Über einige Fragen betreffend die Theorie der Maxima und Minima mehrfacher Integrale

Ohne Zusammenfassung     

Switchable lasing in multimode microcavities

We propose the new concept of a switchable multimode microlaser. As a generic, realistic model of a multimode microresonator a system of two coupled defects in a two-dimensional photonic crystal is considered. We demonstrate theoretically that lasing of the cavity into one selected resonator mode can be caused by injecting an appropriate optical pulse at the onset of laser action (injection seeding). Temporal mode-to-mode switching by reseeding the cavity after a short cooldown period is demonstrated by direct numerical solution. A qualitative analytical explanation of the mode switching in terms of the laser bistability is presented.     

Design and Synthesis of High‐Affinity Dimeric Inhibitors Targeting the Interactions between Gephyrin and Inhibitory Neurotransmitter Receptors

Gephyrin is the central scaffolding protein for inhibitory neurotransmitter receptors in the brain. Here we describe the development of dimeric peptides that inhibit the interaction between gephyrin and these receptors, a process which is fundamental to numerous synaptic functions and diseases of the brain. We first identified receptor‐derived minimal gephyrin‐binding peptides that displayed exclusive binding towards native gephyrin from brain lysates. We then designed and synthesized a series of dimeric ligands, which led to a remarkable 1220‐fold enhancement of the gephyrin affinity (K_D=6.8 nM ). In X‐ray crystal structures we visualized the simultaneous dimer‐to‐dimer binding in atomic detail, revealing compound‐specific binding modes. Thus, we defined the molecular basis of the affinity‐enhancing effect of multivalent gephyrin inhibitors and provide conceptually novel compounds with therapeutic potential, which will allow further elucidation of the gephyrin–receptor interplay.     

Inverse colloidal crystal membranes for hydrophobic interaction membrane chromatography

A collaborative study on the robustness and portability of a capillary electrophoresis‐mass spectrometry method for peptide mapping was performed by an international team, consisting of 13 independent laboratories from academia and industry. All participants used the same batch of samples, reagents and coated capillaries to run their assays, whereas they utilized the capillary electrophoresis‐mass spectrometry equipment available in their laboratories. The equipment used varied in model, type and instrument manufacturer. Furthermore, different types of sheath‐flow capillary electrophoresis–mass spectrometry interfaces were used. Migration time, peak height and peak area of ten representative target peptides of trypsin‐digested bovine serum albumin were determined by every laboratory on two consecutive days. The data were critically evaluated to identify outliers and final values for means, repeatability (precision within a laboratory) and reproducibility (precision between laboratories) were established. For relative migration time the repeatability was between 0.05 and 0.18% RSD and the reproducibility between 0.14 and 1.3% RSD. For relative peak area repeatability and reproducibility values obtained were 3–12 and 9–29% RSD, respectively. These results demonstrate that capillary electrophoresis‐mass spectrometry is robust enough to allow a method transfer across multiple laboratories and should promote a more widespread use of peptide mapping and other capillary electrophoresis‐mass spectrometry applications in biopharmaceutical analysis and related fields.     

Electrogenerated Chemiluminescence of Cationic Triangulene Dyes: Crucial Influence of the Core Heteroatoms

Trianguleniums are fascinating conjugated hexacyclic cations that exhibit interesting electronic and optical properties. Herein, the electrogenerated chemiluminescence (ECL) emission of this family of fluorescent dyes is reported for the first time. Redox behavior and fluorescence properties of eight cationic triangulene luminophores with different heteroatom patterns in the core structure and various pending substituents were examined to rationalize the ECL. Clearly, the more electron‐rich the carbocation, the more efficient the corresponding ECL; two very distinct classes of triangulenes can be drawn from these studies by using an ECL wall sufficiency formalism.     

Ageing of Alkylthiol‐Stabilized Gold Nanoparticles

The ageing of spherical gold nanoparticles having 6‐nm‐diameter cores and a ligand shell of dodecanethiol is investigated under different storage conditions. Losses caused by agglomeration and changes in optical particle properties are quantified. Changes in colloidal stability are probed by analytical centrifugation in a polar solvent mixture. Chemical changes are detected by elementary analysis of particles and solvent. Fractionation occurs under all storage conditions. Ageing is not uniform but broadens the property distributions of the particles. Small‐number statistics in the ligand shell density and the morphological heterogeneity of particles are possible explanations. Washing steps exacerbate ageing, a process that could not be fully reversed by excess ligands. Dry storage is not preferable to storage in solvent. Storage under inert argon atmosphere reduces losses more than all other conditions but could not prevent it entirely.     

