The conformations of cyclic (1-->2)-beta-D-glucans: application of multidimensional clustering analysis to...

Sets containing up to 1.3 x 10(6) energetically accessible conformations of linear (1-->2)-beta-D-glucan oligosaccharides were obtained by Metropolis Monte Carlo (MMC) calculations performed with the GEGOP (GEometry of GlycOProteins) program. Quantitative analyses of the data sets (which were expressed in terms of the glycosidic dihedral angle coordinates) were obtained by two different clustering methods: (i) the three-distance hierarchical clustering method (3-DM), published by Jure Zupan, and (ii) a nonhierarchical clustering method (Population-Density Projection, PDP) which, through a segmentation analysis of two-dimensional projections of the population-density surface, establishes a partitioning of conformational space into a set of "cluster regions", followed by a clustering step where each conformation of the data set is assigned to one of these regions. Computer programs (MCLUST and PDPCLUST) were developed to perform the 3-DM and PDP analyses, respectively. The two types of analysis provided very similar sets of conformational families (clusters), which could be expressed as combinations of distinct conformations of the glycosidic torsional angles (phi, psi) centered at (50 degrees, 10 degrees) for conformation A, (40 degrees, 160 degrees) for conformation B, (55 degrees, -160 degrees) for conformation B', and (170 degrees, 10 degrees) for conformation C. The analysis provided the populations of the families, along with relative rates for transitions between families. Examination of the frequencies of the A, B, and C glycosidic bond conformations with respect to their relative positions in the sequence revealed the tendency of the (1-->2)-beta-D-glucan to adopt conformational repeating structures of the general form [AnB], where n = 3 or 6. These repeating structures combine in an energetically cooperative fashion to give low-energy cyclic conformations having, for example C5 symmetry [AAAB]5 for the eicosamer, and C3 symmetry [AAAAAAB]3 for the heneicosamer.