Glenn P. Johnson

Neutron Crystallography, Molecular Dynamics, and Quantum Mechanics Studies of the Nature of Hydrogen Bonding in Cellulose Iβ

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.

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 β-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of β-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.

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.

HF/6‐31G* energy surfaces for disaccharide analogs

The HF/6‐31G* level of theory was used to calculate relaxed potential energy surfaces for 12 analogs of disaccharides. The analogs were made by replacing glucose with tetrahydropyran and fructose with 2‐methyltetrahydrofuran. Molecules had zero, one or two anomeric carbon atoms, and di‐axial, axial‐equatorial, and di‐equatorial linkages. Despite the absence of hydroxyl groups, the surfaces account well for conformations that are observed in crystals of the parent disaccharides. Thus, torsional energy and the simple bulk of ring structures are major factors in determining disaccharide conformation. The contour shapes around the global minima depend on the number of anomeric carbons involved in the linkage, while the presence of alternative minima that have relative energies less than 4 kcal/mol mostly requires equatorial bonds. However, molecules with two adjacent anomeric centers gave exceptions to these rules. Flexibility values related to a partition function show that the di‐axial trehalose analog is the most rigid. The di‐equatorial pseudodisaccharide analog with no anomeric centers is most flexible. Reproduction of these surfaces is proposed as a simple test of force fields for modeling carbohydrates. Also, these surfaces can be used in a simple hybrid method for calculating disaccharide energy surfaces.

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.

Constructing and evaluating energy surfaces of crystalline disaccharides

This paper focuses on the methods used to construct Ramachandran plots for disaccharides. Our recent work based on a hybrid of molecular mechanics and quantum mechanics energies pointed to the need to take extra care when making these maps. Care is also important in the quantitative validation of these energy surfaces with linkage conformations that were determined by crystallography. To successfully predict conformations that have been observed experimentally, the calculation of the energy should include stereoelectronic effects and correctly weight the hydrogen bonding. Technical concerns include the method used to scan the range of conformations, starting geometries, and finding the zero of relative potential energy on a surface where the values were collected at regular intervals. The distributions of observed conformations on energy maps of sucrose, maltose, and laminarabiose at dielectric constants of 1.5 and 7.5 illustrate the effects of an elevated dielectric constant for the MM3 component of the hybrid energy calculations. At dielectric constants of 3.5 and 7.5, the overall average energies of observed conformations of sucrose and seven disaccharides of glucose were less than 1.0 kcal mol-1. The distribution of corresponding energies of the various crystalline conformations conformed well to a Boltzmann-like equation.

Diffraction from nonperiodic models of cellulose crystals

Powder and fiber diffraction patterns were calculated for model cellulose crystallites with chains 20 glucose units long. Model sizes ranged from four chains to 169 chains, based on cellulose Iβ coordinates. They were subjected to various combinations of energy minimization and molecular dynamics (MD) in water. Disorder induced by MD and one or two layers of water had small effects on the relative intensities, except that together they reduced the low-angle scattering that was otherwise severe enough to shift the 1

Conformational analysis of cellobiose by electronic structure theories.

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