Forest covers and a polyhedral intersection theorem

Aforest cover of a graph is a spanning forest for which each component has at least two nodes. We consider the convex hull of incidence vectors of forest covers in a graph and show that this polyhedron is the intersection of the forest polytope and the cover polytope. This polytope has both the spanning tree and perfect matching polytopes as faces. Further, the forest cover polytope remains integral with the addition of the constraint requiring that, for some integerk, exactlyk edges be used in the solution.Research done while thae authors were visiting the Institut für Ökonometrie und Operations Research, Universität Bonn, West Germany.Financial support provided by the Natural Sciences and Engineering Research Council, Canada and the German Research Association (Deutsche Forschungsgemeneinschaft, SFB 303).     

Interaction of atrazine with Laurentian humic acid

Ultrafiltration fractionation and liquid chromatography have been applied to study the binding and hydrolysis of polar herbicide atrazine on a stoichiometrically well characterized Laurentian humic acid. The main advantage of this method over gas chromatography is the simultaneous determination of both free and bound atrazine, hydroxyatrazine and copper(II) ion with satisfactory accuracy and precision. Atrazine binding requires extensive carboxylate site protonation but the binding sites represent only a very small fraction of total carboxylate of humic acid. The results show that binding of atrazine is not competitive with binding of the hydrolysis product hydroxyatrazine, the binding capacity is reduced at higher ionic strength or by cation competition for carboxylate and the atrazine binding constant and free energy of binding can be fitted by a single value at all pH values. The differences between atrazine binding by fulvic acid and humic acid can be ascribed to the structure difference, one being a flexible linear polymer and the other a three-dimensional colloidal gel particle.     

An investigation of the chemical stability of arsenosugars in simulated gastric juice and acidic environments using IC-ICP-MS and IC-ESI-MS/MS

A more quantitative extraction of arsenic-containing compounds from seafood matrices is essential in developing better dietary exposure estimates. More quantitative extraction often implies a more chemically aggressive set of extraction conditions. However, these conditions may result in undesirable chemical changes in the native arsenicals which may further complicate the toxicological risk assessment. This balance between quantitative extraction and species-specific integrity may be best addressed by using simulated gastric juice as an extraction solvent to mimic 'bioavailability'. This, conceptually, should extract the bioavailable fraction and induce any chemical changes that would occur because of ingestion. The most chemically labile species associated with seafood are thought to be the arsenosugars and for this reason their chemical stability is investigated in this study. Four arsenosugars (3-[5'-deoxy-5'-(dimethylarsinoyl)-beta-ribofuranosyloxy]-2-hydroxypropylene glycol, As(328); 3-[5'-deoxy-5'-(dimethylarsinoyl)-beta-ribofuranosyloxy]-2-hydroxypropanesulfonic acid, As(392); 3-[5'-deoxy-5'-(dimethylarsinoyl)-beta-ribofuranosyloxyl-2-hydroxypropyl hydrogen sulfate, As(408); and 3-[5'-deoxy-5'-(dimethylarsinoyl)-beta-ribofuranosyloxy]-2-hydroxypropyl-2,3-hydroxypropyl phosphate, As(482)) were isolated from seaweed extracts and subjected to simulated gastric juice and acidic conditions which mimic the stomach's pH of 1.1. Three acid solutions were used to test the chemical stability of the arsenosugars: simulated gastric juice, 78 mM nitric acid and 78 mM hydrochloric acid. The composition of the solutions was monitored over time (up to 48 h) using IC-ICP-MS for detection. The arsenosugars were found to degrade at the rate of 1.4% per h at 38 degrees C and 12.2% per h at 60 degrees C. The plots of percent conversion versus time were found to be independent of the starting arsenosugar and all had r2 values of greater than 0.97. A single common degradation product was observed in all the stability studies. A mass balance between the starting arsenosugar (As(392), As(408) and As(482)) and the degradation product was conducted with each set of experiments. This mass balance indicated that the degradation process did not produce any unchromatographable species. This degradation product was tentatively identified as As(254) as determined by ESI-MS/MS spectral data. An acid hydrolysis mechanism was proposed for the formation of As(254) from each of the native arsenosugars by hydrolysis at the C-1 carbon on the ribose ring.     

Adsorption of genetically engineered proteins studied by time‐of‐flight secondary ion mass spectrometry (TOF‐SIMS). Part A: data acquisition and principal component analysis (PCA)

Recent progress in the adaptation of combinatorial biology selection protocols to materials science has created a new class of polypeptides with specific affinity to inorganics. Here, we use one of the genetically engineered proteins, a gold binding protein (GBP‐1), to assess quantitatively its binding specificity to Au, Ag and Pd surfaces by using time‐of‐flight secondary ion mass spectroscopy (TOF‐SIMS). The GBP‐1, originally selected using cell‐surface display techniques, consisting of 14 amino acids with a sequence of MHGKTQATSGTIQS, was used in this study. Three‐repeat and single‐repeat forms of GBP‐1 were prepared. In earlier studies, GBP‐1 was shown to bind to Au particles and self‐assemble on flat Au surfaces. Through the fingerprint analysis of these specific peptides, their role in binding can be investigated in terms of their contribution to surface interaction possibly forming the right molecular architecture for binding. To achieve this purpose, a large‐sized data matrix produced by TOF‐SIMS must be properly treated for analysis. In Part A, we use principal component analysis (PCA) to visualize the spectral variations for a variety of adsorption conditions and suggest possible contribution of the specific types of amino acids (binding site) to the interactions. Copyright © 2007 John Wiley & Sons, Ltd.     

