Diophantine properties of measures invariant with respect to the Gauss map

Motivated by the work of D. Y. Kleinbock, E. Lindenstrauss, G. A. Margulis, and B. Weiss [8, 9], we explore the Diophantine properties of probability measures invariant under the Gauss map. Specifically, we prove that every such measure which has finite Lyapunov exponent is extremal, i.e., gives zero measure to the set of very well approximable numbers. We show, on the other hand, that there exist examples where the Lyapunov exponent is infinite and the invariant measure is not extremal. Finally, we construct a family of Ahlfors regular measures and prove a Khinchine-type theorem for these measures. The series whose convergence or divergence is used to determine whether or not µ-almost every point is ψ-approximable is different from the series used for Lebesgue measure, so this theorem answers in the negative a question posed by Kleinbock, Lindenstrauss, and Weiss [8].     

Separation of a BMS drug candidate and acyl glucuronide from seven glucuronide positional isomers in rat plasma via high-performance liquid chromatography with tandem mass spectrometric detection

A high-performance liquid chromatography/tandem mass spectrometry (LC/MS/MS) method has been developed and validated for the determination of a BMS drug candidate and its acyl glucuronide (1-O-beta glucuronide) in rat plasma. A 50-microL aliquot of each plasma sample was fortified with acetonitrile containing the internal standard to precipitate proteins and extract the analytes of interest. After mixing and centrifugation, the supernatant from each sample was transferred to a 96-well plate and injected into an LC/MS/MS system. Chromatographic separation was achieved isocratically on a Phenomenex Luna C(18), 3 mm x 150 mm, 3 microm column. The mobile phase contained 0.075% formic acid in 70:30 (v/v) acetonitrile/water. Under the optimized chromatographic conditions, the BMS drug candidate and its acyl glucuronide were separated from its seven glucuronide positional isomers within 10 min. Resolution of the parent from all glucuronides and acyl glucuronide from its positional isomers was critical to avoid their interference with quantitation of parent or acyl glucuronide. Detection was by positive ion electrospray MS/MS on a Sciex API 4000. The standard curve, which ranged from 5 to 5000 ng/mL, was fitted to a 1/x(2) weighted quadratic regression model for both the BMS drug candidate and its acyl glucuronide. Whole blood and plasma stability experiments were conducted to establish the sample collection, storage, and processing conditions. The validation results demonstrated that this method was rugged and repeatable. The same methodology has also been used in mouse and human plasma for the determination of the BMS drug candidate and its acyl glucuronide.     

Tandem mass spectrometry of intact GroEL-substrate complexes reveals substrate-specific conformational changes in the trans ring

It has been suggested that the bacterial GroEL chaperonin accommodates only one substrate at any given time, due to conformational changes to both the cis and trans ring that are induced upon substrate binding. Using electrospray ionization mass spectrometry, we show that indeed GroEL binds only one molecule of the model substrate Rubisco. In contrast, the capsid protein of bacteriophage T4, a natural GroEL substrate, can occupy both rings simultaneously. As these substrates are of similar size, the data indicate that each substrate induces distinct conformational changes in the GroEL chaperonin. The distinctive binding behavior of Rubisco and the capsid protein was further investigated using tandem mass spectrometry on the intact 800-914 kDa GroEL-substrate complexes. Our data suggest that even in the gas phase the substrates remain bound inside the GroEL cavity. The analysis revealed further that binding of Rubisco to the GroEL oligomer stabilizes the chaperonin complex significantly, whereas binding of one capsid protein did not have the same effect. However, addition of a second capsid protein molecule to GroEL resulted in a similar stabilizing effect to that obtained after the binding of a single Rubisco. On the basis of the stoichiometry of the GroEL chaperonin-substrate complex and the dissociation behavior of the two different substrates, we hypothesize that the binding of a single capsid polypeptide does not induce significant conformational changes in the GroEL trans ring, and hence the unoccupied GroEL ring remains accessible for a second capsid molecule.     

Phosphine dissociation and diffusion on Si(001) observed at the atomic scale

A detailed atomic-resolution scanning tunneling microscopy (STM) and density functional theory study of the adsorption, dissociation, and surface diffusion of phosphine (PH(3)) on Si(001) is presented. Adsorbate coverages from approximately 0.01 monolayer to saturation are investigated, and adsorption is performed at room temperature and 120 K. It is shown that PH(3) dissociates upon adsorption to Si(001) at room temperature to produce both PH(2) + H and PH + 2H. These appear in atomic-resolution STM images as features asymmetric-about and centered-upon the dimer rows, respectively. The ratio of PH(2) to PH is a function of both dose rate and temperature, and the dissociation of PH(2) to PH occurs on a time scale of minutes at room temperature. Time-resolved in situ STM observations of these adsorbates show the surface diffusion of PH(2) adsorbates (mediated by its lone pair electrons) and the dissociation of PH(2) to PH. The surface diffusion of PH(2) results in the formation of hemihydride dimers on low-dosed Si(001) surfaces and the ordering of PH molecules along dimer rows at saturation coverages. The observations presented here have important implications for the fabrication of atomic-scale P dopant structures in Si, and the methodology is applicable to other emerging areas of nanotechnology, such as molecular electronics, where unambiguous molecular identification using STM is necessary.     

