Agreement between Single Crystal X-Ray and Molecular Mechanical Sugar Ring Conformations

Abstract

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 Å. Most of the experimental values of (q, W) fall within 1.0 Kcal/mol from the calculated minimum.     

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.     

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.     

Vibrational normal modes and dynamical stability of DNA triplex poly(dA). 2poly(dT): S-type structure is more stable and in better agreement with observations in solution.

A normal-mode and statistical mechanical calculation was carried out to determine the vibrational normal modes, contribution of internal fluctuations to the free energy, and hydrogen bond disruption of DNA triplex poly(dA).2poly(dT). The calculation was performed on both the x-ray fiber diffraction model with a N-type sugar conformation, and a newly proposed model with a S-type sugar conformation. Our calculated normal modes for the S-type structure are in better agreement with observed IR spectra for samples in D2O solution. We also find that the contribution of internal fluctuations to free energy, premelting hydrogen bond disruption probability, and hydrogen bond melting temperatures for the Hoogsteen and Watson-Crick hydrogen bonds all show that the S-type structure is dynamically more stable than the N-type structure in a nominal solution environment. Therefore our calculation supports experimental findings that the triplex d(T)n.d(A)nd(T)n most likely adopts a S-type sugar conformation in solution or at high humidity. Our calculations, however, do not preclude the possibility of an N-type conformation at lower humidities.     

Consistent force field calculations on 2,5-diketopiperazine and its 3.6-dimethyl derivatives

The minimum energy conformations are calculated for 2, 5-diketopiperazine (DKP) and its 3,6-dimethyl derivatives (DL-DMDKP and LL-DMDKP), using a consistent force field approach developed previously. The energy function parameters that were not required in earlier calculations on alkanes, amides, mid lactams are fitted to spectral and conformational data on the diketopiperazines. Vibrational assignments are suggested for DKP. Conformational energies are also determined over a range of selected values for ring dihedral angles, and the shape of the potential energy functions is examined over deviations from planarity. DKP and LL-DMDKP are found to have non-planar minimum energy conformations, separated from planar by less than a kcal/mole. DL-DMKP exhibits a nearly flat trough about the planar conformation. Calculations of minimum energies with one dihedral angle coordinate constrainted show a coupling between bond angles and dihedral angles in agreement with recent suggestions of Benedetti.     

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.     

Flexibility of 3',5' deoxyribonucleoside diphosphates

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.     

Solid-state NMR determination of sugar ring pucker in (13)C-labeled 2'-deoxynucleosides

The H3'-C3'-C4'-H4' torsional angles of two microcrystalline 2'-deoxynucleosides, thymidine and 2'-deoxycytidine.HCl, doubly (13)C-labeled at the C3' and C4' positions of the sugar ring, have been measured by solid-state magic-angle-spinning nuclear magnetic resonance (NMR). A double-quantum heteronuclear local field experiment with frequency-switched Lee-Goldberg homonuclear decoupling was used. The H3'-C3'-C4'-H4' torsional angles were obtained by comparing the experimental curves with numerical simulations, including the two (13)C nuclei, the directly bonded (1)H nuclei, and five remote protons. The H3'-C3'-C4'-H4' angles were converted into sugar pucker angles and compared with crystallographic data. The delta torsional angles determined by solid-state NMR and x-ray crystallography agree within experimental error. Evidence is also obtained that the proton positions may be unreliable in the x-ray structures. This work confirms that double-quantum solid-state NMR is a feasible tool for studying sugar pucker conformations in macromolecular complexes that are unsuitable for solution NMR or crystallography.     

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.     

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     

Structure calculations for single-stranded DNA complexed with the single-stranded DNA binding protein GP32 of bacteriophage T4: a remarkable DNA structure

In this study it is established by calculation which regular conformations single-stranded DNA and RNA can adopt in the complex with the single-stranded DNA binding protein GP32 of bacteriophage T4. In order to do so, information from previous experiments about base orientations and the length and diameter of the complexes is used together with knowledge about bond lengths and valence angles between chemical bonds. It turns out that there is only a limited set of similar conformations which are in agreement with experimental data. The arrangement of neighboring bases is such that there is ample space for aromatic residues of the protein to partly intercalate between the bases, which is in agreement with a previously proposed model for the binding domain of the protein [Prigodich, R. V., Shamoo, Y., Williams, K. R., Chase, J. W., Konigsberg, W. H., & Coleman, J. E. (1986) Biochemistry 25, 3666-3671]. Both C2'endo and C3'endo sugar conformations lead to calculated DNA conformations that are consistent with experimental data. The orientation of the O2' atoms of the sugars in RNA can explain why the binding affinity of GP32 for polyribonucleotides is lower than for polydeoxyribonucleotides.     

