Geometric and Combinatorial Realizations of Crystal Graphs

For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type A_n⁽¹⁾, we extend the Young wall construction to arbitrary level, describing a combinatorial realization of the crystals in terms of new objects which we call Young pyramids. Presented by P. Littleman Mathematics Subject Classifications (2000) Primary 16G10, 17B37. Alistair Savage: This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and was partially conducted by the author for the Clay Mathematics Institute.     

Detection of VX contamination in soil through solid-phase microextraction sampling and gas chromatography/mass spectrometry of the VX degradation product bis(diisopropylaminoethyl)disulfide

A solid-phase microextraction (SPME) and gas chromatography-mass spectrometry (GC-MS) sampling and analysis method was developed for bis(diisopropylaminoethyl)disulfide (a degradation product of the nerve agent VX) in soil. A 30-min sampling time with a polydimethylsiloxane-coated fiber and high temperature alkaline hydrolysis allowed detection with 1.0 microg of VX spiked per g of agricultural soil. The method was successfully used in the field with portable GC-MS instrumentation. This method is relatively rapid (less than 1 h), avoids the use of complex preparation steps, and enhances analyst safety through limited use of solvents and decontamination of the soil before sampling.     

Synthesis of PI3K inhibitor GDC-0077 via a stereocontrolled N-arylation of α-amino acids

An efficient synthesis of PI3K inhibitor GDC-0077, featuring two consecutive Cu-catalyzed CN coupling reactions, is reported. The described synthetic route involves a chemoselective Ullmann-type coupling of a chiral difluoromethyl-substituted oxazolidinone, a Cu-catalyzed N-arylation of l-alanine with high stereochemical integrity, and a high-yielding final amide bond formation step to produce GDC-0077 in >99.5 area % HPLC purity.     

Synthesis of lipid A derivatives and their interactions with polymyxin B and polymyxin B nonapeptide

Lipid A is the causative agent of Gram-negative sepsis, a leading cause of mortality among hospitalized patients. Compounds that bind lipid A can limit its detrimental effects. Polymyxin B, a cationic peptide antibiotic, is one of the simplest molecules capable of selectively binding lipid A and may serve as a model for further development of lipid A binding agents. However, association of polymyxin B with lipid A is not fully understood, primarily due to the low solubility of lipid A in water and inhomogeneity of lipid A preparations. To better understand lipid A-polymyxin B interaction, pure lipid A derivatives were prepared with incrementally varied lipid chain lengths. These compounds proved to be more soluble in water than lipid A, with higher aggregation concentrations. Isothermal titration calorimetric studies of these lipid A derivatives with polymyxin B and polymyxin B nonapeptide indicate that binding stoichiometries (peptide to lipid A derivative) are less than 1 and that affinities of these binding partners correlate with the aggregation states of the lipid A derivatives. These studies also suggest that cooperative ionic interactions dominate association of polymyxin B and polymyxin B nonapeptide with lipid A.