Asymptotic symmetries in general relativity

In the context of a recent reformulation of the theory of gravitational radiation from bounded sources in which both shearing and shear-free radiation is manifestly present, we derive the asymptotic symmetry group of the spacetime. The group we obtain contains the Bondi-Metzner-Sachs group as a subgroup. This observation is relevant to the problem of the mysterious role of shear-free radiation in the Bondi-Sachs approach to the theory of gravitational radiation from bounded sources.     

The mathematical miscellany (1836–1839)

Charles Gill (1805–1855), who immigrated to the United States from England in 1830, began to edit The Mathematical Miscellany (1836–1839) while teaching on Long Island (New York, U.S.A.). Most of America's best mathematicians of the day were contributors, including Benjamin Peirce, Theodore Strong, and William Lenhart. The contents of the journal and the correspondence between Gill and its contributors, as well as the journal's troubles, give insights into American mathematics in the middle of the 19th century.     

The maximum reliability location problem and α-reliablep-center problem: Derivatives of the probabilistic location set covering problem

In the last several years, the modeling of emergency vehicle location has focussed on the temporal availability of the vehicles. Vehicles are not available for service when they are engaged in earlier calls. To incorporate this dynamic aspect into facility location decisions, models have been developed which provide additional levels of coverage. In this paper, two new models are derived from the probabilistic location set covering problem. These models allow the examination of the relationships between the number of facilities being located, the reliability that a vehicle will be available, and a coverage standard. In addition, these models incorporate sectoral specific estimates of the availability of the vehicles. Solution of these models reveals that the use of sectoral estimates leads to facility locations which are distributed to a greater spatial extent over the region to be serviced.     

Profiling isoflavonoids found in legume root extracts using capillary electrophoresis

Legumes such as alfalfa (Medicago sativa L.), barrel medic (Medicago truncatula), white sweet clover (Melilotus alba) and fenugreek (Trigonella graecum), normally accumulate (-)-medicarpin and its malonated glucose conjugate as natural inhibitors of fungal pathogens. These plants also accumulate the biosynthetic precursor formononetin as well as the malonated glycoside. We were interested in developing a robust high-throughput method to quantitate the levels of these two isoflavonoids, both free and conjugated, in legume root extracts, for use in screening for mutant plants accumulating altered levels of these compounds. Capillary electrophoresis was examined as an alternative to current high-performance liquid chromatography (HPLC) methods to generate isoflavonoid profiles. The developed assay used micellar electrokinetic capillary chromatography (MEKC) to provide the required selectivity in complex root extracts. The addition of 1,2-hexanediol to the sodium dodecyl sulfate (SDS) electrolyte provided improved resolution of adjacent isoflavonoids. We examined the role of several factors including sample preparation, buffer composition, buffer pH, and organic component in the injected sample. The use of capillaries with longer path lengths were also examined to increase sensitivity. A comparison of results obtained using MEKC and HPLC showed good correlation in the relative amounts of the isoflavonoids studied.     

Negative Electron Transfer Dissociation Sequencing of 3-<Emphasis Type="Italic">O</Emphasis>-Sulfation-Containing Heparan Sulfate Oligosaccharides

Among dissociation methods, negative electron transfer dissociation (NETD) has been proven the most useful for glycosaminoglycan (GAG) sequencing because it produces informative fragmentation, a low degree of sulfate losses, high sensitivity, and translatability to multiple instrument types. The challenge, however, is to distinguish positional sulfation. In particular, NETD has been reported to fail to differentiate 4-O- versus 6-O-sulfation in chondroitin sulfate decasaccharide. This raised the concern of whether NETD is able to differentiate the rare 3-O-sulfation from predominant 6-O-sulfation in heparan sulfate (HS) oligosaccharides. Here, we report that NETD generates highly informative spectra that differentiate sites of O-sulfation on glucosamine residues, enabling structural characterizations of synthetic HS isomers containing 3-O-sulfation. Further, lyase-resistant 3-O-sulfated tetrasaccharides from natural sources were successfully sequenced. Notably, for all of the oligosaccharides in this study, the successful sequencing is based on NETD tandem mass spectra of commonly observed deprotonated precursor ions without derivatization or metal cation adduction, simplifying the experimental workflow and data interpretation. These results demonstrate the potential of NETD as a sensitive analytical tool for detailed, high-throughput structural analysis of highly sulfated GAGs.

