Tree 3-spanners in 2-sep chordal graphs: Characterization and algorithms

A spanning tree T of a graph G is said to be a tree t-spanner if the distance between any two vertices in T is at most t times their distance in G. A graph that has a tree t-spanner is called a tree t-spanner admissible graph. The problem of deciding whether a graph is tree t-spanner admissible is NP-complete for any fixed t >= 4 and is linearly solvable for t <= 2. The case t = 3 still remains open. A chordal graph is called a 2-sep chordal graph if all of its minimal a - b vertex separators for every pair of non-adjacent vertices a and b are of size two. It is known that not all 2-sep chordal graphs admit tree 3-spanners This paper presents a structural characterization and a linear time recognition algorithm of tree 3-spanner admissible 2-sep chordal graphs. Finally, a linear time algorithm to construct a tree 3-spanner of a tree 3-spanner admissible 2-sep chordal graph is proposed. (C) 2010 Elsevier B.V. All rights reserved.

Novel coordination behaviour of gem-bis (pyrazolyl) cyclotriphosphazenes as tridentate NNN-donor ligands: The crystal structure of [Mo(CO)3{N3P3Ph4(3,5-Me2C3HN2)2}]

Reactions of group 6 metal carbonyls with bis(pyrazolyl) phosphazenes yield metal tricarbonyl complexes, [M(CO)3.L] [L = N3P3Ph4 (3, 5-Me2C3HN2)2 (1) or N3P3(MeNCH2CH2O)2 (3,5-Me2C3HN2)2(4)]. The structure of the complex [Mo(CO)3.1], determined by single-crystal X-ray analysis, shows that the (pyrazolyl) phosphazene acts as a tridentate ligand; the two pyridinic pyrazolyl nitrogen atoms and a phosphazene ring nitrogen atom are coordinated to the metal. A similar structure is proposed for the complexes [M(CO)3.4] (M = Mo or W] on the basis of their spectroscopic data.

Organometallic derivatives of diphosphazanes. 2. Seven-coordinated Group 6 metal tricarbonyl complexes of diphosphazane ligands. X-ray crystal structure of [WI2(CO)3{P(OPh)2}2NPh]

The reactions of the complexes [MI2(CO)3-(NCMe)2] (M = Mo, W) with the diphosphazane ligands RN{P(OPh)2}2 (R = Me, Ph) in CH2Cl2 at room temperature afford new seven-coordinated complexes of the type [MI2(CO)3{P(OPh)2}2NR]. The molybdenum complexes are sensitive to air oxidation even in the solid state, whereas the tungsten complexes are more stable in the solid state and in solution. The structure of the tungsten complex [WI2(CO)3{P(OPh)2}2NPh] has been determined by single-crystal X-ray diffraction. It crystallizes in the orthorhombic system with the space group Pna 2(1), a = 19.372 (2) angstrom, b = 11.511 (1) angstrom, c = 15.581 (1) angstrom, and Z = 4. Full-matrix least-squares refinement with 3548 reflections (I > 2.5-sigma-(I)) led to final R and R(w) values of 0.036 and 0.034, respectively. The complex adopts a slightly distorted pentagonal-bypyramidal geometry rarely observed for such a type of complexes; two phosphorus atoms of the diphosphazane ligand, two iodine atoms, and a carbonyl group occupy the equatorial plane, and the other two carbonyl groups, the apical positions.

Oxidation Of Spiroalcohols With 2,3-Dichloro-5,6-Dicyano-1,4-Benzoquinone (Ddq) .4. Structure Of A Novel Dioxepin Derivative

DDQ oxidation of the spiroalcohol 7a gives exclusively a compound to which the 13a-methyl-13aH-7a, 15-methano-15H-dinaphtho[2,1-b:2',1'-e][1,4]-dioxepin structure 8a has been assigned on the basis of two-dimensional homonuclear (H-1-H-1) and heteronuclear (H-1-C-13; FUCOUP) correlation spectroscopy experiments. Similar oxidation of spiroalcohols 7b-h gives the dioxepin derivatives 8b-h.

Synthesis Of (+/-)-2-Isopropyl-5,6-Dimethylbicyclo[3.2.1]Oct-6-En-8-One

Methanolic hydrogen chloride cyclization of the triketone 8, prepared from the Mannich base 7 and 2-methylcyclopentane-1,3-dione, gives ketones 9 and 10. NaBH4 reduction of 9 followed by Grignard reaction with CH3MgI affords the diol 12. Catalytic hydrogenation of 12 followed by PCC oxidation yields the ketoalcohol 13. Dehydration of 13 with SOCl2/pyridine results in a 1:1 mixture of the endo-14 and exo-15 olefins, separated by chromatography.

Synthesis Of (+/-)-Beta-Cuparenone Via 3-Oxa-Beta-Cuparenone

Grignard reaction followed by ozonolysis, or ozonolysis followed by Grignard reaction on the pentenoate 8, generates the diol 9. Cyclodehydration of 9 leads to the 3-oxacuparene (6), whereas PCC oxidation furnishes the 3-oxa-beta-cuparenone (7). Methanesulfonic acid-P2O5 transforms 7 into cyclopentenones 4, 5, known precursors to beta-cuparenone (3), and the naphthalenone 14.

