Analysis of the disaccharides derived from hyaluronic acid and chondroitin sulfate by capillary electrophoresis with sample stacking

CE conditions for monitoring the unsaturated disaccharides of hyaluronic acid (di-HA) and chondroitin sulfate (di-CS) using an alkaline tetraborate buffer, electrokinetic sample injection, and UV absorption detection at 232 nm are reported. Separations were performed in an uncoated fused-silica capillary having reversed polarity and reversed electroosmosis generated with the addition of CTAB to the buffer. The influence of various separation parameters, including the concentration of CTAB, buffer pH, concentration of tetraborate, and applied voltage, on the resolution of the two disaccharides was investigated. Baseline separation was obtained with 25 mM tetraborate at pH 10.0 and having 0.05 mM CTAB. Chloride and phosphate in the sample are beneficial for the stacking of the disaccharides, with di-HA forming a much sharper peak than di-CS. Using samples prepared in 25 mM Tris-HCl (pH 7.5) and electrokinetic injection at the cathode at -10 kV for 40 s, linear relationships between the corrected peak area and the concentration of the disaccharides have been found in the ranges of 1.0-400.0 and 0.1-1.0 microg/mL (0.2-1.0 microg/mL for di-CS), with correlation coefficients being >0.9933 in all cases. The RSDs of detection times and corrected peak areas were between 1.13-1.24 and 1.57-2.13%, respectively. Applied to human serum samples that were prepared by ethanol precipitation and depolymerization of the two polysaccharides with chondroitinase ABC reveals comigration of endogenous compounds with di-HA and a sample-dependent detection time. The di-HA content in the serum sample can be estimated via subtraction of the blank peak that is obtained without enzymatic hydrolysis.     

Gradient extremals and valley floor bifurcations on potential energy surfaces

Gradient extremals are curves in configuration space denned by the condition that the gradient of the potential energy is an eigenvector of the Hessian matrix. Solutions of a corresponding equation go along a valley floor or along a crest of a ridge, if the norm of the gradient is a minimum, and along a cirque or a cliff or a flank of one of the two if the gradient norm is a maximum. Properties of gradient extremals are discussed for simple 2D model surfaces including the problem of valley bifurcations.     

A Highly Stereoselective Synthesis of C(11)-Functionalized Aromatic Steroids by an Intramolecular Benzocyclobutene-Olefin -Cycloaddition. Preliminary Communication

The racemic cis-anti-trans-steroids 9 to 11 have been synthesized in a highly stereoselective manner starting from 4-methoxybenzocyclobutene carboxylic acid via the key step 8 → 9 . (cf. Scheme 2).     

The hyperbolic n-space as a graph in Euclidean (6n−6)-space

We construct for each n2 an isometric C-imbedding HⁿE^6n–6 of the n-dim. hyperbolic space into the Euclidean space E^6n–6 whose image is the graph of a C-map RⁿR^5n–6. This generalizes a well known result of D. Blanusa 1955 (the case n=2).     

Local limits and harmonic functions for nonisotropic random walks on free groups

Summary Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2s) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits.