Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Improving the selectivity of engineered protease inhibitors: Optimizing the P2 prime residue using a versatile cyclic peptide library

Standard mechanism inhibitors are attractive design templates for engineering reversible serine protease inhibitors. When optimizing interactions between the inhibitor and target protease, many studies focus on the nonprimed segment of the inhibitor's binding loop (encompassing the contact β-strand). However, there are currently few methods for screening residues on the primed segment. Here, we designed a synthetic inhibitor library (based on sunflower trypsin inhibitor-1) for characterizing the P2′ specificity of various serine proteases. Screening the library against 13 different proteases revealed unique P2′ preferences for trypsin, chymotrypsin, matriptase, plasmin, thrombin, four kallikrein-related peptidases, and several clotting factors. Using this information to modify existing engineered inhibitors yielded new variants that showed considerably improved selectivity, reaching up to 7000-fold selectivity over certain off-target proteases. Our study demonstrates the importance of the P2′ residue in standard mechanism inhibition and unveils a new approach for screening P2′ substitutions that will benefit future inhibitor engineering studies.

Proximinality in Banach spaces

In this paper, we study approximatively τ-compact and τ-strongly Chebyshev sets, where τ is the norm or the weak topology. We show that the metric projection onto τ-strongly Chebyshev sets are norm-τ continuous. We characterize approximatively τ-compact and τ-strongly Chebyshev hyperplanes and use them to characterize factor reflexive proximinal subspaces in τ-almost locally uniformly rotund spaces. We also prove some stability results on approximatively τ-compact and τ-strongly Chebyshev subspaces.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Identification and characterization of a library of microheterogeneous cyclohexadepsipeptides from the fungus Isaria

Ten new cyclic hexadepsipeptides, six isariins and four isaridins, from the fungus Isaria have been identified and characterized by high-performance liquid chromatography, coupled to tandem electrospray ionization mass spectrometry (LC-ESIMS/MS). The isariins possess a beta-hydroxy acid residue and five alpha-amino acids, while isaridins contain a beta-amino acid, an alpha-hydroxy acid, and four alpha-amino acids. One- and two-dimensional NMR spectroscopy confirmed the chemical identity of some of the isariin fractions. Mass spectral fragmentation patterns of [M + H](+) ions reveal clear diagnostic fragment ions for the isariins and isaridins. Previously described cyclic depsipeptides, isarfelins from Isaria felina (Guo, Y. X.; Liu, Q. H.; Ng, T. B.; Wang H. X. Peptides 2005, 26, 2384), are now reassigned as members of the isaridin family. Examination of isaridin sequences revealed significant similarities with cyclic hexadepsipeptides such as destruxins and roseotoxins. The structure of an isariin (isariin A) investigated by NMR spectroscopy indicated the presence of a hybrid alpha beta C-11 turn, formed by the beta-hydroxy acid and glycine residues and a (D)Leu-(L)Ala type II' beta-turn. Additionally, the inhibitory effect of isariins and an isaridin on the intra-erythrocytic growth of Plasmodium falciparum is presented.