A formula for the determinant of a sum of matrices

We give a formula, involving circular words and symmetric functions of the eigenvalues, for the determinant of a sum of matrices. Theorem of Hamilton-Cayley is deduced from this formula.UQAM and LITPUniversité Paris 7 and LITP.     

Effect of time on the interfacial and foaming properties of beta-lactoglobulin/acacia gum electrostatic complexes and coacervates at pH 4.2

The electrostatic complexation between beta-lactoglobulin and acacia gum was investigated at pH 4.2 and 25 degrees C. The binding isotherm revealed a spontaneous exothermic reaction, leading to a DeltaHobs = -2108 kJ mol(-1) and a saturation protein to polysaccharide weight mixing ratio of 2:1. Soluble electrostatic complexes formed in these conditions were characterized by a hydrodynamic diameter of 119 +/- 0.6 nm and a polydispersity index of 0.097. The effect of time on the interfacial and foaming properties of these soluble complexes was investigated at a concentration of 0.1 wt % at two different times after mixing (4 min, referred as t approximately 0 h and t = 24 h). At t approximately 0 h, the mixture is mainly made of aggregating soluble electrostatic complexes, whereas after 24 h these complexes have already insolubilize to form liquid coacervates. The surface elasticity, viscosity and phase angle obtained at low frequency (0.01 Hz) using oscillating bubble tensiometry revealed higher fluidity and less rigidity in the film formed at t approximately 0 h. This observation was confirmed by diminishing bubble experiments coupled with microscopy of the thin film. It was thicker, more homogeneous and contained more water at t approximately 0 h as compared to t = 24 h (thinner film, less water). This led to very different gas permeability's of Kt approximately 0 h = 0.021 cm s(-1) and Kt=24 h) = 0.449 cm s(-1), respectively. Aqueous foams produced with the beta-lactoglobulin/acacia gum electrostatic complexes or coacervates exhibited very different stability. The former (t approximately 0 h) had a stable volume, combining low drainage rate and mainly air bubble disproportionation as the destabilization mechanism. By contrast, using coacervates aged for 24 h, the foam was significantly less stable, combining fast liquid drainage and air bubble destabilization though fast gas diffusion followed by film rupture and bubble coalescence. The strong effect of time on the air/water interfacial properties of the beta-lactoglobulin/acacia gum electrostatic complexes can be understood by their reorganization at the interface to form a coacervate phase that is more fluid/viscous at t approximately 0 h vs rigid/elastic at t = 24 h.     

Concise synthesis of anhydrovinblastine from leurosine

[reaction: see text] The Cp(2)TiCl-mediated deoxygenation of leurosine (1) afforded anhydrovinblastine (4) in good yield. Furthermore, as the reaction proceeded via a carbon-centered radical intermediate, this transient was also trapped by a hydrogen-atom donor to afford selectively reduced alkaloid 10.     

Easily synthesized antimalarial ferrocene triazacyclononane quinoline conjugates

Starting from triazacyclononane, easily accessible ferrocenic quinoline derivatives were synthesized. Their antiplasmodial properties were investigated against chloroquine sensitive (HB3) and chloroquine-resistant (Dd2) Plasmodium falciparum. One of them, 7-chloro-4-[4-(7-chloro-4-quinolyl)-7-ferrocenylmethyl-1,4,7- triazacyclononan-1-yl]quinoline (4) showed potent antimalarial activity in vitro against the chloroquine-resistant strain Dd2 and therefore revealed to be the most promising lead from the present work for new organometallic antimalarial agents.     

Total synthesis of amaryllidaceae alkaloid buflavine

A concise synthesis of the amaryllidaceae alkaloid buflavine (1) and its regioisomer (2) involving sequential Meyers' biaryl coupling, enecarbamate formation, and hydrogenation followed by ultimate intramolecular reductive amination is presented.     

