Geometry of experimentally observed RNA residues in tRNA and dinucleoside monophosphates: the effect of small variations in the backbone angles.

The polymerization of various experimentally observed conformers of RNA from tRNA and some dinucleoside monophosphates have been examined with a program that computes the basic helix parameters directly from the six backbone torsion angles ω′, ?′, ψ′, ψ, ?, ω to give n (= 360/θ), the number of residues per turn; h, the rise per residue; and r, the radius of the phosphate atoms from the helix axis. The single-stranded regions of tRNA that have A-form residues have a notably lower value of n than the double-stranded regions. The G-U “wobble” base pair is shown to be an energetically strained left-handed form. The A-form dinucleoside monophosphates also have a low value of n. A model of UpAl polymerized as a fourfold left-handed helix with the bases on the outside and phosphates on the inside is investigated for its sharp 90° turn angle characteristics. UpA2 cannot be polymerized due to a low values of h (1.31 Å) and r (2.72 Å), which cause steric hindering. An eightfold model of poly(rA) is discussed as are the nonhelical residues of tRNA. Finally, the effects of small changes in dihedral angles and bond lengths and angles on the helical parameters are investigated and discussed by way of explaining this behavior.     

Parallel Double Helices of DNA. Conformational Analysis of Regular Helices with the Second Order Symmetry Axis

Abstract

We have performed a conformational analysis of DNA double helices with parallel directed backbone strands connected with the second order symmetry axis being at the same time the helix axis. The calculations were made for homopolymers poly(dA) · poly(dA), poly(dC) · poly(dC), poly(dG) poly(dG), and poly(dT) · poly(dT). All possible variants of hydrogen bonding of base pairs of the same name were studied for each polymer. The maps of backbone chain geometrical existence were constructed. Conformational and helical parameters corresponding to local minima of conformational energy of “parallel” DNA helices, calculated at atom-atom approximation, were determined. The dependence of conformational energy on the base pair and on the hydrogen bond type was analysed. Two major conformational advantageous for “parallel” DNA's do not depend much on the hydrogen-bonded base pair type were indicated. One of them coincided with the conformational region typical for “antiparallel” DNA in particular for the B-form DNA Conformational energy of “parallel” DNA depends on the base pair type and for the most part is similar to the conformational energy of “antiparallel” B-DNA.     

Principal component analysis of DNA oligonucleotide structural data

The microstructure of a DNA helix is characterized by several base pair and base step parameters such as twist, rise, roll, propeller twist, etc., in addition to conformational parameters such as the backbone and the glycosidic torsion angles. Among these only a few, which are independent of all others and of each other, may be used to precisely characterize the helix. The problem however is to identify these independent parameters. We have used principal component analysis to identify a relatively small set of independent parameters, with which to characterize each DNA helix. We show that these principal components clearly discriminate between A and B DNA helical types. The calculations further suggest that the microstructure of a DNA helix is better characterized using dinucleotides.     

Flexibility and rigidity of left-handed Z-DNA

The local variation of torsional angles and helical parameters in Z-DNA was analyzed. The sugar phosphate backbone is fairly rigid but the angles at GpC linkage are more changeable than those at CpG linkage in order to form a variety of structures. The water channel at minor groove is important to stabilize and retain the novel Z-DNA helix.     

General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.     

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.     

A molecular dynamics simulation of the (dG)6 . (dC)6 minihelix including counterions and water

The results of a 60 ps molecular dynamics (MD) simulation of (dG)6.(dC)6 including 10 Na+ counterions and 292 water molecules are presented. All backbone angles and helix parameters for the hexamer are reported in this paper along with trajectory plots of selected angles. Hydrogen bonding between the bases along the helical axis was observed to fluctuate with time, showing the dynamic nature of the base-pairing interaction. These fluctuations gave rise to unusual hydrogen-bonding patterns. Good intrastrand base stacking and no interstrand base stacking were also observed. The hexamer minihelix retains an essentially B-DNA conformation throughout the entire simulation even though some helix parameters and backbone angles do not have strict B-DNA values. The most striking feature obtained from the simulation was a high propeller twist, which resulted in a narrow minor groove for the minihelix. It is proposed that (dG)n.(dC)n sequences are resistant to DNAase I because of this narrow minor groove in dilute aqueous solution.     

