Conjectured statistics for the q,t-Catalan numbers

We introduce the distribution function F_n(q,t) of a pair of statistics on Catalan words and conjecture F_n(q,t) equals Garsia and Haiman's q,t-Catalan sequence C_n(q,t), which they defined as a sum of rational functions. We show that F_n,s(q,t), defined as the sum of these statistics restricted to Catalan words ending in s ones, satisfies a recurrence relation. As a corollary we are able to verify that F_n(q,t)=C_n(q,t) when t=1/q. We also show the partial symmetry relation F_n(q,1)=F_n(1,q). By modifying a proof of Haiman of a q-Lagrange inversion formula based on results of Garsia and Gessel, we obtain a q-analogue of the general Lagrange inversion formula which involves Catalan words grouped according to the number of ones at the end of the word.     

Synthese und Reaktionen von Bicyclo[6.4.0]dodecan-3-carbonsäure-Derivaten

Synthesis and Reactions of the Bicyclo[6.4.0]dodecane-3-carboxylic Acid Derivatives The synthesis and some consecutive reactions of the compounds 5-8 , derivatives of bicyclo[6.4.0]dodecane-3-carboxylic acid ( 1 ), are described. The esters 7 and 8 can be obtained by Baeyer-Villiger oxidation of 2-hydroxy-8-methyltricyclo[7.3.1.0^2,7]tridecan-13-one ( 4 ) and subsequent hydrolysis of the lactone 5 . The structure and configuration of these compounds has been evaluated by spectroscopic techniques (mainly 2D-NMR methods). The formation of 7 via 1,2-H shift and subsequent isomerization to 8 has been studied. The esters 11 and 13 are formed stereospecifically from 7 and 8 .     

Influence of calcium on the self-assembly of partially hydrolyzed alpha-lactalbumin

Self-assembly of alpha-lactalbumin after partial hydrolysis by a protease from Bacillus licheniformis can result in nanotubular structures, which show many similarities to microtubules. Calcium plays a crucial role in this process. The objective of this investigation was to study the role of calcium in more detail. The kinetics of the hydrolysis step and the self-assembly step were monitored by respectively liquid chromatography-mass spectrometry and dynamic light scattering. The microstructure of the gels finally formed was investigated by transmission electron microscopy. This investigation demonstrates that calcium accelerated the kinetics of the self-assembly, but it had no effect on the hydrolysis kinetics. As a result of the accelerated self-assembly kinetics at a high calcium concentration, the time of gelation decreased as well. A minimum concentration of calcium needed to obtain the tubular alpha-lactalbumin structures was determined. Below R = 1.5 (mole calcium/mole alpha-lactalbumin), turbid gels with randomlike structure were obtained. Between R = 1.5 and R = 6, translucent gels with a fine stranded network of tubules were formed, while higher calcium concentrations had a negative effect on the tubule formation, resulting in amorphous structures. The optimum calcium concentration for alpha-lactalbumin nanotube formation seemed to be around R = 3.     

Secondary deuterium kinetic isotope effects in irreversible additions of allyl reagents to benzaldehyde

The competitive kinetics of additions of allyl to benzaldehyde-h and -d from allyltributyl tin, from diisopropyltartrylallyl boronate, and from allyl bromide and zinc dust in aqueous tetrahydrofuran have inverse secondary deuterium kinetic isotope effects, SDKIEs. These inverse SDKIEs are in contrast to the normal SDKIEs that were obtained with allyl lithium and allyl Grignard, suggesting rate-determining single-electron transfer in these cases. By various MO calculations the transition state for addition of allyl boronate occurs with substantial B-O bond formation and little C-C bond formation. The magnitudes of the SDKIEs with the other two allylating reagents, when compared with reasonable equilibrium isotope effects for the addition, suggest transition states with substantial C-C bond formation.     