Homolytic displacement at carbon: XI. Intramolecular homolytic displacement as a route to cyclopentane and tetrahydrofuran derivatives from hex-5-enyl- andhex-3-oxo-5-enylcobaloximes

5-Methylhex-5-enylcobaloxime reacts with carbon tetrachloride and with fluorotrichloromethane at 80–100°C to give substantially pure 1-methyl-1-(β,β,β-trichloroethyl)- and 1-methyl-1-β-fluoro-β,β-dichloroethyl)-cyclopentane. Hex-5-enylco-baloxime also gives trichloroethylcyclopentane from carbon tetrachloride, but the yield is dependent on the concentration of carbon tetrachloride. Similar cyclisation to give trichloroethyl- or fluorodichloroethyltetrahydrofuran is observed in the reactions of hex-3-oxo-5-enylcobaloxime with carbon tetrachloride and fluorotrichloromethane. However, no cyclisation was observed in the reactions of the ester, hex-2-one-3-oxo-5-enylcobaloxime, with carbon tetrachloride. These reactions are believed to take place by attack of a polyhalogenomethyl radical at the terminal unsaturated carbon of the organic ligand, followed either by an intramolecular homolytic displacement in which the carbon radical at position-5 attacks carbon-1 with displacement of cobaloxime(II), or by a halogen atom abstraction.     

The assemble,grow and lift-off (AGLO) strategy to construct complex gold nanostructures with pre-designed morphologies

The construction of metallic nanostructures with customizable morphologies and complex shapes has been an essential pursuit in nanoscience. DNA nanotechnology has enabled the fabrication of increasingly complex DNA nanostructures with unprecedented specificity, programmability and sub-nanometer precision, which makes it an ideal approach to rationally organize metallic nanostructures. Here we report an Assemble, Grow and Lift-Off (AGLO) strategy to construct robust standalone gold nanostructures with pre-designed customizable shapes in solution, using only a simple 2D DNA origami sheet as a versatile transient template. Gold nanoparticle (AuNP) seeds were firstly assembled onto the pre-designed binding sites of the DNA origami template and then additional gold was slowly deposited onto the AuNP seeds. The growing seed surfaces eventually merge with adjacent seeds to generate one continuous gold nanostructure in a pre-designed shape, which can then be lifted off the origami template. Diverse customized patterns of templated AuNP seeds were successfully transformed into corresponding gold nanostructures with the target structure transformation percentage over 80%. Moreover, the AGLO strategy can be incorporated with a magnetic bead separation platform to enable the easy recycling of the excess AuNP seeds and DNA components.

The AGLO strategy generates complex gold nanostructures with user-designed morphologies in solution, using only a simple 2D DNA origami sheet as a versatile transient template. The products are robust and stable as standalone gold nanostructures.     

Cyclic PNA-based compound directed against HIV-1 TAR RNA: modelling, liquid-phase synthesis and TAR binding

A cyclic molecule including a hexameric PNA sequence has been designed and synthesized in order to target the TAR RNA loop of HIV-1 through the formation of a "kissing complex". For comparison, its linear analogue has also been investigated. The synthesis of the cyclic and linear PNA has been accomplished following a liquid-phase strategy using mixed PNA and fully N-protected (aminoethylglycinamide) fragments. The interactions of this cyclic PNA and its linear analogue with TAR RNA have been studied and the results indicate clearly that no interaction occurs between the cyclic antisense PNA and TAR RNA, whereas a tenuous interaction has been detected with its linear PNA analogue.     

From anisole to 1,2,4,5‐tetramethoxybenzene: Theoretical study of the factors that determine the conformation of methoxy groups on a benzene ring

Unhindered ortho‐dimethoxy‐substituted phenyl rings often display a coplanar conformation. A theoretical study of a series of methoxybenzenes consisting of methoxybenzene (anisole), the three dimethoxybenzenes, and 1,2,4,5‐tetramethoxybenzene, at the DFT/B3LYP/6‐311++G** level of theory, allows us to identify the factors influencing the conformational preference and attribute the coplanarity of such methoxy groups to mesomeric effects. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007