Anisotropic Reorientation and Intermolecular Interactions of Sucrose Molecules in Aqueous Solution. A Temperature and Concentration-Dependent 13C NMR Relaxation Study

MA'AT Analysis: Probability Distributions of Molecular Torsion Angles in Solution from NMR Spectroscopy

ConspectusMonosaccharides adopt multiple conformations in solution, and this structural complexity increases significantly when they are assembled into oligosaccharides and polysaccharides. Characterization of the conformational properties of saccharides in solution by NMR spectroscopy has been hampered by several complicating factors, including difficulty interpreting spectra because of significant signal overlap, population averaging of NMR parameters, and unique properties of the spectra that make accurate measurements of NMR parameters prone to error (e.g., non-first-order effects on J-couplings). Current conformational assignments rely heavily on theoretical calculations, especially molecular dynamics (MD) simulations, to interpret the experimental NMR parameters. While these studies assert that the available experimental data fit the calculated models well, a lack of independent experimental validation of the force fields from which MD models are derived and an inability to test all possible models that might be compatible with the experimental data in an unbiased manner make the approach less than ideal.NMR spin couplings or J-couplings have been used as structure constraints in organic and other types of molecules for more than six decades. The dihedral angle dependence of vicinal (three-bond) 1H-1H spin couplings (3JHH) first described by Karplus led to an explosion of applications for a wide range of conformational problems. Other vicinal J-couplings (e.g., 3JCCOP, 3JHCOP, and 3JCOCH) have been found to exhibit similar dihedral angle dependencies. 3J values have been used to assign the preferred conformation in molecules that are conformationally homogeneous. However, many molecules, particularly those in biological systems, are conformationally flexible, which complicates structural interpretations of J values in solution. Three-state staggered models are often assumed in order to deconvolute the conformationally averaged J values into conformer populations. While widely applied, this approach assumes highly idealized models of molecular torsion angles that are likely to be poor representations of those found in solution. In addition, this treatment often gives negative populations and neglects the presence of librational averaging of molecular torsion angles.Recent work in this research group has focused on the development of a hybrid experimental-computational method, MA'AT analysis, that provides probability distributions of molecular torsion angles in solution that can be superimposed on those obtained by MD. Ensembles of redundant NMR spin couplings, including 3J (vicinal), 2J (geminal), and sometimes 1J (direct) values, are used in conjunction with circular statistics to provide single- and multistate models of these angles. MA'AT analysis provides accurate mean torsion angles and circular standard deviations (CSDs) of each mean angle that describe the librational motion about the angle. Both conformational equilibria and dynamics are revealed by the method. In this Account, the salient features of MA'AT analysis are discussed, including some applications to conformational problems involving saccharides and peptides.

Using molecular dynamics trajectories to predict nuclear spin relaxation behaviour in large spin systems

Molecular dynamics (MD) trajectories provide useful insights into molecular structure and dynamics. However, questions persist about the quantitative accuracy of those insights. Experimental NMR spin relaxation rates can be used as tests, but only if relaxation superoperators can be efficiently computed from MD trajectories - no mean feat for the quantum Liouville space formalism where matrix dimensions quadruple with each added spin 1/2. Here we report a module for the Spinach software framework that computes Bloch-Redfield-Wangsness relaxation superoperators (including non-secular terms and cross-correlations) from MD trajectories. Predicted initial slopes of nuclear Overhauser effects for sucrose trajectories using advanced water models and a force field optimised for glycans are within 25% of experimental values.

Molecular dynamics simulations of the dielectric properties of fructose aqueous solutions

The static dielectric permittivity and dielectric relaxation properties of fructose aqueous solutions of different concentrations ranging from 1.0 to 4.0 mol l(-1) are investigated by means of molecular dynamics simulations. The contributions from intra- and interspecies molecular correlations were computed individually for both the static and frequency-dependent dielectric properties, and the results were compared with the available experimental data. Simulation results in the time- and frequency-domains were analyzed and indicate that the presence of fructose has little effect on the position of the fast, high-frequency (>500 cm(-1)) components of the dielectric response spectrum. The low-frequency (<0.1 cm(-1)) components, however, are markedly influenced by sugar concentration. Our analysis indicates that fructose-fructose and fructose-water interactions strongly affect the rotational-diffusion regime of molecular motions in the solutions. Increasing fructose concentration not only enhances sugar-sugar and sugar-water low frequency contributions to the dielectric loss spectrum but also slows down the reorientational dynamics of water molecules. These results are consistent with previous computer simulations carried out for other disaccharide aqueous solutions.

Direct NOE simulation from long MD trajectories

A software package, MD2NOE, is presented which calculates Nuclear Overhauser Effect (NOE) build-up curves directly from molecular dynamics (MD) trajectories. It differs from traditional approaches in that it calculates correlation functions directly from the trajectory instead of extracting inverse sixth power distance terms as an intermediate step in calculating NOEs. This is particularly important for molecules that sample conformational states on a timescale similar to molecular reorientation. The package is tested on sucrose and results are shown to differ in small but significant ways from those calculated using an inverse sixth power assumption. Results are also compared to experiment and found to be in reasonable agreement despite an expected underestimation of water viscosity by the water model selected.

