Analysis of a parabolic cross-diffusion population model without self-diffusion

The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large, whereas the self-diffusion terms are assumed to disappear. The last assumption complicates the analysis since these terms usually provide H¹ estimates of the solutions. The existence proof is based on a positivity-preserving backward Euler-Galerkin approximation, discrete entropy estimates, and L¹ weak compactness arguments. Furthermore, employing the entropy-entropy production method, we show for special stationary solutions that the transient solution converges exponentially fast to its steady state. As a by-product, we prove that only constant steady states exist if the inter-specific competition parameters disappear no matter how strong the cross-diffusion constants are.     

Application of quantum calculations in the chemical industry—An overview

The field of quantum chemistry experienced huge progress in the past two decades. The drivers for this have been the availability of more and more powerful computer hardware, the development and implementation of improved methods with a better balanced compromise between accuracy and efficiency, as well as pioneering work how these methods are successfully applied to real‐world problems. Thus, quantum calculations, in particular via density functional theory, became an essential tool in many branches of chemical research. This article tries to give an overview how quantum chemical modeling is used in chemical industry, which is done by reviewing papers written by authors from chemical companies. Various topics of particular industrial relevance are introduced together with strategies how to address them via quantum calculations. Examples are the computation of reaction thermodynamics and kinetics as the key ingredients to understand and predict chemical reactivity, but also solvation models as well as methods to describe electronically excited states. © 2014 Wiley Periodicals, Inc.     

In vivo incorporation of unnatural amino acids to probe structure, dynamics, and ligand binding in a large protein by nuclear magnetic resonance spectroscopy

In vivo incorporation of isotopically labeled unnatural amino acids into large proteins drastically reduces the complexity of nuclear magnetic resonance (NMR) spectra. Incorporation is accomplished by coexpressing an orthogonal tRNA/aminoacyl-tRNA synthetase pair specific for the unnatural amino acid added to the media and the protein of interest with a TAG amber codon at the desired incorporation site. To demonstrate the utility of this approach for NMR studies, 2-amino-3-(4-(trifluoromethoxy)phenyl)propanoic acid (OCF 3Phe), (13)C/(15)N-labeled p-methoxyphenylalanine (OMePhe), and (15)N-labeled o-nitrobenzyl-tyrosine (oNBTyr) were incorporated individually into 11 positions around the active site of the 33 kDa thioesterase domain of human fatty acid synthase (FAS-TE). In the process, a novel tRNA synthetase was evolved for OCF 3Phe. Incorporation efficiencies and FAS-TE yields were improved by including an inducible copy of the respective aminoacyl-tRNA synthetase gene on each incorporation plasmid. Using only between 8 and 25 mg of unnatural amino acid, typically 2 mg of FAS-TE, sufficient for one 0.1 mM NMR sample, were produced from 50 mL of Escherichia coli culture grown in rich media. Singly labeled protein samples were then used to study the binding of a tool compound. Chemical shift changes in (1)H-(15)N HSQC, (1)H-(13)C HSQC, and (19)F NMR spectra of the different single site mutants consistently identified the binding site and the effect of ligand binding on conformational exchange of some of the residues. OMePhe or OCF 3Phe mutants of an active site tyrosine inhibited binding; incorporating (15)N-Tyr at this site through UV-cleavage of the nitrobenzyl-photocage from oNBTyr re-established binding. These data suggest not only robust methods for using unnatural amino acids to study large proteins by NMR but also establish a new avenue for the site-specific labeling of proteins at individual residues without altering the protein sequence, a feat that can currently not be accomplished with any other method.     

Evaluation of two proteomics technologies used to screen the membrane proteomes of wild-type <Emphasis Type="Italic">Corynebacterium glutamicum</Emphasis> and an <Emphasis Type="SmallCaps">L</Emphasis>-lysine-producing strain

The membrane proteomes of a wild-type Corynebacterium glutamicum and an L-lysine-producing strain were quantitatively analyzed by two complementary proteomics techniques—anion exchange chromatography AIEC/SDS-PAGE and 16BAC-PAGE/SDS-PAGE—and the results were compared. Although both techniques allow for the fast screening of differences in protein abundance, AIEC/SDS-PAGE was superior to 16BAC-PAGE/SDS-PAGE with respect to protein separation, it was more suitable for relative protein quantification, and allowed more differentially regulated proteins to be detected (the succinate dehydrogenase complex, an ABC-type cobalamin/Fe³⁺ siderophore transport system, the maltose binding protein, and a subunit of the cytochrome bc-aa₃ supercomplex were upregulated, while a periplasmic component of an ABC-type transporter and an iron-regulated ABC-type transporter were downregulated in the producer). The results indicate the important role of tricarboxylic acid cycle enzymes as well as the adaptation of transport processes in L-lysine-producing cells. Since the only genetic differences between the wild type and the L-lysine producer occur between four central metabolic enzymes in the cytoplasm, our study illustrates the complex effects of metabolic engineering on cell physiology and the power of the new AIEC/SDS-PAGE proteomics approach to detect these effects.      