Alpha helical crossovers favor right‐handed supersecondary structures by kinetic trapping: The phone cord effect in protein folding

The remarkable predominance of right‐handedness in beta‐alpha‐beta helical crossovers has been previously explained in terms of thermodynamic stability and kinetic accessibility, but a different kinetic trapping mechanism may also play a role. If the beta‐sheet contacts are made before the crossover helix is fully formed, and if the backbone angles of the folding helix follows the energetic pathway of least resistance, then the helix would impart a torque on the ends of the two strands. Such a torque would tear apart a left‐handed conformation but hold together a right‐handed one. Right‐handed helical crossovers predominate even in all‐alpha proteins, where previous explanations based on the preferred twist of the beta sheet do not apply. Using simple molecular simulations, we can reproduce the right‐handed preference in beta‐alpha‐beta units, without imposing specific beta‐strand geometry. The new kinetic trapping mechanism is dubbed the “phone cord effect” because it is reminiscent of the way a helical phone cord forms superhelices to relieve torsional stress. Kinetic trapping explains the presence of a right‐handed superhelical preference in alpha helical crossovers and provides a possible folding mechanism for knotted proteins.     

Kinetics of amide proton exchange in helical peptides of varying chain lengths. Interpretation by the Lifson-Roig equation.

The kinetics of amide proton exchange (1H----2H) have been measured by proton nuclear magnetic resonance spectroscopy for a set of helical peptides with the generic formula Ac-(AAKAA)m Y-NH2 and with chain lengths varying from 6 to 51 residues. The integrated intensity of the amide resonances has been measured as a function of time in 2H2O at pH* 2.50. Exchange kinetics for these peptides can be modeled by applying the Lifson-Roig treatment for the helix-to-coil transition. The Lifson-Roig equation is used to compute the probability that each residue is helical, as defined by its backbone (phi, psi) angles. A recursion formula then is used to find the probability that the backbone amide proton of each residue is hydrogen bonded. The peptide helix can be treated as a homopolymer, and direct exchange from the helix can be neglected. The expression for the exchange kinetics contains only three unknown parameters: the rate constant for exchange of a non-hydrogen-bonded (random coil) backbone amide proton and the nucleation (v2) and propagation (w) parameters of the Lifson-Roig theory. The fit of the exchange curves to these three parameters is very good, and the values for v2 and w agree with those derived from circular dichroism studies of the thermally-induced unfolding of related peptides [Scholtz, J.M., Qian, H., York, E.J., Stewart, J.M., & Baldwin, R.L. (1991) Biopolymers (in press]).     

Conformational preferences of helix foldamers of γ‐peptides based on 2‐(aminomethyl)cyclohexanecarboxylic acid

The conformational preferences of helix foldamers having different sizes of the H‐bonded pseudocycles have been studied for di‐ to octa‐γ^2,3‐peptides based on 2‐(aminomethyl)cyclohexanecarboxylic acid (γAmc₆) with a cyclohexyl constraint on the C^α–C^β bond using density functional methods. The helical structures of the γAmc₆ oligopeptides with homochiral configurations are known to be much stable than those with heterochiral configurations in the gas phase and in solution (chloroform and water). In particular, it is found that the (P/M)?2.5₁₄‐helices are most preferred in the gas phase and in chloroform, whereas the (P/M)?2.3₁₂‐helices become most populated in water due to the larger helix dipole moments. As the peptide sequence becomes longer, the helix propensities of 14‐ and 12‐helices are found to increase both in the gas phase and in solution. The γAmc₆ peptides longer than octapeptide are expected to exist as a mixture of 12‐ and 14‐helices with the similar populations in water. The mean backbone torsion angles and helical parameters of the 14‐helix foldamers of γAmc₆ oligopeptides are quite similar to those of 2‐aminocyclohexylacetic acid oligopeptides and γ^2,3,4‐aminobutyric acid tetrapeptide in the solid state, despite the different substituents on the backbone. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 87–95, 2014.     

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.

An 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.     

Sequence-Dependent Anisotropic Flexibility of B-DNA A Conformational Study

Abstract

Bending flexibility of the six tetrameric duplexes was investigated d(AAAA):d(TTTT), d(AATT)₂, d(TTAA) ₂, d(GGGG):d(CCCC), d(GGCC) ₂ and d(CCGG) ₂. The tetramers were extended in the both directions by regular double helices. The stiffness of the B-DNA double helix when bent into the both grooves proved to be less than that in the perpendicular direction by an order of magnitude. Such an anisotropy is a property of the sugar-phosphate backbone structure. The calculated fluctuations of the DNA bending along the dyad axis, 5–7°, are in agreement with experimental value of the DNA persistence length.

Anisotropy of the double helix is sequence-dependent: most easily bent into the minor groove are the tetramers with purine-pyrimidine dimer (RY) in the middle. In contrast, YR dinucleotides prefer bending into the major groove. Moreover, they have an equilibrium bend of 6–12° into this groove. The above inequality is caused by stacking interaction of the bases.

The bend in the central dimer is distributed to some extent between the adjacent links, though the main fraction of the bend remains within the central link. Variation of the sugar-phosphate geometry in the bent helix is inessential, so that DNA remains within the B-family of forms: namely, when the helical axis is bent by 20°, the backbone dihedral angles vary by no more than 15°.

