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.
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.
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. 相似文献
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. 相似文献
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 TmMe 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. 相似文献
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