Gel-phase 19F NMR spectral quality for resins commonly used in solid-phase organic synthesis; a study of peptide solid-phase glycosylations

The spectroscopic properties for seven different commercial resins used in solid-phase synthesis were investigated with (19)F NMR spectroscopy. A fluorine-labeled dipeptide was synthesized on each resin, and the resolution of the (19)F resonances in CDCl(3), DMSO-d(6), benzene-d(6) and CD(3)OD were measured with a conventional NMR spectrometer, i.e. without using magic angle spinning. In general, resins containing poly(ethylene glycol) chains (ArgoGel, TentaGel and PEGA) were found to be favorable for the (19)F NMR spectral quality. Three serine containing tri-, penta-, and heptapeptides were then prepared on an ArgoGel resin functionalized with a fluorine-labeled linker. The resin bound peptides were glycosylated utilizing a thiogalactoside glycosyl donor carrying fluorine-labeled protective groups. Monitoring of the glycosylations with gel-phase (19)F NMR spectroscopy allowed each glycopeptide to be formed in similar 80% yield, using a minimal amount of glycosyl donor (3 x 2 equivalents). In addition, it was found that the glycosylation yields were independent of peptide length.     

Superfluid 3He-A in a cylindrical pore

The Ginzburg-Landau free energy for superfluid ³He is reexpressed in arbitrary curvilinear coordinate systems. Application to ³He-A in a long cylindrical pore with large and small radii yields quantitative predictions for the stable configurations.     

Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

Optimization of preparative chromatographic separation of multiple rare earth elements

This work presents a method to optimize multi-product chromatographic systems with multiple objective functions. The system studied is a neodymium, samarium, europium, gadolinium mixture separated in an ion exchange chromatography step. A homogeneous Langmuir Mobile Phase Modified model is calibrated to fit the experiments, and then used to perform the optimization task. For the optimization a multi-objective Differential Evolution algorithm was used, with weighting based on relative value of the components to find optimal operation points along the Pareto front. The objectives of the Pareto front are weighted productivity and weighted yield with purity as an equality constraint. A prioritizing scheme based on relative values is applied for determining the pooling order. A simple rule of thumb for pooling strategy selection is presented. The multi-objective optimization gives a Pareto front which shows the rule of thumb, as a gap in one of the objective functions.     

Avalanche statistics of sand heaps

Large-scale computer simulations are presented to investigate the avalanche statistics of sandpiles using molecular dynamics. We show that different methods of measurement lead to contradictory conclusions, presumably due to avalanches not reaching the end of the experimental table.     

Construction of the circle in UniMath

We show that the type $\mathrm{T}\mathbb{Z}$ of $\mathbb{Z}$-torsors has the dependent universal property of the circle, which characterizes it up to a unique homotopy equivalence. The construction uses Voevodsky's Univalence Axiom and propositional truncation, yielding a stand-alone construction of the circle not using higher inductive types.     

Future mathematics teachers’ professional knowledge of elementary mathematics from an advanced standpoint

This paper reports a joint research project by researchers from three countries on an international comparative study that examines the professional knowledge of prospective mathematics teachers in elementary mathematics from an advanced standpoint. For this study, mathematical problems on various topics of elementary mathematical content were developed. Using this instrument, the mathematical knowledge of future teachers from Germany, Hong Kong, China (Hangzhou) and South Korea was measured empirically. The paper presents the design of the study, and also results are discussed. The results show that there are systematic differences among the participating countries; for example, the Korean future teachers outperform their counterparts in other countries. A more detailed analysis of the results suggests that the future teachers often do not seem to be able to link school and university knowledge systematically and cannot achieve the crucial “advanced standpoint” from the teacher training programme.     

Separation and characterization of aggregated species of amyloid-beta peptides

We have investigated the use of isoelectric focusing and immunodetection for the separation of low molecular weight species of amyloid-beta (Aβ) peptides from their aggregates. From solutions of Aβ_1–40 or Aβ_1–42 monomeric peptides, low molecular weight material appeared at a pI value of ca. 5, while the presence of aggregates was detected as bands, observed at a pI of 6–6.5. The formation of Aβ aggregates (protofibrils) was verified by a sandwich ELISA, employing the protofibril conformation-selective antibody mAb158. In order to study the aggregation behavior when using a mixture of the monomers, we utilized the IEF separation combined with Western blot using two polyclonal antisera, selective for Aβ_1–40 and Aβ_1–42, respectively. We conclude that both monomers were incorporated in the aggregates. In a further study of the mixed aggregates, we used the protofibril conformation-selective antibody mAb158 for immunoprecipitation, followed by nanoelectrospray mass spectrometry (IP-MS). This showed that the Aβ_1–42 peptide is incorporated in the aggregate in a significantly larger proportion than its relative presence in the original monomer composition. IP-MS with mAb158 was also performed, and compared to IP-MS with the Aβ-selective antibody mAb1C3, where a monomeric Aβ_1–16 peptide was added to the protofibril preparation. Aβ_1–16 is known for its poor aggregation propensity, and acted therefore as a selectivity marker. The results obtained confirmed the protofibril conformation selectivity of mAb158.     

Characterisation of two novel cyclodextrinases using on-line microdialysis sampling with high-performance anion exchange chromatography

In this work, a real-time sampling/analytical method for on-line measurements of two newly discovered cyclomaltodextrinases (CDases) has been developed and evaluated. This novel methodology not only allows the final products to be investigated, but it also reveals enzyme-specific differences in the degradation pathways during the hydrolysis of different substrates, which is a great advantage in the important tasks of investigating the mechanisms of and classifying new hydrolases, and is an advantage that conventional techniques cannot offer. Two different enzymes, one CDase from Laceyella sacchari (LsCda13) and one from Anoxybacillus flavithermus (AfCda13), were investigated during the hydrolysis of α-, β- and γ-cyclodextrin, and the hydrolysis products were sampled via a microdialysis probe and injected on-line every 30 min into a high-performance anion exchange chromatography system equipped with a pulsed amperometric detector (HPAEC–PAD), where they were identified. The enzymes yielded the same end-products, maltose and glucose, in an approximate molar ratio of 2:1, but they exhibited distinctly different patterns of intermediate product formation before reaching the end-point. LsCda13 had a more random distribution of the intermediate products, whereas AfCda13 showed the distinct intermediate production of maltotriose, which in some cases accumulated.