Advection-diffusion equations: Temporal sinc methods

A fully Sinc–Galerkin method for solving advection–diffusion equations subject to arbitrary radiation boundary conditions is presented. This procedure gives rise to a discretization, which has its most natural representation in the form of a Sylvester system where the coefficient matrix for the temporal discretization is full. The word “full” often implies a computationally more complex method compared to, for example, temporal marching. In a comparison of time-marching versus this sinc-temporal procedure, the Sylvester formulation defines a common framework within which these procedures can be evaluated. This framework has been included in the introduction to illustrate an efficiency measure for either method. Similar remarks with regard to fullness versus sparseness in the Sylvester formulation apply when the spatial discretization is spectral or, for example, differencing. Although it is indicated how this sinc-temporal method can be combined with alternative spatial discretizations, the natural affinity between sinc methods for space and time discretizations motivate carrying out the numerical illustrations using the sinc basis in each. © 1995 John Wiley & Sons, Inc.     

The Atlas project-a new pulsed power facility for high energydensity physics experiments

Atlas is a facility being designed at Los Alamos National Laboratory (LANL) to perform high-energy-density experiments in support of weapon physics and basic research programs. It is designed to be an international user facility, providing experimental opportunities to researchers from national laboratories and academic institutions. For hydrodynamic experiments, it will be capable of achieving a pressure exceeding 30 Mbar in a several cubic centimeter volume. With the development of a suitable opening switch, it will be capable of producing more than 3 MJ of soft X-rays. The capacitor bank design consists of a 36 MJ array of 240 kV Marx modules. The system is designed to deliver a peak current of 45-50 MA with a 4-5-μs rise time. The Marx modules are designed to be reconfigured to a 480-kV configuration for opening switch development. The capacitor bank is resistively damped to limit fault currents and capacitor voltage reversal. An experimental program for testing and certifying prototype components is currently under way. The capacitor bank design contains 300 closing switches. These switches are a modified version of a railgap switch originally designed for the DNA-ACE machines. Because of the large number of switches in the system, individual switch prefire rates must be less than 10^-4 to protect the expensive target assemblies. Experiments are under way to determine if the switch-prefire probability can be reduced with rapid capacitor charging     

Opportunities for the use of computer algebra systems in middle secondary mathematics in England and Wales

This paper presents and discusses a number of ways in which mathematical attainment targets specified for pupils aged 11–16 in the revised National Curriculum can be achieved when teachers deploy computer algebra systems.     

Chemistry and Biosynthesis of the Hypothalamic Releasing and Inhibiting Neurohormones

The hypothalamus secretes hormones which in turn affect the release of hormones from the anterior lobe of the pituitary gland. Evidence has so far been adduced for the existence of seven hypothalamic releasing hormones and three inhibiting hormones. These neurohormones are all oligopeptides and occur in only nanogram amounts in the hypothalamus. The study of synthetic analogs has provided valuable information regarding their mechanism of action.     

The stereoisomers of 3,7,11-trimethyldodeca-2,6,10-triene

Four geometrical steroisomers of 3,7,11-trimethyldodeca-2,6,10-triene have been synthesized. The PMR and ¹³C NMR spectra of these compounds provide important information on the geometry of Me substituted double bonds, while the mass spectra distinguish (E and Z,E)-isomers from (E and Z,Z)-isomers.     

Photoaffinity analogues of farnesyl pyrophosphate transferable by protein farnesyl transferase

Farnesylation is a posttranslational lipid modification in which a 15-carbon farnesyl isoprenoid is linked via a thioether bond to specific cysteine residues of proteins in a reaction catalyzed by protein farnesyltransferase (FTase). We synthesized analogues (3-6) of farnesyl pyrophosphate (FPP) to probe the range of modifications possible to the FPP skeleton which allow for efficient transfer by FTase. Photoaffinity analogues of FPP (5, 6) were prepared by substituting perfluorophenyl azide functional groups for the omega-terminal isoprene of FPP. Substituted anilines replace the omega-terminal isoprene in analogues 3 and 4. Compounds 3-5 were prepared by reductive amination of the appropriate anilines with 8-oxo-geranyl acetate, followed by ester hydrolysis, chlorination, and pyrophosphorylation. Additional substitution of three methylenes for the beta-isoprene of FPP gave photoprobe 6 in nine steps. Preparation of the analogues required TiCl(4)-mediated imine formation prior to NaBH(OAc)(3) reduction for anilines with a pK(a) < 1. The azide moiety was not affected by Ph(3)PCl(2) conversion of allylic alcohols 13-16 into corresponding chlorides 17-20. Analogues 3-6 are efficiently transferred to target N-dansyl-GCVLS peptide substrate by mammalian FTase. Comparison of analogue structures and kinetics of transfer to those of FPP reveals that ring fluorination and para substituents have little effect on the affinity of the analogue pyrophosphate for FTase and its transfer efficiency. These results are also supported with models of the analogue binding modes in the active site of FTase. The transferable azide photoprobe 5 photoinactivates FTase. Transferable analogues 5 and 6 allow the formation of appropriately posttranslationally modified photoreactive peptide probes of isoprene function.     

