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.     

Weitere Evidenz für die mikroskopische Gleichzeitigkeit des Bruches zweier Bindungen bei einer E2-Reaktion: H-Isotopeneffekte und Substituentenwirkungen bei der Reaktion von 2,2-Diphenyläthyl-benzolsulfonat mit Methoxid-Ion

Second order rate constants are determined for the E2 reactions of 2,2-diphenyl-ethyl benzenesulfonates Ph₂C^xHCH₂O · O₂S–C₆H₄–X with CH₃ONa in methyl cellosolve solution (^xH = H or D, X = p-CH₃O, p-CH₃, H or p-NO₂). The HAMMETT ? values are of the same order of magnitude as those found in the first order solvolyses of methyl, ethyl or isopropyl benzenesulfonates. The primary deuterium isotope effects k_H/k_D are 5.27, 5.42 and 6.70 for X = p-CH₃O, H and p-NO₂. The ? values as well as the increase of k_H/k_D with introduction of p-NO₂ supply evidence for simultaneous C_αO and C_βH bond cleavages also in the E2 reactions of these compounds.