On the Automorphism Groups of Cayley Graphs of Finite Simple Groups

Let G be a finite nonabelian simple group and let be a connectedundirected Cayley graph for G. The possible structures for thefull automorphism group Aut are specified. Then, for certainfinite simple groups G, a sufficient condition is given underwhich G is a normal subgroup of Aut. Finally, as an applicationof these results, several new half-transitive graphs are constructed.Some of these involve the sporadic simple groups G = J₁, J₄,Ly and BM, while others fall into two infinite families andinvolve the Ree simple groups and alternating groups. The twoinfinite families contain examples of half-transitive graphsof arbitrarily large valency.     

Finding Optimal Routings in Hamming Graphs

A routing R in a graph consists of a simple path p_uvfromu to v for each ordered pair of distinct vertices (u, v). We will call R optimal if all the paths p_uvare shortest paths and if edges of the graph occur equally often in the paths of R. In 1994, Solé gave a sufficient condition involving the automorphism group for a graph to have an optimal routing in this sense. Graphs which satisfy Solé’s condition are called orbital regular graphs. It is often difficult to determine whether or not a given graph is orbital regular. In this paper, we give a necessary and sufficient condition for a Hamming graph to be orbital regular with respect to a certain natural subgroup of automorphisms.     

On Primitive Representations of Finite Alternating and Symmetric Groups with a 2-Transitive Subconstituent

In this paper we analyse primitive permutation representations of finite alternating and symmetric groups which have a 2-transitive subconstituent. We show that either the representation belongs to an explicit list of known examples, or the point stabiliser is a known almost-simple 2-transitive group and acts primitively in the natural representation of the associated alternating or symmetric group.     

On orbital partitions and exceptionality of primitive permutation groups

Let and be transitive permutation groups on a set such that is a normal subgroup of . The overgroup induces a natural action on the set of non-trivial orbitals of on . In the study of Galois groups of exceptional covers of curves, one is led to characterizing the triples where fixes no elements of ; such triples are called exceptional. In the study of homogeneous factorizations of complete graphs, one is led to characterizing quadruples where is a partition of such that is transitive on ; such a quadruple is called a TOD (transitive orbital decomposition). It follows easily that the triple in a TOD is exceptional; conversely if an exceptional triple is such that is cyclic of prime-power order, then there exists a partition of such that is a TOD. This paper characterizes TODs such that is primitive and is cyclic of prime-power order. An application is given to the classification of self-complementary vertex-transitive graphs.

     

Inhibition and acceleration of deuterium exchange in amide-functionalized monolayer-protected gold clusters

Hydrogen/deuterium exchange rates in amide-functionalized monolayer protected gold clusters (MPCs) are controlled by the radial nature of the surface, with inhibition and catalysis observed at different chain lengths.     

Total synthesis of (+/-)-mersicarpine

The first total synthesis of the indole alkaloid mersicarpine is reported. Key steps include a beta-dicarbonyl radical cyclization, as well as an oxidation of the benzopyrrole moiety to establish the masked 1,2-dicarbonyl functionality. An X-ray crystal structure and discussion of the 1H NMR behavior of the natural product are also presented.     

A new method for the preparation of 2-thio substituted furans by methylsulfanylation of gamma-dithiane carbonyl compounds

