DFT studies of the disaccharide, α-maltose: relaxed isopotential maps

Inter-residual Hydrogen Bonding in Carbohydrates Unraveled by NMR Spectroscopy and Molecular Dynamics Simulations

Carbohydrates, also known as glycans in biological systems, are omnipresent in nature where they as glycoconjugates occur as oligo- and polysaccharides linked to lipids and proteins. Their three-dimensional structure is defined by two or three torsion angles at each glycosidic linkage. In addition, transglycosidic hydrogen bonding between sugar residues may be important. Herein we investigate the presence of these inter-residue interactions by NMR spectroscopy in D₂ O/[D₆ ]DMSO (70:30) or D₂ O and by molecular dynamics (MD) simulations with explicit water as solvent for disaccharides with structural elements α-d-Manp-(1→2)-d-Manp, β-d-GlcpNAc-(1→2)-d-Manp, and α-d-Glcp-(1→4)-β-d-Glcp, all of which have been suggested to exhibit inter-residue hydrogen bonding. For the disaccharide β-d-GlcpNAc-(1→2)-β-d-Manp-OMe, the large extent of O5'⋅⋅⋅HO3 hydrogen bonding as seen from the MD simulation is implicitly supported by the ¹ H NMR chemical shift and ³ J_HO3,H3 value of the hydroxy proton. In the case of α-d-Glcp-(1→4)-β-d-Glcp-OMe, the existence of a transglycosidic hydrogen bond O2'⋅⋅⋅HO3 was proven by the presence of a cross-peak in ¹ H,¹³ C HSQC-TOCSY experiments as a result of direct TOCSY transfer between HO3 of the reducing end residue and H2' (detected at C2') of the terminal residue. The occurrence of inter-residue hydrogen bonding, albeit transient, is judged important for the stabilization of three-dimensional structures, which may be essential in maintaining a conformational state for carbohydrate-protein interactions of glycans to take place in biologically important environments.

Predicting the Structures of Glycans, Glycoproteins, and Their Complexes

Complex carbohydrates are ubiquitous in nature, and together with proteins and nucleic acids they comprise the building blocks of life. But unlike proteins and nucleic acids, carbohydrates form nonlinear polymers, and they are not characterized by robust secondary or tertiary structures but rather by distributions of well-defined conformational states. Their molecular flexibility means that oligosaccharides are often refractory to crystallization, and nuclear magnetic resonance (NMR) spectroscopy augmented by molecular dynamics (MD) simulation is the leading method for their characterization in solution. The biological importance of carbohydrate-protein interactions, in organismal development as well as in disease, places urgency on the creation of innovative experimental and theoretical methods that can predict the specificity of such interactions and quantify their strengths. Additionally, the emerging realization that protein glycosylation impacts protein function and immunogenicity places the ability to define the mechanisms by which glycosylation impacts these features at the forefront of carbohydrate modeling. This review will discuss the relevant theoretical approaches to studying the three-dimensional structures of this fascinating class of molecules and interactions, with reference to the relevant experimental data and techniques that are key for validation of the theoretical predictions.

Density functional conformational study of 2-O-sulfated 3,6 anhydro-α-D-galactose and of neo-κ- and ι-carrabiose molecules in gas phase and water

We examined the conformational preferences of the 2-O-sulfated-3,6-α-D-anhydrogalactose (compound I) and two 1,3 linked disaccharides constituting-κ or ι-carrageenans using density functional and ab initio methods in gas phase and aqueous solution. Systematic modifications of two torsion angles leading to 324 and 144 starting geometries for the compound I and each disaccharide were used to generate adiabatic maps using B3LYP/6-31G(d). The lower energy conformers were then fully optimized using B3LYP, B3PW91 and MP2 with several basis sets. Overall, we discuss the impact of full relaxation on the energy and structure of the dominant conformations, present the performance comparison with previous molecular mechanics calculations if available, and determine whether our results are impacted, when polarization and diffuse functions are added to the 6-31G(d) basis set, or when the MP2 level of theory is used.

