Optimality relationships forp-cyclic SOR

Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.Research supported in part by the US Air Force under Grant no. AFOSR-88-0285 and the National Science Foundation under grant no. DMS-85-21154 Present address: Boeing Computer Services, P.O. Box 24346, MS 7L-21, Seattle, WA 98124-0346, USA     

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

Straightforward synthesis of sphinganines via a serine-derived Weinreb amide

Sphinganines can be synthesized in just three steps from easily prepared serine-derived Weinreb amide 4. Pre-deprotonation of the acidic (N-H and O-H) protons of 4 allows for its efficient conversion to amino ketones 5. Such ketones can be selectively reduced to either erythro- or threo-sphinganines. Partially protected sphinganines 11 are also readily accessible in five steps from 4. Thus, Weinreb amide 4 represents one of the most versatile templates described to date for sphinganine synthesis.     

Role of Enterobactin and Intracellular Iron in Cell Lethality During Near-UV Irradiation in Escherichia coli

Abstract— In Escherichia coli, fur mutants that constitutively express their native iron chelating agent, enterobactin, are significantly more sensitive to near-UV radiation (NUV) than wild type. An entA mutant, which is incapable of synthesizing enterobactin, is equal to wild type in resistance to NUV irradiation. However, the addition of Fe⁺³ enterobactin but not Al⁺¹ enterobactin to entA cell suspensions just prior to irradiation results in an increased sensitivity to NUV irradiation. A fes mutant, which is unable to reduce and release iron from enterobactin, is significantly more sensitive to NUV irradiation than wild type. The addition of nontoxic levels of H₂O₂ (5 μ M ) just prior to irradiation significantly increases sensitivity of both fur and fes mutants. These results suggest that one mechanism by which NUV irradiation leads to cell lethality is by creating a transient iron overload, producing very favorable conditions for the production of highly deleterious free radicals through a variety of mechanisms that lead to oxidative stress and DNA damage including lethal and mutagenic lesions. These results are consistent with the hypothesis that enterobactin is an endogenous chromophore for NUV and contributes to cell lethality via the destruction of its ligand, releasing Fe⁺² into the cytoplasm to catalyze the production of highly reactive hydroxyl radicals and other toxic oxygen species via the Haber-Weiss reaction.     

Ruminant pregastric lipases: experimental evidence of their potential as industrial catalysts in food technology

The historical importance of pregastric enzymes in cheese-making is reviewed and the potential for extending their use is discussed in terms of requiring an understanding of their physicochemical parameters. Commericial extracts from the tongues and epiglotti of suckling lambs and calves and adult goats have been processed to yield partially purified samples of the primary pregastric lipase (PGL). The N-terminal sequence and molecular weight of lamb PGL have been determined.

The activity of lamb and goat PGLs against tributyrin has been determined over a range of pH and temperature values. Optimum conditions were pH 6.4, 43°C, and pH 6.0, 52°C, for lamb and goat PGL respectively. The possible influence of the development of a ruminant multi-chambered stomach on the difference in optimal temperature is discussed. A lengthening of the carboxylic acid chain of homoacid triglycerides causes a decrease in hydrolytic activity of lamb PGL but in all cases only a single free fatty acid was released. Against a series of 4-nitrophenylalkanoate esters, maximum activity was observed against the decanoate ester but, in contrast to hydrolysis of the acetate ester which exhibited full Michaelis-Menten kinetics with increasing substrate concentration, activity against the decanoate ester was restricted to the monomeric substrate. Taurocholate inhibits the activity of lamb PGL at concentrations >8 mM. Values of pK₂ equal to 6.69 and 7.92 respectively have been determined for lamb PGL.

Attempts to interesterify coconut oil and cocoa butter, and tributyrin and tricaprylin, catalysed by calf PGL were unsuccessful, although positive results obtained using Candida cylindracea encourage further investigation of alternative methods for immobilizing the PGL. Finally, anhydrous milk fat has been hydrolysed by calf, lamb and goat PGLs and the differences in relative amounts of released free fatty acids have been used to explain the differences in taste which arise when Parmesan cheese is produced using different sources of PGL.     