Reduction of primary freeze-drying time by electric field induced ice nucleus formation

The potential of a high electric field was utilized to induce ice nucleus formation in aqueous solutions. Using this technique it was possible to reduce the primary drying time during lyophilization. Samples of 10% (w/v) hydroxyethylstarch (HES) solution were frozen at a constant rate of −1 K/min, while nucleation was initiated at temperatures of −1.5, −4.5 and −8.5°C. In contrast, spontaneous nucleation was observed in a range between −11.5 and −17.1°C. Electrically induced nucleus formation has proved to be a reliable method to start crystallization at a desired temperature. Continuous measurement of the weight allowed to determine the drying rate and to detect at which time primary drying was completed. The drying time and the drying rate were found to be strongly dependent on the nucleation temperature during freezing. A relation between the nucleation temperature, the structure of the frozen samples and the drying times could be established.

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Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage

We establish large sample approximations for an arbitrary number of bilinear forms of the sample variance–covariance matrix of a high-dimensional vector time series using ${?}_1$-bounded and small ${?}_2$-bounded weighting vectors. Estimation of the asymptotic covariance structure is also discussed. The results hold true without any constraint on the dimension, the number of forms and the sample size or their ratios. Concrete and potential applications are widespread and cover high-dimensional data science problems such as tests for large numbers of covariances, sparse portfolio optimization and projections onto sparse principal components or more general spanning sets as frequently considered, e.g. in classification and dictionary learning. As two specific applications of our results, we study in greater detail the asymptotics of the trace functional and shrinkage estimation of covariance matrices. In shrinkage estimation, it turns out that the asymptotics differ for weighting vectors bounded away from orthogonality and nearly orthogonal ones in the sense that their inner product converges to 0.     

Solid polymers doped with rare earth metal compounds. III. Formation and stability of macromolecular complexes comprising neodymium nitrate and dipivaloylmethane in poly(ethylene oxide)

The solubility, complexation, and morphology in the Nd(NO₃)₃-PEO and Nd(Dpm)₃-PEO systems were investigated using the FTIR, DSC, TGA, WAXD, and SAXS techniques. In both systems, dissolution was verified by the absence of features characteristic of the bulk-phase dopants detectable with WAXD and DSC, and complexation was evident from the FTIR spectral shifts involving the stretching motions of the EO unit. The extent of the Nd³⁺-EO interaction was found to be much stronger with Nd(NO₃)₃ than Nd(Dpm)₃. As a consequence, a T_g elevation from 222K in pure PEO to 335K at an EO/Nd³⁺ ratio (defined as n) of between 4.0 and 5.6 was observed in the Nd(NO₃)₃-PEO system. Moreover, completely dry and amorphous complexes were obtained at n ≥ 5.6, while residual moisture accompanying complexes at n ≤ 4 was found to persist upon prolonged vacuum drying. Being intrinsically hygroscopic at all doping levels, the Nd(NO₃)₃-PEO system was found to absorb moisture from the atmosphere resulting in wet amorphous complexes, although precipitation of Nd(NO₃)₃)·6H₂O was observed at n ≤ 4. It was proposed that moisture present in the Nd(NO₃)₃-PEO system be classified into two categories. One is tightly bound to Nd³⁺ to satisfy its coordination requirement, which was determined to be 11. The other is loosely bound, which is capable of being removed by heating and returning upon exposure to the atmosphere. It is the latter that can be readily quantified by the TGA technique and that lowers T_g via plasticization. In addition to the observed minor FTIR spectral shifts, a relatively weak Nd³⁺-EO interaction in the Nd(Dpm)₃-PEO system resulted in a lack of the T_g elevation for PEO, persistence of the crystalline portion of PEO at all doping levels, and the formation of new crystalline phases as revealed by the WAXD patterns and the DSC thermograms. The short-range order in PEO does not appear to be perturbed, but the SAXS data suggest that the long range-order is disrupted by the presence of Nd(Dpm)³ at an extremely low doping level (i.e., n ≥ 60). © 1994 John Wiley & Sons, Inc.     

Automated immobilized metal affinity chromatography/nano-liquid chromatography/electrospray ionization mass spectrometry platform for profiling protein phosphorylation sites

A versatile integrated system has been developed for the automated enrichment and analysis of phosphopeptides by immobilized metal affinity chromatography/nano-liquid chromatography/electrospray ionization mass spectrometry (IMAC/nano-LC/ESI-MS). This system utilizes two independently controlled high-performance liquid chromatography (HPLC) pumps, an autosampler and microvalves to prepare and elute samples into an ion trap mass spectrometer. The use of robust reversed-phase HPLC columns with integrated ESI emitter tips enables the reproducible detection and identification of low-femtomole quantities of phosphopeptides. The entire system is coordinated through a simple user interface by customized software. The ruggedness of the system is demonstrated by highly reproducible analyses of single and multi-protein digests, while its utility is demonstrated by the thorough evaluation of the relative immunoprecipitation efficiencies of several commercially available anti-phosphotyrosine antibodies.