The greatest common divisor of certain sets of binomial coefficients

A formula is obtained for the greatest common divisor of any number of consecutive terms in any given row of Pascal's triangle.     

Recruitment of receptors at supported lipid bilayers promoted by the multivalent binding of ligand-modified unilamellar vesicles

The development of model systems that mimic biological interactions and allow the control of both receptor and ligand densities, is essential for a better understanding of biomolecular processes, such as the recruitment of receptors at interfaces, at the molecular level. Here we report a model system based on supported lipid bilayers (SLBs) for the investigation of the clustering of receptors at their interface. Biotinylated SLBs, used as cell membrane mimics, were functionalized with streptavidin (SAv), used here as receptor. Subsequently, biotinylated small (SUVs) and giant (GUVs) unilamellar vesicles were bound to the SAv-functionalized SLBs by multivalent interactions and found to induce the recruitment of both SAv on the SLB surface and the biotin moieties in the vesicles. The recruitment of receptors was investigated with quartz crystal microbalance with dissipation monitoring (QCM-D), which allowed the identification of the biotin and SAv densities necessary to obtain receptor recruitment. At approx. 0.6% of biotin in the vesicles, a transition between dense and low vesicle packing was observed, which coincided with the transitions between recruitment in the vesicles vs. recruitment in the SLB and between full and partial use of the biotin moieties in the vesicle. Direct optical visualization of the clustering at the interface of individual GUVs with the SLB platform was achieved with fluorescence microscopy, showing recruitment of SAv at the contact area as well as the deformation of the vesicles upon binding. Different vesicle binding regimes were observed for lower and higher biotin densities in the vesicles and at the SLBs. A more quantitative analysis of the molecular parameters implied in the interaction, indicated that approx. 10% of the vesicle area constitutes the contact area. Moreover, the SUV binding and recruitment appeared to be fast on the analysis time scale, whereas the binding of GUVs is slower due to the larger SLB area over which SAv recruitment needs to occur. The mechanisms revealed in this study may provide insight in biological processes in which recruitment occurs.

The development of model systems that mimic biological interactions and allow the control of both receptor and ligand densities, is essential for a molecular understanding of biomolecular processes, such as the recruitment of receptors at interfaces.     

Zirconium-catalysed N-acylation of lactams using unactivated carboxylic acids

A large number of chemicals including surfactants, nootropic drugs and pesticides contain an N-acylated lactam moiety in their molecular structure. In this work, the direct, catalytic N-acylation of a number of lactams with various unactivated carboxylic acids is reported. Several Lewis acid catalysts were evaluated for their activity in the N-acylation of pyroglutamic acid methyl ester with palmitic acid; the highest activities were observed for zirconium-based catalysts. Yields of up to 97% were obtained utilising 10?mol% Zr(propoxide)₄ in mesitylene at reflux temperature, but ZrOCl₂·8H₂O was determined as the most stable catalyst. The substrate scope was investigated and a number of lactam-carboxylic acid combinations were successfully converted into the desired products in 57–97% yield. This method provides an alternative synthetic pathway towards the drug aniracetam, which can be produced in 84% yield. A plausible catalytic mechanism is presented based on kinetic experiments.     

Photolytic and Reductive Activations of 2-Arsaethynolate in a Uranium–Triamidoamine Complex: Decarbonylative Arsenic-Group Transfer Reactions and Trapping of a Highly Bent and Reduced Form

