On the generation of circuits and minimal forbidden sets

We present several complexity results related to generation and counting of all circuits of an independence system. Our motivation to study these problems is their relevance in the solution of resource constrained scheduling problems, where an independence system arises as the subsets of jobs that may be scheduled simultaneously. We are interested in the circuits of this system, the so-called minimal forbidden sets, which are minimal subsets of jobs that must not be scheduled simultaneously. As a consequence of the complexity results for general independence systems, we obtain several complexity results in the context of resource constrained scheduling. On that account, we propose and analyze a simple backtracking algorithm that generates all minimal forbidden sets for such problems. The performance of this algorithm, in comparison to a previously suggested divide-and-conquer approach, is evaluated empirically using instances from the project scheduling library PSPLIB.Acknowledgement We appreciate the input of two anonymous referees. Particularly the deep remarks of one of them greatly improved our understanding of several issues; he also suggested the simplified Example 1. We thank Marc Pfetsch and Alexander Grigoriev for several enlightening discussions. Marc Pfetsch also pointed us to the paper [15]. Parts of this work were done while the authors were PhD students at the Technische Universität Berlin, Germany, where Frederik Stork was supported by DFG grant Mo 446/3-3, and Marc Uetz was supported by bmb+f grant 03-MO7TU1-3 and GIF grant I 246-304.02/97.     

Confining the Sol-Gel Reaction at the Water/Oil Interface: Creating Compartmentalized Enzymatic Nano-Organelles for Artificial Cells

Living organisms compartmentalize their catalytic reactions in membranes for increased efficiency and selectivity. To mimic the organelles of eukaryotic cells, we develop a mild approach for in situ encapsulating enzymes in aqueous-core silica nanocapsules. In order to confine the sol-gel reaction at the water/oil interface of miniemulsion, we introduce an aminosilane to the silica precursors, which serves as both catalyst and an amphiphilic anchor that electrostatically assembles with negatively charged hydrolyzed alkoxysilanes at the interface. The semi-permeable shell protects enzymes from proteolytic attack, and allows the transport of reactants and products. The enzyme-carrying nanocapsules, as synthetic nano-organelles, are able to perform cascade reactions when enveloped in a polymer vesicle, mimicking the hierarchically compartmentalized reactions in eukaryotic cells. This in situ encapsulation approach provides a versatile platform for the delivery of biomacromolecules.     

LC–MS–MS Study of the Pharmacokinetics of a 9-β-Dihydro-9,10-O-acetal Derivative of Docetaxel in Rats and Beagle Dogs

SHR110008 is a representative 9-β-dihydro-9,10-O-acetal taxane with greater anticancer activity and less toxicity than docetaxel. To support a preclinical study of its pharmacokinetics and to predict the effect of 9-β-dihydro-9,10-O-acetal modification on its pharmacokinetic properties, we have developed a sensitive and rapid liquid chromatographic–tandem mass spectrometric method for quantitative analysis of SHR110008 in rat and dog plasma. Plasma was extracted with ethyl acetate. The analytes were separated on a 150 × 4.6 mm i.d., 5 μm particle, reversed-phase C₁₈ column with 90:10 (v/v) methanol–0.1% formic acid as mobile phase at a flow rate of 0.3 mL min^?1. Detection was performed by triple-quadrupole tandem mass spectrometry in selected reaction monitoring (SRM) mode with an electrospray ionization source. The precursor-to-product ion transition m/z 933 → 142 was used. The method was validated for accuracy and precision, and linearity in the two matrices was good. Lower limits of quantification (LLOQ) in rat and dog plasma were 5 and 2 ng mL^?1, respectively. There were no stability-related problems in the procedure for analysis of SHR110008. The method was successfully used in a preclinical study of the pharmacokinetics of SHR110008 in rats and beagle dogs. The pharmacokinetics of SHR110008 were non-linear in rats and dogs. The elimination half-life ranged from 5.18 to 7.32 h for the rats and from 6.42 to 8.42 h for the dogs.     

Clifford Theory for Glider Representations

Classical Clifford theory studies the decomposition of simple G-modules into simple H-modules for some normal subgroup H ? G. In this paper we deal with chains of normal subgroups 1?G ₁?· · ·?G _d = G, which allow to consider fragments and in particular glider representations. These are given by a descending chain of vector spaces over some field K and relate different representations of the groups appearing in the chain. Picking some normal subgroup H ? G one obtains a normal subchain and one can construct an induced fragment structure. Moreover, a notion of irreducibility of fragments is introduced, which completes the list of ingredients to perform a Clifford theory.     

Plumbonacrite Identified by X‐ray Powder Diffraction Tomography as a Missing Link during Degradation of Red Lead in a Van Gogh Painting

Red lead, a semiconductor pigment used by artists since antiquity, is known to undergo several discoloration phenomena. These transformations are either described as darkening of the pigment caused by the formation of either plattnerite (β‐PbO₂) or galena (PbS) or as whitening by which red lead is converted into anglesite (PbSO₄) or (hydro)cerussite (2 PbCO₃?Pb(OH)₂; PbCO₃). X‐ray powder diffraction tomography, a powerful analytical method that allows visualization of the internal distribution of different crystalline compounds in complex samples, was used to investigate a microscopic paint sample from a Van Gogh painting. A very rare lead mineral, plumbonacrite (3 PbCO₃? Pb(OH)₂?PbO), was revealed to be present. This is the first reported occurrence of this compound in a painting dating from before the mid 20th century. It constitutes the missing link between on the one hand the photoinduced reduction of red lead and on the other hand (hydro)cerussite, and thus sheds new light on the whitening of red lead.     