The obtained results are in accord with x-ray structure of the B-DNA dodecamer; they further substantiate our early model of DNA wrapping in the nucleosome by means of “mini-kinks” separated by a half-pitch of the double helix, i.e. by 5–6 b.p. Sequence-dependent anisotropy of DNA presumably dictates the three-dimentional structure of DNA in solution as well. We have found that nonrandom allocation of YR dimers leads to the systematic bends in equilibrium structure of certain DNA fragments.     

Sequence-dependent structural variations in two right-handed alternating pyrimidine-purine DNA oligomers in solution determined by nuclear Overhauser enhancement measurements

A 500 MHz 1H-n.m.r. study on two right-handed self-complementary double-stranded alternating pyrimidine-purine oligodeoxyribonucleotides, 5'dCGTACG and 5'dACGCGCGT, is presented. Using the proton-proton nuclear Overhauser effect, proton resonances are assigned by a sequential method and a large number of interproton distances, both intra- and internucleotide, are determined (113 for 5'dCGTACG and 79 for 5'dACGCGCGT). The general procedure required to solve the three-dimensional solution structures of oligonucleotides from such distance data is outlined and applied to these two oligonucleotides. In the case of both oligonucleotides the overall solution structure is that of B DNA, namely a right-handed helix with a helical rise of approximately 3.3 A, 10 bp per turn and the base pairs approximately perpendicular to the helix axis. In the case of 5'dCGTACG, subtle local structural variations associated with the pyrimidine and purine nucleotides are superimposed on the overall structure but the mononucleotide repeating unit is preserved. In contrast, 5'dACGCGCGT has a clear alternating structure with a dinucleotide repeat, alternation occurring in the local helical twist and the glycosidic bond, sugar pucker and phosphodiester backbone conformations.     

High-Resolution Crystal Structures of Protein Helices Reconciled with Three-Centered Hydrogen Bonds and Multipole Electrostatics

Theoretical and experimental evidence for non-linear hydrogen bonds in protein helices is ubiquitous. In particular, amide three-centered hydrogen bonds are common features of helices in high-resolution crystal structures of proteins. These high-resolution structures (1.0 to 1.5 Å nominal crystallographic resolution) position backbone atoms without significant bias from modeling constraints and identify Φ = -62°, ψ = -43 as the consensus backbone torsional angles of protein helices. These torsional angles preserve the atomic positions of α-β carbons of the classic Pauling α-helix while allowing the amide carbonyls to form bifurcated hydrogen bonds as first suggested by Némethy et al. in 1967. Molecular dynamics simulations of a capped 12-residue oligoalanine in water with AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications), a second-generation force field that includes multipole electrostatics and polarizability, reproduces the experimentally observed high-resolution helical conformation and correctly reorients the amide-bond carbonyls into bifurcated hydrogen bonds. This simple modification of backbone torsional angles reconciles experimental and theoretical views to provide a unified view of amide three-centered hydrogen bonds as crucial components of protein helices. The reason why they have been overlooked by structural biologists depends on the small crankshaft-like changes in orientation of the amide bond that allows maintenance of the overall helical parameters (helix pitch (p) and residues per turn (n)). The Pauling 3.6₁₃ α-helix fits the high-resolution experimental data with the minor exception of the amide-carbonyl electron density, but the previously associated backbone torsional angles (Φ, Ψ) needed slight modification to be reconciled with three-atom centered H-bonds and multipole electrostatics. Thus, a new standard helix, the 3.6_13/10-, Némethy- or N-helix, is proposed. Due to the use of constraints from monopole force fields and assumed secondary structures used in low-resolution refinement of electron density of proteins, such structures in the PDB often show linear hydrogen bonding.     

Assignments of 31P NMR resonances in oligodeoxyribonucleotides: origin of sequence-specific variations in the deoxyribose phosphate backbone conformation and the 31P chemical shifts of double-helical nucleic acids

It is now possible to unambiguously assign all 31P resonances in the 31P NMR spectra of oligonucleotides by either two-dimensional NMR techniques or site-specific 17O labeling of the phosphoryl groups. Assignment of 31P signals in tetradecamer duplexes, (dTGTGAGCGCTCACA)2, (dTAT-GAGCGCTCATA)2, (dTCTGAGCGCTCAGA)2, and (dTGTGTGCGCACACA)2, and the dodecamer duplex d(CGTGAATTCGCG)2 containing one base-pair mismatch, combined with additional assignments in the literature, has allowed an analysis of the origin of the sequence-specific variation in 31P chemical shifts of DNA. The 31P chemical shifts of duplex B-DNA phosphates correlate reasonably well with some aspects of the Dickerson/Calladine sum function for variation in the helical twist of the oligonucleotides. Correlations between experimentally measured P-O and C-O torsional angles and results from molecular mechanics energy minimization calculations show that these results are consistent with the hypothesis that sequence-specific variations in 31P chemical shifts are attributable to sequence-specific changes in the deoxyribose phosphate backbone. The major structural variation responsible for these 31P shift perturbations appears to be P-O and C-O backbone torsional angles which respond to changes in the local helical structure. Furthermore, 31P chemical shifts and JH3'-P coupling constants both indicate that these backbone torsional angle variations are more permissive at the ends of the double helix than in the middle. Thus 31P NMR spectroscopy and molecular mechanics energy minimization calculations appear to be able to support sequence-specific structural variations along the backbone of the DNA in solution.     

