DNA: role of the glycosydic torsion

Model building studies on helical structures of polynucleotides indicate the glycosydic torsion, χ, and the sugar pucker to be the most important conformational parameters in determining the handedness of the models. Sugar puckers in two typical regions of the pseudorotational space namely, C2′ endo and C3′ endo and the glycosydic torsion in four ranges, namely, anti, high anti, syn and low anti lead to eight conformational combinations for the model bulding of base-paired double helical structures of polynucleotides. Interestingly, not all combinations of sugar pucker and glycosidic torsion lead to structures with Watson-Crick base-pairing. The stereochemical details of the double stranded Watson-Crick base-paired models and their consistency with X-ray diffraction data are discussed.     

Distributed torsion angle grid search in high dimensions: A systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized -turn conformation, an alanine octapeptide restrained to a right-handed helical conformation, and the structured region of the peptide SYPFDV.