Computational experience with general equilibrium problems

We report on computational experience with an implementation of three algorithms for the general economic equilibrium problem. As a result we get that the projection algorithm for variational inequalities increases the size of solvable models by a factor of 5–10 in comparison with the classical homotopy method. As a third approach we implemented a simulated annealing heuristic which might be suitable to estimate equilibria for very large models.Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).     

Gas chromatographic and mass spectrometric determination of nitroaromatics in water

Several methods for the extraction of nitroaromatic compounds from water were compared. High recoveries were achieved with discontinuous or continuous extraction of water with dichloromethane and by adsorption on Amberlite XAD-2, -4 and -8 resins (1:1:1) and elution with dichloromethane. The recoveries obtained with solid-phase extraction using cyano-, phenyl- or octadecyl-bonded phases varied, depending on the compounds studied, and were often low. Nitroaromatic compounds were determined by gas chromatography using an electron-capture or a chemiluminescence detector (thermal energy analyser) and by mass spectrometry using electron impact and positive- and negative-ion chemical ionization.     

Hyphenation of capillary high-performance liquid chromatography with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry for nano-scale screening of single-bead combinatorial libraries

This paper focuses on the technical aspects of chemical screening from 384-well plate nano-scale single-bead combinatorial libraries. The analytical technique utilized is a combination of capillary liquid chromatography with ultraviolet detection and matrix-assisted laser desorption/ionization (MALDI) mass spectrometry. The HPLC/MALDI-MS hyphenation is achieved by means of a micro-fraction collector with a peak detection system that automatically collects the peaks onto the MALDI targets for subsequent characterization. Several experimental parameters such as type of 384-well plate, well-plate sealing foils, and a column-switching procedure were investigated using a small test library of nine components. Additionally, the influence of different MALDI matrices, different MALDI targets and sample-spotting techniques on the MALDI detection sensitivity as well as the ruggedness and sample throughput capacity of this technique were studied. Optimum results for the analytes investigated were obtained with 2,5-dihydroxybenzoic acid using on-line mixing of HPLC effluent and matrix solution. To demonstrate the potential of this capillary HPLC/MALDI-TOFMS method, its application to several single-bead libraries was investigated. The instrumental method allowed for the rapid identification and purity assessment of combinatorial libraries with detection limits down to the higher femtomole level using both UV detection and MALDI mass spectrometry.     

Quantitative analysis of small pharmaceutical drugs using a high repetition rate laser matrix-assisted laser/desorption ionization source

In this work, a high repetition rate laser matrix-assisted laser desorption/ionization (MALDI) source is studied on a quadrupole-time-of-flight (QqTOF) and a triple quadrupole (QqQ) mass spectrometer for rapid quantification of small pharmaceutical drugs. The high repetition rate laser allows an up to 100-fold higher pulse frequency as compared with regular MALDI lasers, resulting in much larger sample throughput and number of accumulated spectra. This increases the reproducibility of signal intensities considerably, with average values being around 5% relative standard deviation after taking into account the area ratio of the analyte to an internal standard. Experiments were conducted in MS/MS mode to circumvent the large chemical background due to MALDI matrix ions in the low mass range. The dynamic range of calibration curves on the QqTOF mass spectrometer extended over at least two orders of magnitude, whereas on the QqQ it extended over at least three orders of magnitude. Detection limits ranged from 60-400 pg/microL on the QqTOF and from 6-70 pg/microL on the QqQ for a series of benzodiazepines. The benzodiazepine content of commercial pill formulations was quantified, and less than 5% error was obtained between the present method and the manufacturer's certified values. Furthermore, a high sample throughput was achieved with this method, so that a single MALDI spot could be quantitatively scanned in as little as 15 s, and an entire 96-well MALDI plate in 24 min.     

Studies on azaspiracid biotoxins. I. Ultrafast high-resolution liquid chromatography/mass spectrometry separations using monolithic columns

In this study, the performance of monolithic columns was evaluated for ultrafast liquid chromatography/mass spectrometry (LC/MS) analyses and for high-resolution separations of several azaspiracid biotoxin analogs. Because of their high permeability, monolithic columns offer a number of advantages over conventional packed columns; viz., very low backpressures and relatively flat van Deemter curves at high flow rates. That is, very high flow rates can be used for ultrafast analyses or, by using longer than normal columns, high-resolution separations are possible. In a series of experiments, we varied the mobile phase flow rates between 1 and 8 mL/min, and studied their impact on chromatographic parameters such as retention time, resolution, number of plates and pressure. The chromatographic run times could be reduced to ca. 30 s without a significant change in the separation efficiency. A signal intensity comparison revealed interesting differences between atmospheric-pressure chemical ionization (APCI) and electrospray ionization (ESI) in their flow-rate dependency. An explanation with respect to the behavior as of a mass-flow or a concentration-dependent device is given in the paper. Additionally, the column length was varied between 10 and 70 cm. As a result, the number of theoretical plates increased substantially. In the example shown in the report, an increase from 13 000 plates for a 10-cm column to 80 000 for a 70-cm column is demonstrated. In addition, the potential of the monolithic columns for high-resolution LC/MS separations is shown for a complex biotoxin mixture, which was separated on a 40-cm-long column.     

Profiling of plasma cholesterol ester and triglyceride fatty acids as their methyl esters by capillary gas chromatography, preceded by a rapid aminopropyl-silica column chromatographic separation of lipid classes

A rapid procedure for the isolation of plasma cholesterol ester and triglyceride fractions with aminopropyl-silica columns, followed by analysis of their fatty acid compositions by capillary gas chromatography with flame ionization detection, is described. Within-series and long-term (six months) series-to-series precision were investigated. The isolation procedure caused minimal cross-over between the two lipid classes. Reference values for 57 apparently healthy Dutch adults were established and compared with data reported from other countries. Feeding of rats with four diets differing in their fatty acid compositions showed the relationship between the composition of the fatty acids in the diet and those esterified to cholesterol in plasma. The method is of potential usefulness to the establishment of the compliance of dietary interventions and basic dietary experiments.     

Screening Dyrk1A inhibitors by MALDI-QqQ mass spectrometry: systematic comparison to established radiometric,luminescence, and LC–UV–MS assays

Enzyme-catalyzed reactions play key roles in disease pathology, thus making them relevant subjects of therapeutic inhibitor screening experiments. Matrix-assisted laser desorption/ionization (MALDI) assays have been demonstrated to be able to replace established screening approaches. They offer increased sample throughput, but care must be taken to avoid instrumental bias from differences in ionization efficiencies. We compared a MALDI-triple-quadrupole (QqQ) method for the Dyrk1A peptide substrate woodtide to LC–MS, liquid chromatography with ultraviolet detection (LC–UV), luminescence, and radiometric assays. MALDI measurements were performed on a MALDI-QqQ instrument in the multiple-reaction monitoring mode. Different MALDI conditions were investigated to address whether matrix type, sample support, and MRM- or SIM-based detection conditions can be used to accommodate the molar responses of substrate peptide and its phosphorylated form. UV detection served as a reference method. The impact of MALDI matrix on IC₅₀ values was small, even considering that matrix preparations were used that are known to alleviate response differences. IC₅₀ values determined by MALDI were ca. 2-fold lower than those determined by LC–UV. Although MALDI generated lower ion yields for the phosphorylated peptide than for the peptide substrate, we found that a correction of compound potencies was readily possible using correction factors based on unbiased LC–UV results. A thorough method development delivered a robust assay with excellent performance (Z′ > 0.91) that was close to that seen for LC–UV.