Sucrose in aqueous solution revisited, Part 2: adaptively biased molecular dynamics simulations and computational analysis of NMR relaxation

We report 100 ns molecular dynamics simulations, at various temperatures, of sucrose in water (with concentrations of sucrose ranging from 0.02 to 4M), and in a 7:3 water-DMSO mixture. Convergence of the resulting conformational ensembles was checked using adaptive-biased simulations along the glycosidic Φ and ψ torsion angles. NMR relaxation parameters, including longitudinal (R₁) and transverse (R₂) relaxation rates, nuclear Overhauser enhancements (NOE), and generalized order parameter (S²) were computed from the resulting time-correlation functions. The amplitude and time scales of molecular motions change with temperature and concentration in ways that track closely with experimental results, and are consistent with a model in which sucrose conformational fluctuations are limited (with 80-90% of the conformations having ϕ-ψ values within 20° of an average conformation), but with some important differences in conformation between pure water and DMSO-water mixtures.

Dynamics of the slow mode in the family of six-carbon monosaccharides monitored by dielectric spectroscopy

Broadband dielectric measurements performed on D-glucose, L-sorbose, D-fructose and D-galactose revealed that, except for the structural relaxation process, one can detect in the liquid phase of these carbohydrates a much slower relaxation mode. Recently we have demonstrated that in D-glucose this relaxation mode might be related to the long range correlation of density fluctuations (LRCDF), also called Fischer clusters (FC). Based on the dielectric data obtained for the four monosaccharides we were able to make a more general conclusion about the characteristic dielectric features of the slow mode in the whole family of carbohydrates. We found out that the timescale separation between structural and considered relaxation reaches up to six decades at the glass transition temperature and the dielectric strength decreases significantly with lowering temperature. Another very interesting feature of the slow process is that it can be described by an almost exponential response function. We have found out that the fragility of the slow process lies within the range m = 44-50. Finally, we have also shown that there is a close link between structural and slow relaxation.

Molecular dynamics studies of the conformation of sorbitol

Molecular dynamics simulations of a 3 molal aqueous solution of D-sorbitol (also called D-glucitol) have been performed at 300 K, as well as at two elevated temperatures to promote conformational transitions. In principle, sorbitol is more flexible than glucose since it does not contain a constraining ring. However, a conformational analysis revealed that the sorbitol chain remains extended in solution, in contrast to the bent conformation found experimentally in the crystalline form. While there are 243 staggered conformations of the backbone possible for this open-chain polyol, only a very limited number were found to be stable in the simulations. Although many conformers were briefly sampled, only eight were significantly populated in the simulation. The carbon backbones of all but two of these eight conformers were completely extended, unlike the bent crystal conformation. These extended conformers were stabilized by a quite persistent intramolecular hydrogen bond between the hydroxyl groups of carbon C-2 and C-4. The conformational populations were found to be in good agreement with the limited available NMR data except for the C-2-C-3 torsion (spanned by the O-2-O-4 hydrogen bond), where the NMR data support a more bent structure.

Carbohydrate Clustering in Aqueous Solutions and the Dynamics of Confined Water

We use molecular dynamics simulations to investigate structure and dynamics of fructose aqueous solutions in the 1-5 M concentration range at ambient conditions. We analyze hydration structures, H-bond statistics, and size distribution of H-bonded carbohydrate clusters as functions of concentration. We find that the local tetrahedral order of water is reasonably well-preserved and that the solute tends to appear as scattered "isolated" molecules at low concentrations and as H-bonded clusters for less diluted solutions. The sugar cluster size distribution exhibits a sharp transition to a percolated cluster between 3.5 and 3.8 M. The percolated cluster forms an intertwined network of H-bonded saccharides that imprisons water. For the dynamics, we find good agreement between simulation and available experimental results for the self-diffusion coefficients. Water librational dynamics is little affected by sugar concentration, whereas reorientational relaxation is described by a concentration-independent bulk-like component attributed to noninterfacial water molecules and a slower component (strongly concentration dependent) that arises from interfacial solvent molecules and, hence, depends on the dynamics of the cluster structure itself. Analysis of H-bonding survival probability functions indicates that the formation of carbohydrate clusters upon increasing concentration enhances the H-bond relaxation time and slows down the entire system dynamics. We find that multiexponential or stretched-exponential fits alone cannot describe the H-bond survival probabilities for the entire postlibrational time span of our data (0.1-100 ps), as opposed to a combined stretched-plus-biexponential function, which provides excellent fits. Our results suggest that water dynamics in concentrated fructose solutions resembles in many ways that of protein hydration water.

Molecular reorientational dynamics of the neat ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate by measurement of 13C nuclear magnetic relaxation data

The reorientational dynamics of the ionic liquid 1-butyl-3-methylimidzolium hexafluorophosphate ([BMIM]PF6) were studied over a wide range of temperatures by measurement of 13C spin-lattice relaxation rates and NOE factors. The reorientational dynamics were evaluated by performing fits to the experimental relaxation data. Thus, the overall reorientational motion was described by a Cole-Davidson spectral density with a Vogel-Fulcher-Tammann temperature dependence of the correlation times. The reorientational motion of the butyl chain was modelled by a combination of the latter model for the overall motion with a Bloembergen-Pur-cell-Pound spectral density and an Arrhenius temperature dependence for the internal motion. Except for C2 in the aromatic ring, an additional reduction of the spectral density by the Lipari-Szabo model had to be employed. This reduction is a consequence of fast molecular motions before the rotational diffusion process becomes effective. The C2 atom did not exhibit this reduction, because the librational motion of the corresponding C2-H vector is severely hindered due to hydrogen bonding with the hexafluorophosphate anion. The observed dynamic features of the [BMIM]+ cation confirm quantum-chemical structures obtained in a former study.