Konstruktion der sämtlichen Lösungen einer Riemannschen Funktionalgleichung durch Dirichletreihen mit Eulerscher Produktentwicklung I

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Minimalist probes for studying protein dynamics: thioamide quenching of selectively excitable fluorescent amino acids

Fluorescent probe pairs that can be selectively excited in the presence of Trp and Tyr are of great utility in studying conformational changes in proteins. However, the size of these probe pairs can restrict their incorporation to small portions of a protein sequence where their effects on secondary and tertiary structure can be tolerated. Our findings show that a thioamide bond-a single atom substitution of the peptide backbone-can quench fluorophores that are red-shifted from intrinsic protein fluorescence, such as acridone. Using steady-state and fluorescence lifetime measurements, we further demonstrate that this quenching occurs through a dynamic electron-transfer mechanism. In a proof-of-principle experiment, we apply this technique to monitor unfolding in a model peptide system, the villin headpiece HP35 fragment. Thioamide analogues of the natural amino acids can be placed in a variety of locations in a protein sequence, allowing one to make a large number of measurements to model protein folding.     

Thioamides as fluorescence quenching probes: minimalist chromophores to monitor protein dynamics

Decreasing the size of spectroscopic probes can afford higher-resolution structural information from fluorescence experiments. Therefore, we have developed p-cyanophenylalanine (Cnf) and backbone thioamides as a fluorophore/quencher pair. Through the examination of a series of thiopeptides, we have determined the working distance for this pair to be 8-30 ?. We have also carried out a proof-of-principle protein-folding experiment in which a Cnf/thioamide-labeled version of villin headpiece HP35 was thermally unfolded while the Cnf/thioamide distance was monitored by fluorescence. For a given protein, thioamide substitutions could be used to track motions with a much greater number of measurements than for current fluorescence probes, providing a dense array of data with which to model conformational changes.     

Theorie der automorphen Formen beliebiger reeller Dimension und ihre Darstellung durch eine neue Art Poincaréscher Reihen

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Über den Bereich Absoluter Konvergenz der Poincaréschen Reihen

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Ein Fundamentalsatz aus der Theorie der ganzen automorphen Formen.

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