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.     

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.     

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.     

Room-temperature catalytic hydrodefluorination of C(sp3)-F bonds

Room-temperature catalytic hydrodefluorination of the strong C(sp3)-F bonds in benzotrifluorides and fluoropentane is catalyzed by Et3Si[B(C6F5)4] and uses Et3SiH as the source of H. Ar-CF3 compounds are converted to Ar-CH3 and fluropentane to pentane. The reaction is thought to proceed via abstraction of F- by Et3Si[B(C6F5)4], and the substituent effects are consistent with this hypothesis.     

The molecular mechanism of stabilization of proteins by TMAO and its ability to counteract the effects of urea

Trimethylamine n-oxide (TMAO) is a naturally occurring osmolyte that stabilizes proteins and offsets the destabilizing effects of urea. To investigate the molecular mechanism of these effects, we have studied the thermodynamics of interaction between TMAO and protein functional groups. The solubilities of a homologous series of cyclic dipeptides were measured by differential refractive index and the dissolution heats were determined calorimetrically as a function of TMAO concentration at 25 degrees C. The transfer free energy of the amide unit (-CONH-) from water to 1 M TMAO is large and positive, indicating an unfavorable interaction between the TMAO solution and the amide unit. This unfavorable interaction is enthalpic in origin. The interaction between TMAO and apolar groups is slightly favorable. The transfer free energy of apolar groups from water to TMAO consists of favorable enthalpic and unfavorable entropic contributions. This is in contrast to the contributions for the interaction between urea and apolar groups. Molecular dynamics simulations were performed to provide a structural framework for the interpretation of these results. The simulations show enhancement of water structure by TMAO in the form of a slight increase in the number of hydrogen bonds per water molecule, stronger water hydrogen bonds, and long-range spatial ordering of the solvent. These findings suggest that TMAO stabilizes proteins via enhancement of water structure, such that interactions with the amide unit are discouraged.     

Partial-filling affinity capillary electrophoresis

Partial-filling affinity capillary electrophoresis (PFACE) is used to examine the binding interactions between two model biological systems: D-Ala-D-Ala terminus peptides to the glycopeptide antibiotic vancomycin (Van) from Streptomyces orientalis, and arylsulfonamides to carbonic anhydrase B (CAB, EC 4.2.1.1, bovine erythrocytes). Using these two systems, modifications in the PFACE technique are demonstrated including flow-through PFACE (FTPFACE), competitive flow-through PFACE (CFTPFACE), on-column ligand synthesis PFACE (OCLSPFACE), and multiple-step ligand injection PFACE (MSLIPFACE). In PFACE small plugs of sample are injected into the capillary column and an equilibrium is established between receptor and ligand during electrophoresis. Binding constants are then obtained by Scatchard analysis using changes in the migration time of the receptor/ligand on changing the concentration of the ligand/receptor. Data demonstrating the quantitative potential of these methods are presented. This review focuses on the unique capabilities of the different PFACE techniques as applied to two model biological systems.