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Oscillatory Perturbations of Linear Problems at Resonance

This paper is concerned with a study of bounded perturbations of resonant linear problems. It follows from our results that for certain types of bounded domains Ω ? Rⁿ, n ≥ 2, the Dirichlet problem $\matrix{\Delta u+\lambda_{1}u+g(u)=h(x),\ \ \ x\in\Omega\cr \quad\quad\quad\quad\quad\quad u=0,\ \ \ x\in\partial\Omega,}$ has infinitely many positive solutions, in case λ₁ is the principal eigenvalue of ?Δ subject to trivial Dirichlet boundary conditions, g is a nontrivial periodic nonlinearity of zero mean and ∫_03A9h(x)?(x)dx = 0, where ? is an eigenfunction corresponding to λ₁.     

Vibrational spectra of cyclopentadienyl chlorides of titanium,zirconium and hafnium. internal rotation and thermodynamic functions

The infrared and Raman spectra of some cyclopentadienyl compounds of the transition metals, namely Ti(C₅H₅)Cl₃ and M(C₅H₅)₂Cl₂ (M = Ti, Zr and Hf), are reported and discussed. The infrared spectra of the gaseous species isolated in argon matrices at 10 K provide structural information about the single molecules. Particular attention has been paid to the low-frequency region in order to achieve more reliable assignments for the internal-rotation modes. The structural data and the fundamental frequencies derived from the spectra are employed in a calculation of the thermodynamic functions for these compounds in the ideal gas state.     

Chiral separation of the four stereoisomers of a novel antianginal agent using a dual cyclodextrin system in capillary electrophoresis

Reported here is an analytical method enabling the stereochemical resolution of a new antianginal compound possessing two stereogenic centers, leading to four stereoisomers. Only one of these isomers is currently under development as a novel antianginal agent and consequently, the other three isomers are considered as unwanted chiral impurities. Therefore, an enantioselective method is required in order to check its enantiomeric purity. This paper presents a method exploiting the high efficiency of capillary electrophoresis and the complexing properties of cyclodextrins to achieve the separation of the four stereoisomers of this weakly basic compound (pKa = 7.4). For this purpose, the combination of a neutral cyclodextrin, hydroxypropyl-gamma-cyclodextrin (HP-gamma-CD), and an anionic cyclodextrin, carboxymethyl-beta-cyclodextrin (CM-beta-CD), was added to the separation buffer running in an uncoated silica capillary. After selection of the suitable cyclodextrin system, satisfactorily separation conditions were as follows: 30 mM phosphate buffer (pH 6.4) containing 10 mM of HP-gamma-CD and 10 mM of CM-beta-CD, running voltage +30 kV. The resulting run time and resolutions were respectively about 17 min and between 1.95 and 2.84. Linearity curves (0.993 < r2 < 0.998) are also shown.     

Sets of tiles with a prescribed number of tilings

Summary For every k2 and r1 there exists a set of k prototiles that admits exactly r distinct tilings. All the tilings obtained are periodic.     

Effect of time on the interfacial and foaming properties of beta-lactoglobulin/acacia gum electrostatic complexes and coacervates at pH 4.2

The electrostatic complexation between beta-lactoglobulin and acacia gum was investigated at pH 4.2 and 25 degrees C. The binding isotherm revealed a spontaneous exothermic reaction, leading to a DeltaHobs = -2108 kJ mol(-1) and a saturation protein to polysaccharide weight mixing ratio of 2:1. Soluble electrostatic complexes formed in these conditions were characterized by a hydrodynamic diameter of 119 +/- 0.6 nm and a polydispersity index of 0.097. The effect of time on the interfacial and foaming properties of these soluble complexes was investigated at a concentration of 0.1 wt % at two different times after mixing (4 min, referred as t approximately 0 h and t = 24 h). At t approximately 0 h, the mixture is mainly made of aggregating soluble electrostatic complexes, whereas after 24 h these complexes have already insolubilize to form liquid coacervates. The surface elasticity, viscosity and phase angle obtained at low frequency (0.01 Hz) using oscillating bubble tensiometry revealed higher fluidity and less rigidity in the film formed at t approximately 0 h. This observation was confirmed by diminishing bubble experiments coupled with microscopy of the thin film. It was thicker, more homogeneous and contained more water at t approximately 0 h as compared to t = 24 h (thinner film, less water). This led to very different gas permeability's of Kt approximately 0 h = 0.021 cm s(-1) and Kt=24 h) = 0.449 cm s(-1), respectively. Aqueous foams produced with the beta-lactoglobulin/acacia gum electrostatic complexes or coacervates exhibited very different stability. The former (t approximately 0 h) had a stable volume, combining low drainage rate and mainly air bubble disproportionation as the destabilization mechanism. By contrast, using coacervates aged for 24 h, the foam was significantly less stable, combining fast liquid drainage and air bubble destabilization though fast gas diffusion followed by film rupture and bubble coalescence. The strong effect of time on the air/water interfacial properties of the beta-lactoglobulin/acacia gum electrostatic complexes can be understood by their reorganization at the interface to form a coacervate phase that is more fluid/viscous at t approximately 0 h vs rigid/elastic at t = 24 h.     

Modelling and mutation studies on the histamine H1-receptor agonist binding site reveal different binding modes for H1-agonists: Asp116 (TM3) has a constitutive role in receptor stimulation

Summary A modelling study has been carried out, investigating the binding of histamine (Hist), 2-methylhistamine (2-MeHist) and 2-phenylhistamine (2-PhHist) at two postulated agonistic binding sites on transmembrane domain 5 (TM5) of the histamine H₁-receptor. For this purpose a conformational analysis study was performed on three particular residues of TM5, i.e., Lys²⁰⁰, Thr²⁰³ and Asn²⁰⁷, for which a functional role in binding has been proposed. The most favourable results were obtained for the interaction between Hist and the Lys²⁰⁰/Asn²⁰⁷ pair. Therefore, Lys²⁰⁰ was subsequently mutated and converted to an alanine, resulting in a 50-fold decrease of H₁-receptor stimulation by histamine. Altogether, the data suggest that the Lys²⁰⁰/Asn²⁰⁷ pair is important for activation of the H₁-receptor by histamine. In contrast, analogues of 2-PhHist seem to belong to a distinct subclass of histamine agonists and an alternative mode of binding is proposed in which the 2-phenyl ring binds to the same receptor location as one of the aromatic rings of classical histamine H₁-antagonists. Subsequently, the binding modes of the agonists Hist, 2-MeHist and 2-PhHist and the H₁-antagonist cyproheptadine were evaluated in three different seven--helical models of the H₁-receptor built in homology with bacteriorhodopsin, but using three different alignments. Our findings suggest that the position of the carboxylate group of Asp¹¹⁶ (TM3) within the receptor pocket depends on whether an agonist or an antagonist binds to the protein; a conformational change of this aspartate residue upon agonist binding is expected to play an essential role in receptor stimulation.Abbreviations 2-MeHist 2-methylhistamine - 2-PEA 2-pyridyl-ethylamine - 2-PhHist 2-phenylhistamine - CHO Chinese hamster ovary - E_int interaction energy - E_str strain energy - GES global energy structure - gpH₁R guinea pig H₁-receptor - GPCR G-protein coupled receptor - Hist histamine - N proximal nitrogen - N tele nitrogen - TM transmembrane domain - WT wild type