Several related methods for the preparation of differentially substituted 2-thiofurans are described. The general procedure involves the formation of a thionium ion from a gamma-dithianyl substituted carbonyl compound followed by cyclization of this reactive intermediate onto the tethered carbonyl group. Two methods for thionium ion generation were explored. One of these involved an acid-catalyzed reaction of beta-ketenedithioacetals, prepared from the condensation of 2,2-bis(methylsulfanyl)acetaldehyde with a variety of ketones. Cyclization followed by loss of methane thiol gave 2-thiofurans 17, 18 and 23, 24 in 70-90% yield. Attempts to prepare 5-heteroatom substituted 2-thiofurans from the corresponding beta-ketenedithioacetal amides or esters were unsuccessful, leading to 1,2-thio rearranged products. A more successful route involved the reaction of beta-acetoxy-gamma-thianyl carbonyl compounds with dimethyl(methylthio)sulfonium tetrafluoroborate (DMTSF). Treatment of the dithiane with this reagent resulted in the smooth generation of a thionium ion. Cyclization followed by loss of acetic acid afforded thiofurans 17, 18, 23, 47-49, 51, and 61-64 in 40-100% yield. The N-butenyl substituted thioamido furan furnished a rearranged hexahydropyrroloquinolin-2-one in high yield when heated at 110 degrees C.     

Ethynyl and Propynylpyrene Inhibitors of Cytochrome P450

Abstract  

The single-crystal X-ray structures and in vivo activities of three aryl acetylenic inhibitors of cytochromes P450 1A1, 1A2, 2A6, and 2B1 have been determined and are reported herein. These are 1-ethynylpyrene, 1-propynylpyrene, and 4-propynylpyrene. To investigate electronic influences on the mechanism of enzyme inhibition, the experimental electron density distribution of 1-ethynylpyrene has been determined using low-temperature X-ray diffraction measurements, and the resulting net atomic charges compared with various theoretical calculations. A total of 82,390 reflections were measured with Mo Kα radiation to a (sinθ/λ)_max = 0.985 Å⁻¹. Averaging symmetry equivalent reflections yielded 8,889 unique reflections. A least squares refinement procedure was used in which multipole parameters were added to describe the distortions of the atomic electron distributions from spherical symmetry. A map of the model electron density distribution of 1-ethynylpyrene was obtained. Net atomic charges calculated from refined monopole population parameters yielded charges that showed that the terminal acetylenic carbon atom (C18) is more negative than the internal carbon (C17). Net atomic charges calculated by ab initio, density functional theory, and semi-empirical methods are consistent with this trend suggesting that the terminal acetylenic carbon atom is more likely to be the site of oxidation. This is consistent with the inhibition mechanism pathway that results in the formation of a reactive ketene intermediate. This is also consistent with assay results that determined that 1-ethynylpyrene acts as a mechanism-based inhibitor of P450s 1A1 and 1A2 and as a reversible inhibitor of P450 2B1. Crystallographic data: 1-ethynylpyrene, C₁₈H₁₀, P2₁/c, a = 14.571(2) Å, b = 3.9094(5) Å, c = 20.242(3) Å, β = 105.042(2)°, V = 1,113.5(2) Å³; 1-propynylpyrene, C₁₉H₁₂, P2₁/n, a = 8.970(2) Å, b = 10.136(1) Å, c = 14.080(3) Å, β = 99.77(2)°, V = 1,261.5(4) Å³; 4-propynylpyrene, C₁₉H₁₂, Pbca, a = 9.904(1) Å, b = 13.174(2) Å, c = 19.401(1) Å, V = 2,531.4(5) Å³.     

In situ vinylindole synthesis. Diels-alder reactions with maleimides to give tetrahydrocarbazoles

Tetrahydrocarbazoles have been prepared in one-flask syntheses from indoles, ketones or aldehydes, and maleimides, with acid catalysis. The reactions involve a condensation of the indole with the ketone or aldehyde, followed by an in situ trapping of the vinylindole in a Diels-Alder addition with a maleimide. Isomerization of the double bond into the indole nucleus gave the tetrahydrocarbazoles which were isolated ( 6, 9 , and 10 ). Variation of the indole, carbonyl compound, and maleimide has been explored. The predominant stereochemistry of the tetrahydro ring in the products is all-cis, although a second stereoisomer has been isolated. Two regioisomers were generated from all unsymmetrical 2-alkanones, except 2-butanone, which gave the single isomer 9a . Aromatization of tetrahydrocarbazoles 6 to carbazoles 7 was accomplished with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone.