Computerized Molecular Modeling of Carbohydrates.

Computerized molecular modeling continues to increase in capability and applicability to carbohydrates. This chapter covers nomenclature and conformational aspects of carbohydrates, perhaps of greater use to computational chemists who do not have a strong background in carbohydrates, and its comments on various methods and studies might be of more use to carbohydrate chemists who are inexperienced with computation. Work on the intrinsic variability of glucose, an overall theme, is described. Other areas of the authors' emphasis, including evaluation of hydrogen bonding by the atoms-in-molecules approach, and validation of modeling methods with crystallographic results are also presented.

Quantum mechanics models of the methanol dimer: OH⋯O hydrogen bonds of ß-d-glucose moieties from crystallographic data.

The interaction of two methanol molecules, simplified models of carbohydrates and cellulose, was examined using a variety of quantum mechanics (QM) levels of theory. Energy plots for hydrogen bonding distance (H⋯O) and angle (OH⋯O) were constructed. All but two experimental structures were located in stabilized areas on the vacuum phase energy plots. Each of the 399 models was analyzed with Bader's atoms-in-molecules (AIM) theory, which showed a widespread ability by the dimer models to form OH⋯O hydrogen bonds that have bond paths and Bond Critical Points. Continuum solvation calculations suggest that a portion of the energy-stabilized structures could occur in the presence of water. A survey of the Cambridge Structural Database (CSD) for all donor-acceptor interactions in ß-D-glucose moieties examined the similarities and differences among the hydroxyl groups and acetal oxygen atoms that participate in hydrogen bonds. Comparable behavior was observed for the O2H, O3H, O4H, and O6H hydroxyls, acting either as acceptors or donors. Ring O atoms showed distinct hydrogen bonding behavior that favored mid-length hydrogen bonds.

Conformational analysis of cellobiose by electronic structure theories.

Adiabatic Φ/ψ maps for cellobiose were prepared with B3LYP density functional theory. A mixed basis set was used for minimization, followed with 6-31+G(d) single-point calculations, with and without SMD continuum solvation. Different arrangements of the exocyclic groups (38 starting geometries) were considered for each Φ/ψ point. The vacuum calculations agreed with earlier computational and experimental results on the preferred gas phase conformation (anti-Φ(H), syn-ψ(H)), and the results from the solvated calculations were consistent with the (syn Φ(H)/ψ(H) conformations from condensed phases (crystals or solutions). Results from related studies were compared, and there is substantial dependence on the solvation model as well as arrangements of exocyclic groups. New stabilizing interactions were revealed by Atoms-In-Molecules theory.

Computerized molecular modeling of carbohydrates.

Computerized molecular modeling continues to increase in capability and applicability to carbohydrates. This chapter covers nomenclature and conformational aspects of carbohydrates, perhaps of greater use to carbohydrate-inexperienced computational chemists. Its comments on various methods and studies might be of more use to computation-inexperienced carbohydrate chemists. New work on intrinsic variability of glucose, an overall theme, is described.

Experimental and theoretical electron density distribution of alpha,alpha-trehalose dihydrate.

alpha,alpha-Trehalose is of interest because of its cryoprotective and antidessicant properties, and because it possesses various technical anomalies such as (13)C NMR spectra that give misleading indications of intramolecular structural symmetry. It is a non-reducing disaccharide, with the glycosidic oxygen atom shared by the anomeric carbon atoms of the two glucose rings, and is therefore subject to a proposed 'overlapping'exo-anomeric effect. We report here a study of the electron density of trehalose with X-ray diffraction and quantum mechanics calculations, similar to a recent study of sucrose, also a non-reducing molecule. In particular we studied the electron density around the glycosidic linkage and the hydrogen bonding with both deformation density and Atoms in Molecules (AIM) analyses. A total of 129,952 single crystal X-ray intensity measurements were collected on alpha,alpha-trehalose dihydrate to a resolution of sintheta/lambda=1.18A(-1) at 100K and refined with an aspherical multipole model to a final agreement factor of R(1)=0.0160. Wavefunctions were calculated at three levels of theory. Redistribution of electron density due to anomeric effects was reduced in trehalose, compared to sucrose. Five new C-Hcdots, three dots, centeredO hydrogen bonds were confirmed with bond critical points and bond paths from AIM analyses, as were the previously proposed O-Hcdots, three dots, centeredO hydrogen bonds.

