A complete set of addition laws for incomplete Edwards curves

Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P₁, P₂ produce the sum P₁+P₂.     

Neurotoxin II bound to acetylcholine receptors in native membranes studied by dynamic nuclear polarization NMR

Methods enabling structural studies of membrane-integrated receptor systems without the necessity of purification provide an attractive perspective in membrane protein structural and molecular biology. This has become feasible in principle since the advent of dynamic nuclear polarization (DNP) magic-angle-spinning NMR spectroscopy, which delivers the required sensitivity. In this pilot study, we observed well-resolved solid-state NMR spectra of extensively (13)C-labeled neurotoxin II bound to the nicotinic acetylcholine receptor (nAChR) in native membranes. We show that TOTAPOL, a biradical required for DNP, is localized at membrane and protein surfaces. The concentration of active, membrane-attached biradical decreases with time, probably because of reactive components of the membrane preparation. An optimal distribution of active biradical has strong effects on the NMR data. The presence of inactive TOTAPOL in membrane-proximal situations but active biradical in the surrounding water/glycerol "glass" leads to well-resolved spectra, yet a considerable enhancement (ε = 12) is observed. The resulting spectra of a protein ligand bound to its receptor are paving the way for further DNP investigations of proteins embedded in native membrane patches.     

Comparative Test of Methods to Determine Particle Size and Particle Size Distribution in the Submicron Range

Among the most important characteristic properties of disperse systems such as latices, pigments, ceramic materials or drug formulations are the particle size and the particle size distribution. To measure these quantities, several methods and measuring instruments based on different physical principles are available. These include turbidimetry, dynamic and static light scattering, electron microscopy with image analysis, ultra- and disc centrifugation, light diffraction and the electrical sensing zone method. All these measuring techniques are doubtless necessary because of the large product variety and the broad particle size range. However, some problems arise if different techniques are used and the results are compared uncritically without considering to the application range and the resolution of the methods. An extensive comparative test was therefore carried out using seven latices in the submicron range with defined monomodal, bimodal and hexamodal particle size distributions. The most important methods of determining average particle size values and particle size distributions were tested and compared. Of the methods to determine only average particle sizes, turbidimetry is the most efficient, followed by dynamic light scattering with cumulants evaluation. Static light scattering only yields accurate results for small particles with narrow particle size distributions. Of the methods to determine particle size distributions, ultracentrifugation and, somewhat less, disc centrifugation and electron microscopy with image analysis are the most efficient. Dynamic light scattering only yields reliable results in the case of small particles with narrow distribution curves. Light diffraction and the electrical sensing zone method are less suitable for the submicron range.     

Cu(I)-catalyzed stereospecific coupling reactions of enantioenriched α-stannylated benzyl carbamates and their application

Enantioenriched α-stannylated benzyl carbamates were used in highly stereospecific coupling reactions employing Cu(I) as catalyzing transition metal. Acid chlorides and allyl bromide derivatives were used as electrophilic coupling partners. The reaction was applied in the synthesis of two highly enantioenriched indanoles and one enantioenriched tetraline via intramolecular cyclization reactions.     

A microcomputer-controlled modulation technique for the detection of transient species in UV photoelectron spectroscopy

A microcomputer-controlled modulation method is described to measure UV photoelectron spectra of transient species generated in a microwave discharge. Spectra at low and high microwave power levels are simultaneously recorded and afterwards linearly combined in order to remove parent compound signals. The method is applied to discharged oxygen where the transition O₂⁺ (²Φ_u) ← O₂ (¹Δ_g) becomes visible without interference from the parent molecule O₂ (³Σ_g^?), and to discharged sulphur dioxide where SO (³Σ^?) and S (³P) photoelectron spectra are obtained free from SO₂ bands. Finally the build-up of transient bands as a function of time is recorded.