Finite domination and Novikov homology over strongly Z-graded rings

Let L be a unital Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent to a bounded complex of finitely generated projective L0-modules, generalising known results for twisted Laurent polynomial rings. The crucial hypothesis is that L is a strongly graded ring. 

Matrix and reservoir-type multipurpose vaginal rings for controlled release of dapivirine and levonorgestrel

A matrix-type silicone elastomer vaginal ring providing 28-day continuous release of dapivirine (DPV) - a lead candidate human immunodeficiency virus type 1 (HIV-1) microbicide compound - has recently demonstrated moderate levels of protection in two Phase III clinical studies. Here, next-generation matrix and reservoir-type silicone elastomer vaginal rings are reported for the first time offering simultaneous and continuous in vitro release of DPV and the contraceptive progestin levonorgestrel (LNG) over a period of between 60 and 180days. For matrix-type vaginal rings comprising initial drug loadings of 100, 150 or 200mg DPV and 0, 16 or 32mg LNG, Day 1 daily DPV release values were between 4132 and 6113μg while Day 60 values ranged from 284 to 454μg. Daily LNG release ranged from 129 to 684μg on Day 1 and 2-91μg on Day 60. Core-type rings comprising one or two drug-loaded cores provided extended duration of in vitro release out to 180days, and maintained daily drug release rates within much narrower windows (either 75-131μg/day or 37-66μg/day for DPV, and either 96-150μg/day or 37-57μg/day for LNG, depending on core ring configuration and ignoring initial lag release effect for LNG) compared with matrix-type rings. The data support the continued development of these devices as multi-purpose prevention technologies (MPTs) for HIV prevention and long-acting contraception.

Intravaginal ring delivery of the reverse transcriptase inhibitor TMC 120 as an HIV microbicide

TMC 120 (Dapivirine) is a potent non-nucleoside reverse transcriptase inhibitor that is presently being developed as a vaginal HIV microbicide. To date, most vaginal microbicides under clinical investigation have been formulated as single-dose semi-solid gels, designed for application to the vagina before each act of intercourse. However, a clear rationale exists for providing long-term, controlled release of vaginal microbicides in order to afford continuous protection against heterosexually transmitted HIV infection and to improve user compliance. In this study we report on the incorporation of various pharmaceutical excipients into TMC 120 silicone, reservoir-type intravaginal rings (IVRs) in order to modify the controlled release characteristics of the microbicide. The results demonstrate that TMC 120 is released in zero-order fashion from the rings over a 28-day period and that release parameters could be modified by the inclusion of release-modifying excipients in the IVR. The hydrophobic liquid excipient isopropyl myristate had little effect on steady-state daily release rates, but did increase the magnitude and duration of burst release in proportion to excipient loading in the IVR. By comparison, the hydrophobic liquid poly(dimethylsiloxane) had little effect on TMC 120 release parameters. A hydrophilic excipient, lactose, had the surprising effect of decreasing TMC 120 burst release while increasing the apparent steady-state daily release in a concentration-dependent manner. Based on previous cell culture data and vaginal physiology, TMC120 is released from the various ring formulations in amounts potentially capable of maintaining a protective vaginal concentration. It is further predicted that the observed release rates may be maintained for at least a period of 1 year from a single ring device. TMC 120 release profiles and the mechanical properties of rings could be modified by the physicochemical nature of hydrophobic and hydrophilic excipients incorporated into the IVRs.

Ring-opening polymerisation of silver-diphosphine [M2L3] coordination cages to give [M2L3](infinity) coordination polymers

[M2L3] coordination cages and linear [M2L3]infinity polymers of the rigid, bridging diphosphines bis(diphenylphosphino)acetylene (dppa) and trans-1,2-bis(diphenylphosphino)ethylene (dppet) with silver(I) salts have been investigated in the solution and solid states. Unlike flexible diphosphines, 1:1 dppa/AgX mixtures do not selectively form discrete [Ag2(diphos)2(X)2] macrocycles; instead dynamic mixtures of one-, two- and three-coordinate complexes are formed. However, 3:2 dppa/AgX ratios (X = SbF6. BF4, O3SCF3 or NO3) do lead selectively to new [M2L3] triply bridged cage complexes [Ag2(dppa)3(X)2] 1a-d (X = SbF6 a, BF4 b, O3SCF3 c, NO3 d), which do not exhibit Ag-P bond dissociation at room temperature on the NMR time scale (121 MHz). Complexes la-d were characterised by X-ray crystallography and were found to have small internal cavities, helical conformations and multiple intramolecular aromatic interactions. The nucleophilicity of the anion subtly influences the cage shape: Increasing nucleophilicity from SbF6 (1a) through BF4 (1b) and O3SCF3 (1c) to NO3 (1d) increases the pyramidal distortion at the AgP3 centres, stretching the cage framework (with Ag...Ag distances increasing from 5.48 in 1a to 6.21 A in 1d) and giving thinner internal cavities. Crystal packing strongly affected the size of the helical twist angle, and no correlation between this parameter and the Ag-Ag distance was observed. When crystalline 1c was stored in its supernatant for 16 weeks, conversion occured to the isostoichiometric [M2L3]infinity coordination polymer [Ag(dppa)2Ag(dppa)(O3SCF3)2]infinity (1c'). X-ray crystallography revealed a structure with ten-membered Ag2(dppa)2 rings linked into infinite one-dimensional chains by a third dppa unit. The clear structural relationship between this polymer and the precursor cage 1c suggests a novel example of ring-opening polymerisation. With dppet, evidence for discrete [M2L3] cages was also found in solution, although 31P NMR spectroscopy suggested some Ag-P bond dissociation. On crystallisation, only the corresponding ring-opened polymeric structures [M2L3]infinity could be obtained. This may be because the greater steric bulk of dppet versus dppa destabilises the cage and favours the ring-opening polymerisation.