Medicines, monopolies and mortars: the chemical laboratory and pharmaceutical trade at the Society of Apothecaries in the eighteenth century

In 1672, a laboratory was founded by the Society of Apothecaries at its premises in Blackfriars, London, to manufacture chemical medicines. By exploring the society's motivations for constructing a laboratory and its development during the eighteenth century, this paper examines the roles that chemistry played within the activities of the institution. While the chemistry's primary utility was in drug manufacturing for the society's pharmaceutical trade, through its laboratory, the society used chemistry to develop its corporate and educational aims, thus helping to secure its institutional authority in London's medical marketplace.     

Absorption and Emission Sensitivity of 2‐(2′‐Hydroxyphenyl)benzoxazole to Solvents and Impurities

2‐(2′‐Hydroxyphenyl)benzoxazole (HBO) is known for undergoing intramolecular proton transfer in the excited state to result in the emission of its tautomer. A minor long‐wavelength absorption band in the range 370–420 nm has been reported in highly polar solvents such as dimethylsulfoxide (DMSO). However, the nature of this species has not been entirely clarified. In this work, we provide evidence that this long‐wavelength absorption band might have been caused by base or metal salt impurities that are introduced into the spectral sample during solvent transport using glass Pasteur pipettes. The contamination by base or metal salt could be avoided by using borosilicate glass syringes or nonglass pipettes in sample handling. Quantum chemical calculations conclude that solvent‐mediated deprotonation is too energetically costly to occur without the aid of a base of an adequate strength. In the presence of such a base, the deprotonation of HBO and its effect on emission are investigated in dichloromethane and DMSO, the latter of which facilitates deprotonation much more readily than the former. Finally, the absorption and emission spectra of HBO in 13 solvents are reported, from which it is concluded that ESIPT is hindered in polar solvents that are also strong hydrogen bond acceptors.     

Bis[N-alkyl-NN-di(2-pyridylmethyl)amine]zinc(II) perchlorates display cis-facial stereochemistry in solid state and solution

N-Alkyl-N,N-di(2-pyridylmethyl)amines are ligands commonly used by supramolecular chemists in molecular recognition and sensing applications. The metal coordination complexes of these ligands, in particular those with 2:1 (ligand:metal) molar ratio, have not been sufficiently characterised in solution. In this work, bis[N-alkyl-N,N-di(2-pyridylmethyl)amine]zinc(II) perchlorates are characterised in both solid and solution phases, using X-ray crystallography and NMR spectroscopy, respectively. Only the cis-facial stereoisomer is observed. Density functional theory calculations support the thermodynamic preference for this stereochemistry, as in one representative case the gas phase energy of the cis-facial configuration is lower than those of the trans-facial and meridional configurations by 4.0 and 4.5 kcal/mol, respectively.     

Experimental investigation on the mechanism of chelation-assisted, copper(II) acetate-accelerated azide-alkyne cycloaddition

A mechanistic model is formulated to account for the high reactivity of chelating azides (organic azides capable of chelation-assisted metal coordination at the alkylated azido nitrogen position) and copper(II) acetate (Cu(OAc)(2)) in copper(II)-mediated azide-alkyne cycloaddition (AAC) reactions. Fluorescence and (1)H NMR assays are developed for monitoring the reaction progress in two different solvents, methanol and acetonitrile. Solvent kinetic isotopic effect and premixing experiments give credence to the proposed different induction reactions for converting copper(II) to catalytic copper(I) species in methanol (methanol oxidation) and acetonitrile (alkyne oxidative homocoupling), respectively. The kinetic orders of individual components in a chelation-assisted, copper(II)-accelerated AAC reaction are determined in both methanol and acetonitrile. Key conclusions resulting from the kinetic studies include (1) the interaction between copper ion (either in +1 or +2 oxidation state) and a chelating azide occurs in a fast, pre-equilibrium step prior to the formation of the in-cycle copper(I)-acetylide, (2) alkyne deprotonation is involved in several kinetically significant steps, and (3) consistent with prior experimental and computational results by other groups, two copper centers are involved in the catalysis. The X-ray crystal structures of chelating azides with Cu(OAc)(2) suggest a mechanistic synergy between alkyne oxidative homocoupling and copper(II)-accelerated AAC reactions, in which both a bimetallic catalytic pathway and a base are involved. The different roles of the two copper centers (a Lewis acid to enhance the electrophilicity of the azido group and a two-electron reducing agent in oxidative metallacycle formation, respectively) in the proposed catalytic cycle suggest that a mixed valency (+2 and +1) dinuclear copper species be a highly efficient catalyst. This proposition is supported by the higher activity of the partially reduced Cu(OAc)(2) in mediating a 2-picolylazide-involved AAC reaction than the fully reduced Cu(OAc)(2). Finally, the discontinuous kinetic behavior that has been observed by us and others in copper(I/II)-mediated AAC reactions is explained by the likely catalyst disintegration during the course of a relatively slow reaction. Complementing the prior mechanistic conclusions drawn by other investigators, which primarily focus on the copper(I)/alkyne interactions, we emphasize the kinetic significance of copper(I/II)/azide interaction. This work not only provides a mechanism accounting for the fast Cu(OAc)(2)-mediated AAC reactions involving chelating azides, which has apparent practical implications, but suggests the significance of mixed-valency dinuclear copper species in catalytic reactions where two copper centers carry different functions.