Conformational flexibility of soluble cellulose oligomers: chain length and temperature dependence.

Structures, dynamics, and stabilities of different sized cellulosic oligomers need to be considered when designing enzymatic cocktails for the conversion of biomass to biofuels since they can be both productive substrates and inhibitors of the overall process. In the present work, the conformational variability, hydrogen bonding, and mechanical properties of short, soluble cellulose chains are investigated as a function of chain length. Cellulose oligomers consisting 2, 4, and 6 beta-d-glucose units are examined in explicit solvent using replica exchange molecular dynamics (REMD) which provides a rigorous evaluation of the relative stabilities of different conformations and their temperature dependencies. This application of REMD to oligosaccharides in solution also allows evaluation of the quality of the force-field and its suitability for sampling carbohydrates efficiently. Simulation results are analyzed in synergy with polymer theory and compared to known measurements of oligomers and crystals. As the chain length is increased, the conformations of the oligomers become more rigid and likely to form intrachain hydrogen bonds, like those found in crystals. Several other conformations and hydrogen bonding patterns distinguish these short cellulose chains from those in cellulose crystals. These studies have also addressed the key role played by solvent on shifting the conformational preferences of the oligosaccharides with respect to vacuum and crystals. Correlation between pyranose ring flipping and the conformation of the 1,4-glycosidic bond was observed.

Twisting of glycosidic bonds by hydrolases.

Patterns of scissile bond twisting have been found in crystal structures of glycoside hydrolases (GHs) that are complexed with substrates and inhibitors. To estimate the increased potential energy in the substrates that results from this twisting, we have plotted torsion angles for the scissile bonds on hybrid Quantum Mechanics::Molecular Mechanics energy surfaces. Eight such maps were constructed, including one for alpha-maltose and three for different forms of methyl alpha-acarviosinide to provide energies for twisting of alpha-(1,4) glycosidic bonds. Maps were also made for beta-thiocellobiose and for three beta-cellobiose conformers having different glycon ring shapes to model distortions of beta-(1,4) glycosidic bonds. Different GH families twist scissile glycosidic bonds differently, increasing their potential energies from 0.5 to 9.5 kcal/mol. In general, the direction of twisting of the glycosidic bond away from the conformation of lowest intramolecular energy correlates with the position (syn or anti) of the proton donor with respect to the glycon's ring oxygen atom. This correlation suggests that glycosidic bond distortion is important for the optimal orientation of one of the glycosidic oxygen lone pairs toward the enzyme's proton donor.

Comparison of different force fields for the study of disaccharides.

Eighteen empirical force fields and the semi-empirical quantum method PM3CARB-1 were compared for studying beta-cellobiose, alpha-maltose, and alpha-galabiose [alpha-D-Galp-(1-->4)-alpha-D-Galp]. For each disaccharide, the energies of 54 conformers with differing hydroxymethyl, hydroxyl, and glycosidic linkage orientations were minimized by the different methods, some at two dielectric constants. By comparing these results and the available crystal structure data and/or higher level density functional theory results, it was concluded that the newer parameterizations for force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF) give results that are reasonably similar to each other, whereas the older parameterizations for Amber, CHARMM or OPLS were more divergent. However, MM3, an older force field, gave energy and geometry values comparable to those of the newer parameterizations, but with less sensitivity to dielectric constant values. These systems worked better than MM2 variants, which were still acceptable. PM3CARB-1 also gave adequate results in terms of linkage and exocyclic torsion angles. GROMOS, GLYCAM06, and MM3 appear to be the best choices, closely followed by MM4, CSFF, and OPLS-2005. With GLYCAM06 and to a lesser extent, CSFF, and OPLS-2005, a number of the conformers that were stable with MM3 changed to other forms.

