The Mathematical Theory of Ito Diffusions on Hypersurfaces, with Applications to NMR Relaxation Problems

A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a Rippled surface are presented.     

Multidimensional separation of isomeric species of chlorinated hydrocarbons such as PCB,PCDD, and PCDF

A multidimensional GC-system containing two capillary columns of different polarities, operated within a double oven instrument, was used for the optimized separation of complex isomeric mixtures of various types of chlorinated aromatic compounds such as PCB, PCDD, or PCDF. Electron capture was applied parallel to flame ionization detection to obtain sensitive signals of the PCB or PCDD and the n-alkane standards required for identification by Kovats indices, respectively. Electron capture detection within a valvelessly operated MDGC system forced changes in the usual instrumental set-up, the live-switching coupling piece being located within the second oven of the double oven instrument. This oven is operated isothermally to ensure optimal and interference-free detection, for stable flow conditions within the coupling piece and for the determination of the isothermal retention indices (Kovats), which are much more suitable for identification by retention than the so-called “linear” indices.     

Molecular modeling of cytochrome P450 3A4

The three-dimensional structure of human cytochrome P450 3A4 was modeled based on crystallographic coordinates of four bacterial P450s: P450 BM-3, P450cam, P450terp, and P450eryF. The P450 3A4 sequence was aligned to those of the known proteins using a structure-based alignment of P450 BM-3, P450cam, P450terp, and P450eryF. The coordinates of the model were then calculated using a consensus strategy, and the final structure was optimized in the presence of water. The P450 3A4 model resembles P450 BM-3 the most, but the B helix is similar to that of P450eryF, which leads to an enlarged active site when compared with P450 BM-3, P450cam, and P450terp. The 3A4 residues equivalent to known substrate contact residues of the bacterial proteins and key residues of rat P450 2B1 are located in the active site or the substrate access channel. Docking of progesterone into the P450 3A4 model demonstrated that the substrate bound in a 6-orientation can interact with a number of active site residues, such as 114, 119, 301, 304, 305, 309, 370, 373, and 479, through hydrophobic interactions. The active site of the enzyme can also accommodate erythromycin, which, in addition to the residues listed for progesterone, also contacts residues 101, 104, 105, 214, 215, 217, 218, 374, and 478. The majority of 3A4 residues which interact with progesterone and/or erythromycin possess their equivalents in key residues of P450 2B enzymes, except for residues 297, 480 and 482, which do not contact either substrate in P450 3A4. The results from docking of progesterone and erythromycin into the enzyme model make it possible to pinpoint residues which may be important for 3A4 function and to target them for site-directed mutagenesis.     

Micellar effect on the electron transfer reaction of chromium(V) ion with organic sulfides

The rate of electron transfer from organic sulfides to [Cr^V(ehba)₂]⁻ (ehba-2-ethyl-2-hydroxy butyric acid) decreases with a decrease in the polarity of the medium. The anionic surfactant, SDS and the cationic surfactant, CTAB have different effects on the kinetics of this reaction. The micellar inhibition observed in the presence of SDS is probably due to the decrease in the polarity and the electrostatic repulsion faced by the anionic oxidant from the anionic micelle and the partition of the hydrophobic substrate between the aqueous and micellar phases. The micellar catalysis in the presence of CTAB is attributed to the increase in the concentration of both reactants in the micellar phase. This micellar catalysis is observed to offset the retarding effects of the less polar micellar medium and the unfavorable charge-charge interaction between the + charge developed on S center in the transition state and the cationic micelle. This catalysis is contrary to the enormous micellar inhibition observed with IO₄⁻, HSO₅⁻ and HCO₄⁻ oxidation of organic sulfides.     