Mass spectrometric analysis of ceramic components for solid oxide fuel cells

For the determination of trace impurities in ceramic components of solid oxide fuel cells (SOFCs), some mass spectrometric methods have been applied such as spark source mass spectrometry (SSMS), laser ionization mass spectrometry (LIMS), laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and inductively coupled plasma mass spectrometry (ICP-MS). Due to a lack of suitable standard reference materials for quantifying of analytical results on La _x Sr _y MnO₃ cathode material a matrix-matched synthetic standard-high purity initial compounds doped with trace elements-was prepared in order to determine the relative sensitivity coefficients in SSMS and LA-ICP-MS. Radiofrequency glow discharge mass spectrometry (rf-GDMS) was developed for trace analysis and depth profiling of thick non-conducting layers. Surface analytical techniques, such as secondary ion mass spectrometry (SIMS) and sputtered neutral mass spectrometry (SNMS), were used to determine the element distribution on surfaces (homogeneity) and the surface contaminants of SOFC ceramic layers.Dedicated to Professor Dr. rer. nat. Hubertus Nickel on the occasion of his 65th birthday     

Terephthalamide derivatives as mimetics of helical peptides: disruption of the Bcl-x(L)/Bak interaction

A series of Bcl-x(L)/Bak antagonists, based on a terephthalamide scaffold, was designed to mimic the alpha-helical region of the Bak peptide. These molecules showed favorable in vitro activities in disrupting the Bcl-x(L)/Bak BH3 domain complex (terephthalamides 9 and 26, K(i) = 0.78 +/- 0.07 and 1.85 +/- 0.32 microM, respectively). Extensive structure-affinity studies demonstrated a correlation between the ability of terephthalamide derivatives to disrupt Bcl-x(L)/Bak complex formation and the size of variable side chains on these molecules. Treatment of human HEK293 cells with the terephthalamide derivative 26 resulted in disruption of the Bcl-x(L)/Bax interaction in whole cells with an IC(50) of 35.0 microM. Computational docking simulations and NMR experiments suggested that the binding cleft for the BH3 domain of the Bak peptide on the surface of Bcl-x(L) is the target area for these synthetic inhibitors.     

Photoactive metallocyclodextrins: sophisticated supramolecular arrays for the construction of light activated miniature devices

The introduction of photoactive metal centres onto cyclodextrin receptors opens up new possibilities for the design of sensors, wires and energy conversion systems. This tutorial review focuses on strategies involving such metallocyclodextrins for the construction of supramolecular arrays with light-activated functions. The assembly procedures for building such arrays are presented, together with the features required for their functions both as sensors for ion or small molecule detection and as wires for photoinduced long-range energy or electron transport. Systems for metal ion sensing are described where the cyclodextrin plays a mediating role in influencing the luminescence properties of an organic probe, responsive to metal binding. Small molecule sensing by the cyclodextrin cavity is realised using luminescent lanthanide or transition metal functionalised cyclodextrins. The light signal of the photoactive metal is switched on or off upon binding an analyte in the cyclodextrin cavity. The metallocyclodextrin systems that function as wires are distinguished by the controlled assembly of transition metal polypyridine and metalloporphyrin units. These units have inherent photoactivity that defines the vectorial direction of energy or electron transfer processes through the wire.     

Systematic quantification of the dynamics of newly synthesized proteins unveiling their degradation pathways in human cells

Proteins are continuously synthesized during cell growth and proliferation. At the same time, excessive and misfolded proteins have to be degraded, otherwise they are a burden to cells. Protein degradation is essential to maintain proteostasis in cells, and dysfunction of protein degradation systems results in numerous diseases such as cancer and neurodegenerative diseases. Despite the importance of protein degradation, the degradation pathways of many proteins remain to be explored. Here, we comprehensively investigated the degradation of newly synthesized proteins in human cells by integrating metabolic labeling, click chemistry, and multiplexed proteomics, and systematic and quantitative analysis of newly synthesized proteins first revealed the degradation pathways of many proteins. Bioinformatic analysis demonstrates that proteins degraded through two major pathways have distinct properties and functions. Proteins degraded through the ubiquitin-proteasome pathway contain more disordered structures, whereas those through the autophagy-lysosome pathway have significantly higher hydrophobicity. Systematic and quantitative investigation of the dynamics of newly synthesized proteins provides unprecedented and valuable information about protein degradation, which leads to a better understanding of protein properties and cellular activities.

Systematic quantification of the dynamics of newly synthesized proteins first reveals the degradation pathways of many proteins in human cells, and proteins degraded through each of the two major pathways have distinct properties and functions.