A procedure to calculate torsion of elliptic curves over ℚ

We present an algorithm which uses the analytic parameterization of elliptic curves to rapidly calculate torsion subgroups, and calculate its running time. This algorithm is much faster than the “traditional” Lutz-Nagell algorithm used by most computer algebra systems to calculate torsion subgroups. This article was processed by the author using the T_EX style filePjour1g from Springer-Verlag     

FT-Raman spectroscopic investigation of a pseudopolymorphic transition in caffeine hydrate

The FT-Raman spectra of caffeine hydrate and anhydrous β-caffeine have been recorded. The accelerated dehydration of the hydrate has been monitored at 30, 35 and 40°C using an environmental chamber. The spectra representing the individual pseudopolymorphic phases differed subtly throughout the entire spectral range. Gradual broadening of the =CH stretching vibration observed at 3121 cm⁻¹ and the progressive appearance of a C=O stretch at 1656 cm⁻¹ were ascribed to intermolecular bonding between CH and C=O in the anhydrous phase. Accompanying loss of resolution of CH deformations in the lower wavenumber region observed at 1475 and 1255 cm⁻¹ supports the suggestion of intermolecular association involving CH. Concurrent loss of resolution of the weak C=N stretch at 1454 cm⁻¹ and recession of the medium intensity H---C=N deformation at 1255 cm⁻¹ were also detected, acknowledging the loss of interaction between N9 of the imidazole ring and the water molecule. The concomitant disappearance of the weak H₂O libration at 890 cm⁻¹ is observed, which suggests the occurrence of molecular realignment associated with corresponding loss of water of crystallisation. On removal of the hydrate backbone of the caffeine hydrate crystal structure, the lattice collapses, resulting in reduction of the intermolecular distance between individual caffeine molecules. The subsequent formation of a less rigid structure is evident, whereby molecules are weakly associated by unconventional CH…O interactions.     

Highly functionalized trans-2,5-disubstituted tetrahydrofurans from ribofuranoside templates: precursors to linked polycyclic ethers

Iodoetherification of C5 allylated ribo-furanosides leads to trans-2,5-disubstituted tetrahydrofurans with high selectivity. The application of this reaction to the synthesis of complex polycyclic ethers is illustrated in the preparation of a truncated, tricyclic analog of monensin A.     

Parameterization of semiempirical methods to treat nucleophilic attacks to biological phosphates: AM1/d parameters for phosphorus

 This paper reports a new AM1/d model for phosphorus that can be used to model nucleophilic attack of phosphates relevant for biological phosphate hydrolysis reactions. The parameters were derived from a quantum dataset calculated with hybrid density-functional theory [B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)] of phosphates and phosphoranes in various charge states, and on transitions states for nucleophilic attacks. A suite of non-linear optimization methods is outlined for semiempirical parameter development based on integrated evolutionary (genetic), Monte Carlo simulated annealing and direction set minimization algorithms. The performance of the new AM1/d model and the standard AM1 and MNDO/d models are compared with the density-functional results. The results demonstrate that the strategy of developing semiempirical parameters specific for biological reactions offers considerable promise for application to large-scale biological problems. Received: 15 January 2002 / Accepted: 6 September 2002 / Published online: 28 March 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: D.M. York e-mail: york@chem.umn.edu Acknowledgements. D.M.Y. is grateful for financial support provided by the National Institutes of Health (grant 1R01-GM62248-01A1) and the Donors of The Petroleum Research Fund, administered by the American Chemical Society, and the Minnesota Supercomputing Institute through a 6-month research scholar award (X.L.). Computational resources were provided by the Minnesota Supercomputing Institute.     

Determination of the enantiomeric composition of phenylalanine samples by chemometric analysis of the fluorescence spectra of cyclodextrin guest-host complexes

A novel strategy for determining the enantiomeric composition of phenylalanine samples that combines ordinary fluorescence spectroscopy, guest-host cyclodextrin chemistry, and multivariate regression modeling is investigated. Partial-least-squares regression (PLS-1) models were developed from fluorescence spectral data obtained with a series of samples containing cyclodextrin guest-host complexes of phenylalanine with different known enantiomeric compositions. The regression models were subsequently validated by determining the enantiomeric composition of a set of independently prepared phenylalanine samples. The ability of the models to correctly predict the enantiomeric compositions of future samples was evaluated in terms of the root-mean-square percent relative error (RMS%RE). The RMS%RE in the mol fraction of D-phenylalanine ranged from 1.3% to 3.0% when beta-cyclodextrin was used as the host molecule for different guest-host concentrations. The RMS%RE in the mol fraction of D-phenylalanine obtained in a similar validation study conducted with gamma-cyclodextrin ranged between 1.8% and 4.0% for different guest-host concentrations. Compared with previous studies done in absorption, fluorescence data were found to be more sensitive and the spectral differences observed as a function of enantiomeric composition were more uniformly spaced, making regression modeling more reliable. As a result, good regression models could be made at lower concentrations than were possible previously when absorption measurements were used.     

Diethylaminosulfur trifluoride-mediated intramolecular cyclization of 2-hydroxycycloalkylureas to fused bicyclic aminooxazoline compounds and evaluation of their biochemical activity against β-secretase-1 (BACE-1)

A series of unique bicyclic aminooxazolines were synthesized and found to exhibit micromolar inhibition of β-secretase-1 (BACE-1). The aminooxazolines were procured by an intramolecular diethylaminosulfur trifluoride (DAST)-mediated ring closure of a benzylic urea onto a secondary alcohol.