Poly(phosphoester)s: A New Platform for Degradable Polymers

Poly(phosphoester)s (PPEs) play an important role in nature. They structure and determine life in the form of deoxy‐ and ribonucleic acid (DNA and RNA), and, as pyrophosphates, they store up chemical energy in organisms. Polymer chemistry, however, is dominated by the nondegradable polyolefins and degradable poly(carboxylic ester)s (PCEs) that are produced on a large scale today. Recent studies have illustrated the potential of PPEs for future applications beyond flame retardancy, and provided a coherent vision to implement this classic biopolymer in modern applications that demand biocompatibility and degradability as well as the possibility to adjust the properties to individual needs.     

Molecular,Macromolecular, and Supramolecular Glucuronide Prodrugs: Lead Identified for Anticancer Prodrug Monotherapy

In this work, a tumor growth intervention by localized drug synthesis within the tumor volume, using the enzymatic repertoire of the tumor itself, is presented. Towards the overall success, molecular, macromolecular, and supramolecular glucuronide prodrugs were designed for a highly potent toxin, monomethyl auristatin E (MMAE). The lead candidate exhibited a fold difference in toxicity between the prodrug and the drug of 175, had an engineered mechanism to enhance the deliverable payload to tumours, and contained a highly potent toxin such that bioconversion of only a few prodrug molecules created a concentration of MMAE sufficient enough for efficient suppression of tumor growth. Each of these points is highly significant and together afford a safe, selective anticancer measure, making tumor-targeted glucuronides attractive for translational medicine.     

Catalytic Oxidation of CO on a Curved Pt(111) Surface: Simultaneous Ignition at All Facets through a Transient CO-O Complex**

The catalytic oxidation of CO on transition metals, such as Pt, is commonly viewed as a sharp transition from the CO-inhibited surface to the active metal, covered with O. However, we find that minor amounts of O are present in the CO-poisoned layer that explain why, surprisingly, CO desorbs at stepped and flat Pt crystal planes at once, regardless of the reaction conditions. Using near-ambient pressure X-ray photoemission and a curved Pt(111) crystal we probe the chemical composition at surfaces with variable step density during the CO oxidation reaction. Analysis of C and O core levels across the curved crystal reveals that, right before light-off, subsurface O builds up within (111) terraces. This is key to trigger the simultaneous ignition of the catalytic reaction at different Pt surfaces: a CO-Pt-O complex is formed that equals the CO chemisorption energy at terraces and steps, leading to the abrupt desorption of poisoning CO from all crystal facets at the same temperature.     

Synthesis of the thiazole-thiazoline fragment of largazole analogues

The thiazole-thiazoline fragment of the marine natural product largazole, a potent histone deacetylase 1 inhibitor, has been synthesized in five steps. The methodology provides rapid access to thiazole-4-carbonitrile, thiazole-4-carbimidate, thiazole-oxazoline, and other thiazole-thiazoline derivatives that are important intermediates in the total synthesis of many natural products with important biological properties.     

Analysis of chorismate mutase catalysis by QM/MM modelling of enzyme-catalysed and uncatalysed reactions

Chorismate mutase is at the centre of current controversy about fundamental features of biological catalysts. Some recent studies have proposed that catalysis in this enzyme does not involve transition state (TS) stabilization but instead is due largely to the formation of a reactive conformation of the substrate. To understand the origins of catalysis, it is necessary to compare equivalent reactions in different environments. The pericyclic conversion of chorismate to prephenate catalysed by chorismate mutase also occurs (much more slowly) in aqueous solution. In this study we analyse the origins of catalysis by comparison of multiple quantum mechanics/molecular mechanics (QM/MM) reaction pathways at a reliable, well tested level of theory (B3LYP/6-31G(d)/CHARMM27) for the reaction (i) in Bacillus subtilis chorismate mutase (BsCM) and (ii) in aqueous solvent. The average calculated reaction (potential energy) barriers are 11.3 kcal mol(-1) in the enzyme and 17.4 kcal mol(-1) in water, both of which are in good agreement with experiment. Comparison of the two sets of reaction pathways shows that the reaction follows a slightly different reaction pathway in the enzyme than in it does in solution, because of a destabilization, or strain, of the substrate in the enzyme. The substrate strain energy within the enzyme remains constant throughout the reaction. There is no unique reactive conformation of the substrate common to both environments, and the transition state structures are also different in the enzyme and in water. Analysis of the barrier heights in each environment shows a clear correlation between TS stabilization and the barrier height. The average differential TS stabilization is 7.3 kcal mol(-1) in the enzyme. This is significantly higher than the small amount of TS stabilization in water (on average only 1.0 kcal mol(-1) relative to the substrate). The TS is stabilized mainly by electrostatic interactions with active site residues in the enzyme, with Arg90, Arg7 and Glu78 generally the most important. Conformational effects (e.g. strain of the substrate in the enzyme) do not contribute significantly to the lower barrier observed in the enzyme. The results show that catalysis is mainly due to better TS stabilization by the enzyme.