Conformational and dynamical properties of disaccharides in water: a molecular dynamics study

Explicit-solvent molecular dynamics simulations (50 ns, 300 K) of the eight reducing glucose disaccharides (kojibiose, sophorose, nigerose, laminarabiose, maltose, cellobiose, isomaltose, and gentiobiose) have been carried out using the GROMOS 45A4 force field (including a recently reoptimized carbohydrate parameter set), to investigate and compare their conformational preferences, intramolecular hydrogen-bonding patterns, torsional dynamics, and configurational entropies. The calculated average values of the glycosidic torsional angles agree well with available experimental data, providing validation for the force field and simulation methodology employed in this study. These simulations show in particular that: 1) (1-->6)-linked disaccharides are characterized by an increased flexibility, the absence of any persistent intramolecular hydrogen bond and a significantly higher configurational entropy (compared to the other disaccharides); 2) cellobiose presents a highly persistent interresidue hydrogen bond and a significantly lower configurational entropy (compared to the other disaccharides); 3) persistent hydrogen bonds are observed for all disaccharides (except (1-->6)-linked) and typically involve a hydrogen donor in the reducing residue and an acceptor in the nonreducing one; 4) the probability distributions associated with the glycosidic dihedral angles and psi are essentially unimodal for all disaccharides, and full rotation around these angles occurs at most once or twice for (never for psi) on the 50-ns timescale; and 5) the timescales associated with torsional transitions (except around and psi) range from approximately 30 ps (rotation of hydroxyl groups) to the nanosecond range (rotation of the lactol and hydroxymethyl groups, and around the omega-glycosidic dihedral angle in (1-->6)-linked disaccharides).     

An improved hydrogen bond potential: impact on medium resolution protein structures

A new semi-empirical force field has been developed to describe hydrogen-bonding interactions with a directional component. The hydrogen bond potential supports two alternative target angles, motivated by the observation that carbonyl hydrogen bond acceptor angles have a bimodal distribution. It has been implemented as a module for a macromolecular refinement package to be combined with other force field terms in the stereochemically restrained refinement of macromolecules. The parameters for the hydrogen bond potential were optimized to best fit crystallographic data from a number of protein structures. Refinement of medium-resolution structures with this additional restraint leads to improved structure, reducing both the free R-factor and over-fitting. However, the improvement is seen only when stringent hydrogen bond selection criteria are used. These findings highlight common misconceptions about hydrogen bonding in proteins, and provide explanations for why the explicit hydrogen bonding terms of some popular force field sets are often best switched off.     

Direct nuclear Overhauser effect refinement of crambin from two-dimensional nmr data using a slow-cooling annealing protocol

The solution structure of crambin has been refined using a direct nuclear Overhauser effect (NOE) simulation approach (DINOSAUR) following a slow-cooling simulated annealing protocol starting from eight previously obtained nmr and the x-ray structures of crambin. Theoretical NOE intensities calculated with inclusion of local motions were directly compared to the experimental nmr data and forces were derived using a simple first-order approximation for the calculation of the NOE gradient. A dynamic assignment procedure was applied for the peaks involving unassigned diastereotopic proton pairs or equivalent aromatic protons. With this approach, R factors could be minimized in a reasonable simulation time to low values (around 0.26) while deviations from ideal bond lengths and angles are still acceptable. The improvement in R factors is accompanied by an improvement of the precision of the structures, the rms deviations (rmsd; from the average) calculated on the ensemble of nine structures decreasing from 0.65 to 0.55 Å for backbone atoms and from 1.0 to 0.85 Å for all heavy atoms. The solution structure is significantly different from the x-ray structure with rmsd for all atoms of 1.35 Å compared to 0.85 Å between solution structures. The largest differences are found for residues Thr-21 and Pro-22 in the loop region between the two α-helices and for the side chain of Tyr-29. © 1994 John Wiley & Sons, Inc.     