Biotransformation of Substituted Pyridines with Dioxygenase-containing Microorganisms.

A series of 2-, 3- and 4-substituted pyridines was metabolised using the mutant soil bacterium Pseudomonas putida UV4 which contains a toluene dioxygenase (TDO) enzyme. The regioselectivity of the biotransformation in each case was determined by the position of the substituent. 4-Alkylpyridines were hydroxylated exclusively on the ring to give the corresponding 4-substituted 3-hydroxypyridines, while 3-alkylpyridines were hydroxylated stereoselectively on C-1 of the alkyl group with no evidence of ring hydroxylation. 2-Alkylpyridines gave both ring and side-chain hydroxylation products. Choro- and bromo-substituted pyridines, and pyridine itself, while being poor substrates for P. putida UV4, were converted to some extent to the corresponding 3-hydroxypyridines. These unoptimised biotransformations are rare examples of the direct enzyme-catalysed oxidation of pyridine rings and provide a novel synthetic method for the preparation of substituted pyridinols. Evidence for the involvement of the same TDO enzyme in both ring and side-chain hydroxylation pathways was obtained using a recombinant strain of Escherichia coli (pKST11) containing a cloned gene for TDO. The observed stereoselectivity of the side-chain hydroxylation process in P. putida UV4 was complicated by the action of an alcohol dehydrogenase enzyme in the organism which slowly leads to epimerisation of the initial (R)-alcohol bioproducts by dehydrogenation to the corresponding ketones followed by stereoselective reduction to the (S)-alcohols.

Tetrodotoxin-sensitive sodium current in sheep lymphatic smooth muscle.

1. Fast inward currents were elicited in freshly isolated sheep lymphatic smooth muscle cells by depolarization from a holding potential of -80 mV using the whole-cell patch-clamp technique. The currents activated at voltages positive to -40 mV and peaked at 0 mV. 2. When sodium chloride in the bathing solution was replaced isosmotically with choline chloride inward currents were abolished at all potentials. 3. These currents were very sensitive to tetrodotoxin (TTX). Peak current was almost abolished at 1 microM with half-maximal inhibition at 17 nM. 4. Examination of the voltage dependence of steady state inactivation showed that more than 90% of the current was available at the normal resting potential of these cells (-60 mV). 5. The time course of recovery from inactivation was studied using a double-pulse protocol and showed that recovery was complete within 100 ms with a time constant of recovery of 20 ms. 6. Under current clamp, action potentials were elicited by depolarizing current pulses. These had a rapid upstroke and a short duration and could be blocked with 1 microM TTX. 7. Spontaneous contractions of isolated rings of sheep mesenteric lymphatic vessels were abolished or significantly depressed by 1 microM TTX.

Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Design optimisation of ring elements for broadband reflectarray antennas

Plane wave scattering from a flat surface consisting of two periodic arrays of ring elements printed on a grounded dielectric sheet is investigated. It is shown that the reflection phase variation as a function of ring diameter is controlled by the difference in the centre resonant frequency of the two arrays. Simulated and measured results at X-band demonstrate that this parameter can be used to reduce the gradient and improve the linearity of the reflection phase versus ring size slope. These are necessary conditions for the re-radiating elements to maximise the bandwidth of a microstrip reflectarray antenna. The scattering properties of a conventional dual resonant multilayer structure and an array of concentric rings printed on a metal backed dielectric substrate are compared and the trade-off in performance is discussed.

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

The equilibrium polymerization of sulfur is investigated by Monte Carlo simulations. The potential energy model is based on density functional results for the cohesive energy, structural, and vibrational properties as well as reactivity of sulfur rings and chains [Part I, J. Chem. Phys. 118, 9257 (2003)]. Liquid samples of 2048 atoms are simulated at temperatures 450less than or equal toTless than or equal to850 K and P=0 starting from monodisperse S-8 molecular compositions. Thermally activated bond breaking processes lead to an equilibrium population of unsaturated atoms that can change the local pattern of covalent bonds and allow the system to approach equilibrium. The concentration of unsaturated atoms and the kinetics of bond interchanges is determined by the energy DeltaE(b) required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15less than or equal toDeltaE(b)less than or equal to21 kcal/mol over a wide temperature range (Tgreater than or equal to450 K), within which polymerization occurs readily, with entropy from the bond distribution overcompensating the increase in enthalpy. There is a maximum in the polymerized fraction at temperature T-max that depends on DeltaE(b). This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for Tless than or equal toT(max), because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm-Schulz function, plus an isolated peak for S-8. Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S-8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on DeltaE(b) give estimates of the polymerization temperature T-f=450+/-20 K. (C) 2003 American Institute of Physics.