Monte Carlo-based searching as a tool to study carbohydrate structure

A torsion angle-based Monte Carlo searching routine was developed and applied to several carbohydrate modeling problems. The routine was developed as a Unix shell script that calls several programs, which allows it to be interfaced with multiple potential functions and various utilities for evaluating conformers. In its current form, the program operates with several versions of the MM3 and MM4 molecular mechanics programs and has a module to calculate hydrogen-hydrogen coupling constants. The routine was used to study the low-energy exo-cyclic substituents of β-D-glucopyranose and the conformers of D-glucaramide, both of which had been previously studied with MM3 by full conformational searches. For these molecules, the program found all previously reported low-energy structures. The routine was also used to find favorable conformers of 2,3,4,5-tetra-O-acetyl-N,N'-dimethyl-D-glucaramide and D-glucitol, the latter of which is believed to have many low-energy forms. Finally, the technique was used to study the inter-ring conformations of β-gentiobiose, a β-(1→6)-linked disaccharide of D-glucopyranose. The program easily found conformers in the 10 previously identified low-energy regions for this disaccharide. In 6 of the 10 local regions, the same previously identified low-energy structures were found. In the remaining four regions, the search identified structures with slightly lower energies than those previously reported. The approach should be useful for extending modeling studies on acyclic monosaccharides and possibly oligosaccharides.

DFTMD studies of β-cellobiose: conformational preference using implicit solvent

Previous DFT in vacuo studies on the conformational preferences for cellobiose showed that upon optimization the φ(H)-anti conformations were of lower energy than the syn forms. Upon optimization using an implicit solvation method, COSMO, the syn or observed form was still not predicted to be of lower energy than the φ(H)-anti form, even though optimization after addition of several explicit water molecules did show a relative energy difference favoring the syn form. In order to examine the predictive ability of COSMO on this carbohydrate, constant energy dynamics, DFTMD, simulations were carried out on low energy syn and φ(H)-anti conformations with and without COSMO included during the dynamics. The resulting analysis confirmed that when COSMO is included in the dynamics, the syn conformations become energetically favored over the φ(H)-anti forms suggesting that both solvent and entropy play roles in dictating the solution conformation of cellobiose. Analysis of the dynamic runs includes distributions of selected dihedral angles versus time, conformational transitions, and populations of some quasi-planar, boat, skew forms during the simulations.

Conformational properties of glucose-based disaccharides investigated using molecular dynamics simulations with local elevation umbrella sampling

Explicit-solvent molecular dynamics (MD) simulations of the 11 glucose-based disaccharides in water at 300K and 1bar are reported. The simulations were carried out with the GROMOS 45A4 force-field and the sampling along the glycosidic dihedral angles phi and psi was artificially enhanced using the local elevation umbrella sampling (LEUS) method. The trajectories are analyzed in terms of free-energy maps, stable and metastable conformational states (relative free energies and estimated transition timescales), intramolecular H-bonds, single molecule configurational entropies, and agreement with experimental data. All disaccharides considered are found to be characterized either by a single stable (overwhelmingly populated) state ((1-->n)-linked disaccharides with n=1, 2, 3, or 4) or by two stable (comparably populated and differing in the third glycosidic dihedral angle omega ; gg or gt) states with a low interconversion barrier ((1-->6)-linked disaccharides). Metastable (anti-phi or anti-psi) states are also identified with relative free energies in the range of 8-22 kJ mol(-1). The 11 compounds can be classified into four families: (i) the alpha(1-->1)alpha-linked disaccharide trehalose (axial-axial linkage) presents no metastable state, the lowest configurational entropy, and no intramolecular H-bonds; (ii) the four alpha(1-->n)-linked disaccharides (n=1, 2, 3, or 4; axial-equatorial linkage) present one metastable (anti-psi) state, an intermediate configurational entropy, and two alternative intramolecular H-bonds; (iii) the four beta(1-->n)-linked disaccharides (n=1, 2, 3, or 4; equatorial-equatorial linkage) present two metastable (anti-phi and anti-psi) states, an intermediate configurational entropy, and one intramolecular H-bond; (iv) the two (1-->6)-linked disaccharides (additional glycosidic dihedral angle) present no (isomaltose) or a pair of (gentiobiose) metastable (anti-phi) states, the highest configurational entropy, and no intramolecular H-bonds. The observed conformational preferences appear to be dictated by four main driving forces (ring conformational preferences, exo-anomeric effect, steric constraints, and possible presence of a third glycosidic dihedral angle), leaving a secondary role to intramolecular H-bonding and specific solvation effects. In spite of the weak conformational driving force attributed to solvent-exposed H-bonds in water (highly polar protic solvent), intramolecular H-bonds may still have a significant influence on the physico-chemical properties of the disaccharide by decreasing its hydrophilicity. Along with previous work, the results also complete the suggestion of a spectrum of approximate transition timescales for carbohydrates up to the disaccharide level, namely: approximately 30 ps (hydroxyl groups), approximately 1 ns (free lactol group, free hydroxymethyl groups, glycosidic dihedral angleomega in (1-->6)-linked disaccharides), approximately 10 ns to 2 micros (ring conformation, glycosidic dihedral angles phi and psi). The calculated average values of the glycosidic torsional angles agree well with the available experimental data, providing validation for the force-field and simulation methodology employed.