ω-Helices in Proteins

A modification of the α-helix, termed the ω-helix, has four residues in one turn of a helix. We searched the ω-helix in proteins by the HELFIT program which determines the helical parameters—pitch, residues per turn, radius, and handedness—and p = rmsd/(N ? 1)^1/2 estimating helical regularity, where “rmsd” is the root mean square deviation from the best fit helix and “N” is helix length. A total of 1,496 regular α-helices 6–9 residues long with p ≤ 0.10 Å were identified from 866 protein chains. The statistical analysis provides a strong evidence that the frequency distribution of helices versus n indicates the bimodality of typical α-helix and ω-helix. Sixty-two right handed ω-helices identified (7.2% of proteins) show non-planarity of the peptide groups. There is amino acid preference of Asp and Cys. These observations and analyses insist that the ω-helices occur really in proteins.     

Interaction of paired homologous series of diacridines and triacridines with deoxyribonucleic acid

Viscometric measurements using covalently closed circular DNA and sonicated rod-like DNA fragments were performed to investigate unwinding and extension of the DNA helix associated with binding of paired homologous series of diacridines and triacridines. The maximum interchromophore distance for members of the diacridine series spans from 15.1 to 27.5 A, permitting the largest of these ligands to cover up to 4 or 5 base-pairs, allowing for helical twist and local unwinding in a bisintercalated complex lacking severe bending or kinking of the DNA backbone. Helix unwinding angles and increments in DNA contour length are characteristic of bifunctional reaction for all the diacridines studied, the DNA lattice appearing to saturate with one ligand molecule bound per 4 base-pairs. The triacridines, whose maximum end-to-end interchromophore distances are the same as those of their paired diacridines, have maximum central-to-terminal interchromophore distances covering the range 7.5-13.8 A and thus have the potential to form trisintercalated complexes with one or two base-pairs sandwiched between each chromophore. However, helix extension and unwinding parameters for the triacridines are similar to those of the diacridines, and we find no evidence of a transition from bifunctional to trifunctional reaction as the homologous series is ascended. In general, the binding site size appears to be 5 base-pairs for the triacridines. The stereochemical requirements for trisintercalation of triacridines are discussed with reference to the present findings and to the work of others.     

Conformational characteristics and correlations in crystal structures of nucleic acid oligonucleotides: evidence for sub-states

Sugar phosphate backbone conformations are a structural element inextricably involved in a complete understanding of specific recognition nucleic acid ligand interactions, from early stage discrimination of the correct target to complexation per se, including any structural adaptation on binding. The collective results of high resolution DNA, RNA and protein/DNA crystal structures provide an opportunity for an improved and enhanced statistical analysis of standard and unusual sugar-phosphate backbone conformations together with corresponding dinucleotide sequence effects as a basis for further exploration of conformational effects on binding. In this study, we have analyzed the conformations of all relevant crystal structures in the nucleic acids data base, determined the frequency distribution of all possible epsilon, zeta, alpha, beta and gamma backbone angle arrangements within four nucleic acid categories (A-RNA and A-DNA, free and bound B-DNA) and explored the relationships between backbone angles, sugar puckers and selected helical parameters. The trends in the correlations are found to be similar regardless of the nucleic acid category. It is interesting that specific structural effects exhibited by the different unusual backbone sub-states are in some cases contravariant. Certain alpha/gamma changes are accompanied by C3' endo (north) sugars, small twist angles and positive values of base pair roll, and favor a displacement of nucleotide bases towards the minor groove compared to that of canonical B form structures. Unusual epsilon/zeta combinations occur with C2' (south) sugars, high twist angles, negative values of base pair roll, and base displacements towards the major groove. Furthermore, any unusual backbone correlates with a reduced dispersion of equilibrium structural parameters of the whole double helix, as evidenced by the reduced standard deviations of almost all conformational parameters. Finally, a strong sequence effect is displayed in the free oligomers, but reduced somewhat in the ligand bound forms. The most variable steps are GpA and CpA, and, to a lesser extent, their partners TpC and TpG. The results provide a basis for considering if the variable and non-variable steps within a biological active sequence precisely determine morphological structural features as the curvature direction, the groove depth, and the accessibility of base pair for non covalent associations.