An Eulerian exposition

An overview of Eulerian graphs is presented. In particular, characterizations of Eulerian graphs and digraphs as well as algorithms for constructing Eulerian circuits are discussed. A solution to the Chinese postman problem is followed by a study of subgraphs and supergraphs of Eulerian graphs. After an introduction to randomly Eulerian graphs and digraphs, we conclude with a summary of a variety of results involving enumeration.     

Reaction pathways to dimer in polystyrene pyrolysis: A mechanistic modeling study

A detailed mechanistic model for polystyrene pyrolysis was created that built on a modeling framework developed in our previous work and was used to probe three competing pathways to dimer formation: benzyl radical addition, 1,3-hydrogen shift, and 7,3-hydrogen shift, based on recent literature reports. To incorporate the chemistry involved in the 7,3-hydrogen shift pathway, the 1,7- and 7,3-hydrogen shift reaction families were added to the model. The updated version of the model tracks 75 species and over 3500 reactions. Rate parameters for all families were specified based on our previous work, more recent literature reports, and regression against limited experimental data. The model was able to accurately predict the experimental results for polystyrene pyrolysis for different reactor configurations for a temperature range of 100 °C and two orders of magnitude of initial molecular weight for experimental data collected in our own lab and from Bouster and coworkers and Bockhorn and coworkers. The results from our model were studied using net rate analysis to gain insight into the competitiveness of the various reaction pathways to dimer formation. The net rate analysis demonstrated that 7,3-hydrogen shift is the dominant reaction pathway to dimer formation at the temperatures studied. Benzyl radical addition becomes a more competitive reaction pathway as the temperature increases, which is caused predominantly by an increase in the benzyl radical concentration with increasing temperature. Overall, it is quantitatively shown that both 7,3-hydrogen shift and benzyl radical addition are important pathways for dimer formation, with their relative competitiveness influenced by temperature.     

Surface-induced dissociation and chemical reactions of C2D 4 + on stainless steel, carbon (HOPG), and two different diamond surfaces

Surface-induced interactions of the projectile ion C₂D₄⁺ with room-temperature (hydrocarbon covered) stainless steel, carbon highly oriented pyrolytic graphite (HOPG), and two different types of diamond surfaces (O-terminated and H-terminated) were investigated over the range of incident energies from a few eV up to 50 eV. The relative abundance of the product ions in dependence on the incident energy of the projectile ion [collision-energy resolved mass spectra, (CERMS) curves] was determined. The product ion mass spectra contained ions resulting from direct dissociation of the projectile ions, from chemical reactions with the hydrocarbons on the surface, and (to a small extent) from sputtering of the surface material. Sputtering of the surface layer by low-energy Ar⁺ ions (5–400 eV) indicated the presence of hydrocarbons on all studied surfaces. The CERMS curves of the product ions were analyzed to obtain both CERMS curves for the products of direct surface-induced dissociation of the projectile ion and CERMS curves of products of surface reactions. From the former, the fraction of energy converted in the surface collision into the internal excitation of the projectile ion was estimated as 10% of the incident energy. The internal energy of the surface-excited projectile ions was very similar for all studied surfaces. The H-terminated room-temperature diamond surface differed from the other surfaces only in the fraction of product ions formed in H-atom transfer surface reactions (45% of all product ions formed versus 70% on the other surfaces).     

Monte Carlo Model of Stricture Formation in Photodynamic Therapy of Normal Pig Esophagus

Photodynamic therapy (PDT) is FDA-approved for use in patients with Barrett's esophagus using porfimer sodium (2 mg per kg) and a recommended light dose of 130 J cm⁻¹ for high grade dysplasia. Despite uniform drug and light doses, the clinical outcome of PDT is variable. A significant number of PDT cases result in esophageal strictures, a side effect related to excessive energy absorption. The purpose of this project was to model esophageal stricture formation with a Monte Carlo simulation. An original multilayer Monte Carlo computer simulation was developed for esophageal PDT. Optical absorption and scattering coefficients were derived for mucosal and muscle layers of normal porcine esophagus. Porfimer sodium was added to each layer by increasing the absorption coefficient by the appropriate amount. A threshold-absorbed light dose was assumed to be required for stricture formation and ablation. The simulation predicted irreversible damage to the mucosa with a 160 J cm⁻¹ light dose and damage to the muscle layer with an additional 160 J cm⁻¹ light dose for a tissue porfimer sodium content of 3.5 mg kg⁻¹. The simulation accurately modeled photodynamic stricture formation in normal pig in vivo esophageal tissue. This preliminary work suggests that the absorbed light threshold for stricture formation may be between 2 and 4 J per gram of tissue.     