Equilibrium polymerization of cyclic carbonate oligomers. III. Chain branching and the gel transition

Ring-opening polymerization of cyclic polycarbonate oligomers, where monofunctional active sites act on difunctional monomers to produce an equilibrium distribution of rings and chains, leads to a "living polymer." Monte Carlo simulations [two-dimensional (2D) and three-dimensional (3D)] of the effects of single [J. Chem. Phys. 115, 3895 (2001)] and multiple active sites [J. Chem. Phys. 116, 7724 (2002)] are extended here to trifunctional active sites that lead to branching. Low concentrations of trifunctional particles c(3) reduce the degree of polymerization significantly in 2D, and higher concentrations (up to 32%) lead to further large changes in the phase diagram. Gel formation is observed at high total density and sizable c(3) as a continuous transition similar to percolation. Polymer and gel are much more stable in 3D than in 2D, and both the total density and the value of c(3) required to produce high molecular weight aggregates are reduced significantly. The degree of polymerization in high-density 3D systems is increased by the addition of trifunctional monomers and reduced slightly at low densities and low c(3). The presence of branching makes equilibrium states more sensitive (in 2D and 3D) to changes in temperature T. The stabilities of polymer and gel are enhanced by increasing T, and-for sufficiently high values of c(3)-there is a reversible polymer-gel transformation at a density-dependent floor temperature. (C) 2002 American Institute of Physics.

Equilibrium polymerization of cyclic carbonate oligomers. II. Role of multiple active sites

Ring opening polymerization of bisphenol A polycarbonate is studied by Monte Carlo simulations of a model comprising a fixed number of Lennard-Jones particles and harmonic bonds [J. Chem. Phys. 115, 3895 (2001)]. Bond interchanges produced by a low concentration (0.10%less than or equal toc(a)less than or equal to0.36%) of chemically active particles lead to equilibrium polymerization. There is a continuous transition in both 2D and 3D from unpolymerized cyclic oligomers at low density to a system of linear chains at high density, and the polymeric phase is much more stable in three dimensions than in two. The steepness of the polymerization transition increases rapidly as c(a) decreases, suggesting that it is discontinuous in the limit c(a)-->0. The transition is entropy driven, since the average potential energy increases systematically upon polymerization, and there is a steady decline in the degree of polymerization as the temperature is lowered. The mass distribution functions for open chains and for rings are unimodal, with exponentially decaying tails that can be fitted by Zimm-Schulz functions and simpler exponential forms. (C) 2002 American Institute of Physics.

Perovskite lead zirconium titanate nanorings: Towards nanoscale ferroelectric

Rings of perovskite lead zirconium titanate (PZT) with internal diameters down to similar to 5 nm and ring thicknesses of similar to 5-10 nm have been fabricated and structurally, crystallographically, and chemically characterized using an analytical transmission electron microscope. Ring fabrication involved conformal solution deposition of a thin layer of PZT on the inside of a thin film of anodized aluminum oxide nanopores, and subsequent sectioning of the coated pores perpendicular to their cylinder axes. Although the starting solution used for the solution deposition was made from morphotropic phase boundary PZT, the nanorings were found to be on the zirconium-rich side of the PZT phase diagram. Nevertheless, coatings were found to be of perovskite crystallography. The dimensions of these nanorings are such that they have the potential to demonstrate polarization vortices, as modeled by Naumov [Nature (London) 432, 737 (2004)], and moreover represent the perfect morphology to allow vortex alignment and the creation of the ferroelectric "solenoid" as modeled by Gorbatsevich and Kopaev [Ferroelectrics 161, 321 (1994)].

Simulation of the surface structure of butylmethylimidazolium ionic liquids

Molecular dynamics simulations of the liquid/vacuum surfaces of the room temperature ionic liquids [bmim][PF6], [bmim][BF4] and [bmim][Cl] have been carried out at various temperatures. The surfaces are structured with a top monolayer containing oriented cations and anions. The butyl side chains tend to face the vacuum and the methyl side chains the liquid. However, as the butyl chains are not densely packed, both anions and rings are visible from the vacuum phase. The effects of temperature and the anion on the degree of cation orientation is small, but the potential drop from the vacuum to the interior of the liquid is greater for liquids with smaller anions. We compare the simulation results with a range of experimental observations and suggest that neutron reflection from samples with protiated butyl groups would be a sensitive probe of the structure.