Agreement between single crystal X-ray and molecular mechanical sugar ring conformations

We have calculated the deoxyribose sugar energy for a wide range of puckering parameters, (q, W), using different force fields. The intra-ring bond lengths, bond angles, and dihedral angles are calculated for every energy minimized structure and compared with 224 sugar ring structures available from DNA single crystal x-ray data. A modified Weiner's force field yields an excellent agreement with x-ray data. The calculated energy surface shows a variable amplitude repuckering path, with an average distortion of 0.42 A. Most of the experimental values of (q, W) fall within 1.0 Kcal/mol from the calculated minimum.     

Molecular Mechanics Studies of Molybdenum Disulphide Catalysts Parameterisation of Molybdenum and Sulphur

Abstract

A method for the parameterisation of molybdenum disulphide is presented which reproduces the crystal structure accurately. The method involves calculating parameters such that there is no net force contribution from any individual term of the potential on any atom. Ideal bond lengths and bond angles are taken from the X-ray crystal structure; stretching and bending force constants are calculated from a combination of spectroscopic data and quantum mechanics calculations, whereby the energy function with bond length or bond angle is calculated and fitted with an harmonic potential. For the non-bonded Lennard-Jones parameters, the dispersion coefficient C was calculated by an interpolation of existing published parameters using a multiple regression and then the crystal energy was minimised with respect to the van der Waals radius r₀ using a fixed crystal fragment.

These parameters were tested for various models of the hexagonal and rhombohedral forms of MoS₂. RMS fits between structures minimised with molecular mechanics and experimental models ranged from 0.006 Å to 0.012 Å.     

Flexibility of 3′,5′ Deoxyribonucleooside Diphosphates

Abstract

In 3′,5′ deoxyribonucleoside diphosphates, in addition to the nature of the base and the sugar puckering, there are six single bond rotations. However, from the analysis of crystal structure data on the constituents of nucleic acids, only three rotational angles, that are about glycosyl bond, about C4′-C5′ and about C3′-O3′ bonds, are flexible. For a given sugar puckering and a base, potential energy calculations using non-bonded, electrostatic and torsional functions were carried out by varying the three torsion angles. The energies are represented as isopotential energy surfaces. Since the availability of the real-time color graphics, it is possible to analyse these isopotential energy surfaces. The calculations were carried out for C3′ exo and C3′ endo puckerings for deoxyribose and also for four bases. These calculations throw more light not only on the allowed regions for the three rotational angles but also on the relationships among them. The dependence of base and the puckering of the sugar on these rotational angles and thereby the flexibility of the 3′,5′ deoxyribonucleoside diphosphates is discussed. From our calculations, it is now possible to follow minimum energy path for interconversion among various conformers.     

Towards the simulation of biomolecules: optimisation of peptide-capped glycine using FFLUX

Abstract

The optimisation of a peptide-capped glycine using the novel force field FFLUX is presented. FFLUX is a force field based on the machine-learning method kriging and the topological energy partitioning method called Interacting Quantum Atoms. FFLUX has a completely different architecture to that of traditional force fields, avoiding (harmonic) potentials for bonded, valence and torsion angles. In this study, FFLUX performs an optimisation on a glycine molecule and successfully recovers the target density-functional-theory energy with an error of 0.89 ± 0.03 kJ mol^?1. It also recovers the structure of the global minimum with a root-mean-squared deviation of 0.05 Å (excluding hydrogen atoms). We also show that the geometry of the intra-molecular hydrogen bond in glycine is recovered accurately.     

Conformational studies on polynucleotide chains. IV. Backbone structure of ribonucleic acids.