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Graphical Abstract

     

Ethylene polymerization catalysis over chromium oxide

A study of the nature of polymerization catalysis over CrO₃–silica and of the nature of the polyethylene obtained is presented. A fixed surface chromate (or possibly dichromate) species was shown to be activated for polymerization by an oxidation–reduction reaction with the monomer or with other reactive compounds such as CO. A change in catalyst color from orange to blue occurred simultaneously, and an indigoblue color was present only during ethylene addition, indicating involvement of Cr d orbitals. A spectacular chemiluminescence, due to excitation of oxygen, occurred when CO-treated catalyst was exposed to air. Active site population and the rate at which each site produced polymer molecules were calculated. A reaction mechanism compatible with the experimental data is depicted.     

Morpholino‐Functionalized and Heteroaryl‐Substituted Titanocene Anti‐Cancer Drugs: Synthesis and Cytotoxicity Studies

From the carbolithiation of 6‐morpholino fulvene ( 3a ) and different ortho‐lithiated heterocycles (furan, thiophene and N‐methylpyrrole), the corresponding lithium cyclopentadienide intermediate ( 4a – c ) was formed. These three lithiated intermediates underwent a transmetallation reaction with TiCl₄ resulting in morpholino‐functionalised titanocenes 5a – c . When these titanocenes were tested against LLC‐PK cells, the IC₅₀ values obtained were of 58, 63 and 115 μM for titanocenes 5a – c respectively. The most cytotoxic titanocene 5a with an IC₅₀ value of 58 μM is found to be approximately 20 times less cytotoxic than cis‐platin, which showed an IC₅₀ value of 3.3 μM, when tested on the LLC‐PK cell line, and 10 times less cytotoxic than its dimethylamino‐functionalised analogue (Titanocene C , IC₅₀ = 5.5 μM).     

Charge state dependent collision-induced dissociation of native and reduced porcine elastase

The [M + 20H](20+)-[M + 12H](12+) charge states of native and reduced porcine elastase, a 25.9 kDa serine protease, were subjected to collisional activation in a quadrupole ion trap. For most charge states, ion parking was used to increase the number of parent ions over that yielded directly by electrospray. Ion-ion proton transfer reactions were used to reduce product ion charge states largely to +1 to simplify spectral interpretation. Both forms of the protein show charge state dependent fragmentation behavior. The native protein, which contains four disulfide linkages, shows almost no evidence for fragmentation within the regions of the protein linked by disulfide bonds. However, at the lowest charge states studied, evidence for cleavage of a least one of the disulfide bonds was evident in the appearance of a c-type ion. The highest charge states of native elastase showed several prominent cleavages C-terminal to valine residues. As the charge state decreased, however, preferential cleavages at acidic amino acid residues became important. The reduced form of the protein did not show particularly prominent cleavages at valine residues. However, many of the same preferential cleavages at acidic amino acid residues noted for the native protein were also observed in the same charge states of the reduced protein. The reduced protein also showed additional cleavages from regions of the protein that are ordinarily protected by disulfide linkages in the native form.     

SO<Stack><Subscript>2</Subscript><Superscript>−·</Superscript></Stack> electron transfer ion/ion reactions with disulfide linked polypeptide ions

Multiply-charged peptide cations comprised of two polypeptide chains (designated A and B) bound via a disulfide linkage have been reacted with SO2-* in an electrodynamic ion trap mass spectrometer. These reactions proceed through both proton transfer (without dissociation) and electron transfer (with and without dissociation). Electron transfer reactions are shown to give rise to cleavage along the peptide backbone, loss of neutral molecules, and cleavage of the cystine bond. Disulfide bond cleavage is the preferred dissociation channel and both Chain A (or B)-S* and Chain A (or B)-SH fragment ions are observed, similar to those observed with electron capture dissociation (ECD) of disulfide-bound peptides. Electron transfer without dissociation produces [M + 2H]+* ions, which appear to be less kinetically stable than the proton transfer [M + H]+ product. When subjected to collision-induced dissociation (CID), the [M + 2H]+* ions fragment to give products that were also observed as dissociation products during the electron transfer reaction. However, not all dissociation channels noted in the electron transfer reaction were observed in the CID of the [M + 2H]+* ions. The charge state of the peptide has a significant effect on both the extent of electron transfer dissociation observed and the variety of dissociation products, with higher charge states giving more of each.