Hydration of small peptides

The results for the sequential hydration of small peptides (<15 residues) obtained in our group are reviewed and put in perspective with other work published in the literature where appropriate. Our findings are based on hydration equilibrium measurements in a high-pressure drift cell inserted into an electrospray mass spectrometer and on calculations employing molecular mechanics and density functional theory methods. It is found that the ionic functional groups typically present in peptides, the ammonium, guanidinium, and carboxylate groups, are the primary target of water molecules binding to peptides. Whereas the water–guanidinium binding energy is fairly constant at 9 ± 1 kcal/mol, the water binding energy of an ammonium group ranges from 7 to 15 kcal/mol depending on how exposed the ammonium group is. A five-residue peptide containing an ammonium group is in favorable cases large enough to fully self-solvate the charge, but a pentapeptide containing a guanidinium group is too small to efficiently shield the charge of this much larger ionic group. The water–carboxylate interaction amounts to 13 kcal/mol with smaller values for a shielded carboxylate group. Both water bound to water in a second solvation shell and charge remote water molecules on the surface of the peptide are bound by 7–8 kcal/mol. The presence of several ionic groups in multiply charged peptides increases the number of favorable hydration sites, but does not enhance the water–peptide binding energy significantly. Water binding energies measured for the first four water molecules bound to protonated bradykinin do not show the declining trend typically observed for other peptides but are constant at 10 kcal/mol, a result consistent with a molecule containing a salt bridge with several good hydration sites. Questions regarding peptide structural changes as a function of number of solvating water molecules are discussed. Not much is known at present about the effect of individual water molecules on the conformation of peptides and on the stability of peptide zwitterions.     

Amyloid beta-protein: monomer structure and early aggregation states of Abeta42 and its Pro19 alloform

The amyloid beta-protein (Abeta) is a seminal neuropathic agent in Alzheimer's disease (AD). Recent evidence points to soluble Abeta oligomers as the probable neurotoxic species. Among the naturally occurring Abeta peptides, the 42-residue form Abeta42 is linked particularly strongly with AD, even though it is produced at approximately 10% of the levels of the more abundant 40-residue form Abeta40. Here, we apply mass spectrometry and ion mobility to the study of Abeta42 and its Pro19 alloform. The Phe19 --> Pro19 substitution blocks fibril formation by [Pro19]Abeta42. Evidence indicates that solution-like structures of Abeta monomers are electrosprayed and characterized. Unfiltered solutions of Abeta42 produce only monomers and large oligomers, whereas [Pro19]Abeta42 solutions produce abundant monomers, dimers, trimers, and tetramers but no large oligomers. When passed through a 10,000 amu filter and immediately sampled, Abeta42 solutions produce monomers, dimers, tetramers, hexamers, and an aggregate of two hexamers that may be the first step in protofibril formation. These results are consistent with recently published photochemical cross-linking data and lend support to recent aggregation mechanisms proposed by Bitan, Teplow, and co-workers [J. Biol. Chem. 2003, 278, 34882-34889].     

Studying and switching electron transfer: from the ensemble to the single molecule

We report here on the systematic investigation of photoinduced intramolecular electron transfer (IET) in a series of donor-bridge-acceptor molecules as a means of understanding electron transport through the bridge. Perylenebisimide chromophores connected by various oligophenylene bridges are studied because their electron-transfer behavior can readily be monitored by following changes in the fluorescence intensity. We find dramatic switching of the IET behavior as the solvent polarity (dielectric constant) is increased. By combining steady-state and time-resolved fluorescence spectroscopy in a variety of solvents at multiple temperatures with standard theories of electron transfer, we determine parameters governing the IET behavior of these dimers, such as the electronic coupling through the bridges. We also deploy available ab initio quantum chemical methods to calculate the through-space component of the electronic coupling matrix element. Single-molecule investigations of the electron-transfer behavior also show that IET can be switched reversibly by a similar mechanism in an isolated individual molecule.