Dipolar relaxations in an epoxy-amine system

Dipolar relaxations in a reactive epoxy-amine system based on diglycidyl ether of bisphenol A with 4,4^′-diaminodiphenylsulfone were studied with the Havriliak-Negami function. The system was cured isothermally at 140 °C using simultaneous kinetic and microdielectric studies.The relaxation time was calculated from the frequency f_max of the peak of the loss factor ε^′′ versus frequency f. A linear relation exists between the logarithm of the relaxation time τ and the glass transition temperature T_g. Then, logτ follows the Di Benedetto equation revisited by Pascault and Williams allowing the prediction of the relaxation time τ during cure.The unrelaxed permittivity at high frequency ε_u, the relaxed or static permittivity ε_s and the skewness parameter β were found independent on the conversion or the curing time. The distribution parameter α decreases as curing time t increases. The difficulty of orientation of dipoles in the electric field due to vitrification is responsible of these behaviours.     

Electron beam irradiated textile cellulose fibres.: ESR studies and derivatisation with glycidyl methacrylate (GMA)

Powdered samples of cotton, flax and viscose from textile fibres were subjected to electron beam irradiation (20-400 KGy). ESR signals were observed after irradiation. The intensity of the signals depended on the administered dose and exhibited an exponential decay with time. The ESR spectra, whose pattern depended drastically on the crystallinity of the samples, indicated the simultaneous presence of at least three carbon-centred radical species. When the whole irradiated textile fibres were quenched in a solution of glycidyl methacrylate (GMA) a significant increase of the weight was observed, the increase being strongly dependent on the administered dose and on the time interval elapsed between irradiation and quenching. Spectroscopic characterisation evidenced that GMA acted as cellulose radicals scavenger on the unsubstituted carbon of the double bond and was covalently linked to the fibre through a new C-C bond while maintaining unaltered the ester and the epoxide groups, available for further derivatisations. Because irradiation of the whole textile fibres in the range 20-200 KGy does not result in significant degradation of the material, GMA quenching of fibres irradiated in this dose range may represent an attractive route to their functionalisation.     

Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison

We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b]. Problem P: find a globally-optimal value off and a corresponding point; Problem Q: find a set of disjoint subintervals of [a, b] containing only points with a globally-optimal value and the union of which contains all globally optimal points. A two-phase algorithm is proposed for Problem P. In phase I, this algorithm obtains rapidly a solution which is often globally-optimal. Moreover, a sufficient condition onf for this to be the case is given. In phase II, the algorithm proves the-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globally-optimal value. The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen. For small, the new algorithm requires only a few percent more function evaluations than the best possible one. An extended version of Piyavskii's algorithm is proposed for problem Q. A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals. This result is achieved for all twenty test problems.The research of the authors has been supported by AFOSR grants 0271 and 0066 to Rutgers University. Research of the second author has been also supported by NSERC grant GP0036426, FCAR grant 89EQ4144 and partially by AFOSR grant 0066. We thank Nicole Paradis for her help in drawing the figures.     

ESCA: Electron Spectroscopy for Chemical Analysis

A substance on which X-rays fall emits photoelectrons and Auger electrons. The energy spectra of the electrons emitted provide information about the electronic structure in the specimen, ranging from the innermost atomic levels and their dependence on the chemical environment to the molecular orbitals of the valence electrons and the band structure in solids. Electron spectra of this nature can now be recorded with high-resolution instruments; their analysis offers new aspects for investigation of chemical composition. The method of electron spectroscopy developed for this purpose, which has now been developed to a high degree of perfection, will be referred to in the following discussion as ESCA (Electron Spectroscopy for Chemical Analysis).     

Highly selective conversion of N-aroyl-α-dehydronaphthylalaninamides into 3,4-dihydrobenzoquinolinone derivatives via photoinduced intermolecular electron transfer

The irradiation of substituted (Z)-N-aroyl-α-dehydronaphthylalaninamides [(Z)-1] in methanol containing triethylamine (TEA) with Pyrex-filtered light was found to give 3,4-dihydrobenzoquinolinone derivatives (2) in high yields along with minor amounts of 4,5-dihydrooxazole derivatives (3). Analysis of the substituent effects on product composition revealed that both the photoreactivity of 1 and the selectivity of 2 are decreased with increasing electron-withdrawing ability of the substituent introduced at the para-position on the N-benzoyl benzene ring. From the analysis of the dependence of the quantum yield for the formation of 2 on the TEA concentration, it was found that back electron transfer occurs efficiently within an (E)-1 anion radical-TEA cation radical pair intermediate.