Commutative Algebras of Toeplitz Operators on the Reinhardt Domains

Let D be a bounded logarithmically convex complete Reinhardt domain in centered at the origin. Generalizing a result for the one-dimensional case of the unit disk, we prove that the C ^*-algebra generated by Toeplitz operators with bounded measurable separately radial symbols (i.e., symbols depending only on is commutative. We show that the natural action of the n-dimensional torus defines (on a certain open full measure subset of D) a foliation which carries a transverse Riemannian structure having distinguished geometric features. Its leaves are equidistant with respect to the Bergman metric, and the orthogonal complement to the tangent bundle of such leaves is integrable to a totally geodesic foliation. Furthermore, these two foliations are proved to be Lagrangian. We specify then the obtained results for the unit ball.     

Methyl rotation barriers in proteins from 2H relaxation data. Implications for protein structure

Side-chain 2H and backbone 15N relaxation data have been collected at multiple temperatures in the samples of the SH3 domain from alpha-spectrin. Combined analyses of the data allowed for determination of the temperature-dependent correlation times tauf characterizing fast methyl motion. Molecular dynamics simulations confirmed that tauf are dominated by methyl rotation; the corresponding activation energies approximate methyl rotation barriers. For 33 methyl groups in the alpha-spectrin SH3 domain the average barrier height was thus determined to be 2.8 +/- 0.9 kcal/mol. This value is deemed representative of the "fluid" hydrophobic protein core where some barriers are increased and others are lowered because of the contacts with surrounding atoms, but there is no local order that could produce systematically higher (lower) barriers. For comparison, the MD simulation predicts the average barrier of 3.1 kcal/mol (calculated via the potential of mean force) or 3.4-3.5 kcal/mol (rigid barriers after appropriate averaging over multiple MD snapshots). The latter result prompted us to investigate rigid methyl rotation barriers in a series of NMR structures from the Protein Databank. In most cases the barriers proved to be higher than expected, 4-6 kcal/mol. To a certain degree, this is caused by tight packing of the side chains in the NMR structures and stems from the structure calculation procedure where the coordinates are first annealed toward the temperature of 0 K and then subjected to energy minimization. In several cases the barriers >10 kcal/mol are indicative of van der Waals violations. The notable exceptions are (i) the structures solved using the GROMOS force field where tight methyl packing is avoided (3.0-3.6 kcal/mol) and (ii) the structure solved by means of the dynamic ensemble refinement method (Lindorff-Larsen, K.; Best, R. B.; DePristo, M. A.; Dobson, C. M.; Vendruscolo, M. Nature 2005, 433, 128) (3.5 kcal/mol). These results demonstrate that methyl rotation barriers, derived from the experiments that are traditionally associated with studies of protein dynamics, can be also used in the context of structural work. This is particularly interesting in view of the recent efforts to incorporate dynamics data in the process of protein structure elucidation.     

Alcohol biomarker analysis: simultaneous determination of 5-hydroxytryptophol glucuronide and 5-hydroxyindoleacetic acid by direct injection of urine using ultra-performance liquid chromatography-tandem mass spectrometry

A direct ultra-performance liquid chromatography-tandem mass spectrometry method (UPLC-MS/MS) for simultaneous measurement of urinary 5-hydroxytryptophol glucuronide (GTOL) and 5-hydroxyindoleacetic acid (5-HIAA) was developed. The GTOL/5-HIAA ratio is used as an alcohol biomarker with clinical and forensic applications. The method involved dilution of the urine sample with deuterated analogues (internal standards), reversed-phase chromatography with gradient elution, electrospray ionisation and monitoring of two product ions per analyte in selected reaction monitoring mode. The measuring ranges were 6.7-10 000 nmol/l for GTOL and 0.07-100 micromol/l for 5-HIAA. The intra- and inter-assay imprecision, expressed as the coefficient of variation, was below 7%. Influence from ion suppression was noted for both compounds but was compensated for by the use of co-eluting internal standards. The accuracy in analytical recovery of added substance to urine samples was 96 and 98%, respectively, for GTOL and 5-HIAA. Method comparison with GC-MS for GTOL in 25 authentic patient samples confirmed the accuracy of the method with a median ratio between methods (GC-MS to UPLC-MS/MS) of 1.14 (r(2) = 0.975). The difference is explained by the fact that the GC-MS method also measures unconjugated 5-hydroxytryptophol naturally present in urine. The comparison with data for 5-HIAA obtained by an HPLC method demonstrated a median ratio of 1.05 between the methods. The UPLC-MS/MS method was capable of measuring endogenous GTOL and 5-HIAA levels in urine, which agreed with the literature data. In conclusion, a fully validated and robust direct method for the routine measurement of urinary GTOL and 5-HIAA was developed.     

