Discrete mathematics in primary and secondary schools in the United States

This article provides a status report on discrete mathematics in America's schools, including an overview of publications and programs that have had major impact. It discusses why discrete mathematics should be introduced in the schools and the authors' efforts to advocate, facilitate, and support the adoption of discrete mathematics topics in the schools. Their perspective is that discrete mathematics should be viewed not only as a collection of new and interesting mathematical topics, but, more importantly, as a vehicle for providing teachers with a new way to think about traditional mathematical topics and new strategies for engaging their students in the study of mathematics.     

Cytochrome-c detection

Following a myocardial infarction (MI) cells die or are damaged and their contents leak into the blood circulation, resulting in elevated serum levels of various enzymes, proteins, and organic molecules. Over the past few decades, it has become standard practice to employ the detection of these elevated substances as markers for the confirmation of MIs and to monitor MI patients’ response to treatment. Although it has previously been shown that cytochrome-c, a small respiratory protein, is among those elevated, the lack of a suitable detection system has prevented its routine use in the diagnosis of MIs. We present a preliminary study in which chemiluminescence was employed to detect elevated levels of cytochrome-c in the serum of MI patients. The technique, which is specific for c-type proteins, is approx 30 times more sensitive than the traditional Coomassie blue stain and can detect as little as 0.03 μg of protein. It also has potential for diagnostic use in other diseases that are characterized by mitochondrial damage.     

Ionization of carbonic acid in sodium chloride solutions at 25°C

The stoichiometric pK ₁ ^* and pK ₂ ^* for the ionization of carbonic acid has been determined from emf measurements in NaCl soluions to 6.0m at 25°C. Our results at low concentrations are in good agreement with the results of Harned and Bonner, of Dyrssen and Hansson and of Roy et al. The calculated values of pK ₁ ^* using Pitzer's equations agree with the measured values to ±0.01 pK units provided higher order terms are used. It was necessary to use a triplet interaction parameter () and higher order electrostatic terms (^E) to calculate reliable values of pK ₂ ^* (±0.03 pK units) over the entire concentration range. These results demonstrate the reliability of the Pitzer equations to estimate activity coefficients in concentrated salt solutions.     

On-line on-chip post-column derivatisation reactions for pre-ionisation of analytes and cluster analysis in gradient micro-liquid chromatography/electrospray mass spectrometry

A system is presented that demonstrates the principle of on-line and on-chip post-column derivatisation reactions in micro-high-performance liquid chromatography (micro-HPLC) hyphenated to electrospray time-of-flight mass spectrometry (ESI-TOFMS). In this micro-HPLC-chip-MS set-up, the analytes are separated using gradient micro-HPLC and subsequently derivatised on-chip and detected. One of the major limitations of MS detection is its dependency on the degree of ionisation, which is widely variable and compound-specific. Optimising and controlling the degree of ionisation in a simple manner would allow MS detection to be truly generic. One way of achieving this is by pre-ionisation of analytes using simple derivatisation procedures that are both rapid and quantitative. Performing this in situ on the system described here overcomes issues of sample handling and efficiency losses when time-consuming "bench chemistry" is necessary prior to analysis. The power of the system is demonstrated by the separation of primary and secondary amines, which are subsequently derivatised with a positively charged phosphonium complex and detected in an enhanced manner. Typically, molecular cations (M(+)) are detected showing that the ionisation process is dominated by the phosphonium species, leading to more constant ionisation for a variety of compounds. In addition, stable isotopically labelled ((12)C/(13)C)-phosphonium reagent is used for the reactions, allowing for inherent signal/noise (S/N) improvement and automated data processing using cluster analysis. A similar reaction scheme is used for the derivatisation of ketones and aldehydes, also demonstrating dramatic increases in sensitivity, especially with increasing temperature. Minimal loss in chromatographic fidelity in terms of retention times is observed by the introduction of the micromixer chip into the system. Optimal flow rates in micro-HPLC and ESI-MS are compatible with flow rates for the chip as well as a multitude of in-line optical detectors including UV and fluorescence. In addition, the micromixer chip can be positioned pre-column if preferred. The system is robust, easily fully automated and applicable to a wide variety of reactions. The system has a major advantage in its simple robust connection to the "normal scale" outside world.     

A general and efficient synthesis of sulfonylbenzotriazoles from N-chlorobenzotriazole and sulfinic acid salts

One-pot reactions of sulfinic acid salts (produced from organometallic reagents with SO2) with N-chlorobenzotriazole gave the corresponding N-alkane-, N-arene-, and N-heteroenesulfonylbenzotriazoles 3a-j in 41-93% yields. Reagents 3a-j are efficient sulfonylating agents, reacting at 20-80 degrees C with various primary and secondary aliphatic amines to yield the corresponding sulfonamides in 64-100% yields.     

NMR and X-ray crystallography, complementary tools in structural proteomics of small proteins

NMR spectroscopy and X-ray crystallography, the two primary experimental methods for protein structure determination at high resolution, have different advantages and disadvantages in terms of sample preparation and data collection and analysis. It is therefore of interest to assess their complementarity when applied to small proteins. Structural genomics/proteomics projects provide an ideal opportunity to make such comparisons as they generate data in a systematic manner for large enough numbers of proteins to allow firm conclusions to be drawn. Here we report a comparison for 263 unique proteins screened by both NMR spectroscopy and X-ray crystallography in our structural proteomics pipeline. Only 21 targets (8%) were deemed amenable to both methods based on an initial 2D 15N-HSQC NMR spectrum and optimized crystallization trials. However, the use of both methods in the pipeline increased the total number of targets amenable to structure determination to 107, with 43 amenable to NMR only and 43 amenable to X-ray crystallographic methods only. We did not observe a correlation between 15N-HSQC spectral quality and the success of the same protein in crystallization screens. Similar results were found for an independent set of 159 proteins as reported in the accompanying paper by Snyder et al. Thus, we conclude that both methods are highly complementary, and in order to increase the number of proteins suited for structure determination, we suggest that both methods be used in parallel in screening of all small proteins for structure determination.     

The isolation of new norcycloartene triterpenoids from the tropical marine alga Tydemaniaexpeditionitis (chlorophyta)

Three new Δ³-norcycloartene triterpenoids, with differing side chain functionalities, have been isolated from the tropical green alga $\text{Tydemania}$$\text{expeditionitis}$ collected in Guam. The structures of these new compounds were secured by x-ray crystallography and by chemical interconversion.     

Calculating the knowledge-based similarity of functional groups using crystallographic data

A knowledge-based method for calculating the similarity of functional groups is described and validated. The method is based on experimental information derived from small molecule crystal structures. These data are used in the form of scatterplots that show the likelihood of a non-bonded interaction being formed between functional group A (the `central group') and functional group B (the `contact group' or `probe'). The scatterplots are converted into three-dimensional maps that show the propensity of the probe at different positions around the central group. Here we describe how to calculate the similarity of a pair of central groups based on these maps. The similarity method is validated using bioisosteric functional group pairs identified in the Bioster database and Relibase. The Bioster database is a critical compilation of thousands of bioisosteric molecule pairs, including drugs, enzyme inhibitors and agrochemicals. Relibase is an object-oriented database containing structural data about protein-ligand interactions. The distributions of the similarities of the bioisosteric functional group pairs are compared with similarities for all the possible pairs in IsoStar, and are found to be significantly different. Enrichment factors are also calculated showing the similarity method is statistically significantly better than random in predicting bioisosteric functional group pairs.     

A self-consistent reaction field model of solvation using distributed multipoles. I. Energy and energy derivatives

The self-consistent reaction field model developed previously by the authors in the case of single center multipole expansion of the electronic structure of the solute has been extended to the case of a distributed multipole expansion. Three different expansions have been tested and two of them have proved to be rapidly convergent. The performances of the code are illustrated by the density functional theory treatment of few test systems: guanine, cytosine, and cytosine hydrated with one and three water molecules. A robust fast computer code has been tested to get the electronic structure, the electrostatic contribution to the solute-solvent free energy of interaction, and the optimized molecular geometry in solution.