Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.     

A Network Simulation of High-congestion Road-traffic Flows in Cities with Marine Container Terminals

Port cities where marine cargo terminals are located are generally near urban areas characterized by high-congestion road traffic. Changes in cargo traffic volumes into a marine terminal, or in the surrounding traffic arteries, which carry this traffic, can significantly affect the terminal's operations. Conversely, activity at the terminal can have an impact on the traffic levels and congestion for a considerable distance from the terminal. This paper demonstrates a methodology useful for studying the impact of road traffic flows on marine container terminals located in highly congested areas. This model was developed at the request of the Virginia Center for World Trade and was used to answer three planning questions in the port of Hampton Roads, Virginia, USA-what would be the impact of: opening a new section of interstate highway, a projected doubling of container traffic at one terminal, and a daily unit train in the vicinity of another terminal. The problem was made more challenging by limited data-collection funds. None the less, the model was deemed valid by a panel of traffic experts and officials from several major state and private agencies involved in marine traffic management. The model results were subsequently a factor in two major decisions related to terminal management.     

The isolation and structure determination of cryptomisrine,a novel indolo[3,2-b]quinoline dimeric alkaloid from cryptolepis sanguinolenta

The isolation and structure determination of cryptomisrine, a novel indolo[3,2-b]quinoline dimeric alkaloid obtained from extracts of the roots of the Ghanaian medicinal plant Cryptolepis sanguinolenta is reported. The structure determination was made via a consideration of the spectral data, including uv, ir, nmr, and mass spectra. In particular, one-dimensional proton/carbon nmr, one-dimensional nOe difference nmr, and a series of homonuclear (COSY) and inverse-detected heteronuclear two-dimensional (HMQC, HMBC) experiments were utilized, as well as high resolution FABMS. Cryptomisrine is most unusual in that its two monomeric parts apparently exist in such a C₂ symmetric environment that only one set of proton and carbon nmr resonances are observed. Cryptomisrine is the first example of a dimeric indolo-[3,2-b]quinoline alkaloid to have been isolated from nature.     

Inverted and suppressed direct response HMQC-TOCSY spectra - a convenient method of spectral editing

HMQC-TOCSY spectra provide a convenient means of establishing proton-proton connectivities in congested spectra of complex aromatic heterocycles. Advantage is taken of the greater dispersion of the ¹³C nmr spectrum to circumvent overlap which would preclude spectral interpretation through the usual COSY spectrum. A recently reported method for inverting direct responses (IDR) in HMQC-TOCSY spectra is demonstrated for [1]benzothieno[2,3-c]naphtho[2,1-g]quinoline. A modification of the IDR-HMQC-TOCSY method is also demonstrated which is capable of fully suppressing direct responses (SDR) without resorting to the timing of the onset of decoupling as in the original report of the HMQC-TOCSY experiment. SDR-HMQC-TOCSY has the further advantage of allowing the use of higher levels of digitization in F₂ than can be attained when broadband heteronuclear decoupling is employed.     

Broadband and band-selective IMPRESS-gHMBC: compensation of refocusing inefficiency with synchronized inversion sweep

Compensation of refocusing inefficiency in a gHMBC experiment by replacing the rectangular pi pulse with a pair of adiabatic pulses with synchronized inversion sweep (CRISIS) significantly improves the performance of the gHMBC experiment. The CRISIS-gHMBC experiment retains the pure absorptive shapes in F1 and hence results in better lineshape and higher resolution than the current versions of magnitude mode gHMBC spectra. When used as a broadband experiment, CRISIS-gHMBC, owing to better refocusing efficiency of the adiabatic pulse pairs, gives improved performance across the 13C spectral width. Moreover, it is shown that CRISIS-gHMBC is a robust and improved alternative and when used along with the IMPRESS (Improved Resolution using Symmetrically Shifted pulses) technique further increases the sensitivity and resolution without additional experimental time. The IMPRESS-CRISIS combination is demonstrated for broadband gHMBC and band-selective gHMBC experiments. The ICbs-gHMBC [IMPRESS-CRISIS-band-selective gHMBC] experiment is an attractive and better alternative to individual band-selective gHMBC.     