Mechanistic implications for the formation of the diiron cluster in ribonucleotide reductase provided by quantitative EPR spectroscopy

The small subunit of Escherichia coli ribonucleotide reductase (R2) is a homodimeric (betabeta) protein, in which each beta-peptide contains a diiron cluster composed of two inequivalent iron sites. R2 is capable of reductively activating O(2) to produce a stable tyrosine radical (Y122*), which is essential for production of deoxyribonucleotides on the larger R1 subunit. In this work, the paramagnetic Mn(II) ion is used as a spectroscopic probe to characterize the assembly of the R2 site with EPR spectroscopy. Upon titration of Mn(II) into samples of apoR2, we have been able to quantitatively follow three species (aquaMn(II), mononuclear Mn(II)R2, and dinuclear Mn(2)(II)R2) and fit each to a sequential two binding site model. As previously observed for Fe(II) binding within apoR2, one of the sites has a greater binding affinity relative to the other, K(1) = (5.5 +/- 1.1) x 10(5) M(-)(1) and K(2) = (3.9 +/- 0.6) x 10(4) M(-)(1), which are assigned to the B and A sites, respectively. In multiple titrations, only one dinuclear Mn(2)(II)R2 site was created per homodimer of R2, indicating that only one of the two beta-peptides of R2 is capable of binding Mn(II) following addition of Mn(II) to apoR2. Under anaerobic conditions, addition of only 2 equiv of Fe(II) to R2 (Fe(2)(II)R2) completely prevented the formation of any bound MnR2 species. Upon reaction of this sample with O(2) in the presence of Mn(II), both Y122* and Mn(2)(II)R2 were produced in equal amounts. Previous stopped-flow absorption spectroscopy studies have indicated that apoR2 undergoes a protein conformational change upon binding of metal (Tong et al. J. Am. Chem. Soc. 1996, 118, 2107-2108). On the basis of these observations, we propose a model for R2 metal incorporation that invokes an allosteric interaction between the two beta-peptides of R2. Upon binding the first equiv of metal to a beta-peptide (beta(I)), the aforementioned protein conformational change prevents metal binding in the adjacent beta-peptide (beta(II)) approximately 25 A away. Furthermore, we show that metal incorporation into beta(II) occurs only during the O(2) activation chemistry of the beta(I)-peptide. This is the first direct evidence of an allosteric interaction between the two beta-peptides of R2. Furthermore, this model can explain the generally observed low Fe occupancy of R2. We also demonstrate that metal uptake and this newly observed allosteric effect are buffer dependent. Higher levels of glycerol cause loss of the allosteric effect. Reductive cycling of samples in the presence of Mn(II) produced a novel mixed metal Fe(III)Mn(III)R2 species within the active site of R2. The magnitude of the exchange coupling (J) determined for both the Mn(2)(II)R2 and Fe(III)Mn(III)R2 species was determined to be -1.8 +/- 0.3 and -18 +/- 3 cm(-)(1), respectively. Quantitative spectral simulations for the Fe(III)Mn(III)R2 and mononuclear Mn(II)R2 species are provided. This work represents the first instance where both X- and Q-band simulations of perpendicular and parallel mode spectra were used to quantitatively predict the concentration of a protein bound mononuclear Mn(II) species.     

