The structure and maximum number of maximum independent sets in trees

A subset of vertices is a maximum independent set if no two of the vertices are joined by an edge and the subset has maximum cardinality. in this paper we answer a question posed by Herb Wilf. We show that the greatest number of maximum independent sets for a tree of n vertices is We give the families of trees on which these maxima are achieved. Proving which trees are extremal depends upon the structure of maximum independent sets in trees. This structure is described in terms of adjacency rules between three types of vertices, those which are in all, no, or some maximum independent sets. We show that vertices that are in some but not all maximum independent sets of the tree are joined in pairs by the α-critical edges (edges whose removal increases the size of a maximum independent set). The number of maximum independent sets is shown to depend on the structure within the tree of the α-critical edges.     

Assay development and high-throughput screening of caspases in microfluidic format

Caspase proteases are familiar targets in drug discovery. A common format for screening to identify caspase inhibitors employs fluorogenic or colorimetric tetra-peptide substrates in 96, 384, or 1536 -well microtiter plates. The primary motivation for increasing the number of wells per plate is to reduce the reagent cost per test and increase the throughput of HTS operations. There are significant challenges, however, to moving into or beyond the 1536-well format, such as submicroliter liquid handling, liquid evaporation, increased surface area-to-volume ratios, and the potential for artifacts and interference from small air-borne particles such as lint. Therefore, HTS scientists remain keenly interested in technologies that offer alternatives to the ever-shrinking microtiter plate well. Microfluidic assay technology represents an attractive option that, in theory, consumes only subnanoliter volumes of reagents per test. We have successfully employed a microfluidic assay technology in fluorogenic screening assays for several caspase isoforms utilizing the Caliper Technologies Labchip platform. Caspase-3 is used as a representative case to describe microfluidic assay development and initial high-throughput screening results. In addition, microfluidic screening and plate-based screening are compared in terms of reagent consumption, data quality, and ease of operation.     

A L-RNA aptamer chiral stationary phase for the resolution of target and related compounds

In this paper, we report for the first time an aptamer-based chiral stationary phase (CSP) able to resolve racemates of both target and various related compounds. The enantiomers of tyrosine and analogues (11 enantiomeric pairs) were separated using an immobilized tyrosine-specific L-RNA aptamer as CSP and an aqueous buffer (8 mM Tris-HCl buffer, 25 mM NaCl, 5 mM MgCl2; pH 7.4) as mobile phase, at a column temperature of 10 degrees C. It appeared that the carboxylic and amino groups as well as the aromatic side chain of amino acid controlled the stereospecific recognition. Modifications on the polar groups were strongly detrimental for enantioselectivity while the replacement of the phenolic group by some bicyclic aromatic residues of different polarity, size or shape did not impair the enantioselective interaction. In addition, the effects of the mobile phase composition and column temperature upon the retention and stereoselective properties of the CSP were assessed. Finally, it was found that the immobilized RNA aptamer could be used under hydro-organic mobile phase conditions without alteration of the stationary phase stability.     

Solvothermal syntheses of Cu3P via reactions of amorphous red phosphorus with a variety of copper sources

Polycrystalline Cu₃P was successfully prepared under a wide variety of solvothermal conditions. The reaction of red phosphorus with several copper sources (copper metal, copper (I) iodide, copper (I) chloride and copper (II) chloride) at 150-200 °C for 1-2 days in water produced Cu₃P. Products were examined with powder X-ray diffraction, scanning electron microscopy and energy dispersive spectroscopy. Thermal analyses and optical spectroscopy were also performed. A detailed list of reaction conditions, products and impurity phases (where applicable) are reported.     

Rearrangement of epoxynitriles: a convenient homologation of acyclic and cyclic ketones to carboxylic acids

A convenient two-step homologation of both aliphatic and aromatic ketones to the corresponding carboxylic acid has been developed. First ketones were converted to epoxynitriles with the Darzens reaction. Second, a Lewis acid mediated rearrangement of these epoxynitriles with lithium bromide was achieved to give homologated secondary alkanoic acids (as well as aryl-alkanoic) in good yields. The mechanism and the scope of the rearrangement reaction were investigated. This strategy constitutes a two-step homologation of ketones to secondary carboxylic acids.     

Synthesis and Circular Dichroism of Both Enantiomers of 2-deuterofluoroacetic acid ( Fluoro[2H1]acetic acid)

Sharpless epoxidation of (E)-1-(trimethylsilyl)[1-²H₁]oct-1-en-3-o1 ( 3a ) yielded (1S,2S,3S)- and (1R,2R,3R)-1-(trimethylsilyl)-1,2-epoxy[1-²H₁]octan-3-ols ( 4a and 4b , resp.) which were converted in three steps into (S)- and (R)-fluoro[ ²H₁]acetic acid ( 7a and 7b , resp.) in good yields. Their high isotopic and optical purity was established by ¹H- and ¹⁹F-NMR, mass, and circular-dichroism spectroscopy.     

Use of a native affinity ligand for the detection of G proteins by capillary isoelectric focusing with laser-induced fluorescence detection

Affinity probe capillary isoelectric focusing (CIEF) with laser-induced fluorescence was explored for detection of Ras-like G proteins. In the assay, a fluorescent BODIPY FL GTP analogue (BGTPgammaS) and G protein were incubated resulting in formation of BGTPgammaS-G protein complex. Excess BGTPgammaS was separated from BGTPgammaS-G protein complex by CIEF using a 3-10 pH gradient and detected in whole-column imaging mode. In other cases, a single point detector was used to detect zones during the focusing step of CIEF using a 2.5-5 pH gradient. In this case, analyte peaks passed the detector in approximately 5 min at an electric field of 350 V/cm. Detection during focusing allowed for more reproducible assays at shorter times but with a sacrifice in sensitivity compared to detection during mobilization. Resolution was adequate to separate BGTPgammaS-Ras and BGTPgammaS-Rab3A complexes. Formation of specific complexes was confirmed by adding GTPgammaS to samples containing BGTPgammaS-G protein. GTPgammaS competed with BGTPgammaS for G protein binding sites resulting in decreased BGTPgammaS-G protein peak heights. The concentrating effect of CIEF enabled detection limits of 30 pM.     

Structural analysis of metal interactions with the dinucleotide duplex, dCG x dCG, using ion mobility mass spectrometry

The metal binding properties of the dinucleotide duplex, dCG x dCG, were analyzed in the gas phase with ion mobility mass spectrometry. Both MALDI and ESI were used to generate [M(dCG x dCG)]+ complexes. The collision cross section of each complex was measured in helium using ion mobility based methods and compared to calculated cross sections of theoretical structures. When metal cations classified as hard acids were combined with dCG x dCG, the [M(dCG x dCG)]+ complex organized into a globular structure. However, when soft acid metal cations were examined, a structure was observed where the two C-G base pairs were Watson-Crick bound.