New entry of coupling reaction of phenacylamine derivatives with silylstannane

The new coupling reaction of phenacylamines with silylstannane and lithium diisopropylamide (LDA) is reported. The treatment of a phenacylamine iodide 1 with (trimethylsilyl)tributylstannane (Me3SiSnBu3) and cesium fluoride (CsF) gave a dimerization product 2 having no iodine atom. Reaction of 1 with LDA afforded a dimerization product 3 with an iodine atom. The products 2 and 3 were separated to the meso and racemic isomers, respectively.     

Screening of inhibitors of uridine diphosphate glucuronosyltransferase with a miniaturized on-line drug-metabolism system

Inhibition of uridine diphosphate glucuronosyltransferase (UGT), a major drug-metabolyzing enzyme, has been studied using an on-line drug-metabolism system integrated into capillary electrophoresis. Microsomes isolated from rat liver were encapsulated in tetramethoxysilane (TMOS)-based silica matrices within a capillary in a single step under mild conditions. This microsome-immobilized capillary column allows both the metabolism of drugs and determination of the metabolites in a single capillary simultaneously, just by injecting the substrate-coenzyme mixture onto the column. Glucuronidation of acetaminophen, a widely used pharmaceutical analgesic and antipyretic agent, was investigated using this system. The glucuronidation was inhibited by 4-nitrophenol (4NP) or probenecid that was injected onto a column along with the substrate-coenzyme mixture. On the other hand, valproate did not inhibit the metabolizing reaction. The extents of inhibition using encapsulated UGT were almost the same as those obtained using free UGT. On the other hand, this electrophoretic enzyme-inhibitor assay in microfabricated devices consumes 10(4) less sample and 10(3) less microsome per experiment compared to the conventional reaction schemes. These results demonstrate that this on-line system can circumvent laborious procedures for the isolation and determination of drug metabolites from the reaction mixtures required in the conventional schemes and can provide an attractive alternative technique for the analysis of drug interactions in the metabolic pathways.     

A new proof of Masser's vanishing theorem

We give a simple proof of Masser's vanishing theorem, which is important in investigating the algebraic independence of the values of Mahler functions.

     

Loop-erased random walk on the Sierpinski gasket

In this paper the loop-erased random walk on the finite pre-Sierpiński gasket is studied. It is proved that the scaling limit exists and is a continuous process. It is also shown that the path of the limiting process is almost surely self-avoiding, while having Hausdorff dimension strictly greater than 1. The loop-erasing procedure proposed in this paper is formulated by erasing loops, in a sense, in descending order of size. It enables us to obtain exact recursion relations, making direct use of ‘self-similarity’ of a fractal structure, instead of the relation to the uniform spanning tree. This procedure is proved to be equivalent to the standard procedure of chronological loop-erasure.     

Inclusion Properties and Crystal Structure of Clathrates Constructed Based on “π-sandwich”

Abstract

Inclusion behavior of structurally similar host compounds, 1,4-bis[1-(9-anthryl)-3-propen-1-on-3-yl]benzene (1) and 1,4-bis[3-(9-anthryl)-3-propen-1-on-1-yl]benzene (2), has been studied. Both hosts preferred cyclic, non-branched small molecules as a guest component, to yield 1:2 clathrates specifically. X-ray powder diffraction studies revealed that those 1:2 clathrates of 1 and 2 were respectively isostructural. X-ray analyses of (1)(THF)₂ (P 1, a = 10.910(2), b = 19.656(5), c = 9.172(4) Å, α = 95.58(3), β = 93.67(2), γ = 103.30(2)°, D _calc = 1.195 g cm^?3, Z = 2, and R = 0.067 for 8644 observed reflections) and (2)(1,4-dioxane)₂, (P2₁/n, a = 5.661(1), b = 17.971(3), c = 18.619(3) Å, β = 91.37(2)°, D _calc = 1.254 g cm^?3, Z = 2, and R = 0.097 for 4353 observed reflections) illuminated that their guest preference should be ascribed to the commonly observed π-sandwich” structure, in which guest molecules are enclathrated between two anthracene planes of the host molecules.     

Total Synthesis and Structure Revision of Didemnaketal B

Didemnaketal B, a structurally complex spiroacetal that exhibits potent HIV‐1 protease inhibitory activity, was originally discovered by Faulkner and his colleagues from the ascidian Didemnum sp. collected at Palau. Its absolute configuration was proposed on the basis of degradation/derivatization experiments of the authentic sample. However, our total synthesis of the proposed structure of didemnaketal B questioned the stereochemical assignment made by Faulkner et al. Here we describe in detail our first total synthesis of the proposed structure 2 of didemnaketal B, which features 1) a convergent synthesis of the C7–C21 spiroacetal domain by means of a strategy exploiting Suzuki–Miyaura coupling, 2) an Evans syn‐aldol reaction and a vinylogous Mukaiyama aldol reaction for the assembly of the C1–C7 acyclic domain, and 3) a Nozaki–Hiyama–Kishi reaction for the construction of the C21–C28 side chain domain. The NMR spectroscopic discrepancies observed between synthetic 2 and the authentic sample as well as careful inspection of the Faulkner’s stereochemical assignment led us to postulate that the absolute configuration of the C10–C20 domain of 2 has been erroneously assigned. Accordingly, the total synthesis of the revised structure 65 was achieved to show that the NMR spectroscopic properties of synthetic 65 were in good agreement with those of the authentic sample. Furthermore, application of the phenylglycine methyl ester (PGME) method to the C7–C21 spiroacetal domain enabled us to establish the absolute configuration of didemnaketal B.     

Algebraic theory of difference equations and Mahler functions

Algebraic independence of certain Mahler functions constructed from Rudin–Schapiro sequences and Baum–Sweet sequences is proved, using difference Riccati equations and the notion of difference field extension of valuation ring type.     

Linear response theory in stochastic many-body systems revisited

The Green–Kubo relation, the Einstein relation, and the fluctuation–response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green–Kubo relation is a direct result of the local detailed balance condition, the fluctuation–response relation represents the dynamic extension of both the Green–Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.