Aggregation-fragmentation in a model of DNA-mediated colloidal assembly

We present results from an off-lattice Monte Carlo simulation of DNA-mediated colloidal assembly. In this simulation, the aggregation-fragmentation of a binary mixture of DNA-coated colloidal particles is studied through a simplified model of base-pair hybridization. Bonding between monomers is modeled as a simple temperature-sensitive A/B-type interaction, where type A and B monomers can bond to only the opposite type (no A/A or B/B attachments are allowed). The actual chemistry of base-pair hybridization is not included in the model. The morphological structures of the clusters formed as well as the kinetics of growth are analyzed in our 2D simulations. The fractal dimension and kinetic growth exponents for clusters formed near the DNA "melting" temperature agree with those seen previously for 2D diffusion-limited cluster aggregation (DLCA) models. The clusters appear more compact, exhibiting signs of local order at intermediate temperature values. At higher temperatures, the formation of large clusters is not favorable under the action of temperature-dependent fragmentation, and the system eventually reaches a steady state as a collection of small aggregates. The temperature profile for this dissolution of the colloidal assembly is sharp, indicating that the selective hybridization process provides a highly sensitive measurement tool. At high temperatures, we analyze the steady-state behavior of the average cluster size in terms of an aggregation-fragmentation model.     

Metal-directed synthesis and photophysical studies of trinuclear v-shaped and pentanuclear x-shaped ruthenium and osmium metallorods and metallostars based upon 4'-(3,5-dihydroxyphenyl)-2,2':6',2''-terpyridine divergent units

A new series of V-shaped trinuclear metallorods and X-shaped pentanuclear metallostars has been prepared by the reaction of metal complexes bearing pendant phenolic functionalities with complexes containing electrophilic ligands. Specifically, {M(tpy)2} motifs (M=Ru or Os; tpy=2,2':6',2'-terpyridine) bearing one or two pendant 3,5-dihydroxyphenyl substituents at the 4-position of the central ring of the tpy have been reacted with the complexes [Ru(tpy)(Xtpy)]2+ (X=Cl or Br) to form new ether-linked species. The energy transfer from ruthenium to osmium in these complexes has been investigated in detail and the efficiency of transfer shown to be highly temperature dependent; the energy transfer is highly efficient at low temperature, whereas at room temperature nonradiative and nontransfer deactivation of the excited {Ru(tpy)2}* domains is most significant.     

Classification of gasoline data obtained by gas chromatography using a piecewise alignment algorithm combined with feature selection and principal component analysis

A fast and objective chemometric classification method is developed and applied to the analysis of gas chromatography (GC) data from five commercial gasoline samples. The gasoline samples serve as model mixtures, whereas the focus is on the development and demonstration of the classification method. The method is based on objective retention time alignment (referred to as piecewise alignment) coupled with analysis of variance (ANOVA) feature selection prior to classification by principal component analysis (PCA) using optimal parameters. The degree-of-class-separation is used as a metric to objectively optimize the alignment and feature selection parameters using a suitable training set thereby reducing user subjectivity, as well as to indicate the success of the PCA clustering and classification. The degree-of-class-separation is calculated using Euclidean distances between the PCA scores of a subset of the replicate runs from two of the five fuel types, i.e., the training set. The unaligned training set that was directly submitted to PCA had a low degree-of-class-separation (0.4), and the PCA scores plot for the raw training set combined with the raw test set failed to correctly cluster the five sample types. After submitting the training set to piecewise alignment, the degree-of-class-separation increased (1.2), but when the same alignment parameters were applied to the training set combined with the test set, the scores plot clustering still did not yield five distinct groups. Applying feature selection to the unaligned training set increased the degree-of-class-separation (4.8), but chemical variations were still obscured by retention time variation and when the same feature selection conditions were used for the training set combined with the test set, only one of the five fuels was clustered correctly. However, piecewise alignment coupled with feature selection yielded a reasonably optimal degree-of-class-separation for the training set (9.2), and when the same alignment and ANOVA parameters were applied to the training set combined with the test set, the PCA scores plot correctly classified the gasoline fingerprints into five distinct clusters.     

Computer simulation of selective aggregation in binary colloids

The morphology of clusters formed by selective aggregation of binary colloids is studied in a two-dimensional Monte Carlo simulation for a large range of number fractions (200:1, 100:1, 10:1, 2:1). We find remarkable similarity in morphology to those observed in experiments, from the formation of closed "micelles" to large branched clusters. Quantitative studies of the fractal dimension, kinetics, and cluster size distribution are also carried out and compared with diffusion-limited cluster aggregation and reaction-limited cluster aggregation models.