On shredders and vertex connectivity augmentation

We consider the following problem: given a k-(node) connected graph G find a smallest set F of new edges so that the graph G+F is (k+1)-connected. The complexity status of this problem is an open question. The problem admits a 2-approximation algorithm. Another algorithm due to Jordán computes an augmenting edge set with at most (k−1)/2 edges over the optimum. CV(G) is a k-separator (k-shredder) of G if |C|=k and the number b(C) of connected components of G−C is at least two (at least three). We will show that the problem is polynomially solvable for graphs that have a k-separator C with b(C)k+1. This leads to a new splitting-off theorem for node connectivity. We also prove that in a k-connected graph G on n nodes the number of k-shredders with at least p components (p3) is less than 2n/(2p−3), and that this bound is asymptotically tight.     

Structural and optical isomers of nonamethoxy cyclotriveratrylene: separation and physical characterization

The paper concerns the structural and optical isomers of nonamethoxy-tribenzocyclononene (compound 1). In the first part of the paper it is shown that 1 exists in two structural isomers: a rigid crown (c-1) with C3 symmetry and a flexible saddle (s-1) with C1 symmetry. The latter, not previously known, can be prepared from the as-synthesized c-1 by quenching a hot solution (or the melt) followed by HPLC separation. The crown/saddle equilibrium, isomerization kinetics, and associated thermodynamic parameters in various organic solvents are reported. Carbon-13 MAS NMR, X-ray diffraction, and differential scanning calorimetry (DSC) of polycrystalline c-1 and s-1 racemates are also reported. The different melting points of the isomers and their rapid isomerization in the melt result in unconventional DSC thermograms involving multiple endothermic and exothermic transitions. The second part of the paper concerns the chiral properties of 1. Both the saddle and crown isomers are structurally chiral, but due to the fast pseudorotation of s-1 in solution, it cannot be separated into its enantiomers. Those of c-1 were separated by HPLC using a chiral column. Their X-ray structure and melting points differ considerably from those of the racemate. This and their fast racemization in the melt lead to complex DSC thermograms with multiple transitions. Solutions of the neat enantiomers exhibit a relatively small specific optical rotation. In the UV they show circular dichroism for the B1u and B2u transitions, with the latter exhibiting a clear couplet structure. Infrared and vibrational circular dichroism spectra of the enantiomers in solution are reported. Comparison of these spectra with quantum mechanical simulations provides unambiguous identification of the enantiomers.     

Chiral discrimination in the 13C and 2H NMR of the crown and saddle isomers of nonamethoxy-cyclotriveratrylene in chiral liquid-crystalline solutions

We report 2H and 13C NMR spectra of the crown and saddle isomers of nonamethoxy-tribenzocyclononene (1), dissolved in lyotropic achiral and chiral liquid-crystalline solutions based on poly-gamma-benzyl-glutamate and poly-gamma-benzyl-L-glutamate (PBG and PBLG). The 2H-[1H] measurements include spectra of compound 1 deuterated in the ring methylene and in the aromatic sites as well as of the methyl groups in natural abundance. Carbon-13 spectra were recorded in natural abundance as well as in two isotopomers enriched in the ring methylene and one of the methoxy groups. The crown isomer (c-1) is rigid with C3 symmetry and can be separated into its enantiomers using a chiral high-performance liquid chromatography column. The NMR spectra of racemic c-1 in PBLG solutions exhibit two sets of lines due to the enantiomers. The peaks were identified by comparing the spectra with those of the neat enantiomers. Analysis of the 2H quadrupolar splittings and the 13C residual chemical shift anisotropies shows that the dominant factor determining the chiral discrimination is the difference in the ordering of the two enantiomers in the chiral liquid crystals. The saddle isomer (s-1) is highly flexible, undergoing fast pseudorotation between six conformers. The "frozen" conformers have C1 symmetry and are therefore chiral. Three of these comprise one enantiomer, and the other three the second one. However, the rapidly interconverting species has, on the average, a C3h symmetry and is therefore achiral. The methylene groups in the latter are, however, prostereogenic, and their hydrogen/deuterium-carbon bonds constitute enantiotopic pairs. The 2H NMR spectra of the s-1 methylene-deuterated in PBLG solutions exhibit, in fact, enantio-discrimination with two quadrupolar doublets. This is in contrast to rigid prochiral molecules with a threefold symmetry axis, which normally do not show such discrimination. A detailed analysis of the effect is presented, and it is argued that the discrimination observed for s-1 reflects the different ordering of its enantiomers during the pseudorotation cycle.     