Amplified analysis of DNA by the autonomous assembly of polymers consisting of DNAzyme wires

A systematic study of the amplified optical detection of DNA by Mg(2+)-dependent DNAzyme subunits is described. The use of two DNAzyme subunits and the respective fluorophore/quencher-modified substrate allows the detection of the target DNA with a sensitivity corresponding to 1 × 10(-9) M. The use of two functional hairpin structures that include the DNAzyme subunits in a caged, inactive configuration leads, in the presence of the target DNA, to the opening of one of the hairpins and to the activation of an autonomous cross-opening process of the two hairpins, which affords polymer DNA wires consisting of the Mg(2+)-dependent DNAzyme subunits. This amplification paradigm leads to the analysis of the target DNA with a sensitivity corresponding to 1 × 10(-14) M. The amplification mixture composed of the two hairpins can be implemented as a versatile sensing platform for analyzing any gene in the presence of the appropriate hairpin probe. This is exemplified with the detection of the BRCA1 oncogene.     

The Rearrangement of 2,2‐Diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane to 3,4,4‐Triphenylcyclopent‐1‐ene: a DFT Analysis

A computational study on the rearrangement of 2,2‐diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane ( 1 ) is presented, using density functional theory (DFT), (U)B3LYP with the 6‐31G* basis set (DFT1) and (U)M05‐2X with the 6‐311+G** basis set (DFT2). In agreement with a biradical character of the transition structure (TS) or intermediate, the potential‐energy hypersurface is lowered by the influence of three conjugated Ph groups. Surprisingly, two conformations of the geminal diphenyl group (different twist angles) induce two different minimum‐energy pathways for the rearrangement. Independent of the functional used, the first hypersurface harbors true biradical intermediates, whereas the second energy surface is a flat, slightly ascending slope from the starting material to the TS. The functional (U)M05‐2X with the basis set 6‐311+G** provides realistic energies which seem to be close to experiment. The activation energy for racemization of enantiomers of 1 is lower than that of rearrangement by 2.5 kcal mol^?1, in agreement with experiment.     

Qualitative and Quantitative Analysis of 17 Different Types of Tetra- and Pentacyclic Triterpenic Acids in Boswellia papyrifera by a Semi-Automatic Homomodal 2D HPLC method

A semi-automatic two dimensional high-performance liquid chromatography (HPLC) gradient method with photo diode array detection was developed, capable of separating and quantifying up to 17 different triterpenic acids in the gum resin of the frankincense species Boswellia papyrifera. The here reported quantitation of 14 of the possible 17 compounds contains boswellic, tirucallic and lupeolic acids. All compounds were isolated from B. papyrifera and used as external standards. Quantitation of these compounds was performed after minimizing the matrix by liquid?Cliquid separation, using alkaline, acidic and organic media to separate the acids from interfering matrix compounds. Therefore, two different extraction procedures were tested, giving two different extraction profiles. Within the first run (1st dimension) 13 compounds could be quantified. Quantitation of ??-boswellic acid, which was proved to elute as inhomogeneous peak, was achieved by introduction of a second dimension, leading to a fully validated semi-automatic homomodal 2D chromatography. The method is applicable for determination of compounds occurring in different types of frankincense and their pharmaceutical products. It also can be applied to distinguish between different kinds of frankincense. Moreover, it is the first published method feasible of separating and quantifying five different types of tirucallic acids.     

A novel approach to improve operation and performance in flow field-flow fractionation

A new system design and setup are proposed for the combined use of asymmetrical flow field-flow fractionation (AF4) and hollow-fiber flow field-flow fractionation (HF5) within the same instrumentation. To this purpose, three innovations are presented: (a) a new flow control scheme where focusing flow rates are measured in real time allowing to adjust the flow rate ratio as desired; (b) a new HF5 channel design consisting of two sets of ferrule, gasket and cap nut used to mount the fiber inside a tube. This design provides a mechanism for effective and straightforward sealing of the fiber; (c) a new AF4 channel design with only two fluid connections on the upper plate. Only one pump is needed to deliver the necessary flow rates. In the focusing/relaxation step the two parts of the focusing flow and a bypass flow flushing the detectors are created with two splits of the flow from the pump. In the elution mode the cross-flow is measured and controlled with a flow controller device. This leads to reduced pressure pulsations in the channel and improves signal to noise ratio in the detectors. Experimental results of the separation of bovine serum albumin (BSA) and of a mix of four proteins demonstrate a significant improvement in the HF5 separation performance, in terms of efficiency, resolution, and run-to-run reproducibility compared to what has been reported in the literature. Separation performance in HF5 mode is shown to be comparable to the performance in AF4 mode using a channel with two connections in the upper plate.