Evaluation of Density Functionals and Basis Sets for Carbohydrates.

Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of α- and ß-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of ß-d-glucopyranose. For each set, conformational energies varied by about 7 kcal/mol. Results obtained with the Hartree-Fock method, with pure density functional approximations (DFAs) like LSDA, PBEsol, PBE, and TPSS and with hybrid DFAs like B3PW91, B3LYP, PBEh, and M05-2X, were then compared to the reference and local MP2 relative energies. Basis sets included 6-31G*, 6-31G**, 6-31+G*, 6-31+G**, 6-311+G**, 6-311++G**, cc-pVTZ(-f), cc-pVTZ, and aug-cc-pVTZ(-f). The smallest basis set that gives good DFA relative energies is 6-31+G**, and more converged results can be obtained with 6-311+G**. The optimized geometries obtained from a smaller basis set, 6-31+G*, were useful for subsequent single point energy calculations with larger basis sets. The best agreement with MP2 was shown by M05-2X, but only when using a dense DFT grid. The popular B3LYP functional is not the best for saccharide conformational studies. The B3PW91 functional gives systematically better results, but other hybrid functionals like PBEh or TPSSh are even better. Overall, the nonempirical PBE GGA and TPSS meta-GGA functionals also performed better than B3LYP.

Neutron crystallography, molecular dynamics, and quantum mechanics studies of the nature of hydrogen bonding in cellulose Ibeta.

In the crystal structure of cellulose I beta, disordered hydrogen bonding can be represented by the average of two mutually exclusive hydrogen bonding schemes that have been designated A and B. An unanswered question is whether A and B interconvert dynamically, or whether they are static but present in different regions of the microfibril (giving temporally or a spatially averaged structures, respectively). We have used neutron crystallographic techniques to determine the occupancies of A and B at 295 and 15 K, quantum mechanical calculations to compare the energies of A and B, and molecular dynamics calculations to look at the stability of A. Microfibrils are found to have most chains arranged in a crystalline I beta structure with hydrogen bonding scheme A. Smaller regions of static disorder exist, perhaps at defects within or between crystalline domains in which the hydrogen bonding is complex but with certain features that are found in B.

Linkage and pyranosyl ring twisting in cyclodextrins.

Acylated beta-cyclodextrins (beta-CDs) were studied to gain perspective on maltose octapropanoate, the crystal structure of which was reported in the preceding paper in this issue. Acylated beta-CDs are distorted so we looked at other CDs and gained increased understanding of distortion in CDs and possibly, shapes in starch. Classic CDs have six to eight glucose residues in a doughnut shape that is stabilized by a ring of inter-residue O3,,,O2' hydrogen bonds. On a phi,psi energy map for a maltose analog that does not form hydrogen bonds, classic CD linkages have higher energies than structures that are stabilized by the exo-anomeric effect. In distorted beta-CDs, which lack hydrogen bonding, some linkages attain low-energies from the exo-anomeric effect and acyl stacking. Those linkages result in left-handed helical geometry so other linkages are forced by the CD macrocycle to have counter-balancing right-handed character. Permethylated gamma-CDs have two 'flipping' linkages as do some larger native CDs. Flipping linkages allow two left-handed segments to join into a macrocycle, thus avoiding the higher-energy, right-handed forms. Some glucose rings in derivatized beta-CDs have substantial positive twists of the pseudo torsion angle O1-C1...C4-O4, adding right-handed character to balance the left-handed linkages. In substituted gamma-CD, all residues have negative twists, giving extra left-handed character to the short, pseudo-helical segments. In non-macrocyclic molecules the twists ranged from -14 degrees to +2 degrees , averaging -6.1 degrees. In these beta- and gamma-CDs, the twists ranged from -22 degrees to +16 degrees for (4)C(1) rings, and the (O)S(2) ring in acetylated beta-CD has a twist of +34 degrees . Glucose residues in other CDs were less twisted.

Octa-O-propanoyl-beta-maltose: crystal structure, acyl stacking, related structures, and conformational analysis.

