Fourier analysis of the approximation power of principal shift-invariant spaces

The approximation order provided by a directed set {S _h } _h>0 of spaces, each spanned by thehZ ^d -translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs _h to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s _h } is obtained froms ₁ by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions.     

Abbau von Palustrin zu (−)-Dihydropalustraminsäure ((2R, 6S, 1′S)-[6-(1′-Hydroxypropyl)-2-piperidyl]essigsäure) und Struktur von Palustrin und Palustridin. Mitteilung über Schachtelhalmalkaloide

Degradation of palustrin to (?)-dihydropalustramic acid ((2R,6S,1′S)-[6-(1′-hydroxypropyl)-2-piperidyl]acetic acid), and the structure of palustrin and palustridin The structure of the macrocyclic alkaloid palustrin is shown to be 1a . Its piperidine unit can be obtained as (?)-dihydropalustramic acid ( 6a ) by the following sequence of degradation reactions (Scheme 1): catalytic hydrogenation of 1a followed by methylation and Hofmann degradation provides the allyl base 4 . the regioselectivity of the Hofmann elimination is explained by intramolecular proton abstraction at C(3) by C(18)-O^?. Catalytic reduction of 4 and subsequent acidic hydrolysis yielded 6a and N, N-dimethylputrescine (?N,N-dimethyl-1,4-butanediamine; 7 ). Loss of the N-alkyl group in the formation of 6a occurs during the catalytic hydrogenation step. This interpretation is supported by the results of model experiments. The position of the double bond in 1a is deduced from the IR. spectrum of the bromo-δ-lactone 19 prepared by treatment of 1a with N-bromosuccinimide at pH 4 (Scheme 3). Some of our previously published results on the degradation of dihydropalustrin ( 2a ) are obviously at variance with the newly proposed structure for palustrin ( 1a ). They can easily be explained by assuming a partial hydrogenolysis of the C(17)-N(1) bond during the preparation of dihydropalustrin from palustrin. Periodate cleavage of dihydropalustramic acid methyl ester ( 6b ) liberates propionaldehyde, which can be trapped by working at pH 7.5 (Scheme 2); at lower pH values it condenses rapidly with the simultaneously generated 3,4,5,6-tetrahydropyridine derivative 15 . The structure of the condensation product is proposed to be 16 on the basis of the isolation of its hydrogenation product, an isomeric dihydropalustramic acid ( 17 ).     

ESCA: Electron Spectroscopy for Chemical Analysis

A substance on which X-rays fall emits photoelectrons and Auger electrons. The energy spectra of the electrons emitted provide information about the electronic structure in the specimen, ranging from the innermost atomic levels and their dependence on the chemical environment to the molecular orbitals of the valence electrons and the band structure in solids. Electron spectra of this nature can now be recorded with high-resolution instruments; their analysis offers new aspects for investigation of chemical composition. The method of electron spectroscopy developed for this purpose, which has now been developed to a high degree of perfection, will be referred to in the following discussion as ESCA (Electron Spectroscopy for Chemical Analysis).     

On the existence of SH3, SeH3, and TeH3: Discrepancies between all-electron and pseudopotential calculations

Ab initio calculations using both pseudopotential and double and triple-ζ all-electron basis sets, with and without electron correlation (MP2, QCISD), have been performed on the λ⁴-sulfanyl (SH₃), λ⁴-selanyl (SeH₃), and λ⁴-tellanyl (TeH₃) radicals. All-electron basis sets of double-ζ quality predict that SH₃ and SeH₃ correspond to transition states on their respective potential energy surfaces. In contrast, the pseudopotentials of Hay and Wadt predict that SH₃ and SeH₃ correspond to local minima at the QCISD level of theory while the pseudopotentials of Christiansen and Stevens predict transition states. By comparison, TeH₃ proved to be a local minimum at all levels of theory. Interestingly, when a very large (triple-ζ) all-electron basis set was used, SH₃ proved to be a transition state; however, in this instance the potential energy surface was found to be much flatter than in the case for which a double-ζ basis set was used, suggesting that further improvements in the basis set may lead to a local minimum. Further improvements in the all-electron selenium basis also led to a local minimum for SeH₃ at the QCISD level of theory. © 1995 by John Wiley & Sons, Inc.     

An approach to computer-aided inhibitor design: Application to cathepsin L

Summary We have developed an approach to search for molecules that can be used as lead compounds in designing an inhibitor for a given proteolytic enzyme when the 3D structure of a homologous protein is known. This approach is based on taking the cast of the binding pocket of the protease and comparing its dimensions with that of the dimensions of small molecules. Herein the 3D structure of papain is used to model cathepsin L using the comparative modeling technique. The cast of the binding pocket is computed using the crystal structure of papain because the structures of papain and the model of cathepsin L are found to be similar at the binding site. The dimensions of the cast of the binding site of papain are used to screen for molecules from the Cambridge Structural Database (CSD) of small molecules. Twenty molecules out of the 80 000 small molecules in the CSD are found to have dimensions that are accommodated by the papain binding pocket. Visual comparison of the shapes of the cast and the 20 screened molecules resulted in identifying brevotoxin b, a toxin isolated from the red tide dinoflagellate Ptycho brevis (previously classified as Gymonodium breve), as the structure that best fits the binding pocket of papain. We tested the proteolytic activity of papain and cathepsin L in the presence of brevotoxin b and found inhibition of papain and cathepsin L with K_is of 25 M and 0.6 M, respectively. We also compare our method with a more elaborate method in the literature, by presenting our results on the computer search for inhibitors of the HIV-1 protease.     