Synthetic investigations on illudinine: a new synthesis of methyl 8-methoxy-2,2-dimethyl-7-oxo-1,2,3,5,6,7-hexahydro-s-indacene-4-carboxylate

A new strategy for the total synthesis of methyl 8-methoxy-2,2-dimethyl-7-oxo-1,2,3,5,6,7-hexahydro-s-indacene-4-carboxylate 4, a key intermediate in the synthesis of illudalanes, is reported. The key step in this strategy is a new method of preparation of indanones from tetralones. Thus, the furfurylidene derivative of 6-methoxy-3,4-dihydronaphthalen-1-(2H)-one is oxidised to the dicarboxylic acid 9a which is cyclodehydrated to methyl 7-methoxy-1-oxoindan-4-carboxylate 10. Similar reactions on the tetrahydronaphthalenone 25, obtained from 6-methoxy-1,2,3,4-tetrahydronaphthalene-7-carbaldehyde 11 by sequential transformations including a regiospecific benzylic oxidation resulted in the hexahydro-s-indacenone 4, thus completing a formal synthesis of illudinine 1.

The identification of 14 alpha,17 beta-dihydroxyandrost-4-en-3-one monohydrate and 14 alpha,17 beta-dihydroxyandrosta-1,4-dien-3-one monohydrate, metabolites of androstenedione in Mucor piriformis

The microorganism Mucor piriformis transforms androst-4-ene-3,17-dione into a major and several minor metabolites. X-ray crystallographic analysis of two of these metabolites was undertaken to determine unambiguously their composition and chirality. Crystals belong to the orthorhombic space-group P2(1)2(1)2(1), with a = 7.199(4) angstrom and a = 6.023(3) angstrom, b = 11.719(3) angstrom and b = 13.455(4) angstrom, c = 20.409(3) angstrom and c = 20.702(4) angstrom for the two title compounds, respectively. The structures have been refined to final R values of 0.060 and 0.040, respectively.

The nature of inhibition of 3-hydroxy-3-methylglutaryl CoA reductase by garlic-derived diallyl disulfide

A concentration dependent inhibition of 3-hydroxy-3-methylglutaryl CoA (HMG CoA) reductase was found on preincubation of microsomal preparations with diallyl disulfide, a component of garlic oil. This inhibited state was only partially reversed even with high concentrations of DTT. Glutathione, a naturally occurring reducing thiol agent, was ineffective. The substrate, HMG CoA, but not NADPH, was able to give partial protection for the DTT-dependent, but not glutathione-dependent activity. The garlic-derived diallyl disulfide is the most effective among the sulfides tested for inhibition of HMG CoA reductase. Formation of protein internal disulfides, inaccessible for reduction by thiol agents, but not of protein dimer, is likely to be the cause of this inactivation.

Src Homology 3-interacting Domain of Rv1917c of Mycobacterium tuberculosis Induces Selective Maturation of Human Dendritic Cells by Regulating PI3K-MAPK-NF-kappa B Signaling and Drives Th2 Immune Responses

Mycobacterium tuberculosis, an etiological agent of pulmonary tuberculosis, causes significant morbidity and mortality worldwide. Pathogenic mycobacteria survive in the host by subverting host innate immunity. Dendritic cells (DCs) are professional antigen-presenting cells that are vital for eliciting immune responses to infectious agents, including pathogenic mycobacteria. DCs orchestrate distinct Th responses based on the signals they receive. In this perspective, deciphering the interactions of the proline-glutamic acid/proline-proline-glutamic acid (PE/PPE) family of proteins of M. tuberculosis with DCs assumes significant pathophysiological attributes. In this study, we demonstrate that Rv1917c (PPE34), a representative member of the proline-proline-glutamic-major polymorphic tandem repeat family, interacts with TLR2 and triggers functional maturation of human DCs. Signaling perturbations implicated a critical role for integrated cross-talk among PI3K-MAPK and NF-kappa B signaling cascades in Rv1917c-induced maturation of DCs. However, this maturation of DCs was associated with a secretion of high amounts of anti-inflammatory cytokine IL-10, whereas Th1-polarizing cytokine IL-12 was not induced. Consistent with these results, Rv1917c-matured DCs favored secretion of IL-4, IL-5, and IL-10 from CD4(+) T cells and contributed to Th2-skewed cytokine balance ex vivo in healthy individuals and in patients with pulmonary tuberculosis. Interestingly, the Rv1917c-skewed Th2 immune response involved induced expression of cyclooxygenase-2 (COX-2) in DCs. Taken together, these results indicate that Rv1917c facilitates a shift in the ensuing immunity toward the Th2 phenotype and could aid in immune evasion by mycobacteria.

A simple local 3-approximation algorithm for vertex cover

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required. (c) 2009 Elsevier B.V. All rights reserved.