The external-anomeric torsional effect

Combining Computational Chemistry and Crystallography for a Better Understanding of the Structure of Cellulose

The approaches in this article seek to enhance understanding of cellulose at the molecular level, independent of the source and the particular crystalline form of cellulose. Four main areas of structure research are reviewed. Initially, the molecular shape is inferred from the crystal structures of many small molecules that have β-(1→4) linkages. Then, conformational analyses with potential energy calculations of cellobiose are covered, followed by the use of Atoms-In-Molecules theory to learn about interactions in experimental and theoretical structures. The last section covers models of cellulose nanoparticles. Controversies addressed include the stability of twofold screw-axis conformations, the influence of different computational methods, the predictability of crystalline conformations by studies of isolated molecules, and the twisting of model cellulose crystals.

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.

Insights into furanose solution conformations: beyond the two-state model

A two-state model is commonly used for interpreting ring conformations of furanoses based on NMR scalar (3) J-coupling constants, with the ring populating relatively narrow distributions in the North and the South of the pseudorotation itinerary. The validity of this simple approach has been questioned, and is examined here in detail employing molecular dynamics (MD) simulations with a new GLYCAM force field parameter set for furanoses. Theoretical (3) J-coupling constants derived from unrestrained MD simulations with the new furanose-specific parameters agreed with the experimental coupling constants to within 1 Hz on average. The results confirm that a two state model is a reasonable description for the ring conformation in the majority of methyl furanosides. However, in the case of methyl α-D-arabinofuranoside the ring populates a continuum of states from North to South via the eastern side of the pseudorotational itinerary. Two key properties are responsible for these differences. Firstly, East and West regions in β- and α-anomers, respectively, are destabilized by the absence of the anomeric effect. And, secondly, East or West conformations can be further destabilized by repulsive interactions among vicinal hydroxyl groups and ring oxygen atoms when the vicinal hydroxyl groups are in syn-configurations (such as in ribose and lyxose) more so than when in anti (arabinose, xylose).

Energy maps for glycosidic linkage conformations

Glycosidic linkage conformations are the main factors in determining the shapes of disaccharide, oligosaccharide, and polysaccharide molecules. The conformations are expressed in terms of the torsion angles about the bonds from each ring of the disaccharide moiety to its glycosidic oxygen atom, and the probability of a given conformation is often expressed in terms of its free or potential energy. The energy surface or map for a disaccharide is a display of the energy plotted against the two torsion angles. Successful mapping allows a particular kind of energy calculation to provide the energy values for each conformation and avoids possible pitfalls. Although different methods are discussed, the main emphasis of this chapter is on the technical production of the maps and their exploitation in further understanding the shape of the molecule in question.

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.

Understanding molecular structure from molecular mechanics

Molecular mechanics gives us a well known model of molecular structure. It is less widely recognized that valence bond theory gives us structures which offer a direct interpretation of molecular mechanics formulations and parameters. The electronic effects well-known in physical organic chemistry can be directly interpreted in terms of valence bond structures, and hence quantitatively calculated and understood. The basic theory is outlined in this paper, and examples of the effects, and their interpretation in illustrative examples is presented.

Selenoglycosides in silico: ab initio-derived reparameterization of MM4, conformational analysis using histo-blood group ABH antigens and lectin docking as indication for potential of bioactivity

The identification of glycan epitopes such as the histo-blood group ABH determinants as docking sites for bacterial/viral infections and signals in growth regulation fuels the interest to develop non-hydrolysable mimetics for therapeutic applications. Inevitably, the required substitution of the linkage oxygen atom will alter the derivative's topology. Our study addresses the question of the impact of substitution of oxygen by selenium. In order to characterize spatial parameters and flexibility of selenoglycosides, we first performed ab initio calculations on model compounds to refine the MM4 force field. The following application of the resulting MM4R version appears to reduce the difference to ab initio data when compared to using the MM4 estimator. Systematic conformational searches on the derivatives of histo-blood group ABH antigens revealed increased flexibility with acquisition of additional low-energy conformer(s), akin to the behavior of S-glycosides. Docking analysis using the Glide program for eight test cases indicated potential for bioactivity, giving further experimental investigation a clear direction to testing Se-glycosides as lectin ligands.

Bioinformatics and molecular modeling in glycobiology

The field of glycobiology is concerned with the study of the structure, properties, and biological functions of the family of biomolecules called carbohydrates. Bioinformatics for glycobiology is a particularly challenging field, because carbohydrates exhibit a high structural diversity and their chains are often branched. Significant improvements in experimental analytical methods over recent years have led to a tremendous increase in the amount of carbohydrate structure data generated. Consequently, the availability of databases and tools to store, retrieve and analyze these data in an efficient way is of fundamental importance to progress in glycobiology. In this review, the various graphical representations and sequence formats of carbohydrates are introduced, and an overview of newly developed databases, the latest developments in sequence alignment and data mining, and tools to support experimental glycan analysis are presented. Finally, the field of structural glycoinformatics and molecular modeling of carbohydrates, glycoproteins, and protein-carbohydrate interaction are reviewed.

CHARMM Additive All-Atom Force Field for Glycosidic Linkages between Hexopyranoses

We present an extension of the CHARMM hexopyranose monosaccharide additive all-atom force field to enable modeling of glycosidic-linked hexopyranose polysaccharides. The new force field parameters encompass 1→1, 1→2, 1→3, 1→4, and 1→6 hexopyranose glycosidic linkages, as well as O-methylation at the C(1) anomeric carbon, and are developed to be consistent with the CHARMM all-atom biomolecular force fields for proteins, nucleic acids, and lipids. The parameters are developed in a hierarchical fashion using model compounds containing the key atoms in the full carbohydrates, in particular O-methyl-tetrahydropyran and glycosidic-linked dimers consisting of two molecules of tetrahyropyran or one of tetrahydropyran and one of cyclohexane. Target data for parameter optimization include full two-dimensional energy surfaces defined by the Φ/Ψ glycosidic dihedral angles in the disaccharide analogs as determined by quantum mechanical MP2/cc-pVTZ single point energies on MP2/6-31G(d) optimized structures (MP2/cc-pVTZ//MP2/6-31G(d)). In order to achieve balanced, transferable dihedral parameters for the Φ/Ψ glycosidic dihedral angles, surfaces for all possible chiralities at the ring carbon atoms involved in the glycosidic linkages are considered, resulting in over 5000 MP2/cc-pVTZ//MP2/6-31G(d) conformational energies. Also included as target data are vibrational frequencies, pair interaction energies and distances with water molecules, and intramolecular geometries including distortion of the glycosidic valence angle as a function of the glycosidic dihedral angles. The model-compound optimized force field parameters are validated on full disaccharides through comparison of molecular dynamics results to available experimental data. Good agreement is achieved with experiment for a variety of properties including crystal cell parameters and intramolecular geometries, aqueous densities, and aqueous NMR coupling constants associated with the glycosidic linkage. The newly-developed parameters allow for the modeling of linear, branched, and cyclic hexopyranose glycosides both alone and in heterogenous systems including proteins, nucleic acids and/or lipids when combined with existing CHARMM biomolecular force fields.

Molecular mechanics (MM4) study of amines

The MM4 force field has been extended to include aliphatic amines. About 20 amines have been examined to obtain a set of useful molecular mechanics parameters for this class. The vibrational spectra of seven amines (172 frequencies) calculated by MM4 have an overall rms error of 27 cm(-1), compared with corresponding MM4 value of 24 cm(-1) for alkanes. The rms and signed average errors of the moments of inertia of nine simple amines compared with the experimental data were 0.18% and -0.004%, respectively. The heats of formation of 30 amines were also studied. The MM4 weighted standard deviation is 0.41 kcal/mol, compared with experiment. Electronegativity effects occur in the hydrocarbon portion of an amine from the nitrogen, and are accounted for by including electronegativity induced changes in bond lengths and angles, and induced dipole-dipole interactions in the molecule. Negative hyperconjugation results from the presence of the lone pair of electrons on nitrogen, and leads to the Bohlmann bands in the infrared, and also to strong and unusual geometric changes in the molecules (Bohlmann effect), all of which are fairly well accounted for. The conformational energies in amines appear to be less straightforward than those for most other classes of molecules, apparently because of the Bohlmann effect, and these are probably not yet completely understood. In general, the agreement between the MM4 calculated results and the available data is reasonably good.

Octa-O-propanoyl-β-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.

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.

Molecular Mechanics (MM4) Study of Fluorinated Hydrocarbons

A molecular mechanics study of small saturated hydrocarbons (up to C-6) substituted by up to six fluorines has been carried out with the MM4 force field. A parameter set has been developed for use in the calculation of bond lengths, bond angles, torsion angles, conformational energies, barriers to rotation, dipole moments, moments of inertia, and vibrational frequencies for these compounds. The results are mostly in fair to good agreement with experiment and ab initio calculations. The high electronegativity of fluorine leads to serious geometric consequences in these compounds, but these consequences can be dealt with adequately by suitable cross-terms in the force constant matrix, and by recognizing that some of the reference bond lengths and angles (l(0), theta(0)) and the corresponding stretching and bending constant parameters (k(s), k(theta)) that are usually thought of as constants must in fact be treated as functions of the electronegativity of the substituents. Additionally, the heavy mass of the fluorine (relative to the mass of hydrogen in alkanes) leads to large values for other cross-terms that were found to be unimportant in hydrocarbons. Conformational equilibria for polyfluorinated compounds are affected by the delta-two effect well-known in carbohydrates. A few larger fluorinated and polyfluorinated alkanes, including perfluoropropane, perfluorobutane, and Teflon, have also been studied.

Quantum mechanics studies of cellobiose conformations

Three regions of the conformation space that describes the relative orientations of the two glucose residues of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 × 9 grid of 20° increments of the linkage torsion angles ϕ and ψ. Besides these 81 constrained minimizations, we studied two central subregions and two regions at the edges of our maps of complete ϕ,ψ space with unconstrained minimization, for a total of 85 target geometries. HF/6-31G(d) and single-point HF/6-311+G(d) calculations were used to find the lowest energies for each geometry. B3LYP/6-31G+G(d) and single point B3LYP/6-11+G(d) calculations were also used for all unconstrained minimizations. For each target, 181 starting geometries were tried (155 for the unconstrained targets). Numerous different starting geometries resulted in the lowest energies for the various target structures. The starting geometries came from five different sets that were based on molecular mechanics energies. Although all five sets contributed to the adiabatic map, use of any single set resulted in discrepancies of 3–7 kcal/mol (1 cal = 4.184 J) with the final map. For most of the targets, the starting geometry that gave the lowest energy depended on the basis set and whether the HF or B3LYP method was used. However, each of the above four calculations gave the same overall lowest energy structure that was found previously by Strati et al. This global minimum, stabilized by highly cooperative hydrogen bonds, is in a region that is essentially not populated by crystal structures. HF/6-31G(d) energy contours of the mapped central region were compatible with the observed crystal structures. Observed structures that lacked O3···O5′ hydrogen bonds were about 1 kcal/mol above the map's minimum, and observed structures that have a pseudo twofold screw axis ranged from about 0.4 to 1.0 kcal/mol. The HF/6-311+G(d) map accommodated the observed structures nearly as well.Key words: cellulose, carbohydrate, conformation, energy, flexibility, folding, helix, shape.