Synthesis, X-ray crystallographic structures of thio substituted N-acetyl N'-methylamide alanine and evaluation of sp sulfur parameters of the CFF91 force field.

Acetyl thioalanine N-methyl (Ac-Alat-NHMe) and thioacetyl alanine N-methyl (Act-Ala-NHMe) were synthesized, crystallized and their X-ray diffraction structures determined for the first time. Both molecules adopted beta-sheet conformations and showed similar hydrogen bonding patterns with one molecular surface forming two oxo hydrogen bonds and the other forming two thio hydrogen bonds. The crystal structure data for the two thioamides provided a validation of the thioamide parameters for the newly derived CFF91 force field because the observed crystal (phi, psi) angles were situated in the global minimum regions of the theoretical (phi, psi) map predicted using the parameters. In addition, the parameters were further validated because conformational energy minimization of the crystal structure produced low deviations in unit cell dimensions, bond lengths, bond angles and torsional angles, and a 120-ps molecular dynamics simulation also gave a low deviation for the most probable N-H...S=C bond distance.     

Molecular Mechanics: The Conjugate Nitro Group Parameters in the MM2 Force Field

The conjugated nitro group has been included in the π system calculation within the MM2 force field. New parameters have been estimated by a statistical process from X-ray molecular structures recorded in the C.S.D.S. Comparison of the corresponding results with those given by the MM2(91) force field parameters show a clear improvement for dihedral and bond angles. For N-O and C-N bond lengths a slight global improvement is also observed. A closer examination of the results for the latter bond shows that sometimes MM2(91) gives better results for six membered ring nitro compounds. By contrast the parameters proposed here are more adapted to five membered ring derivatives. The derived linear relations permit the study of molecules over a wider range of π indices. The introduction of a correction factor to the calculated molecular π dipole moment in conjunction with a necessary reestimation of some σ-bond dipole moments also leads to improved total molecular dipole moments.     

Application of a genetic algorithm in the conformational analysis of methylene-acetal-linked thymine dimers in DNA: Comparison with distance geometry calculations

The three-dimensional spatial structure of a methylene-acetal-linked thymine dimer presentin a 10 base-pair (bp) sense–antisense DNA duplex was studied with a geneticalgorithm designed to interpret NOE distance restraints. Trial solutions were represented bytorsion angles. This means that bond angles for the dimer trial structures are kept fixed duringthe genetic algorithm optimization. Bond angle values were extracted from a 10 bpsense–antisense duplex model that was subjected to energy minimization by means ofa modified AMBER force field. A set of 63 proton–proton distance restraints definingthe methylene-acetal-linked thymine dimer was available. The genetic algorithm minimizesthe difference between distances in the trial structures and distance restraints. A largeconformational search space could be covered in the genetic algorithm optimization byallowing a wide range of torsion angles. The genetic algorithm optimization in all cases ledto one family of structures. This family of the methylene-acetal-linked thymine dimer in theduplex differs from the family that was suggested from distance geometry calculations. It isdemonstrated that the bond angle geometry around the methylene-acetal linkage plays animportant role in the optimization.     

Molecular Mechanics: The Conjugate Nitro Group Parameters in the MM2 Force Field

The conjugated nitro group has been included in the π system calculation within the MM2 force field. New parameters have been estimated by a statistical process from X-ray molecular structures recorded in the C.S.D.S. Comparison of the corresponding results with those given by the MM2(91) force field parameters show a clear improvement for dihedral and bond angles. For N-O and C-N bond lengths a slight global improvement is also observed. A closer examination of the results for the latter bond shows that sometimes MM2(91) gives better results for six membered ring nitro compounds. By contrast the parameters proposed here are more adapted to five membered ring derivatives. The derived linear relations permit the study of molecules over a wider range of π indices. The introduction of a correction factor to the calculated molecular π dipole moment in conjunction with a necessary reestimation of some σ-bond dipole moments also leads to improved total molecular dipole moments.