Minimization Problems with Singular Data

This work contains a survey of some results on minimization problems with singular data and some new contributions (not previously published) presented in my lecture at the “Seminario Matematico e Fisico di Milano”. Lecture held in the Seminario Matematico e Fisico on October 10, 2005 Received: June 2006     

A possible helical model for sodium glycocholate micellar aggregates

Sodium glycocholate crystallizes in the tetragonal space group14 witha =b = 27.793(4),c = 7.937(1) Å andZ = 8. Refinement based on 2290 observed reflections led to a conventionalR = 0.10. The bile salt molecules are arranged in a helix with 2₁ symmetry stabilized mainly by polar interactions. Four helices are held together by hydrogen bonds involving water molecules, giving rise to hydrophilic channels, with a small cross section, which can include water molecules. The packing of these tetramers form hydrophobic channels containing some disordered acetone and water molecules. The helices will be checked as a model for the micellar aggregates of this important conjugated bile salt, following the same strategy successfully applied to sodium deoxycholate. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82107 (20 pages).     

Enantioselective hydrogen transfer reactions from propan-2-ol to ketones catalyzed by pentacoordinate iridium(I) complexes with chiral Schiff bases

Some diastereoisomeric pentacoordinate complexes of the type [Ir(COD)-(NNR)I] (COD = cis,cis-1,5-cyclooctadiene; NNR = 2-pyridinal-1-phenylethylimine (PPEI) (I), 2-acetylpyridine-1-phenylethylimine (APPEI) (II)) have been synthesized. The complexes are active and selective catalysts for asymmetric hydrogen transfer from propan-2-ol to prochiral ketones. Optical yields of up to 84% have been obtained in the reduction of t-butyl phenyl ketone. The structure and absolute configuration of complexes I and II were determined by X-ray diffraction.     

Single-scan NMR spectroscopy at arbitrary dimensions

Multidimensional nuclear magnetic resonance (NMR) provides one of the foremost analytical tools available to elucidate the structure and dynamics of complex molecules in their native states. Executing this kind of experiment generally requires collecting an n-dimensional time-domain signal S, from which the spectrum arises via an appropriate Fourier analysis of its various time variables. This time-domain signal is actually measured directly only along one of the time axes, while the effects introduced by the remaining time variables are monitored via a parametric incrementation of their values throughout independent experiments. Two-dimensional (2D) NMR experiments thus usually require longer acquisition times than unidimensional experiments, 3D NMR is orders-of-magnitude more time consuming than 2D spectroscopy, etc. Very recently, we proposed and demonstrated an approach whereby data acquisition in 2D NMR can be parallelized, enabling the collection of complete 2D spectral sets within a single transient. The present paper discusses the extension of this 2D NMR methodology to an arbitrary number of dimensions. The principles of the ensuing ultrafast n-dimensional NMR approach are described, and a variety of homo- and heteronuclear 3D and 4D NMR spectra collected within a fraction of a second are presented.     

CO2 poisoning effect on HY zeolite dehydration catalyst

The poisoning effect of CO₂ on a HY catalyst for the dehydration of 2-(2-hydroxyethyl)-pyridine (HEP) to 2-vinylpyridine (VP) has been investigated by FT-IR analysis in the presence and absence of pyridine. CO₂ was found to adsorb on sites not occupied by pyridine,i.e. on weak basic sites accompanying the strongly acidic sites, characteristic of Y zeolites in the protonated form. When the basic sites are occupied by preadsorbed CO₂, HEP dehydration cannot take place any more through the minor mechanism, involving a couple of acid-base sites, and the reaction proceeds only through the major mechanism, involving a carbocation intermediate, on Br?nsted acid sites only.     

GC/MS-based metabolomics reveals fatty acid biosynthesis and cholesterol metabolism in cell lines infected with influenza A virus

Metabolomics is the downstream of systems biology and has drawn significant interest for studying the metabolic networks from cells to organisms. To profile the metabolites in two different cell lines (A549 and AGS) infected with influenza A virus, gas chromatography coupled with mass spectrometry (GC/MS) was employed. Some differentiating metabolites in the cell lines were tentatively identified using reference library, interpreted and visualized by applying principal components analysis (PCA) and cluster heat map. Consequently, metabolic flux profiling allowed the differentiation of fatty acid biosynthesis and cholesterol metabolism during viral replication in the cell lines. The change in fatty acid turnover was also observed. Metabolomics investigation also revealed the different responses between A549 and AGS cell lines to the virus infection. From the pattern recognition results, AGS cell line might be more susceptible to influenza A virus. Regarding the fact that AGS is a poorly differentiated gastric adenocarcinoma cell line whereas A549 is a relatively differentiated lung tumor one, it is speculated that viral replication might be associated with the cell differentiations.     

A capacitively coupled temperature‐jump arrangement for high‐resolution biomolecular NMR

A simple design for performing rapid temperature jumps within a high‐resolution nuclear magnetic resonance (NMR) setting is presented and exemplified. The design is based on mounting, around a conventional NMR glass tube, an inductive radiofrequency (RF) irradiation coil that is suitably tuned by a resonant circuit and is driven by one of the NMR's console high‐power RF amplifiers. The electric fields generated by this coil's thin metal strips can lead to a fast and efficient heating of the sample, amounting to temperature jumps of ≈ 20 °C in well within a second—particularly in the presence of lossy dielectric media like those provided by physiological buffers. Moreover, when wound around a 4‐mm NMR tube, the resulting device fits a conventional 5‐mm inverse probe and is wholly compatible with the field homogeneities and sensitivities expected for high‐resolution biomolecular NMR conditions. The performance characteristics of this new system were tested using saline solutions, as well as on a lyotropic liquid crystal capable of undergoing nematic → isotropic transitions in the neighborhood of ambient temperature. These settings were then incorporated into the performance of a new kind of single‐scan 2D NMR spectroscopy acquisition, correlating the anisotropic and isotropic patterns elicited by solutes dissolved in such liquid‐crystalline systems, before and after a sudden temperature jump occurring during an intervening mixing period. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthesis of New Silybin Derivatives and Evaluation of Their Antioxidant Properties

Silibinin, the major flavonolignan of silymarin, displays a broad spectrum of biological features that are generally ascribed to its antioxidant properties. Silibinin occurs in two diastereoisomeric forms, i.e., silybins A and B, in a ratio of ca. 1 : 1. With a simple and robust purification method, it is now possible to obtain silybins A and B in pure forms, in g‐scale amounts, and within a short period of time. Herein, we describe an efficient synthesis strategy to obtain a variety of new and more H₂O‐soluble derivatives from the single silybins in which the 9″‐OH group was converted to a sulfate, N₃, phosphodiester, or NH₂ group via a solution‐phase approach. Thus, eight new compounds have been synthesized, purified by HPLC analysis, and characterized by NMR and MS analyses. To conduct experiments to clarify the many biological properties of pure silibinin diastereoisomers and their derivatives, the synthetic compounds were tested by using the DPPH assay to evaluate their antioxidant activities. The results, even if only for a small number of derivatives, revealed that some of these compounds are much more active than their parent compounds. It is also interesting to consider the synergetic effects.