Flexible and adaptive use of strategies and representations in mathematics education

The flexible and adaptive use of strategies and representations is part of a cognitive variability, which enables individuals to solve problems quickly and accurately. The development of these abilities is not simply based on growing experience; instead, we can assume that their acquisition is based on complex cognitive processes. How these processes can be described and how these can be fostered through instructional environments are research questions, which are yet to be answered satisfactorily. This special issue on flexible and adaptive use of strategies and representations in mathematics education encompasses contributions of several authors working in this particular field. They present recent research on flexible and adaptive use of strategies or representations based on theoretical and empirical perspectives. Two commentary articles discuss the presented results against the background of existing theories.     

Resonance structures of the amide bond: the advantages of planarity

Delocalization indexes based on magnitudes derived from electron-pair densities are demonstrated to be useful indicators of electron resonance in amides. These indexes, based on the integration of the two-electron density matrix over the atomic basins defined through the zero-flux condition, have been calculated for a series of amides at the B3LYP/6-31+G* level of theory. These quantities, which can be viewed as a measure of the sharing of electrons between atoms, behave in concordance with the traditional resonance model, even though they are integrated in Bader atomic basins. Thus, the use of these quantities overcomes contradictory results from analyses of atomic charges, yet keeps the theoretical appeal of using nonarbitrary atomic partitions and unambiguously defined functions such as densities and pair densities. Moreover, for a large data set consisting of 24 amides plus their corresponding rotational transition states, a linear relation was found between the rotational barrier for the amide and the delocalization index between the nitrogen and oxygen atoms, indicating that this parameter can be used as an ideal physical-chemical indicator of the electron resonance in amides.     

Pyrolysis mass spectrometry for distinguishing potential hoax materials from bioterror agents

Pyrolysis mass spectrometry (PyMS) was investigated as a rapid tool to distinguish potential bioterror hoax materials from samples containing pathogenic bacteria. A pyrolysis time-of-flight (TOF) mass spectrometer equipped with an alternative ionization technique, metastable atom bombardment (MAB), was used to produce sample spectra. These spectra were analyzed by principal component and discriminant analysis for pattern recognition. Materials investigated were two strains of Vibrio parahaemolyticus, one of which produced the tdh toxin, two Salmonella enterica serotypes, a biological mosquito control product containing spores of Bacillus thuringiensis, and several white to off-white powders (which could be used as hoax materials), such as flour, corn starch, methyl cellulose, and xanthan gum. PyMS distinguished bacterial samples from hoax materials. Furthermore, pattern analysis differentiated Vibrios from Salmonellae, Salmonella enterica Anatum from S. enterica Heidelberg, and the two V. parahaemolyticus strains from each other. The B. thuringiensis mixture was distinguished from other bacteria and powders, suggesting that PyMS with pattern recognition may differentiate samples containing pathogens, including Bacillus spp., from nonbiological agents and that it can be a rapid method for detection of bacteria. MS data acquisition took only 7 min for each sample.     

Electronic structure of mononuclear bis(1,2-diaryl-1,2-ethylenedithiolato)iron complexes containing a fifth cyanide or phosphite ligand: a combined experimental and computational study

A series of mononuclear square-based pyramidal complexes of iron containing two 1,2-diaryl-ethylene-1,2-dithiolate ligands in various oxidation levels has been synthesized. The reaction of the dinuclear species [Fe(III)2(1L*)2(1L)2]0, where (1L)2- is the closed shell di-(4-tert-butylphenyl)-1,2-ethylenedithiolate dianion and (1L*)1- is its one-electron-oxidized pi-radical monoanion, with [N(n-Bu)4]CN in toluene yields dark green crystals of mononuclear [N(n-Bu)4][Fe(II)(1L*)2(CN)] (1). The oxidation of 1 with ferrocenium hexafluorophosphate yields blue [Fe(III)(1L*)2(CN)] (1ox), and analogously, a reduction with [Cp2Co] yields [Cp2Co][N(n-Bu)4][Fe(II)(1L*)(1L)(CN)] (1red); oxidation of the neutral dimer with iodine gives [Fe(III)(1L*)2I] (2). The dimer reacts with the phosphite P(OCH3)3 to yield [Fe(II)(1L*)2{P(OCH3)3}] (3), and [Fe(III)2(3L*)2(3L)2] reacts with P(OC6H5)3 to give [Fe(II)(3L*)2{P(OC6H5)3}] (4), where (3L)2- represents 1,2-diphenyl-1,2-ethylenedithiolate(2-). Both 3 and 4 were electrochemically one-electron oxidized to the monocations 3ox and 4ox and reduced to the monoanions 3red and 4red. The structures of 1 and 4 have been determined by X-ray crystallography. All compounds have been studied by magnetic susceptibility measurements, X-band EPR, UV-vis, IR, and M?ssbauer spectroscopies. The following five-coordinate chromophores have been identified: (a) [Fe(III)(L*)2X]n, X = CN-, I- (n = 0) (1ox, 2); X = P(OR)3 (n = 1+) )3ox, 4ox) with St = 1/2, SFe = 3/2; (b) [Fe(II)(L*)2X]n, X = CN-, (n = 1-) (1); X = P(OR)3 (n = 0) (3, 4) with St = SFe = 0; (c) [Fe(II)(L*)(L)X]n <--> [Fe(II)(L)(L*)X]n, X = CN- (n = 2-) (1red); X = P(OR)3 (n = 1-) (3red, 4red) with St = 1/2, SFe = 0 (or 1). Complex 1ox displays spin crossover behavior: St = 1/2 <--> St = 3/2 with intrinsic spin-state change SFe = 3/2 <--> SFe = 5/2. The electronic structures of 1 and 1(ox) have been established by density functional theoretical calculations: [Fe(II)(1L*)2(CN)]1- (SFe = 0, St = 0) and [Fe(III)(1L*)2(CN)]0 (SFe = 3/2, St = 1/2).     

