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We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretisation, outline the implementation, and showcase numerical examples.

Belactosins and cystargolides are natural product proteasome inhibitors from Actinobacteria. Both feature dipeptidic backbones and a unique beta-lactone building block. Herein, we present a detailed investigation of their biosynthesis. Identification and analysis of the corresponding gene clusters indicated that both compounds are assembled by rare single-enzyme amino acid ligases. Feeding experiments with isotope-labeled precursors and in vitro biochemistry showed that the formation of the beta-lactone warhead is unprecedented and reminiscent of leucine biosynthesis, and that it involves the action of isopropylmalate synthase homologues.

Belactosine und Cystargolide sind von Actinobakterien produzierte Naturstoffe mit proteasominhibitorischen Eigenschaften. Beide weisen ein Peptidruckgrat aus zwei Aminosauren sowie einen einzigartigen β-Lacton-Baustein auf. Hier wird eine detaillierte Untersuchung der Biosynthese der beiden Naturstoffe beschrieben. Die Identifizierung und Analyse der entsprechenden Gencluster weist darauf hin, dass beide Stoffe uber seltene Aminosaure-Ligasen gebildet werden. Futterungsversuche mit isotopenmarkierten Vorstufen und In-vitro-Biochemie zeigen einen bislang unbeschriebenen Mechanismus zur β-Lacton-Biosynthese, der sich aus der Leucin-Bildung ableitet und die Beteiligung eines Isopropylmalat-Synthase-ahnlichen Enzyms vorsieht.

Arene diazonium salts undergo Matsuda–Heck reactions with vinylsulfonates and -sulfonamides to give styrylsulfonic acid derivatives in high to excellent yields and with high to excellent selectivities. By quantifying the evolution of nitrogen over time in a gas-meter apparatus, the reactivities of ethylvinylsulfonate and the benchmark olefin methyl acrylate were compared for an electron-rich and an -deficient arene diazonium salt. Tertiary sulfonamides react in Matsuda–Heck couplings with high conversions, but require long reaction times, which prevents the determination of kinetic data through the measurement of nitrogen evolution. Secondary sulfonamides were found to be unreactive. From these results, the following order of reactivity could be deduced: H2C=CHCO2Me > H2C=CHSO2OEt > H2C=CHSO2N(Me)Bn >> H2C=CHSO2NHBn. Through the Matsuda–Heck coupling of 5-indolyldiazonium salt and a tertiary vinylsulfonamide, the synthesis of the C-5-substituted indole part of the antimigraine drug naratriptan was accomplished in high yield.