A new proof for the first-fit decreasing bin-packing algorithm

This paper provides a new proof of a classical result of bin-packing, namely the $\text{11}\text{9}$ performance bound for the first-fit decreasing algorithm. In bin-packing, a list of real numbers in (0,1] is to be packed into a minimal number of bins, each of which holds a total of at most 1. The first-fit decreasing (FFD) algorithm packs each number in order of nonincreasing size into the first bin in which it fits. In his doctoral dissertation, D. S. Johnson (“Near-Optimal Bin Packing Algorithms,” Doctoral thesis, MIT, Cambridge, Mass., 1973) proved that for every list L, $\text{FFD}\text{(L) ?}\text{11}\text{9}\text{OPT}\text{(L) + 4}$, where FFD(L) and OPT(L) denote the number of bins used by FFD and an optimal packing, respectively. Unfortunately, his proof required more than 100 pages! This paper contains a much shorter and simpler proof that $\text{FFD}\text{(L) ?}\text{11}\text{9}\text{OPT}\text{(L) + 3}$.     

Analysis of acidic drugs in the effluents of sewage treatment plants using liquid chromatography-electrospray ionization tandem mass spectrometry

Azaspiracid poisoning (AZP) is a new human toxic syndrome that is caused by the consumption of shellfish that have been feeding on harmful marine microalgae. A liquid chromatography–mass spectrometry (LC–MS) method has been developed for the determination of the three most prevalent toxins, azaspiracid (AZA1), 8-methylazaspiracid (AZA2) and 22-demethylazaspiracid (AZA3) as well as the isomeric hydroxylated analogues, AZA4 and AZA5. Separation of five azaspiracids was achieved on a C₁₈ column (Luna-2, 150×2 mm, 5 μm) with isocratic elution using acetonitrile–water containing trifluoroacetic acid and ammonium acetate as eluent modifiers. Using an electrospray ionisation (ESI) source with an ion-trap mass spectrometer, the spectra showed the protonated molecules, [M+H]⁺, with most major product ions due to the sequential loss of two water molecules. A characteristic fragmentation pathway that was observed in each azaspiracid was due to the cleavage of the A-ring at C₉–C₁₀ for each toxin. It was possible to select unique ion combinations to distinguish between the isomeric azaspiracids, AZA4 and AZA5. Highly sensitive LC–MS³ analytical methods were compared and the detection limits were 5–40 pg on-column. Linear calibrations were obtained for AZA1 in shellfish in the range 0.05–1.00 μg/ml (r²=0.9974) and good reproducibility was observed with a relative standard deviation (%RSD) of 1.8 for 0.9 μg AZA1/ml (n=5). The %RSD values for the minor toxins, AZA4 and AZA5, using LC–MS³ (A-ring fragmentation) were 12.3 and 8.1 (0.02 μg/ml; n=7), respectively. The selectivity of toxin determination was enhanced using LC–MS–MS with high energy WideBand activation.     

Suicide inactivation of peroxidases and the challenge of engineering more robust enzymes

As the number of industrial applications for proteins continues to expand, the exploitation of protein engineering becomes critical. It is predicted that protein engineering can generate enzymes with new catalytic properties and create desirable, high-value, products at lower production costs. Peroxidases are ubiquitous enzymes that catalyze a variety of oxygen-transfer reactions and are thus potentially useful for industrial and biomedical applications. However, peroxidases are unstable and are readily inactivated by their substrate, hydrogen peroxide. Researchers rely on the powerful tools of molecular biology to improve the stability of these enzymes, either by protecting residues sensitive to oxidation or by devising more efficient intramolecular pathways for free-radical allocation. Here, we discuss the catalytic cycle of peroxidases and the mechanism of the suicide inactivation process to establish a broad knowledge base for future rational protein engineering.     

A Series of Collaborations Between Various Pharmaceutical Companies and Regulatory Authorities Concerning the Analysis of Biomolecules Using Capillary Electrophoresis

An international project team (including members from US, Canada and UK) has been formed from a number of interested biopharmaceutical companies and regulatory authorities to conduct a cross-organisation collaboration exercise. The results from this exercise demonstrate the robustness of CE-SDS across eight different organisations that used instruments of the same equipment model, the same reagents, and the same methodology. Data generated from the analysis of a series of molecular weight markers showed very good precision with regards to relative migration time (RMT) both within and between organisations. The apparent molecular weight of bovine serum albumin (BSA) was measured with good precision to within approximately 2% RSD across the participants. A representative IgG sample showed similar results with regards to relative migration time of its 3 main components, IgG Light Chain, IgG Non-glycosylated Heavy Chain, and IgG Heavy Chain. Fractional peak area for each peak also showed good agreement, with less than 9% RSD for all peaks. This exercise will facilitate both increased regulatory and industrial opinion of CE for biopharmaceutical analysis.CE in the Biotechnology & Pharmaceutical Industries: 7th Symposium on the Practical Applications for the Analysis of Proteins, Nucleotides and Small Molecules, Montreal, Canada, August 12–16, 2005     

Family communication about genetic risk: the little that is known

Although family communication is important in clinical genetics only a small number of studies have specifically explored the passing on of genetic knowledge to family members. In addition, many of these present exploratory or tentative findings based upon small sample sizes, or data collected only a short time after testing. Nevertheless, if health professionals are to develop effective strategies to help patients' deal with communication issues, we need to know more about what actually happens in families. The aim of this commentary is to identify factors which appear to influence whether patients share information about genetic risk with relatives who are unaware of that risk, with whom they share it and how they go about it. The paper draws upon evidence and thinking from the disciplines of psychology (including family therapy), sociology, medicine and genetic counselling. It is presented under the following headings: disease factors, individual factors, family factors and sociocultural factors. It concludes by highlighting a number of key issues which are relevant for health professionals.     

Ytterbium(III) Triflate–Catalyzed Stereoselective Synthesis of β‐Lactams via [2+2] Cyclocondensation in Ionic Liquid

Catalyzed by ytterbium(III) triflate [Yb(OTf)₃], β‐lactams were stereoselectively synthesized from imines and acetyl chlorides in ionic liquid under mild conditions. The ionic liquid and catalyst could be recycled and reused as opposed to traditional solvent–catalyst systems.     

Cobalt(II) and copper(II) complexes ofN,N′,N″,N‴-tetra(2-cyanoethyl)-1,4,8,11-tetraazacyclotetradecane

Summary Cobalt(II) and copper(II) complexes of the title ligand, TCEC, as well as a cobalt(II) complex ofN,N,N",N'-tetra (1-methyl-2-cyanoethyl)-1,4,8,11-tetraazacyclotetradecane, TMCEC, have been isolated and spectrally characterized.     

Synthesis of a NO-releasing prodrug of rofecoxib

[reaction: see text] A newly developed synthesis of a NO-releasing prodrug of rofecoxib is described. The highly productive process consists of five chemical steps and produces prodrug 1 in an overall 64% yield from commercially available 3-phenyl-2-propyn-1-ol (4). The synthesis is highlighted by the carbometalation reaction of propargyl alcohol 4 to generate the tetrasubstituted olefin core, sulfone acid 2. Additionally, two alternate end-game strategies to prepare NO-COXIB 1 from this intermediate were explored and developed: (1) a convergent synthesis where a bromonitrate side chain is introduced in one step and (2) a two-step sequence that first installs the requisite six-carbon ester side chain followed by chemoselective nitration.