Recent developments in solid-phase microextraction coatings and related techniques

During the last decade, solid-phase microextraction (SPME) has gained widespread acceptance for analyte matrix separation and preconcentration. Relatively few data are currently available dealing with in-house production of fibres with tailor-made properties to be used for SPME, though recently the number of publications evaluating new coatings has been considerably growing. This review, centred on publications that appeared during the last five years, is resuming different approaches which can be used for fibre production and further summarises alternative techniques closely related to SPME, such as in-tube extraction or single-drop microextraction (SDME). The aim is to give the reader a concise overview of recent developments in new coating procedures and materials, including the respective applications.     

Laser-driven shock experiments on precompressed water: Implications for "icy" giant planets

Laser-driven shock compression of samples precompressed to 1 GPa produces high-pressure-temperature conditions inducing two significant changes in the optical properties of water: the onset of opacity followed by enhanced reflectivity in the initially transparent water. The onset of reflectivity at infrared wavelengths can be interpreted as a semiconductor<-->electronic conductor transition in water, and is found at pressures above approximately 130 GPa for single-shocked samples precompressed to 1 GPa. Our results indicate that conductivity in the deep interior of "icy" giant planets is greater than realized previously because of an additional contribution from electrons.     

Natural product diversification using a non-natural cofactor analogue of S-adenosyl-L-methionine

Adenosine analogues bearing either 5'-aziridine or 5'-N-mustard electrophiles are methyltransferase-dependent DNA alkylating agents. We present here a novel synthetic cofactor bearing a pendant 5'-amino acid N-mustard. Unlike previously studied synthetic cofactors, this material is very efficiently used by the natural product biosynthetic enzyme rebeccamycin methyltransferase (RebM) to generate a number of new rebeccamycin analogues. These data promote the notion that natural product methyltransferases can be used with non-natural cofactors to enhance the molecular diversity of natural product analogues for drug discovery. To our knowledge, this is the first documentation of a biological methyltransferase, other than DNA methyltransferases, that can exploit such synthetic cofactors.     

A biosynthetic gene cluster for the acetyl-CoA carboxylase inhibitor andrimid

Increasing bacterial resistance to antibiotics with conventional targets has focused attention on antibiotics with unconventional targets. One promising candidate, the acetyl-CoA carboxylase (ACC) inhibitor andrimid, is a potent, broad-spectrum antibiotic with high selectivity for prokaryotic ACC. Here, we report the use of a DNA-based approach to clone the andrimid biosynthetic gene cluster from Pantoea agglomerans, yielding a cosmid that confers robust andrimid production on Escherichia coli. This gene cluster encodes a hybrid nonribosomal peptide/polyketide (NRP/PK) synthase with several unusual features, including three enzymes that form and insert beta-phenylalanine, two transglutaminase-like enzymes that likely serve as condensation catalysts, and four densely hybrid modules that form the succinimide precursor. Unlike most type I NRPSs and PKSs, the andrimid gene cluster is a dissociated system comprised of small proteins. Therefore, future efforts can exploit the genetic manipulability of E. coli to engineer the andrimid synthase with the goal of producing a diverse set of andrimid analogues for clinical evaluation.     

Synthesis and characterization of oligoproline-based molecular assemblies for light harvesting

Helical oligoproline arrays provide a structurally well-defined environment for building photochemical energy conversion assemblies. The use of solid-phase peptide synthesis (SPPS) to prepare four such arrays, consisting of 16, 17, 18, and 19 amino acid residues, is described here. Each array contains the chromophore [Rub'(2)m](PF(6))(2) (b' = 4,4'-diethylamidocarbonyl-2,2'-bipyridine; m = 4-methyl-2,2'-dipyridine-4'-carboxylic acid) and the electron transfer donor PTZ (phenothiazine). The arrays differ systematically in the distance between the redox-active metal complex and PTZ sites. They have been used in photophysical studies to provide insight into the distance dependence of electron transfer. (J. Am. Chem. Soc. 2004, 126, 14506-14514). This work describes the synthesis, purification, and characterization of the oligoproline arrays, including a general procedure for the synthesis of related arrays.     

A microfluidic-based system for analysis of single cells based on Ca2+ flux

A microfluidic format-based system has been developed for in situ monitoring of the calcium flux response to agonists using Chinese hamster ovary (CHO) cells. The assay is based on measuring the fluorescent intensity of the calcium-sensitive indicator, Fluo-4 AM, and was performed in a modified glass chip channel, whose surface was functionalised using a silanisation method with 3-aminopropyltriethoxysilane (APTS) (enabling the cells to be immobilised on the channel surface). CHO cells calcium flux response was measured for different agonists over a range of concentrations. Cells and reagents were introduced into the chip in a continuous flow as a series of plugs in a given sequence.