Morphological Effects of Glycosaminoglycans on Calcium Oxalate Monohydrate Crystals

The effects of individual glycosaminoglycan (GAG) species on calcium oxalate monohydrate (COM) crystal growth were studied in vitro by the observation of crystal morphology grown in a supersaturated calcium oxalate solution in the presence of GAGs using optical and scanning electron microscopes. GAGs affected the morphology of COM crystals differently depending on the species. The growth rates of the crystals formed in the presence of chondroitin-6-sulfate (ChS-C) were higher in length and lower in width and thickness than those of control crystals. The incorporation of dermatan sulfate or heparin into the crystals formed in the presence of these GAGs was revealed by X-ray microanalysis, whereas ChS-C was not detected in the crystals grown with it. The experiment using dicarboxylates, as a simple model of GAG molecules, showed that a distance between the side groups was important for their morphological effects. These findings suggested that the different effects of GAGs on the crystal morphology resulted from the differences in their interaction modes with COM crystal faces, that is, the differences in their binding behavior, their inhibition modes of crystal growth, and other roles played after binding to the crystals

Hierarchy of the Selberg zeta functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Comment: 14 page