In preceding papers the energies associated with the internal rotations in the sugar–phosphate–sugar complex were described with an analytical potential consisting of a Lennard-Jones 6–12 term and an intrinsic torsional term and representing the best fit to a large number of energies computed with a quantum mechanical ab initio technique. The complex considered there (of 37 atoms and with the chemical formula C₁₀H₁₈O₈P) is repesentative of deoxyribonucleic acids. In this paper we apply our potential to evaluating the intramolecular energies of the 39-atom complex C₁₀H₁₈O₁₀P, representative of the ribonucleic acids. The potential energies for the internal rotations (considered independent from one another) and the energy maps for rotations about consecutive bonds of the backbone chain are critically compared, both with those obtained for the deoxy system and with those obtained from different theoretical approaches as available from literature. It is shown that, at least for certain combinations of the internal rotation angles, the choice of the starting geometry for the sugarphosphate–sugar molecule (bond lengths and valence angles) strongly affects the value of the computed energy. If a proper geometry is used, very low energies are predicted by our potential in correspondence of the sets of torsional angles found in various RNAs by x-ray crystallography.     

Structure of guanosine-3',5'-cytidine monophosphate. I. Semi-empirical potential energy calculations and model-building

The conformation and packing scheme for guanosine-3′, 5′-cytidine monophosphate, GpC, were computed by minimizing the classical potential energy. The lowest energy conformation of the isolated molecule had dihedral angles in the range of helical RNA's and the sugar pucker was C3′ endo. This was used as the starting conformation in a packing search over orientation space, the dihedral angles being flexible in this step also. The packing search was restricted by constraints from our x-ray data, namely, (1) the dimensions of the monoclinic unit cell and its pseudo-C2 symmetry (the real space group is P2₁), (2) the location of the phosphorous atom, and (3) the orientation of the bases. In addition, a geometric function was devised to impose Watson-Crick base pairing. Thus, a trial structure could be sought without explicit inclusion of intermolecular potentials. An interactive computer graphics system was used for visualizing the calculated structures. The packing searches yielded two lowest energy schemes in which the molecules had the same conformation (similar to double-helical RNA) but different orientations within the unit cell. One of these was refined by standard x-ray methods to a discrepancy index of 14.4% in the C2 pseudocell. This served as the starting structure for the subsequent refinement in the real P2₁ cell.⁵     

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.     

Conformational Studies of Dextran [α-(1⇒6)-D-Glucan]

Abstract

A theoretical conformational study of dextran, a (l?6)-linked α-D-glucan polysaccharide, has been made to allow an explicit comparison with earlier results on pustulan, the corresponding (1 ?6)-linked β-D-glucan. The nonbonded, torsional and hydrogen bond contributions to potential energy were calculated as a function of rotational angles φ, ψ, and ω The (φ, ψ, ω)-space of the disaccharide and of helices contain many local energy minima with very small energy differences. A comparison of (1?6)-α-D-glucans with (1?6)-β-D-glucans indicates significant differences in conformational behavior. Specifically, our results shed light on the fact that dextran does not gel, whereas pustulan does. The difference in tendency to gel may be related to the fact that dextran has no particularly favored conformations with structural regularity whereas pustulan does.     

Interactions of Molecules with Nucleic Acids. X. Covalent Intercalat e Binding of the Carcinogenic BPDE I(+) to Kinked DNA

Abstract

A theoretical model is proposed for the covalent binding of (+) 7 β,8α-dihydroxy-9α, 10α- epoxy-7,8,9,10-tetrahydrobenzo[a]pyrene denoted by BPDE I(+), to N2 on guanine. The DNA must kink a minimum of 39° to allow proper hybrid configurations about the C10 and N2 atoms involved in bond formation and to allow stacking of the pyrene moiety with the non-bonded adjacent base pair. Conservative (same sugar puckers and glycosidic angles as in B-DNA) and non-conservative (alternating sugar puckers as in intercalation sites) conformations are found and they are proposed structures in pathways connecting B-DNA, an intercalation site, and a kink site in the formation of a covalently intercalative bound adduct of BPDE I(+) to N2 on guanine. Stereographic projections are presented for (3′) and (5′) binding in the DNA. Experimental data for bending of DNA by BPDE, orientation of BPDE in DNA and unwinding of superhelical DNA is explained. The structure of a covalent intercalative complex is predicted to result from the reaction. Also, an anti ? syn transition of guanine results in a structure which allows the DNA to resume its overall B-form. The only change is that guanine has been rotated by 200° about its glycosidic bond so that the BPDE I(+) is bound in the major groove. The latter step may allow the DNA to be stored with an adduct which may produce an error in the genetic code.     