Development of a liquid chromatography/tandem mass spectrometry assay for the quantification of PM00104, a novel antineoplastic agent, in mouse, rat, dog, and human plasma

A rapid and sensitive liquid chromatography/tandem mass spectrometry (LC/MS/MS) assay was developed and validated to quantify a novel antineoplastic agent, PM00104, in mouse, rat, dog, and human plasma. The method was validated to demonstrate the specificity, limit of quantification (LOQ), accuracy, and precision of measurements. The calibration range for PM00104 was established using PM00104 standards from 0.01-5.0 ng/mL in blank plasma. The selected reaction monitoring (SRM), based on the m/z 692.2 --> 218.2 transition, was specific for PM00104, and that based on the m/z 697.2 --> 218.2 transition was specific for PM00104 ((13)C(2),(2)H(3)) (the internal standard, IS); no endogenous materials interfered with the analysis of PM00104 and IS from blank plasma. The assay was linear over the concentration range 0.01-5.0 ng/mL. The correlation coefficients for the calibration curves ranged from 0.9981-0.9999. The mean intra-day and inter-day accuracies for all calibration standards (n = 8) ranged from 97-105% (< or =5% bias) in human plasma, and the mean inter-day precision for all calibration standards was less than 8.5%. The mean intra- and inter-day assay accuracy for all quality control (QC) replicates in human plasma (n = 9), determined at each QC level throughout the validated runs, ranged from 96-112% (< or =12% bias) and from 102-105% (< or =5% bias), respectively. The mean intra- and inter-day assay precision was less than 15.0 and 11.8% for all QC levels, respectively. For the QC samples prepared in animal species plasma, the %CV values of the assays ranged from 1.8-8.8% in mouse plasma, from 3.7-13.8% in rat plasma, and from 3.0-7.2% in dog plasma. The assay accuracies ranged from 92-102% (< or =8% bias) for all QC levels prepared in mouse plasma; ranged from 93-106% (< or =7% bias) in rat plasma; and ranged from 95-114% (< or =14% bias) in dog plasma. The assay has been used to support preclinical pharmacokinetic and toxicokinetic studies and is currently used to measure PM00104 plasma concentrations to support clinical trials.     

A computational study of radical haloacetal cyclizations controlled by the acetal center

The stereochemical outcome of the radical haloacetal cyclization reaction (Ueno-Stork reaction) has been examined by ab initio and other molecular orbital techniques. It was found that the stereochemistry of 5-exo- and 6-exo trig cyclizations can be accurately predicted from calculations using moderate levels of theory (UHF/6-311G** or B3LYP/6-311G**). A simplified computational procedure, easily run on a standard desktop computer, has been developed that provides excellent predictive ability for the stereochemical outcome for the reactions in question. Interestingly, a novel twist transition state has been identified for the first time in 5-exo-trig radical cyclization reactions.     

Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 19. Preparation and Characterization of Films of Quaternized Poly(4‐vinylpyridine)‐silica

Quaternized poly(4‐vinylpyridine) (QPVP) has been incorporated as an anion exchanger into sol‐gel derived silica films for use in a spectroelectrochemical sensor. The preparation, characteristics and performance of these films are described. The films, which are spin‐coated onto the surface of a planar optically transparent electrode, are optically transparent and uniform. Scanning electron microscopy and spectroscopic ellipsometry have been used to examine film structure, thickness and optical properties. These films have been shown both spectroscopically and electrochemically to preconcentrate ferrocyanide, a model analyte for the sensor. The films can be regenerated for multiple measurements by exposure to 1 M KNO₃. The effects of polymer molecular weight and storage conditions on film performance are described. The overall response of this film is comparable to the poly(dimethyldiallylammonium chloride)‐silica films previously used for this sensor.     

Mass spectrometry in structural and stereochemical problems—CLXXXIV: Charge localization in fragment ions of amino ketones and esters

The mass spectral fragmentation of a number of specially synthesized amino esters and ketones has been studied in which the distance between the two functionalities has been varied. The principal fragments formed following initial ionization are the even-electron immonium ions a and b. Further fragmentation of ion a in the amino esters occurs via non-specific processes. Therefore it is difficult to establish the degree of mobility of the positive charge in the fragment ions, notably whether the species with the charge present on the oxygen atom makes a significant contribution to the fragmentation. The β-(IIb) and γ-(IV) amino ketones show no McLafferty rearrangements after α-fission, thus demonstrating that uncoupling of the carbonyl π electrons is not a feasible trigger in lieu of charge localization.     

Synthesis and in vitro degradation of poly(N‐vinyl‐2‐pyrrolidone)‐based graft copolymers for biomedical applications

This work is devoted to the design of a novel family of hydrosoluble biomaterials: poly(N‐vinyl‐2‐pyrrolidone) (PVP)‐based graft copolymers. A synthesis route has been elaborated in which ω‐functionalized PVP is prepared via chain‐transfer radical polymerization, end‐group modified, and subsequently grafted onto a polyhydroxylated backbone, typically dextran or poly(vinyl alcohol). The resulting graft copolymer biomaterials are designed for use in various biomedical applications, particularly as materials with a stronger potential for plasma expansion than already existing products have. The graft copolymers are potentially degradable because the PVP grafts are connected to the polyol backbone via a hydrolytically labile carbonate or ester linkage. The degradation of the graft copolymers was performed in vitro over a period of 6 weeks. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3652–3661, 2002