MA'AT: A Web-Based Application to Determine Rotamer Population Distributions in Solution from Nuclear Magnetic Resonance Spin-Coupling Constants.

A hybrid experimental-computational method to determine conformational equilibria of molecules in solution has been developed based on the use of redundant nuclear magnetic resonance (NMR) spin-spin coupling constants (spin-couplings; J-couplings), density functional theory (DFT) calculations, and circular statistics. The mathematics that underpins the method, known as MA'AT analysis, is presented, and key components of a computer program that applies this algorithm are discussed. The method was tested using single-state and multi-state models to identify the factors required to obtain reliable results, to establish the limitations of the method, and to highlight techniques to evaluate the uniqueness of solution.

Conformational Populations of ß-(1→4) O-Glycosidic Linkages Using Redundant NMR J-Couplings and Circular Statistics.

Twelve disaccharides containing ß-(1→4) linkages and displaying systematic structural variations in the vicinity of these linkages were selectively labeled with 13C to facilitate measurements of multiple NMR spin-spin (scalar; J) coupling constants (JCH and JCC values) across their O-glycosidic linkages. Ensembles of spin-couplings (2JCOC, 3JCOCH, 3JCOCC) sensitive to the two linkage torsion angles, phi (ϕ) and psi (ψ), were analyzed by using parametrized equations obtained from density functional theory (DFT) calculations, Fredholm theory, and circular statistics to calculate experiment-based rotamer populations for ϕ and ψ in each disaccharide. With the statistical program MA'AT, torsion angles ϕ and ψ were modeled as a single von Mises distribution, which yielded two parameters, the mean position and the circular standard deviation (CSD) for each angle. The NMR-derived rotamer populations were compared to those obtained from 1 µs aqueous molecular dynamics (MD) simulations and crystallographic database statistical analyses. Conformer populations obtained exclusively from the MA'AT treatment of redundant J-couplings were in very good agreement with those obtained from the MD simulations, providing evidence that conformational populations can be determined by NMR for mobile molecular elements such as O-glycosidic linkages with minimal input from theory. The approach also provides an experimental means to validate the conformational preferences predicted from MD simulations. The conformational behaviors of ϕ in the 12 disaccharides were very similar, but those of ψ varied significantly, allowing a classification of the 12 disaccharides based on preferred linkage conformation in solution.

O-Acetyl Side-Chains in Monosaccharides: Redundant NMR Spin-Couplings and Statistical Models for Acetate Ester Conformational Analysis.

α- and ß-d-glucopyranose monoacetates 1-3 were prepared with selective 13C enrichment in the O-acetyl side-chain, and ensembles of 13C-1H and 13C-13C NMR spin-couplings (J-couplings) were measured involving the labeled carbons. Density functional theory (DFT) was applied to a set of model structures to determine which J-couplings are sensitive to rotation of the ester bond θ. Eight J-couplings (1JCC, 2JCH, 2JCC, 3JCH, and 3JCC) were found to be sensitive to θ, and four equations were parametrized to allow quantitative interpretations of experimental J-values. Inspection of J-coupling ensembles in 1-3 showed that O-acetyl side-chain conformation depends on molecular context, with flanking groups playing a dominant role in determining the properties of θ in solution. To quantify these effects, ensembles of J-couplings containing four values were used to determine the precision and accuracy of several 2-parameter statistical models of rotamer distributions across θ in 1-3. The statistical method used to generate these models has been encoded in a newly developed program, MA'AT, which is available for public use. These models were compared to O-acetyl side-chain behavior observed in a representative sample of crystal structures, and in molecular dynamics (MD) simulations of O-acetylated model structures. While the functional form of the model had little effect on the precision of the calculated mean of θ in 1-3, platykurtic models were found to give more precise estimates of the width of the distribution about the mean (expressed as circular standard deviations). Validation of these 2-parameter models to interpret ensembles of redundant J-couplings using the O-acetyl system as a test case enables future extension of the approach to other flexible elements in saccharides, such as glycosidic linkage conformation.