A Method for the Determination of Furanose Ring Coordinates in its Pseudorotation Circuit for Different Amplitudes of Pucker

Abstract

Interconversion between energetically favored molecular conformations must proceed through less favored intermediate states. Thus, a knowledge of the nucleotide furanose ring conformations, other than the crystallographically well-determined ones, are of interest in investigating nucleotide conformational energies and dynamics. The sugar ring flexibility affects the conformation and dynamics of the monomer and determines the range of feasible nucleic acid secondary and tertiary structures. We have generated furanose geometries for varying amplitudes of pucker over its entire range of pseudorotation by making use of a ring closure procedure and the empirical dependence of endocyclic bond lengths and bond angles on sugar pucker. Atomic coordinates are tabulated here for the furanose ring at pseudorotation phase angle intervals of 9° for the average amplitude (τ_m) of pucker of 39° as well as for decreased (20° and 30°) and increased (44°) values of τ_m. However, the coordinates for any values of P and τ_m can be readily calculated.     

Thermodynamic and Structural Properties of r(ACC) as Revealed by Ultraviolet Electronic Absorption,Circular Dichroism, 1H-NMR Spectroscopy and Monte Carlo Simulations

Abstract

UV absorption, circular dichroïsm (CD) and ¹H NMR, associated with Monte Carlo (MC) molecular structure simulations have been applied to the study of the trinucleoside diphosphate: r(ACC).

The MC study which has been conducted as a function of temperature, is based on random variations of the nucleotide conformational angles, i.e. phosphodiester chain torsional angles and sugar pucker pseudorotational angles. All of the chemical bond lengths and valence angles remained fixed during the structural simulation, except those of the sugar pucker. Six different initial structures have been selected in order to explore the molecular conformational space as completely as possible. This simulation procedure led to distinct families of equilibrium conformations at 283,298 and 318 K.

The thermodynamical parameters such as variations in entropy, enthalpy and also melting temperature (ΔS⁰ _x, ΔH⁰ _x and T_m) of the stacking (X) equilibrium were obtained from UV absorption and circular dichroïsm (CD) spectra recorded over a 80K temperature range. Chemical shifts (δ), vicinal coupling constants(³J _k) and cross-relaxation rates (σ_k,l) of trimers were measured at 400.13 MHz over a range of concentrations (2–13mM) and temperatures (283–333K). Least-squares fitting of the experimental chemical shifts to simple models of association (A) and stacking equilibria allowed separation of the variations in the δ values (Δδ_x and Δδ_A) due to either phenomenon. The three NMR data sets (Δδ_x, ³J^k,l and σ_k.l) were then evaluated for the minima conformers obtained with the MC simulations. Theoretical values of Δδ_x were estimated using the results of an ab initio study while the coupling constant data were simulated with Karplus-type equations. Finally, the relaxation data were simulated from the distance matrices using treatment for cases of both slow conformational exchange accompanied by rapid small-amplitude fluctuations about the minima structures.

A consistent picture of the large amplitude deformations (torsional angle variation) of these trimers has emerged from the present study. Optimized conformational blends at 283, 296 and 318K were obtained by least-squares fitting of the experimental data to the theoretical ones, while considering the populations as adjustable parameters. As it would be expected, the right-handed helical conformation (A-RNA type) is found to be the major stacked species, in the temperature range of 283 to 318K. Limited evidence for bulged structures has been obtained, whereas novel reverse-stacked and half-stacked conformers also presented theoretical data compatible with the NMR observables of aqueous r(ACC).     