Relaxed energetic maps of kappa-carrabiose: a DFT study

The B3LYP density function was used with the 6-31G(d) basis set to perform relaxed energetic contour maps of the charged form of kappa-carrabiose in the gas phase and for the neutral form first in the gas phase and then by simulating the presence of water as solvent using the Onsager model. Only one starting conformation has been considered to perform all the calculations. Rigid energetic maps have been then constructed either by addition of diffuse or polarization functions to the basis set obtaining in that way 6-31+G(d)//6-31G(d), 6-31+G(d,p)//6-31G(d), and 6-311++G(d,p)//6-31G(d) energetic maps that have been carefully examined. The obtained structures corresponding to the lower energy conformers have been then fully optimized using different basis sets with the B3LYP method, a reversion in term of energy has been observed for the two first minima in the case of the charged disaccharide in the gas phase, this was attributed to the large grid of 30 degrees that could lead to the exclusion of an intermediate value corresponding to the real minimum of energy. We thus suggest that after establishing potential energy maps it is essential to proceed to full optimizations of the lower energy conformers. Calculations using the more accurate correlated method MP2 with the 6-31G(d) basis set have also been performed for conformers of the two disaccharides in the gas phase.

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.

DFT conformation and energies of amylose fragments at atomic resolution. Part 1: Syn forms of alpha-maltotetraose

DFT optimization studies of 90 syn alpha-maltotetraose (DP-4) amylose fragments have been carried out at the B3LYP/6-311++G** level of theory. The DP-4 fragments studied include V-helix, tightly bent conformations, a boat, and a (1)C(4) conformer. The standard hydroxymethyl rotamers (gg, gt, tg) were examined at different locations in the residue sequence, and their influence on the bridge conformations phi/psi values and conformer energy is described. Hydroxyl groups were considered to be homodromic, that is, they are either in the all clockwise, 'c', or all counterclockwise, 'r'. Energy differences between conformations are examined in order to assess the stability of the different conformations and to identify the sources of energy that dictate amylose polymer formation. A small nearly cyclic compact structure is of low energy as one would expect when these flexible molecules are studied in vacuo. Many conformations in which the only differences are a single hydroxymethyl variation in the residue sequence show similar energies and bridge conformations, with trends being a result of the hydroxymethyl as well as hydroxyl orientation. In general the 'c' structures are of lower energy than the 'r' structures, although this is only true for the in vacuo state. The solvent dependence on conformational preference of several low-energy DP-4 structures was investigated via the continuum solvation method COSMO. These results suggest that the 'r' structures may be favored for fully solvated molecules.