The crystal structure of beta-maltose octapropanoate (1) was solved to improve understanding of di-, oligo-, and polysaccharide conformations. The O6 and O6' atoms are in gg and gt orientations, respectively. Extrapolation of the coordinates of the non-reducing residue and observed linkage bond and torsion angles of 1 [Formula: see text] yields a left-handed helix similar to amylose triacetate I. The phi and psi values of 1 are also similar to those of other crystalline, acylated maltose compounds as well as some hydroxyl-bearing molecules. Acylated maltose moieties are often stabilized by stacking of the carbonyl groups and alpha-carbons on O3 and O2' as well as by the exo-anomeric effect. The conformation of 1 is within the 1-kcal/mol contour on a hybrid energy map built with a dielectric constant of 7.5, but corresponds to higher energies on maps made with lower dielectric constants. In one region of phi,psi space, both hydroxyl-bearing and derivatized maltose moieties are found but no inter-residue, intramolecular hydrogen-bonding occurs. In another region, only hydroxyl-bearing molecules crystallize and O2'...O3 hydrogen bonds are always found. In agreement with the energy surfaces, amylose helices extrapolated from available linkage geometries were almost all left-handed.

Determining the crystal structure of cellulose III(I) by modeling.

Recently, a one-chain monoclinic unit cell for cellulose III(I) having P2(1) symmetry and a single glucose in the asymmetric unit was proposed, based on high-resolution diffraction patterns. The new work challenged a two-chain structure that was published 25 years earlier, although it did not provide new three-dimensional coordinates. Our goals were to solve the structure by modeling, find whether modeling would reject the previously determined two-chain unit cell, and compare the model with the anticipated experimental structure. Combinations of three rotamers of the O-2, O-3, and O-6 hydroxyl groups produced 27 'up' and 27 'down' starting structures. Clusters ('minicrystals') of 13 cellotetraose chains terminated by methyl groups for each of the 54 starting structures were optimized with MM3(96). Hydroxyl groups on 16 of these 54 structures reoriented to give very similar hydrogen-bonding schemes in the interiors, along with the lowest energies. Hydrogen bonds included the usual intramolecular O-3H...O-5' linkage, with O-6' also accepting from O-3H. Interchain hydrogen bonds form an infinite, cooperative O-6H...O-2H...O-6 network. Direct comparison of total minicrystal energies for the one- and two-chain unit cell was inappropriate because the two-chain cell's alternate chains are shifted 0.9 A along the z-axis. To get comparable energy values, models were built with both cellotetraose and cellohexaose chains. The differences in their energies represent the energies for the central layers of cellobiose units. The one-chain cell models had much lower energy. The eight best 'up' one-chain models agree reasonably well with the structure newly determined by experiment.

The external-anomeric torsional effect.

The rotational barrier for a methyl group at the end of an anomeric system is sometimes lower than we might have anticipated. Thus, in the trans-trans conformation of dimethoxymethane, the barrier to methyl rotation is calculated (B3LYP/6-311++G(2d,2p)) to be 2.22 kcal/mol, just slightly smaller than the corresponding barrier to rotation of the methyl group in methyl propyl ether of 2.32 kcal/mol. However, if the methyl being rotated in dimethoxymethane is placed into a gauche conformation, that rotational barrier is reduced to 1.52 kcal/mol. This substantial (0.80 kcal/mol relative to methyl propyl ether) reduction in barrier height in the latter case is attributed mainly to the change in the bond order of the C-O bond to which the methyl is attached, as a function of conformation, which in turn is a result of the anomeric effect. We have called this barrier lowering the external-anomeric torsional effect. This effect is apparently widespread in carbohydrates, and it results in the changing of conformational energies by up to about 2 kcal/mol. If polysaccharide potential surfaces are to be accurately mapped by molecular mechanics, this effect clearly needs to be accounted for.

Incremented alkyl derivatives enhance collision induced glycosidic bond cleavage in mass spectrometry of disaccharides.