Ab initio study of phenyl benzoate: structure,conformational analysis,dipole moment,IR and Raman vibrational spectra

The molecular structure (bond distances and angles), conformational properties, dipole moment and vibrational spectroscopic data (vibrational frequencies, IR and Raman intensities) of phenyl benzoate were calculated using Hartree–Fock (HF), density functional (DFT), and second order Møller–Plesset perturbation theory (MP2) with basis sets ranging from 6-31G* to 6-311++G**. The theoretical results are discussed mainly in terms of comparisons with available experimental data. For geometric data, good agreement between theory and experiment is obtained for the MP2, B3LYP and B3PW91 levels with basis sets including diffuse functions. The B3LYP/6-31+G* theory level estimates the shape of the experimental functions for phenyl torsion around the Ph–O and Ph–C bonds well, but reproduces the height of the rotational barriers poorly. The B3LYP/6-31+G* harmonic force constants were scaled by applying the scaled quantum mechanical force field (SQM) technique. The calculated vibrational spectra were interpreted and band assignments were reported. They are in excellent agreement with experimental IR and Raman spectra.Figure Calculated and experimental (GED) potential energy functions for torsional motion of phenyl benzoate relative to the minimum value. a The potential function for torsion about the O₃–C₄ bond. b The potential function for torsion about the C₂–C₁₀ bond.     

Necessary conditions for avoiding incorrect polypeptide folds in conformational search by energy minimization

Low energy conformations have been generated for melittin, pancreatic polypeptide, and ribonuclease S-peptide, both in the vicinity of x-ray structures by energy refinement and by an unconstrained search over the entire conformational space. Since the structural polymorphism of these medium-sized peptides in crystal and solution is moderate, comparing the calculated conformations to x-ray and nmr data provides information on local and global behavior of potential functions. Local analysis includes standardization calculations, which show that models with standard geometry can approximate good resolution x-ray data with less than 0.5 Å rms deviation (RMSD). However, the atomic coordinates are shifted up to 2 Å RMSD by local energy minimization, and thus 2 Å is generally the smallest RMSD value one can target in a conformational search using the same energy evaluation models. The unconstrained search was performed by a buildup-type method based on dynamic programming. To accelerate the generation of structures in the conformational search, we used the ECEPP potential, defined in terms of standard polypeptide geometry. A number of low energy conformations were further refined by relaxing the assumption of standard bond lengths and bond angles through the use of the CHARMM potential, and the hydrophobic folding energies of Eisenberg and McLachlan were calculated. Each conformation is described in terms of the RMSD from the native, hydrogen-bonding structure, solvent-acessible surface area, and the ratio of surfaces corresponding to nonpolar and polar residues. The unconstrained search finds conformations that are different from the native, sometimes substantially, and in addition, have lower conformational energies than the native. The origin of deviations is different for each of the three peptides, but in all examples the refined x-ray structures have lower energies than the calculated incorrect folds when (1) the assumption of standard bond lengths and bond angles is relaxed; (2) a small and constant effective dielectric permittivity (ε < 10) is used; and (3) the hydrophobic folding energy is incorporated into the potential. © 1993 John Wiley & Sons, Inc.     

Conformational studies on polynucleotide chains. III. Intramolecular energy maps and comparison with experiments

Conformational energy maps for the four combinations of two consecutive torsional angles of the backbone structure of polydeoxyribonucleotides are presented. Both the C(2′)-endo and the C(3′)-endo conformation of sugar rings were considered. The energies were evaluated with an analytical expression representing the best fit to ab initio energies computed in the Hartree-Fock approximation, and consisting of a contribution from nonbonded interactions of the Lennard-Jones 6-12 type and an intrinsic torsional potential. It is shown that the minima of these maps are in excellent agreement with the most stable conformations as obtained from x-ray crystallographic analysis of nucleic acids and polynucleotides.     

Computation of the bond dissociation enthalpies and free energies of hydroxylic antioxidants using the ab initio Hartree–Fock method

Abstract

Introduction

A new method for calculating theoretical bond dissociation enthalpy (BDE) and bond dissociation free energy (BDFE) of hydroxylic antioxidants is forwarded. BDE and BDFE may be understood as activation energies accompanying the formation of transition states, which may undergo downhill homolytic dissociation. The new method does not involve the complete fission of O–H bonds.

