The primal-dual method for approximation algorithms

In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to NP-hard problems in combinatorial optimization. Because of parallels with the primal-dual method commonly used in combinatorial optimization, we call it the primal-dual method for approximation algorithms. We show how this technique can be used to derive approximation algorithms for a number of different problems, including network design problems, feedback vertex set problems, and facility location problems. Received: June 19, 2000 / Accepted: February 7, 2001?Published online October 2, 2001     

Taveuniamides: new chlorinated toxins from a mixed assemblage of marine cyanobacteria

Brine shrimp toxicity guided fractionation of the extracts from two mixed Fijian collections of the cyanobacteria Lyngbya majuscula and Schizothrix sp. led to the isolation of eleven novel chlorinated lipids. All of these metabolites show an intriguing constellation of unsaturation (olefinic and acetylenic bonds) and chlorination at the two termini of a 15-carbon chain. The central carbon atom of the chain (C-8) is substituted in each case with an N-acetate function. Taveuniamides A-E have an adjacent carbomethoxy group at C-9 to form a protected β-amino acid while taveuniamides F-K have a methylene group at this position. A standard assortment of 2D NMR techniques in concert with mass spectrometry and other analytical techniques were used to define the structures of these novel metabolites. Taveuniamides F, G and K were the most potent brine shrimp toxins with LD₅₀s between 1.7-1.9 μg/mL.     

Multiple binding modes of the camptothecin family to DNA oligomers

The binding constants of camptothecin, topotecan and its lactone ring-opened carboxylate derivative to DNA octamers were measured by UV and NMR spectroscopy. The self-association of topotecan (TPT) was also measured. The carboxylate form of TPT binds in the same way as the lactone, but more weakly. Titration of TPT into d(GCGATCGC)2 shows a preferred location stacked onto the terminal G1 base. However, the intermolecular NOEs cannot be reconciled with a single conformation of the complex, and suggest a model of a limited number of conformations in fast exchange. MD calculations on four pairs of starting structures with TPT stacked onto the G1-C8 base pair in different orientations were therefore performed. The use of selected experimental "docking" restraints yielded ten MD trajectories covering a wide conformational space. From a combination of calculated free energies, NOEs and chemical shifts, some of the structures produced could be eliminated, and it is concluded that the data are consistent with two major families of conformations in fast exchange. One of these is the conformation found in a crystal of a TPT/DNA/topoisomerase I ternary complex [Proc. Natl. Acad. Sci. USA 2002, 99, 15 387-15 392].     

Continuous flow hydroformylation of alkenes in supercritical fluid-ionic liquid biphasic systems

A process for the hydroformylation of relatively low volatility alkenes (demonstrated for 1-dodecene) in a continuous flow system is described. The catalyst is dissolved in an ionic liquid while the substrate and gaseous reagents are transported into the reactor dissolved in supercritical CO(2), which simultaneously acts as a transport vector for aldehyde products. Decompression of the fluid mixture downstream yields products which are free of both reaction solvent and catalyst. The use of rhodium complexes of triaryl phosphites leads to ligand degradation through reaction of the ionic liquid with water and subsequent attack of the released HF on the phosphite. Sodium salts of sulfonated phosphines are insufficiently soluble in the ionic liquids to obtain acceptable rates, but replacing the sodium by a cation similar to that derived from the ionic liquid, allows good solubility and activity to be obtained. The nature of the ionic liquid is very important in achieving high rates, with 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amides giving the best activity if the alkyl chain is at least C(8). Catalyst turnover frequencies as high as 500 h(-1) have been observed, with the better rates at higher substrate flow rates. Rhodium leaching into the product stream can be as low as 0.012 ppm, except at low partial pressures of CO/H(2), when it is significantly higher. Oxygen impurities in the CO(2) feed can lead to oxidation of the phosphine giving higher rates, lower selectivities to the linear aldehyde, increased alkene isomerization and greater leaching of rhodium. However, it is found that under certain process conditions, the supercritical fluid-ionic liquid (SCF-IL) system can be operated continuously for several weeks without any visible sign of catalyst degradation. Comparisons with commercial hydroformylation processes are provided.     

The annealing behavior of implanted nitrogen in fcc stainless steel

Post-implantation annealing of N-implanted 304 stainless steel at 400 °C has been investigated by conversion electron Mössbauer spectroscopy, X-ray diffraction and Auger electron spectroscopy. After a 1 h anneal, the near complete dissolution of the as-implanted Fe₂N-like nitride phase results in a 9 at.% N fcc solid-solution phase. After the final anneal (64 h), N has diffused to a depth of about 2 m and remains in solid solution with an average content of 4 at.%. An average N diffusion coefficient at 400 °C is estimated to be 10^-12-10^-14 cm²/s, depending on anneal time, too small to explain the deep penetration observed in high-flux, high-dose N-implanted stainless steel. The present results provide additional evidence for beam controlled N migration where Cr plays an important role.     

Determination of internuclear distances in uniformly labeled molecules by rotational-resonance solid-state NMR

Rotational-resonance magic-angle spinning NMR experiments are frequently used to measure dipolar couplings and to determine internuclear distances. So far most measurements were performed on samples containing isolated spin pairs. Thus, extensive structure elucidation, for example in biomolecules, requires the preparation of a whole set of doubly labeled samples. Here, we describe the analysis of the rotational-resonance polarization-exchange curves obtained from a single, uniformly labeled sample. It is shown experimentally that, at a magnetic field of 14.09 T, the rotational-resonance conditions in uniformly (13)C-labeled threonine are sufficiently narrow to permit the measurement of five distances between the four carbon spins with an accuracy of better than 10%. The polarization-exchange curves are analyzed using a modified two-spin model consisting of the two active spins. The modified model includes an additional offset in the final polarization, which comes from the coupling to the additional, passive, spins. The validity of this approach is experimentally verified for uniformly (13)C-labeled threonine. The broader applicability of such a model is demonstrated by numerical simulations which quantify the errors as a function of the most relevant parameters in the spin system.     

