A Pregenerator for Burgers Equation¶Forced by Conservative Noise

We consider the stationarity of a Burgers equation with an external random force of gradient type in one space dimension. The expected stationary measure is the white noise measure on the space of tempered distributions. As a consequence, the nonlinearity of the formal equation u _t +λu u _x =νu _xx +η _x is ill-defined. Introducing a pregenerator we can formulate a generalized martingale problem leading to a meaningful version of the formal equation which was an open problem. Received: 9 March 2001 / Accepted: 10 October 2001     

Heavy element research at GSI — Recent results and perspectives

The nuclear shell model predicts that the next doubly magic shellclosure beyond ²⁰⁸Pb is at a proton number between Z=114 and 126 and at a neutron number N=184. The outstanding aim of experimental investigations is the exploration of this region of spherical ‘Superheavy Elements’. This article describes the experiments that were performed recently at the GSI SHIP. They resulted in an unambiguous identification of elements 110 to 112. They were negative so far in searching for elements 113, 116, and 118. The measured decay data are compared with theoretical predictions. Some aspects concerning the reaction mechanism are also presented.     

Synthesis and solid-state organization of coil-ring-coil block copolymers

Shape-persistent macrocycles based on the phenyl-ethynyl-butadienyl backbone containing two extraannular hydroxyl groups were prepared by the oxidative coupling of the appropriate phenylethynyl oligomers. Carbodiimide-directed coupling with independently synthesized polystyrene carboxylic acid oligomers led to ABA coil-ring-coil block copolymers in which the central macrocycle serves as rigid and the polystyrene oligomers as flexible elements. Depending on the size of the coil blocks, these structures aggregate in cyclohexane into supramolecular hollow cylindrical brushes in which the rigid core is surrounded by the flexible matrix. However, in the solid state it is not possible to identify a morphology in which isolated channels based on aggregated macrocycles are embedded in a matrix of polystyrene. Detailed X-ray and electron diffraction studies on samples prepared from a solution in cyclohexane under equilibrium conditions show that the material adopts a lamellar morphology in the solid state in which columns of macrocycles are aggregated into layers which are separated by polystyrene.     

Diffusion of reagents in macrobeads

A simple and effective method of measuring diffusion rates of various acylating reagents in macro beads (in this work diameters greater than 570 microm) of amino-functionalized resins is presented. The extent of diffusion at various points of time was determined by treating beads with a staining reagent ("chloranil", 2,3,5,6-tetrachloro-1,4-benzoquinone) that colored the regions of the beads that had not yet been permeated by reagent (the central part of the beads). The volume of unstained resin (permeated part) was compared with the volume of the stained part, and diffusion rate constants were calculated. Factors influencing diffusion such as reagent concentration, solvent, temperature, resin type, and mechanical effects were investigated. The results showed that diffusion was promoted by increased temperature, good swelling of the resin, small reagents, and high concentrations but not by sonication or mechanical agitation.     

Solvent triggering between conformational states in amphiphilic shape-persistent macrocycles

The amphiphilic shape-persistent macrocycle 1 containing four phenol-OH groups as polar side groups and four hexyloxy groups as nonpolar side groups in an adaptable arrangement was recrystallized from solvents of different polarity. X-ray crystallography reveals that the conformation of the macrocycle is solvent dependent such that in the pyridine solvate only two of the nonpolar side groups point outward while in the THF solvate all four of them point outward. Moreover, in the latter case the three-dimensional packing leads to the formation of a supramolecular channel structure with a large pore size.     

SPOCC-194, a new high functional group density PEG-based resin for solid-phase organic synthesis

A novel polymer matrix for solid-phase synthesis, SPOCC(194) resin (1), was designed featuring a backbone of homogeneous tetraethylene glycol (TEG(194)) macromonomer linked by quaternary carbon junctions and terminating in primary alcohol functionality. Beaded SPOCC(194) resin was effectively prepared by suspension polymerization of oxetanylated TEG macromonomer 5 in stirred silicon oil. Mechanically stable and inert to a diverse range of reaction conditions, SPOCC(194) possessed a high hydroxyl group loading (0.9-1.2 mmol/g) for substrate attachment and swelled effectively ( approximately 2-4 mL/g) in a variety of organic and aqueous solvents. Developed for solid-phase synthesis at high reactant concentrations for driving organic and aqueous reactions to completion, SPOCC(194) exhibited high functional group density (mmol/mL) similar to that of low-loaded aminomethylated polystyrene-divinylbenzene copolymer (PS-1%DVB) yet significantly higher than that of PEGA(1900), SPOCC(1500), and TentaGel S. High-resolution MAS NMR spectra of Fmoc-derivatized SPOCC(194) indicate that monitoring of functional group transformation is possible. Moreover, by employment of a nonaromatic resin-linker combination, electrophilic chemistry, such as Lewis acid catalyzed glycosylation and Friedel-Crafts acylation, was selectively performed on substrate bound to SPOCC(194) resin. Such properties make SPOCC(194) resin a promising new polymer matrix for the support-bound construction of small organic molecules by parallel and combinatorial synthesis and the scavenging of solution-phase reactants or byproducts.     

Solid-phase glycosylation of peptide templates and on-bead MAS-NMR analysis: perspectives for glycopeptide libraries

The efficient solid-phase glycosylation of amino acid side chains (serine (Ser), threonine (Thr), and tyrosine (Tyr)) in peptides was demonstrated with a variety of glycosyl trichloroacetimidate donors in high yields and purities. A novel photolabile linker, with no chiral centre, was introduced to facilitate analysis by both matrix-assisted laser desorption ionisation time of flight (MALDI-TOF) mass spectrometry and nanoprobe magic angle spinning (MAS) NMR spectroscopy. Product analysis by nanoprobe MAS NMR spectroscopy, LC-MS and MALDI-TOF mass spectrometry of the glycosylation reactions indicated that the reactivity order of the hydroxy side-chain functions of amino acids in peptides on the solid-phase was Tyr>Ser>Thr. The nearly quantitative glycosylation yields and the efficient on-bead product analysis by nanoprobe MAS NMR spectroscopy have made a truly solid-phase approach for the synthesis and analysis of glycopeptide libraries possible.     

Fluorescence-quenched solid phase combinatorial libraries in the characterization of cysteine protease substrate specificity

To map the substrate specificity of cysteine proteases, two combinatorial peptide libraries were synthesized and screened using the archetypal protease, papain. The use of PEGA resin as the solid support for library synthesis facilitated the application of an on-resin fluorescence-quenched assay. Results from the screening of library 2 indicated a preference for Pro or Val in the S3 subsite and hydrophobic residues in S2; the most prevalent residue not being Phe but Val. The S1 subsite exhibited a dual specificity for both small, nonpolar residues, Ala or Gly, as well as larger, Gln, and charged residues, Arg. Small residues predominated in the S1'-S4' subsites. Active peptides from the libraries and variations thereof were resynthesized and their kinetics of hydrolysis by papain assessed in solution phase assays. Generally, there was a good correlation between the extent of substrate cleavage on solid phase and the kcat/KM's obtained in solution phase assays. Several good substrates for papain were obtained, the best substrates being Y(NO2)PMPPLCTSMK(Abz) (kcat/KM = 2109 (mM s)-1), Y(NO2)PYAVQSPQK(Abz) (kcat/KM = 1524 (mM s)-1), and Y(NO2)PVLRQQRSK(Abz) (kcat/KM = 1450 (mM s)-1). These results were interpreted in structural terms by the use of molecular dynamics (MD). These MD calculations indicated two different modes for the binding of substrates in the narrow enzyme cleft.