Method

Theoretical gas phase BDE values were calculated with the ab initio unrestricted Hartree–Fock (UHF) method, as changes in enthalpy between ground singlet states (GS) and triplet dissociative states (DS). Similarly, gas phase BDFEs were estimated from the corresponding changes in Gibbs free energy. The results were then compared with reliable experimental reports.

Results

The proposed theoretical approach of BDE and BDFE determination was tested using 10 simple phenols, 5 flavonoids, and l-ascorbic acid derivatives. The agreement between our calculated gas phase results and the adopted experimental values were generally within 0.5 kcal mol^?1, with a very few exceptions.

Discussion

Generally, steric interactions as well as intramolecular hydrogen bonding involving the dissociating OH group should be minimized in the GS. The DS are both electronically and vibrationally exited transition states. They have one unpaired electron on the carbon atom, which bears the homolytically dissociating OH group and are second order saddle points with a fixed <C–O–H bond angel of 180°.

Conclusion

It was concluded that ab initio UHF was well suited for the estimation of gas phase BDE and BDFE. The method presented has a good potential for application across a range of hydroxylic antioxidants. Currently, work is underway to extend its application in other class of antioxidants.     

A Modified Version of the Cornell et al. Force Field with Improved Sugar Pucker Phases and Helical Repeat

Abstract

We have examined some subtle parameter modifications to the Cornell et al. force field, which has proven quite successful in reproducing nucleic acid properties, but whose C2′-endo sugar pucker phase and helical repeat for B DNA appear to be somewhat underestimated. Encouragingly, the addition of a single V₂ term involving the atoms C(sp³)-O-(sp³)-C(sp³)- N(sp²), which can be nicely rationalized because of the anomeric effect (lone pairs on oxygen are preferentially oriented relative to the electron withdrawing N), brings the sugar pucker phase of C2′-endo sugars to near perfect agreement with ab initio calculations (W near 162°). Secondly, the use of high level ab initio calculations on entire nucleosides (in contrast to smaller model systems necessitated in 1994–95 by computer limitations) lets one improve the % torsional potential for nucleic acids. Finally, the O(sp³)-C(sp³)- C(sp³)-O(sp³) V₂ torsional potential has been empirically adjusted to reproduce the ab initio calculated relative energy of C2′- endo and C3′-endo nucleosides. These modifications are tested in molecular dynamics simulations of mononucleosides (to assess sugar pucker percentages) and double helices of DNA and RNA (to assess helical and sequence specific structural properties). In both areas, the modified force field leads to improved agreement with experimental data.     

Molecular Mechanics and Dynamics of an Abasic Frameshift in DNA and Comparison to NMR Data

Abstract

In a previous publication (Ph. Cuniasse, L.C. Sowers, R. Eritja, B. Kaplan, M.F. Goodman, J.A.H. Cognet, M. Le Bret, W. Guschlbauer and G.V. Fazakerley, Biochemistry 28, 2018 (1989), we determined by two dimensional NMR studies and molecular mechanics calculations the three-dimensional structure of a non-selfcomplementary oligonucleotide:

5′d(C1 P1 G2 P2 G3 P3 dr4 P4 G5 P5 G6 P6 C7)3′

3′d(G13P12C12PllCll P10 C10 P9 C9 P8 G8)5′

where dr, at the center of the first strand, is a model abasic site. In order to explain all the results arising from NMR measurements, we found that an equilibrium between two conformations was necessary. These conformations differ mainly by the sugar pucker of G5 which is C2′ endo or C3′ endo. The latter is stabilized by addition of counterions between phosphate residues P3 and P4.

