THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Dynamics of Multisection Semiconductor Lasers

We consider a mathematical model (the so-called traveling-wave system) which describes longitudinal dynamical effects in semiconductor lasers. This model consists of a linear hyperbolic system of PDEs, which is nonlinearly coupled with a slow subsystem of ODEs. We prove that a corresponding initial-boundary value problem is well posed and that it generates a smooth infinite-dimensional dynamical system. Exploiting the particular slow-fast structure, we derive conditions under which there exists a low-dimensional attracting invariant manifold. The flow on this invariant manifold is described by a system of ODEs. Mode approximations of that system are studied by means of bifurcation theory and numerical tools.     

Chemoenzymatic approach to enantiopure streptogramin B variants: characterization of stereoselective pristinamycin I cyclase from Streptomyces pristinaespiralis

Streptogramin B antibiotics are cyclic peptide natural products produced by Streptomyces species.In combination with the synergistic group A component, they are "last line of defense" antimicrobial agents against multiresistant cocci. The racemization sensitivity of the phenylglycine (Phg(7)) ester is a complex challenge in total chemical synthesis of streptogramin B molecules. To provide fast and easy access to novel streptogramin antibiotics, we introduce a novel chemoenzymatic strategy in which diversity is generated by standard solid phase protocols and stereoselectivity by subsequent enzymatic cyclization. For this approach, we cloned, overproduced, and biochemically characterized the recombinant thioesterase domain SnbDE TE of the pristinamycin I nonribosomal peptide synthetase from Streptomyces pristinaespiralis. SnbDE TE catalyzes regioselective ring closure of linear peptide thioester analogues of pristinamycin I as well as stereoselective cyclization out of complex in situ racemizing substrate mixtures, enabling synthesis of Streptogramin B variants via a dynamic kinetic resolution assay. A remarkable substrate tolerance was detected for the enzymatic cyclization including all the seven positions of the peptide backbone. Interestingly, SnbDE TE was observed to be the first cyclase from a macrolactone forming NRPS which is additionally able to catalyze macrolactamization of peptide thioester substrates. An N-methylated peptide bond between positions 4 and 5 is mandatory for a high substrate turnover. The presented strategy is potent to screen for analogues with improved activity and guides our understanding of structure--activity relationships in the important class of streptogramin antibiotics.     

Synthesis and derivatization of daptomycin: a chemoenzymatic route to acidic lipopeptide antibiotics

Daptomycin is a branched cyclic nonribosomally assembled acidic lipopeptide, which is the first clinically approved antibiotic of this class. Here we show that the recombinant cyclization domain of the Streptomyces coelicolor calcium-dependent antibiotic (CDA) nonribosomal peptide synthetase (NRPS) is a versatile tool for the chemoenzymatic generation of daptomycin derivatives. Linear CDA undecapeptide thioesters with single exchanges at six daptomycin-specific residues were successfully cyclized by CDA cyclase. Simultaneous incorporation of all six of these residues into the peptide backbone and elongation of the N-terminus of CDA by two residues yielded a daptomycin derivative that lacked only the beta-methyl group of l-3-methylglutamate. Bioactivity studies with several substrate analogues revealed a significant role of nonproteinogenic constituents for antibacterial potency. In accordance with acidic lipopeptides, the bioactivity of the chemoenzymatic assembled daptomycin analogue is dependent on the concentration of calcium ions. Single deletions of the four acidic residues in the peptide backbone suggest that only two aspartic acid residues are essential for antimicrobial potency. These two residues are strictly conserved among other nonribosomal acidic lipopeptides and the EF-motif of ribosomally assembled calmodulin. Based on these findings CDA cyclase is a versatile catalyst that can be used to generate novel daptomycin derivatives that are otherwise difficult to obtain by chemical modification of the parental tridecapeptide to improve further its therapeutic activity.     

Fluorescence study of an immobilized ligand—metal ion complex

A ligand known to form a fluorescent complex with aluminum ion was immobilized on silica gel. The immobilization sequence was verified by cross-polarization magicangle spinning n.m.r. spectroscopy and diffuse reflectance u.v. spectroscopy. The solid-state fluorescence of the immobilized ligand complexed with aluminum ion was similar to the fluorescence of a solvated complex of a model ligand. The potential to eliminate possible interfering species by isolating the complex from solution was demonstrated.     

Selective acidolytic cleavage of aralkyl carbonyl amino protecting groups

The acidolytic cleavage of a series of new N-aralkyloxycarbonyl protecting groups has been found to proceed as a first-order reaction, the rate of cleavage being dependent on the stability of the corresponding aralkyl carbonium ions. Some of the groups are cleaved at much the same rate as the N-trityl residue and up to 60000 times faster than the t-butyloxycarbonyl (Boc) group. The rate is also strongly influenced by the acidity of the reaction media. The relative rates at which aralkyloxycarbonyl and Boc groups are split off can be largely controlled by appropriate selection of the reaction conditions. The implications of these findings for peptide syntheses are discussed and the use of the 2-(p-diphenyl)-isopropyloxycarbonyl residue as an especially suitable N-protecting group is proposed.     

Copper passivity and its breakdown in sodium bicarbonate solutions: A scanning electron microscopy and x-ray photoelectron and auger spectroscopy study

Effect of bicarbonate ions on the copper passivity and its local breakdown is studied by cyclic voltammetry, Auger spectroscopy, x-ray photoelectron spectroscopy, and scanning electron microscopy. Comparing data for solutions with various sodium bicarbonate concentrations shows copper to undergo pitting in 0.02 M NaHCO₃, whereas it remains stably passive in 0.10 M NaHCO₃. Independent studies suggest that carbonates play a protective role in stabilization of the oxide-hydroxide passive film on copper.