On the convexity of the sum of the first eigenvalues of operators depending on a real parameter

Let ₁ (k) ₂ (k) be the eigenvalues of an operator of a certain type depending on a real parameterk. The paper shows that under certain requirements on the operator and on the nature of its dependence onk, the sum ₁ (k)++ _N (k) is a concave function ofk, for any positive integerN.

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Zusammenfassung Seien ₁ (k) ₂ (k) die Eigenwerte eines von einem reellen Parameterk abhängigen Operators. Man zeigt, daß unter gewissen Voraussetzungen über den Operator und seine Abhängigkeit vonk die Summe ₁ (k)++ _N (k) für jedesN eine konkave Funktion vonk ist.

     

Highly Conjugated π-Systems Arising from Cannibalistic Hexadehydro-Diels–Alder Couplings: Cleavage of C−C Single and Triple Bonds

We have investigated the cannibalistic self-trapping reaction of an ortho-benzyne derivative generated from 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne in an HDDA reaction. Without adding any specific trapping agent, the highly reactive benzyne is trapped by another bisdiyne molecule in at least three different modes. We have isolated and characterized the resulting products and performed high-level calculations concerning the reaction mechanism. During the cannibalistic self-trapping process, either a C≡C triple bond or an sp–sp³ C−C single bond is cleaved. Up to seven rings and nine C−C bonds are formed starting from two 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne molecules. Our experiments and calculations provide considerable insight into the variety of reaction pathways which the ortho-benzyne derivative, generated from a bisdiyne, can take when reacting with another bisdiyne molecule.     

Mycotoxin profile of Fusarium langsethiae isolated from wheat in Italy: production of type‐A trichothecenes and relevant glucosyl derivatives

Fusarium langsethiae, formally described as a new species over a decade ago, has been identified as the main producer of HT‐2 (HT2) and T‐2 (T2) toxins in Europe in small cereal grains. Mycotoxin contamination caused by this Fusarium species can represent a food safety hazard that deserves further attention. In the present work, the mycotoxin profile in wheat cultures of F. langsethiae is presented with particular reference to the production of major type‐A trichothecenes and their glucosyl derivatives. F. langsethiae isolates, representative of the major Italian wheat cultivation areas, were tested for the production of T2, HT2, diacetoxyscirpenol (DAS) and neosolaniol (NEO), and relevant glucosyl derivatives. Liquid chromatography‐tandem mass spectrometry (LC‐MS/MS) was used for the identification and chemical characterization of these metabolites. F. langsethiae isolates under investigation resulted to be potent producers of T2, HT2 and NEO. Furthermore, a well‐defined set of isolates, all originating from Central Italy, produced also DAS. All isolates were found to be able to produce HT2 glucosyl derivatives, whereas only traces of T2 glucoside were detected in one sample. Furthermore, two mono‐glucosyl derivatives of NEO and one mono‐glucoside derivative of DAS were identified and characterized. The screening for the presence/absence of glucosylated trichothecenes in analyzed fungal extracts revealed a general co‐occurrence of these derivatives with the parent toxin at levels that could be roughly estimated to account up to 37% of the relevant unconjugated toxin. This is the first report of the production of glucosylated trichothecenes by F. langsethiae cultured on small grains. Copyright © 2013 John Wiley & Sons, Ltd.     

NMR-assisted computational studies of peptidomimetic inhibitors bound in the hydrophobic pocket of HIV-1 glycoprotein 41

Due to the inherently flexible nature of a protein–protein interaction surface, it is difficult both to inhibit the association with a small molecule, and to predict how it might bind to the surface. In this study, we have examined small molecules that mediate the interaction between a WWI motif on the C-helix of HIV-1 glycoprotein-41 (gp41) and a deep hydrophobic pocket contained in the interior N-helical trimer. Association between these two components of gp41 leads to virus–cell and cell–cell fusion, which could be abrogated in the presence of an inhibitor that binds tightly in the pocket. We have studied a comprehensive combinatorial library of α-helical peptidomimetics, and found that compounds with strongly hydrophobic side chains had the highest affinity. Computational docking studies produced multiple possible binding modes due to the flexibility of both the binding site and the peptidomimetic compounds. We applied a transferred paramagnetic relaxation enhancement experiment to two selected members of the library, and showed that addition of a few experimental constraints enabled definitive identification of unique binding poses. Computational docking results were extremely sensitive to side chain conformations, and slight variations could preclude observation of the experimentally validated poses. Different receptor structures were required for docking simulations to sample the correct pose for the two compounds. The study demonstrated the sensitivity of predicted poses to receptor structure and indicated the importance of experimental verification when docking to a malleable protein–protein interaction surface.     

S‐Alkylation of Soft Scorpionates

The alkylation reactions of soft scorpionates are reported. The hydrotris(S‐alkyl‐methimazolyl)borate dications (alkyl=methyl, allyl, benzyl), which were prepared by the reaction of Tm^Me anion and primary alkyl halides, have been isolated and structurally characterised. The reaction is, however, not universally successful. DFT analysis of these alkylation reactions (C?S versus B? H alkylation) indicates that the observed outcome is driven by kinetic factors. Extending the study to incorporate alternative imine thiones (mercaptobenzothiazole, bz; thiazoline, tz) led to the structural characterisation of di[aquo‐μ‐aquohydrotris(mercaptobenzothiazolyl)boratosodium], which contains sodium atoms in the κ³‐S,S,S coordination mode. Alkylation of Na[Tbz] and Na[tzTtz] leads to decomposition resulting in the formation of the simple S‐alkylated heterocycles. The analysis of the species involved in these reactions shows an inherent weakness in the B? N bond in soft scorpionates, which has implications for their use in more advanced chemistry.     

X‐Band DNP Hyperpolarization of Viscous Liquids and Polymer Melts

NMR studies of synthetic polymers and biomacromolecules, which provide insight into the conformation and dynamics of these materials, can benefit strongly from the increased sensitivity offered by dynamic nuclear polarization (DNP) and other hyperpolarizing methods. In this study ¹H DNP nuclear spin hyperpolarization of two polybutadiene samples, representing a supercooled liquid and an entangled polymer melt, is demonstrated at 0.35 T magnetic field strength and at temperatures between −80 and +50 °C. Electron spin polarization transfer from the α,γ‐bisdiphenylene‐β‐phenylallyl radical to the sample nuclei is achieved by the Overhauser and solid effect. DNP signal enhancements are studied, varying the electron spin resonance offset, microwave power, and sample temperature. The influence of spin relaxation times, line widths, and molecular dynamics are discussed. The results show promising, up to 15‐fold NMR signal enhancements using noncryogenic temperatures and an inexpensive setup that is less technically demanding than current high‐field DNP setups.