In this paper, we have constructed systematically, all possible structures as a function of torsion angles delta of dr4 and of G5 by molecular mechanics in the presence or absence of counterions. Since these conformations were not forced with NMR distance measurements, this method allows detailed comparisons between all possible conformations and NMR data. Maps of contour lines of the potential energy, of fits to NMR distance measurements, and of helical twist as a function of torsion angles delta of dr4 and of G5 unravel the difficulties associated with the study of the G5 sugar pucker conformation equilibrium.

Sugar puckers and proton distances are very sensitive criteria to monitor molecular dynamics. Relying on these experimental criteria, we have tested many molecular dynamics preparation phases and we propose a new warm-up and equilibration procedure for molecular dynamics. Thus we show with a 290 ps molecular dynamic run that G5 is in conformational equilibrium and that all NMR data are well reproduced.     

Distortions of the DNA Double Helix Induced by 1,3-trans-Diamminedichloroplatinum(II)-intrastrand Cross-link: An Internal Coordinate Molecular Modeling Study

Abstract

A trans-diamminedichloroplatinum(II) (trans-DDP) intrastrand adduct within the sequence d(TCTG*TG*TC)·d(GACACAGA) (where G* represents a platinated guanine) is modeled on the basis of qualitative experimental data concerning global unwinding and curvature as well as information on base pairing. Modeling is performed using the internal coordinate JUMNA program, specific to nucleic acids, and modified to include the possibility of covalently bound ligands. Calibration of the energy functions representing the Pt-N7 bond with guanine is described. The platinum atom and the platinum-nitrogen bonds are parameterized for use in the Hückel Del Re method to calculate monopoles at each atom. These monopoles are consistent with the Flex force field included in Jumna. By developing an appropriate minimization protocol we are able to generate stable, distorted three-dimensional structures compatible with the experimental data and including an unusually high global unwinding. No a priori geometric assumptions are made in generating these structures.     

UV Photoelectron Spectroscopy and Ab Initio Characterization of Valence Orbital Structures and Conformations of Neutral Phosphate Esters

Abstract

The Hel UV photoelectron spectrum of trimethyl phosphate (TMP) has been measured and interpreted with the aid of SCF molecular orbital calculations carried out with STO-3G, STO-3G* and 4–31G basis functions. The photoelectron spectrum of TMP is more accurately reproduced by results from 4–31G calculations than by results from STO-3G or STO-3G* calculations. However, all three basis sets yield results which predict the same assignment of the photoelectron spectrum. Results at the 4–31G level indicate that whether calculations are based on crystallographic bond angles and bond lengths or on STO-3G optimized geometries has little effect on the energetic ordering of the upper occupied orbitals. The energetic ordering of orbitals is also found to be only weakly dependent upon the torsional angle φ, describing rotation of ester groups about P-O bonds and upon the torsional angle ψ, describing rotation of methyl groups about C-O bonds. For trimethyl phosphate, with C₃ symmetry, the vertical ionization potentials of the upper occupied orbitals are 10.81 eV (8e), 11.4 eV (9a), 11.93 eV (7e), 12.6–12.9 eV (8a and 6e), 14.4 eV (7a) and 15.0–16.0 eV(5e and 6a). Calculations at the 4–31G level indicate that many of the highest occupied orbitals in neutral dimethyl phosphate and methyl phosphate have energies and electron distributions similar to orbitals in TMP.

For TMP, a search for optimized values of φ and ψ has been carried out at the STO-3G* level. In agreement with previous NMR studies and with classical potential calculations, the STO- 3G* results indicate that both the gauche φ= 53.1 °) and anticlinal (φ = 141.9°) conformations are thermally accessible. Also in agreement with the classical potential calculations, the STO-3G* results predict that in the all gauche conformation energy is minimized when the methyl groups assume a staggered geometry (ψ= 60° to 80°) and that an energy maximum occurs for an eclipsed geometry (ψ = 0° to 20°). A study of the dependence of optimized values of O-P-O ester bond angles on the torsional angles, φ, was carried out at the STO-3G, STO-3G* and 4–31G levels. The results demonstrate that for C₃ symmetry, the coupling of O-P-O angles to φ is influenced by repulsive steric interactions.