Synthesis of fluorous fullerene adducts: reversible solubilization of fullerenes in perfluorinated solvents

Fullerene (C60) Diels-Alder adducts with perfluoroalkylated 1,3-cyclopentadiene (1a,b) were synthesized and studied. The perfluoroalkylated cyclopentadiene was found to be less reactive toward C60 than cyclopentadiene itself, possibly because of the electron-withdrawing effect of the side chain. Because of the same effect, the temperature of the retro-Diels-Alder reaction for the fluorinated adducts was lower (70 degrees C) than the reported value (95 degrees C) for the cyclopentadiene adducts of C60. Higher adducts of the fluorous diene and C60 were found to be soluble in perfluorohexane and to show visible partitioning between organic (toluene) and fluorous phases. Also, the Diels-Alder addition of the fluorous diene was accompanied by extensive oxidation of the fullerene core, as revealed by MALDI-TOF data.     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

A novel 3D mammalian cell perfusion-culture system in microfluidic channels

Mammalian cells cultured on 2D surfaces in microfluidic channels are increasingly used in drug development and biological research applications. These systems would have more biological or clinical relevance if the cells exhibit 3D phenotypes similar to the cells in vivo. We have developed a microfluidic channel based system that allows cells to be perfusion-cultured in 3D by supporting them with adequate 3D cell-cell and cell-matrix interactions. The maximal cell-cell interaction was achieved by perfusion-seeding cells through an array of micropillars; and 3D cell-matrix interactions were achieved by a polyelectrolyte complex coacervation process to form a thin layer of matrix conforming to the 3D cell shapes. Carcinoma cell lines (HepG2, MCF7), primary differentiated (hepatocytes) and primary progenitor cells (bone marrow mesenchymal stem cells) were perfusion-cultured for 72 hours to 1 week in the microfluidic channel, which preserved their 3D cyto-architecture and cell-specific functions or differentiation competence. This transparent 3D microfluidic channel-based cell culture system also allows direct optical monitoring of cellular events for a wide range of applications.     

Raman spectroscopic investigation on the microenvironment of the liver tissues of Zebrafish (Danio rerio) due to titanium dioxide exposure

Nano titanium dioxide (nTiO₂), generally considered to be toxicologically inert, is manufactured in large quantities and extensively applied in consumer products. The small size and large surface area endow them with an active group or intrinsic toxicity. Advances in instrumentation are making Raman spectroscopy the tool of choice for an increasing number of (bio) chemical applications. One of the great advantages of this technique is its ability to provide information on the concentration, structure and interaction of biochemical molecules in their microenvironments within intact cells and tissues, non-destructively. Zebrafish (Danio rerio), one of the most important vertebrate model organisms used in developmental biology, are increasingly used in biomedical research, particularly as a model of human disease. In the present work, an attempt is made to study the effect of titanium dioxide, both nano and bulk, on the microenvironment of the liver tissues of Zebrafish using FT-Raman spectroscopy. The results of the present study suggest that TiO₂ exposure demonstrate a marked influence on the microenvironments of the liver tissues of Zebrafish. A shift to a higher wavenumber and an increase in the intensity of the band at ∼1087 cm⁻¹ in the TiO₂ exposed tissues suggest that some of the conformational changes resulting from the alkali recovery process takes place due to TiO₂ exposure. The decreased intensity ratio (I₃₂₂₀/I₃₄₀₀) observed in the titanium-exposed tissues suggests a decreased water domain size, which could be interpreted in terms of weaker hydrogen-bonded molecular species of water in the TiO₂ exposed tissues. The observed shift of COO⁻ bands to higher frequencies shows the disruption of salt bridges as a result of a change in the oppositely charged partners and due to the enhanced random coil conformation. The variation in the intensity ratio of the tyrosyl doublet (I₈₅₈/I₈₂₅) indicates variation in the hydrogen bonding of the phenolic hydroxyl group due to TiO₂ exposure. The results further suggest that the microenvironments are greatly altered due to titanium nano exposure when compared to titanium bulk. In conclusion, the results indicate that FT-Raman spectroscopy might be a useful tool for rapid assessment of nano particle biological interactions.     

Some relations between additive functions,II

Aequationes mathematicae -     

On the system of functional equationsf(x + y) = f(x) + f(y) andf(xy) = p (x)f(y) + q(y)f(x)

Aequationes mathematicae -