The influence of ionic liquid's nature on free radical polymerization of vinyl monomers and ionic conductivity of the obtained polymeric materials

Various 1,3‐dialkylimidazolium and tetraalkylphosphonium ionic liquids (ILs), including novel ones, have been studied as reaction media for free radical polymerization of methyl methacrylate (MMA), acrylonitrile (AN) and 1‐vinyl‐3‐ethylimidazolium salts (ViEtIm⁺)Y^?. The influence of IL's nature upon the polymer formulation was investigated. The use of different ionic liquids allows not only to obtain the polymers with high molecular weight (PMMA, up to 5,770,000 g/mol; PAN, up to 735,000 g/mol and poly[(ViEtIm⁺)Y^?], up to 1,130,000 g/mol) in high yields, but also to control the polymerization rate and molecular mass. The physicochemical characteristics, including mechanical properties, thermal stability and heat‐resistance of the obtained polymers were studied in order to compare with those of polymers prepared in a traditional media. It was found that elongation, tensile modulus and strength of PAN, which was synthesized in ionic liquid, are reliatively higher. The influence of IL's nature upon their ionic conductivity and the formation of conductive polymers from molten‐salt‐type vinyl monomers was investigated. Molecular design of the polymers simultaneously with the influence of IL's nature in order to achieve higher ionic conductivity is discussed. Flexible, transparent polymer films, obtained in different ways, show relatively high ionic conductivity (of about 10^?5 S cm^?1 at 20°C). Copyright © 2006 John Wiley & Sons, Ltd.     

Frustrated-total-internal-reflection-based thin-film color separator

The frustrated-total-internal-reflection thin-film color filtering device operating in a visible spectral range is designed. Such a device splits an incident light beam into spatially separated red, green, and blue color beams. Spectral shape and angular spread of transmitted light for s and p polarizations are calculated at different values of refractive indices and thicknesses of layers.     

Tetranitromethane as an efficient reagent for the conversion of epoxides into β-hydroxy nitrates

A convenient regioselective method for the preparation of β-hydroxy nitrates based on the ring opening reaction of epoxides by tetranitromethane in the presence of triethylamine is described. A series of substituted β-hydroxy nitrates were obtained in high yields under mild conditions.     

Unbiased and biased chemometric analysis of LC-MS data from human urine following coffee intake

We carried out a human volunteer study with 14 participants, eight of whom were asked to consume one cup of coffee at four different time points. Urine samples were collected at eight time points and analyzed by HPLC-MS analysis. The LC-MS data were subjected to unsupervised multivariate statistical analysis (principal component analysis) followed by supervised multivariate analysis (linear discriminant analysis). In an unbiased approach, in the absence of data preselection and filtering, the most important features explaining differences between coffee consumers and the control group observed showed variations in endogenous human hormonal steroid metabolites as well as xanthine derivatives. Only after a biased data treatment data revealed differences between the sample groups based on literature reported chlorogenic acid metabolites resulting directly from coffee intake. Such analysis could confirm the presence of 21 previously reported chlorogenic acid plasma metabolites as urinary metabolites. The application of tandem MS molecular networking revealed the presence of five bioavailable chlorogenic acid derivatives in urine previously not reported, including both quinic acid lactone and dimethoxy caffeoyl esters. Selected cinnamic acids were quantified in urine.     

Gas permeation parameters and other physicochemical properties of a polymer of intrinsic microporosity: Polybenzodioxane PIM-1

A detailed study of gas permeation, thermodynamic properties and free volume was performed for a novel polymer of intrinsic microporosity (PIM-1). Gas permeability was measured using both gas chromatographic and barometric methods. Sorption of vapors was studied by means of inverse gas chromatography (IGC). In addition, positron annihilation lifetime spectroscopy (PALS) was employed for investigation of free volume in this polymer. An unusual property of PIM-1 is a very strong sensitivity of gas permeability and free volume to the film casting protocol. Contact with water in the process of film preparation resulted in relatively low gas permeability (P(O₂) = 120 Barrer), while soaking with methanol led to a strong increase in gas permeability (P(O₂) = 1600 Barrer) with virtually no evidence of fast aging (decrease in permeability) that is typical for highly permeable polymers. For various gas pairs (O₂/N₂, CO₂/CH₄, CO₂/N₂) the data points on the Robeson diagrams are located above the upper bound lines. Hence, a very attractive combination of permeability and selectivity is observed. IGC indicated that this polymer is distinguished by the largest solubility coefficients among all the polymers so far studied. Free volume of PIM-1 includes relatively large microcavities (R = 5 Å), and the results of the PALS and IGC methods are in reasonable agreement.