Thermoresponsive behavior of charged <Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide-based hydrogels containing gold nanostructures

We report the synthesis of N-isopropylacrylamide-based hydrogels containing either an anionic (acrylic acid) or cationic ([2-(acryloyloxy)ethyl]trimethylammonium chloride) co-monomer. These hydrogels were cross-linked with a cleaveable (N,N′-cystaminebisacrylamide) and/or inert (N,N′-methylenebisacrylamide) molecule in four combinations. Gold nanostructures were then synthesized within these hydrogel matrices by in situ reduction of a metal ion precursor. The resulting eight nanocomposites and their non-gold-containing (native) analogs were characterized with several analytical methods. UV–visible and infrared spectroscopy revealed differences among the samples based largely on the concentration and identity of cross-linking agent. Equilibrium swelling masses and phase transition behavior point to differences among samples on charge of the hydrogel backbone, cross-linker type, and presence or absence of gold nanostructures. A molecular level explanation for these observations is described.     

Two isomers of 2,4‐di­benzyl‐8‐azabicyclo­[3.2.1]­octan‐3‐ol

The crystal structures of the title compounds, 2α,4α‐di­benzyl‐3α‐tropanol (2α,4α‐di­benzyl‐8‐methyl‐8‐aza­bi­cyclo­[3.2.1]­octan‐3α‐ol), C₂₂H₂₇NO, (I), and 2α,4α‐di­benzyl‐3β‐tropanol (2α,4α‐di­benzyl‐8‐methyl‐8‐aza­bi­cyclo­[3.2.1]­octan‐3β‐ol), C₂₂H₂₇NO, (II), show that both compounds have a piperidine ring in a chair conformation and a pyrrolidine ring in an envelope conformation. Isomer (I) is asymmetric, the benzyl groups having different orientations, whereas isomer (II) is mirror symmetric, and the N and O atoms, the C atom attached to the hydroxy group, and the methyl C atom attached to the N atom lie on the mirror plane. In the crystal structures of both (I) and (II), the mol­ecules are linked together by intermolecular O—H⋯N hydrogen bonds to form chains that run parallel to the a direction in (I) and parallel to b in (II).     

Reactions in Nitroimidazole Triggered by Low‐Energy (0–2 eV) Electrons: Methylation at N1‐H Completely Blocks Reactivity

Low‐energy electrons (LEEs) at energies of less than 2 eV effectively decompose 4‐nitroimidazole (4NI) by dissociative electron attachment (DEA). The reactions include simple bond cleavages but also complex reactions involving multiple bond cleavages and formation of new molecules. Both simple and complex reactions are associated with pronounced sharp features in the anionic yields, which are interpreted as vibrational Feshbach resonances acting as effective doorways for DEA. The remarkably rich chemistry of 4NI is completely blocked in 1‐methyl‐4‐nitroimidazole (Me4NI), that is, upon methylation of 4NI at the N1 site. These remarkable results have also implications for the development of nitroimidazole based radiosensitizers in tumor radiation therapy.     

Specific ion effects on the electrophoretic mobility of small,highly charged peptides: A modeling study

In this work, we use coarse‐grained modeling to study the free solution electrophoretic mobility of small highly charged peptides (lysine, arginine, and short oligos thereof (up to nonapeptides)) in NaCl and Na₂SO₄ aqueous solutions at neutral pH and room temperature. The experimental data are taken from the literature. A bead modeling methodology that treats the electrostatics at the level of the nonlinear Poisson Boltzmann equation developed previously in our laboratory is able to account for the mobility of all peptides in NaCl, but not Na₂SO₄. The peptide mobilities in Na₂SO₄ can be accounted for by including sulfate binding in the model and this is proposed as one possible explanation for the discrepancy. Oligo arginine peptides bind more sulfate than oligo lysines and sulfate binding increases with the oligo length.     

Tailoring Chimeric Ligands for Studying and Biasing ErbB Receptor Family Interactions

Described is the development and application of a versatile semisynthetic strategy, based on a combination of sortase‐mediated coupling and tetrazine ligation chemistry, which can be exploited for the efficient incorporation of tunable functionality into chimeric recombinant proteins. To demonstrate the scope of the method, the assembly of a set of bivalent ligands, which integrate members of the epidermal growth factor (EGF) ligand family, is described. By using a series of bivalent EGFs with variable intraligand spacing, the differences in structure were correlated with the ability to bias signaling in the ErbB receptor family in a cell motility assay. Biasing away from EGFR‐HER2 dimerization with a bivalent EGF was observed to reduce cell motility in an intraligand distance‐dependent fashion, thus demonstrating the utility of the approach for acutely perturbing receptor‐mediated cell signaling pathways.