Electrospray ionization and collision induced dissociation on a triple quadrupole mass spectrometer were used to determine the effect of spatial crowding of incremented alkyl groups of two anomeric pairs of peralkylated (methyl to pentyl) disaccharides (maltose/cellobiose and isomaltose/gentiobiose). Protonated molecules were generated which underwent extensive fragmentation under low energy conditions. For both the 1 --> 4 and 1 --> 6 alpha and beta isomers, at comparable collision energies the methyl derivative exhibited the least fragmentation followed by ethyl, propyl, butyl, and pentyl. Collision energy is converted to rotational-vibrational modes in competition with bond cleavage, as represented by the slope of product/parent ion (D/P) ratio versus offset energy. Variable rotational freedom at the glycosidic linkage with incremented alkyl groups is hypothesized to be responsible for this effect. Discrimination of anomeric configuration was also assessed for these stereoiosmeric disaccharides. A systematic study showed that an increasing discrimination was attained for the 1 --> 4 isomeric pair as the size of the derivative increased from methyl to pentyl. No anomeric discrimination was attained for the 1 --> 6 isomeric pair. Parent and product ion scans confirmed the consistency of fragmentation pathways among derivatives. Chem-X and MM3 molecular modeling programs were used to obtain minimum energy structures and freedom of motion volumes for the permethylated disaccharides. The modeling results correlated with the fragmentation ratios obtained in the mass spectrometer giving strong indication that the collision induced spectra are dependent on the freedom of rotational motion around the glycosidic bond.

Crystal structure of penta-O-acetyl-beta-D-galactopyranose with modeling of the conformation of the acetate groups.

The crystal structure of penta-O-acetyl-beta-D-galactopyranose was determined with Mo K(alpha) radiation at 150 K to R = 0.029. The space group is P2(1)2(1)2(1), and the unit cell dimensions are, a = 8.348, b = 9.021 and c = 25.418 A. The ring has the usual 4C(1) shape and O-6 is in the tg position as frequently observed for sugars having the axial galacto configuration at C-4. Conformations of the acetate groups were compared with those from the literature. Nearly eclipsed, 'Z' conformations are found for the ester moieties, and the torsion angles for the sequence involving the ring hydrogen, carbon, alkoxy oxygen and carbonyl carbon for both 1 and related compounds are eclipsed-to-gauche. Orientations and conformations of the acetate substituents were modeled with both MM3 molecular mechanics and various levels of quantum mechanics theory. Higher levels of theory and more complete models provided better prediction of the experimental observations.

The crystal structure of the alpha-cellobiose.2 NaI.2 H(2)O complex in the context of related structures and conformational analysis.

The crystal structure of beta-D-glucopyranosyl-(1-->4)-alpha-D-glucopyranose (alpha-cellobiose) in a complex with water and NaI was determined with Mo K(alpha) radiation at 150 K to R=0.027. The space group is P2(1) and unit cell dimensions are a=9.0188, b=12.2536, c=10.9016 A, beta=97.162 degrees. There are no direct hydrogen bonds among cellobiose molecules, and the usual intramolecular hydrogen bond between O-3 and O-5' is replaced by a bridge involving Na+, O-3, O-5', and O-6'. Both Na+ have sixfold coordination. One I(-) accepts six donor hydroxyl groups and three C-H***I(-) hydrogen bonds. The other accepts three hydroxyls, one Na+, and five C-H***I(-) hydrogen bonds. Linkage torsion angles phi(O-5) and psi(C-5) are -73.6 and -105.3 degrees, respectively (phi(H)=47.1 degrees and psi(H)=14.6 degrees ), probably induced by the Na+ bridge. This conformation is in a separate cluster in phi,psi space from most similar linkages. Both C-6-O-H and C-6'-O-H are gg, while the C-6'-O-H groups from molecules not in the cluster have gt conformations. Hybrid molecular mechanics/quantum mechanics calculations show <1.2 kcal/mol strain for any of the small-molecule structures. Extrapolation of the NaI cellobiose geometry to a cellulose molecule gives a left-handed helix with 2.9 residues per turn. The energy map and small-molecule crystal structures imply that cellulose helices having 2.5 and 3.0 residues per turn are left-handed.