Gold nanoparticle-quantum dot-polystyrene microspheres as fluorescence resonance energy transfer probes for bioassays

The paper describes the development of highly sensitive particle-based fluorescence resonance energy transfer (FRET) probes that do not use molecular fluorophores as donors and acceptors. In these probes, CdSe/ZnS luminescent quantum dots (QDs) were capped with multiple histidine-containing peptides to increase their aqueous solubility while maintaining their high emission quantum yield and spectral properties. The peptide-modified QDs (QD-His) were covalently attached to carboxyl-modified polystyrene (PS) microspheres to form highly emitting PS microspheres (QD-PS). Gold nanoparticles (AuNPs) were then covalently attached to the QD-PS surface to form AuNP-QD-PS composite microspheres that were used as FRET probes. Attachment of AuNPs to QD-PS completely quenched the QD emission through FRET interactions. The emission of QD-PS was restored when the AuNPs were removed from the surface by thiol ligand displacement. The new AuNP-QD-PS FRET platform is simple to prepare and highly stable, and it opens many new possibilities for carrying out FRET assays on microparticle-based platforms and in microarrays. The versatility of these assays could be greatly increased by replacing the linkers between the QDs and AuNPs with ones that selectively respond to specific cleaving agents or enzymes.     

Quality assurance for molecular epidemiology of tuberculosis methods in the mycobacterium reference laboratory

In the National Mycobacterium Reference Laboratory of the Israeli National Public Health Laboratory (hereafter referred to as “the laboratory”), three methods are employed for the molecular epidemiology of Mycobacterium tuberculosis: IS6110 restriction fragment length polymorphism typing (RFLP typing), 43 spacer oligonucleotide typing (spoligotyping), and 24 loci Mycobacterial Interspersed Repeating Unit—Variable Number of Tandem Repeats typing (MIRU-VNTR typing). In this article, we describe the main practical aspects concerning quality assurance of these methods that are based on standardized, internationally agreed upon conditions, including consensus reference strains and markers. All three methods were validated by classical epidemiology (confirmed transmission) and clinical information. The laboratory has introduced a new 5 colors, 4 primer sets multiplex modification of the optimal 24-miru typing system that includes an easily produced in-house internal standard for the high-throughput capillary electrophoresis system. Quantitative measurement of the internal standards yielded statistics for measurement uncertainty that include the frequency distribution, mean, standard deviation, 95% confidence interval and coefficient of variation. Use of the new internal standard developed in our laboratory allowed us to introduce the first quantitative evaluation of the system performance of the AB3130xl capillary electrophoresis genetic analyzer for MIRU-VNTR typing. The results are discussed in terms of expected accuracy and precision of MIRU-VNTR results, and possible implications for forensic microsatellite typing which may be much more sensitive to the observed intra- and inter-plate variation.     

Kinetic bromine isotope effect: example from the microbial debromination of brominated phenols

The increasing use of kinetic isotope effects for environmental studies has motivated the development of new compound-specific isotope analysis techniques for emerging pollutants. Recently, high-precision bromine isotope analysis in individual brominated organic compounds was proposed, by the coupling of gas chromatography to a multi-collector inductively coupled plasma mass spectrometer using strontium as an external spike for instrumental bias correction. The present study, for the first time, demonstrates an application of this technique for determining bromine kinetic isotope effects during biological reaction, focusing on the reductive debromination of brominated phenols under anaerobic conditions. Results show bromine isotope enrichment factors (ε) of ?0.76?±?0.08, ?0.46?±?0.19, and ?0.20?±?0.06?‰ for the debromination of 4-bromophenol, 2,4-dibromophenol, and 2,4,6-tribromophenol, respectively. These values are rather low, yet still high enough to be obtained with satisfying certainty. This further implies that the analytical method may be also appropriate for future environmental applications.     

Coulomb Explosion Imaged Cryptochiral (R,R)‐2,3‐Dideuterooxirane: Unambiguous Access to the Absolute Configuration of (+)‐Glyceraldehyde

The absolute configuration of (R,R)‐2,3‐dideuterooxirane, which has been independently determined using Coulomb explosion imaging, has been unambiguously chemically correlated with the stereochemical key reference (+)‐glyceraldehyde. This puts the absolute configuration of D (+)‐glyceraldehyde on firm experimental grounds.