Classification of partitions of all triples on ten points into copies of Fano and affine planes

We continue our study of partitions of the full set of triples chosen from a v-set into copies of the Fano plane PG(2,2) (Fano partitions) or copies of the affine plane AG(2,3) (affine partitions) or into copies of both of these planes (mixed partitions). The smallest cases for which such partitions can occur are v=8 where Fano partitions exist, v=9 where affine partitions exist, and v=10 where both affine and mixed partitions exist. The Fano partitions for v=8 and the affine partitions for v=9 and 10 have been fully classified, into 11, two and 77 isomorphism classes, respectively. Here we classify (1) the sets of i pairwise disjoint affine planes for i=1,…,7, and (2) the mixed partitions for v=10 into their 22 isomorphism classes. We consider the ways in which these partitions relate to the large sets of AG(2,3).     

Accurate mass measurement using Fourier transform ion cyclotron resonance mass spectrometry for structure elucidation of designer drug analogs of tadalafil, vardenafil and sildenafil in herbal and pharmaceutical matrices

Phosphodiesterase type 5 (PDE-5) inhibitors are a class of drugs used primarily in the treatment of erectile dysfunction. The Food and Drug Administration (FDA) approved PDE-5 inhibitors include sildenafil citrate, vardenafil hydrochloride and tadalafil. In this study, accurate mass measurements were made by electrospray ionization (ESI) using Fourier transform ion cyclotron resonance mass spectrometry (FTICRMS) to elucidate the structures of sildenafil, tadalafil and vardenafil analogs that were found in products marketed as dietary supplements. Initial detection of these analogs was accomplished through routine screening of suspect samples by liquid chromatography/electrospray ionization multi-stage mass spectrometry (LC/ESI-MS(n)) on a low-resolution ion trap instrument. The chromatographic behavior and mass spectrometric fragmentation patterns observed were often similar to those observed for FDA approved PDE-5 inhibitors. The mass accuracy and resolving power associated with FTICRMS allows for the determination of elemental compositions. Elucidation of the product ion structures for the analogs was accomplished through the use of accurate mass measurements with the aid of Mass Frontier software (version 4.0). Using FTICRMS, accurate masses with measurement errors averaging <0.4 ppm were achieved, allowing assignment of one possible elemental formula to each fragment ion. The mass measurement errors associated with [M + H](+) for the analogs aminotadalafil, piperidino vardenafil, hydroxyacetildenafil and piperidino acetildenafil were 0.1, 0.0, 0.1 and 0.5 ppm, respectively. Based on the accuracy of the measurements, structural assignments could be made with a high degree of confidence.     

Microcontact printed antibodies on gold surfaces: function, uniformity, and silicone contamination

The function of microcontact printed protein was investigated using surface plasmon resonance (SPR) imaging, X-ray photoelectron spectroscopy spectroscopy (XPS), and XPS imaging. We chose to analyze a model protein system, the binding of an antibody from solution to a microcontact printed protein antigen immobilized to a gold surface. SPR imaging experiments indicated that the microcontact printed protein antigen was less homogeneous, had increased nonspecific binding, and bound less antibody than substrates to which the protein antigen had been physically adsorbed. SPR images of substrates contacted with a poly(dimethylsiloxane) stamp inked with buffer alone (i.e., no protein) revealed that significant amounts of silicone oligomer were transferred to the surface. The transfer of the silicone oligomer was not homogeneous, and the oligomer nonspecifically bound protein (BSA and IgG) from solution. XPS spectroscopy and imaging were used to quantify the amount of silicon (due to the presence of silicone oligomer), as well as the amounts of other elements, transferred to the surface. The results suggest that the silicone oligomer introduced by the printing process reduces the overall binding capacity of the microcontact-printed protein compared to physically adsorbed protein.     

Development and characterization of a high-throughput system for assessing cell-surface receptor-ligand engagement

A nonfouling interfacial interpenetrating polymer network (IPN) of poly(acrylamide-co-ethylene glycol/acrylic acid) [p(AAm-co-EG/AAc)] was grafted to polystyrene for use as a novel platform for the development of high-throughput assays for screening of specific bimolecular interactions (i.e., receptor-ligand engagement). For the development of the IPN, a water-soluble hydrogen-abstracting photoinitiator was investigated: (4-benzoylbenzyl)trimethylammonium chloride. IPN-modified polystyrene surfaces were characterized using XPS, contact angle goniometry, and protein adsorption analysis. These IPN surfaces minimized fibrinogen adsorption compared to tissue culture polystyrene (>96% reduction), prevented mammalian cell adhesion, and served as nonfouling surfaces to graft biological ligands. For bimolecular interaction studies, a model peptide ligand from bone sialoprotein (Ac-CGGNGEPRGDTYRAY-NH(2)) was grafted to p(AAm-co-EG/AAc) via a 3400 M(w) linear pEG spacer. Ligand density measurements, cell culture, and a centrifugal adhesion assay were used to study cell adhesion to peptide-modified IPNs (i.e., receptor-ligand engagement). Ligand density (Gamma) was controllable from approximately 1 to 20 pmol/cm(2) by modulating the peptide input concentration (0.02-20 microM). Cell adhesion was directly dependent on the ligand density. This technology creates a powerful high-throughput system to simultaneously probe a myriad of cell-surface receptor-ligand interactions.