Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Elastic properties of crosslinked poly(vinyl alcohol) gels: Network topology

Current network theory exhibits inconsistencies which show up particularly clearly in deformation of networks prepared by crosslinking a polymer in solution. A check of theory can be obtained if one knows precisely the number of crosslinks in the network and if a range of deformations is applied to the network. In an effort to explore this problem we have examined the relation of shear modulus to crosslink density, primary molecular weight, and polymer concentration for a series of poly(vinyl alcohol) gels at low to intermediate concentrations. Aqueous poly(vinyl alcohol) solutions were crosslinked to form infinite networks using terephthalaldehyde. We find a large discrepancy with these poly(vinyl alcohol) gels between measured shear modulus and that calculated from classical elasticity theory assuming quantitative reaction of crosslinking. The ratio of measured to calculated modulus is independent of crosslink density for a given primary molecular weight and concentration. It shows linear dependence on polymer concentration prior to crosslinking and extrapolates to a critical concentration which is consistent with the effective sizes of the polymer molecules.     

DMC: A multifunctional hybrid dynamics/Monte Carlo simulation algorithm for the evaluation of conformational space

A hybrid conformational search algorithm (DMC) is described that combines a modified form of molecular dynamics with Metropolis Monte Carlo sampling, using the COSMIC(90) force field. Trial configurations are generated by short bursts of high-temperature dynamics in which the initial kinetic energy is focused into single bond rotations or alternatively into “corner-flapping” motions in ring systems. Constant temperature and simulated annealing search protocols have been applied to the conformational analysis of several model hydrocarbons (cyclopentane, cyclohexane, cycloheptane, cyclooctane, cycloheptadecane, decane, and tetradecane), and the performance compared with conventional molecular dynamics and Monte Carlo sampling methods. Optimum Metropolis sampling temperatures have been determined and range from 1000–2000 K for acyclic molecules to 3000 K for cyclic systems. Simulated annealing runs are most successful at locating the global minimum when cooling slowing from these optimum temperatures.     

Rapid imaging, using a cooled charge-coupled-device, of fluorescent two-dimensional polyacrylamide gels produced by labelling proteins in the first-dimensional isoelectric focusing gel with the fluorophore 2-methoxy-2,4-diphenyl-3(2H)furanone

A new method for visualising proteins in two-dimensional polyacrylamide gels was developed. Proteins were labelled with the fluorophore 2-methoxy-2,4-diphenyl-3(2H)furanone (MDPF) while present in the first-dimensional gel after isoelectric focusing and subsequently electrophoresed into the second-dimensional gel. High resolution spot patterns were produced and compared with other methods of visualisation. A new rapid imaging system based on a cooled charge-coupled-device was used to view the two-dimensional fluorescent protein spot patterns. The method allows the immediate and rapid imaging of two-dimensional gels at the end of electrophoresis with no further processing.     

Mutagenesis approaches to deduce structure-function relationships in terpene synthases

This review highlights mutagenesis studies of terpene synthases, specifically sesquiterpene synthases and oxidosqualene cyclases. Mutagenesis studies of these enzymes have provided mechanistic insights, structure-function relationships for specific enzymatic residues, novel terpene structures and enzymes with novel activities. The literature through 2002 is reviewed and 113 references cited.     

Photoinduzierte Cycloadditionen von 3-Benzyl-2H-azirin

Irradiation of 2-azido-3-phenyl-propene ( 5 ) in pentane or benzene solution with a high pressure lamp (pyrex filter) yields 3-benzyl-2H-azirin ( 6 ), which on further irradiation behind quartz or vycor in the presence of trifluoroacetic acid methylester or carbon dioxide yields 4-benzyl-5-methoxy-5-trifluoromethyl-3-oxazolin ( 8 ) and 4-benzyl-3-oxazolin-5-one ( 9 ), respectively (scheme 2). A small amount of 3-phenylacetonitrile is also formed.     

Fragmentation of N-linked glycans with a matrix-assisted laser desorption/ionization ion trap time-of-flight mass spectrometer

N-Linked glycans were ionized from several matrices with a Shimadzu-Biotech AXIMA-QIT matrix-assisted laser desorption/ionization quadrupole ion trap time-of-flight mass spectrometer. [M+Na]+ ions were produced from all matrices and were accompanied by varying amounts of in-source fragmentation products. The least fragmentation was produced by 2,5-dihydroxybenzoic acid and the most by alpha-cyano-4-hydroxycinnamic acid and 6-aza-2-thiothymine. Sialic acid loss was extensive but could be prevented by formation of methyl esters. Fragmentation produced typical low-energy-type spectra dominated by ions formed by glycosidic cleavages. MS(n) spectra (n = 3 and 4) were used to probe the pathways leading to the major diagnostic ions. Thus, for example, an ion that was formed by loss of the core GlcNAc residues and the 3-antenna was confirmed as being formed by a B/Y rather than a C/Z mechanism. The proposed structures of several cross-ring cleavage ions were confirmed and it was shown that MS3 spectra could be obtained from as little as 10 fmol of glycan.     

Peptides—XXXVII: Synthesis of the 1–37 fragment of a lysozyme analogue

Combination of the protected peptide fragments 1–16, 17–26 and 27–37 to yield the 1–37 portion of a lysozyme analogue is described. The fragments were combined using DCCI with the addition of HONSu, and the products purified mainly by gel filtration.