Little is known about the chemistry of the 2-arsaethynolate anion, but to date it has exclusively undergone fragmentation reactions when reduced. Herein, we report the synthesis of [U(Tren^TIPS)(OCAs)] ( 2 , Tren^TIPS=N(CH₂CH₂NSiiPr₃)₃), which is the first isolable actinide-2-arsaethynolate linkage. UV-photolysis of 2 results in decarbonylation, but the putative [U(Tren^TIPS)(As)] product was not isolated and instead only [{U(Tren^TIPS)}₂(μ-η²:η²-As₂H₂)] ( 3 ) was formed. In contrast, reduction of 2 with [U(Tren^TIPS)] gave the mixed-valence arsenido [{U(Tren^TIPS)}₂(μ-As)] ( 4 ) in very low yield. Complex 4 is unstable which precluded full characterisation, but these photolytic and reductive reactions testify to the tendency of 2-arsaethynolate to fragment with CO release and As transfer. However, addition of 2 to an electride mixture of potassium-graphite and 2,2,2-cryptand gives [{U(Tren^TIPS)}₂{μ-η²(OAs):η²(CAs)-OCAs}][K(2,2,2-cryptand)] ( 5 ). The coordination mode of the trapped 2-arsaethynolate in 5 is unique, and derives from a new highly reduced and bent form of this ligand with the most acute O-C-As angle in any complex to date (O-C-As ≈128°). The trapping rather than fragmentation of this highly reduced O-C-As unit is unprecedented, and quantum chemical calculations reveal that reduction confers donor–acceptor character to the O-C-As unit.     

Deconstructing Oligomer Distributions: Discrete Species and Artificial Distributions

The separation of an oligo(methyl acrylate) distribution, obtained from reversible addition–fragmentation chain transfer (RAFT) polymerization, in a discrete (dispersity=1) oligomeric library (degree of polymerization between 1 and 22) is presented. The properties of this library in terms of diffusivity, glass transition temperature, and viscosity are determined, filling a significant knowledge gap associated with these materials. The obtained oligomer library is used to construct artificial oligomer distributions on demand. These artificial oligomer distributions are used to highlight the potential to tailor physical properties of a material, while concomitantly demonstrating the limitations associated with size‐exclusion chromatography analysis of molecular weight and dispersity in particular.     

Thermal stability and spectroscopic properties of erbium-doped niobic-tungsten–tellurite glasses for laser and amplifier devices

Er³⁺ doped niobic-tungsten–tellurite glasses doped with concentration of Er³⁺ ion up to 3 wt% were fabricated. The effect of Er³⁺ doping concentration on thermal stability and optical properties was investigated in order to obtain the most suitable rare earth content for developing 1.5 μm compact fiber amplifier pumped with a commercial telecom 980 nm laser diode. The maximum doping concentration allowed was found to be around 1.77×10²⁰ ions/cm³, for which a broad 1.5 μm emission spectra of 65 nm FWHM and a lifetime of 3.4 ms for the ⁴I_13/2 level was measured.     

Temperature Controlled Sequential Gelation in Composite Microgel Suspensions

Depending on the volume fraction and interparticle interactions, colloidal suspensions can exhibit a variety of physical states, ranging from fluids, crystals, and glasses to gels. For microgel particles made of thermoresponsive polymers, both parameters can be tuned using environmental parameters such as temperature and ionic strength, making them excellent systems to experimentally study state transitions in colloidal suspensions. Using a simple two‐step synthesis it is shown that the properties of composite microgels, with a fluorescent latex core and a responsive microgel shell, can be finely tuned. With this system the transitions between glass, liquid, and gel states for suspensions composed of a single species are explored. Finally, a suspension of two species of microgels is demonstrated, with different transition temperatures, gels in a sequential manner. Upon increasing temperature a distinct core–sheath structure is formed with a primary gel composed of the species with lowest transition temperature, which acts as a scaffold for the aggregation of the second species.     

Magnetic circular dichroism spectroscopy on the Cr₈ antiferromagnetic ring

A Magnetic Circular Dichroism (MCD) spectroscopic study of the antiferromagnetic ring [Cr?F?Piv??] (Piv = pivalate) is reported. From the splitting of the MCD bands, the single ion anisotropy parameters in the cluster spin ground state at different fields were determined to be d(Cr) = -0.33 ± 0.02 cm?1, e(Cr) = 0.11 ± 0.01 cm?1. Analysis of the MCD intensity as a function of field and temperature revealed the influence of spin mixing effects and yielded independent estimates of the single ion anisotropies (d(Cr) = -0.19 cm?1, e(Cr) = 4.3 × 10-4 cm?1), as well as yielding the isotropic exchange interaction strength (J = -6.00 cm?1). Thus it is shown that MCD is a powerful method to unravel the relation between single-ion and cluster anisotropy, furthering the design of molecular magnets with desired properties.