Laser-initiated polymerization of charge-transfer monomer systems

The laser-initiated polymerization of charge-transfer monomer complexes was investigated with a pulsed nitrogen laser and an argon laser. Several donor-acceptor monomer charge-transfer systems were screened for polymerization in different solvents. Polymerization by laser initiation was achieved in two of these systems; that is, 2-vinylnaphthalene/fumaronitrile and 9-vinylanthracene/fumaronitrile. The best polymer yields were obtained with the 2-vinylnaphthalene/fumaronitrile system in sulfolane solvent. The influences on the polymer yield and composition of solvents, varying focal path length, glass conditioning, initiation sources, environment, and monomer feed ratios were evaluated. Infrared (IR) spectral studies, gel permeation chromatography (GPC), and chemical analyses were performed to characterize the polymer products arising from the polymerization of 2-vinylnaphthalene/fumaronitrile in sulfolane. The polymer contained a high percentage of sulfolane (ca. 1/3 mol fraction), presumably arising from solvent transfer to the growing polymer chains during the propagation phase of the polymerization.     

PHOTOCHEMISTRY OF TYPE I ACID-SOLUBLE CALF SKIN COLLAGEN: DEPENDENCE ON EXCITATION WAVELENGTH

Although previous studies have demonstrated that the predominant photochemistry of type I collagen under 254 nm irradiation may be attributed either to direct absorption by tyrosine/phenylalanine or to peptide bonds, direct collagen photochemistry via solar UV wavelengths is much more likely to involve several age- and tissue-related photolabile collagen fluorophores that absorb in the latter region. In this study, we compare and contrast results obtained from irradiation of a commercial preparation of acid-soluble calf skin type I collagen in solution with UVC (primarily 254 nm), UVA (335–400nm) and broad-band solar-simulating radiation (SSR; 290^1–00nm). Excitation spectroscopy and analysis of photochemically induced disappearance of fluorescence (fluorescence fading) indicates that this preparation has at least four photolabile fluorescent chromophores. In addition to tyrosine and L-3,4-dihydroxyphenylalanine, our sample contains two other fluorophores. Chromophore I, with emission maximum at 360 nm, appears to be derived from interacting aromatic moieties in close mutual proximity. Chromophore II, with broad emission at430–435 nm, may be composed of one or more age-related molecules. Collagen fluorescence fading kinetics are sensitive to excitation wavelength and to conformation. Under UVC, chromophore I fluorescence disappears with second-order kinetics, indicating a reaction between two proximal like molecules. Adherence to second-order kinetics is abrogated by prior denaturation of the collagen sample. A new broad, weak fluorescence band at400–420 nm, attributable to dityrosine, forms under UVC, but not under solar radiation. This band is photolabile to UVA and UVB wavelengths. Amino acid analysis indicates significant destruction of aromatic amino acids under UVC, but not under UVA or SSR. When properly understood, collagen fluorescence fading phenomena may act as a sensitive molecular probe of structure, conformation and reactivity.     

Does alpha-fluorination affect the structural trans-influence and kinetic trans-effect of an alkyl ligand? Molecular structures of Pd(TMEDA)(CH(3))(R(F)) and a kinetic study of the trans to cis isomerization of Pt(TMEDA)(CH(3))(2)I(R(F)) [R(F) = CF(2)CF(3), CFHCF(3), CH(2)CF(3)

Reaction of Pd(TMEDA)(CH(3))(2) [TMEDA = tetramethylethylenediamine] with fluoroalkyl iodides R(F)I affords a series of square planar Pd(II) complexes Pd(TMEDA)(CH(3))(R(F)) [R(F) = CF(2)CF(3) (9), CFHCF(3) (10), CH(2)CF(3) (11)], presumably by oxidative addition followed by reductive elimination of CH(3)I. The solid-state structures of each compound have been determined by single crystal X-ray diffraction studies, allowing the effect of increasing alpha-fluorination on the structural trans-influence of alkyl ligands to be examined. In these compounds there is no significant difference observed in the trans-influence of the three fluorinated alkyl ligands toward the trans-N atom, although a significant cis-influence on the neighboring methyl ligand is apparent. Oxidative addition of the same series of fluoroalkyl ligands to the corresponding Pt(TMEDA)(CH(3))(2) affords octahedral Pt(IV) complexes trans-Pt(TMEDA)(CH(3))(2)(R(F))I [R(F) = CF(2)CF(3) (12), CFHCF(3) (13), CH(2)CF(3) (14)] as the kinetic products. In each case, subsequent isomerization to the corresponding all cis-isomers is observed; in the case of 13, the stereocenter at the alpha-carbon results in two diastereomeric cis-isomers, which are formed at different rates. The molecular structures of 13 and its more stable all cis-isomer 16b have been crystallographically determined. Kinetic studies of the trans-cis isomerization reactions show the mechanism to involve a polar transition state, presumably involving iodide dissociation, followed by rearrangement of the cation, and iodide recombination. High dielectric solvents increase the rate, but solvent coordinating ability has no effect. Dissolved salts (LiI, LiOTf) show normal accelerative salt effects, with no inhibition in the case of added iodide, consistent with the formation of an intimate ion pair intermediate. The kinetic parameters show that the trans-effects of fluoroalkyl ligands in these compounds follow the order expected from the relative sigma-donor properties of the ligands, with CF(2)CF(3) < CFHCF(3) < CH(2)CF(3).