The synthesis of novel polycyclic heterocyclic ring systems via photocyclization. 11. Synthesis and total assignment of the 1H and 13C NMR spectra of isomeric benzothienonaphthoquinolines using multiple inverse detected two-dimensional NMR methods

Two novel heterocyclic ring systems, namely, [1]benzothieno[2,3-c]naphtho[1,2-f]quinoline and [1]benzothieno[2,3-c]naphtho[2,1-g]quinoline have been synthesized and characterized by inverse detected two-dimensional nmr methods. Unequivocal total assignments of the proton and carbon nmr spectra were made through the concerted utilization of HMQC (Heteronuclear Multiple Quantum Correlation) and a combination of HMBC (Heteronuclear Multiple Bond Correlation) and HMQC-TOCSY (HMQC with proton TOtal Correlation Spectroscopy).     

Elucidation of the structure of quindolinone,a minor alkaloid of cryptolepis sanguinolenta: Submilligram 1H-13c and 1H-15N heteronuclear shift correlation experiments using micro inverse-detection

Elucidation of minor natural product structures has been significantly augmented by inverse-detection; further improvement has been afforded by the development of micro inverse-detection probes. We report here the elucidation of the structure of a new alkaloid, quindolinone (5H, 10H-indolo[3,2-b]quinolin-11-one), from the West African plant Cryptolepis sanguinolenta. All nmr data for this minor, preparative hplc-isolated alkaloid, including ¹H-¹⁵N one? bond heteronuclear shift correlation (HMQC) data, were recorded on an 800 μg sample of the alkaloid dissolved in 140 μl of 100% d₆-DMSO using a 400 MHz spectrometer.     

Mass spectrometric analysis of porcine rhodopsin

Rhodopsin is the dim light photosensitive pigment of animals. In this work, we undertook to study the structure of rhodopsin from swine and compare it with bovine and rat rhodopsin. Porcine rhodopsin was analyzed using methodology developed previously for mass spectrometric analysis of integral membrane proteins. Combining efficient protein cleavage and high performance liquid chromatography separation with the sensitivity of mass spectrometry (MS), this technique allows the observation of the full protein map and the posttranslational modifications of the protein in a single experiment. The rhodopsin protein from a single porcine eye was sequenced completely, with the exception of two single-amino acid fragments and one two-amino acid fragment, and the gene sequence reported previously was confirmed. The posttranslational modifications, similar to the ones reported previously for bovine and rat rhodopsin, were also identified. Although porcine rhodopsin has a high degree of homology to bovine and rat rhodopsins and most of their posttranslational modifications are identical, the glycosylation and phosphorylation patterns observed were different. These results show that rhodopsin from a single porcine eye can be characterized completely by MS. This technology opens the possibility of rhodopsin structural and functional studies aided by powerful mass spectrometric analysis, using the fellow eye as an internal control.     

Application of high-field NMR and cryogenic probe technologies in the structural elucidation of poecillastrin a,a new antitumor macrolide lactam from the sponge poecillastra species

Poecillastrin A (1), a new polyketide-derived macrolide lactam, was isolated from a deep-water collection of the marine sponge Poecillastra species. The structure of poecillastrin A (1) was assigned using NMR data acquired at 500 MHz with an inverse-detection cryogenic probe and at 800 MHz with a room-temperature probe.     

The quantitative analysis of 1-alpha-acetylmethadol and its principal metabolites in biological specimens by gas chromatography-chemical ionization-multiple ion monitoring mass spectrometry.

1-alpha-acetylmethadol (LAAM) is a new drug under development for the treatment of heroin dependence. A new analytical method applicable to the accurate biodispositional study of the drug and its metabolities is described and critically discussed in this report. The procedure involves sample preparation and direct organic solvent extraction using eta-butyl chloride, amide derivatization by molecular rearrangement, and gas chromatography-chemical ionization mass spectrometry-selected ion monitoring, with methane as the carrier and ammonia as reagent gases. Deuterated (d3 stable isotopes of LAAM and its metabolites are used as internal standards. The method is free from qualitative interferences and has quantitative sensitivity to 5 ng/ml for 2.0 ml samples with 10-15% accuracy and precision in the range 5-100 ng/ml; and 2-5% at concentrations up to 750 ng/ml. Specimens of plasma, whole blood, urine, bile, brain, liver, and other visceral samples have been successfully analyzed, as well as in vitro preparations such as hepatic microsomes. By appropriate data processing, the method lends itself to routine analysis and high volume work; even manually the method is capable of at least 50 samples per week. A simplified procedure for the analysis of LAAM and its metabolites in urine only is also presented and discuet up and use the methods.