Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

Contributions to the synthesis of some ferrocene-containing antibiotics

This Review discusses the synthesis and characterization by our Group of new antibiotics belonging to the class of penicillins, cephalosporins and rifamycins with ferrocenyl and 1, 1′-ferrocenilene residues in the molecule. As reactants for 6-aminopenicillanic acid (6-APA) and 7-aminocephalosporanic acid (7-ACA) the following were used: 1, 1-bis(chlorocarbonyl)ferrocene, ferrocenyl sulfochloride, 1, 1′-ferrocenylenedisulfochloride and thioglycolic acids S-modified with ferrocene. In the synthesis of rifamycins, the hydrazides of the thioglycolic acids, S-modified with ferrocene, were employed as nucleophilic agents. The synthesized intermediates were characterized by elemental analysis, TLC, IR, UV and ¹H NMR spectra. The characterization of new antibiotics was made by TLC, IR and UV spectral analysis. Biological activity was tested on Gram-negative and Gram-positive bacteria. Good activity is reported towards Gram-positive bacteria in the case of derivatives containing residues of thioglycolic acid S-modified with ferrocene, the antibacterial activity being similar to that of amoxicillin, carbenicillin and cephalothin. All compounds are inactive towards Gram-negative bacteria.     

On a class of elliptic operators with nonpolynomial degeneracy on a boundary

Rostov-on-Don. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 91–99, September–October, 1992.     

Access to Paullone Analogues by Intramolecular Heck Reaction

The syntheses of paullone ( 1a ) and three paullone derivatives, including a sulfur analogue ( 2a ), a tricyclic derivative ( 2b ), and a ring‐enlarged variant ( 2c ), are described, Pd‐catalyzed intramolecular Heck reaction being the key step. The kinase‐inhibitory properties of the novel paullone analogues were investigated.     

Bounded speed of propagation for solutions to radiative transfer equations

The Radiative Transfer Equation is the nonlinear transport equation

Utilization of an Hg(2+)-sensitive membrane-electrode in the complexometric determination of Bi(3+), Fe(3+) and Cr(3+)

The paper reports the results obtained in the complexometric determination of Bi(3+), Fe(3+) and Cr(3+) by using an Hg(2+)-sensitive membrane-electrode for the end-point indication. The determination of Bi(3+) and Fe(3+) is performed after addition of mercuric complexonate from which these cations release Hg(2+) by means of which the electrode senses the equivalence point. In the case of Cr(3+) an excess of complexone is added and the surplus is titrated with a standard solution of Hg(2+) in the presence of the Hg(2+)-sensitive membrane-electrode.     

Interactions between hen egg-white lysozyme, PEG2,000, and PLA50 at the air-water interface

In this paper, we compared the efficiency of polymer films, made of a poly(ethylene glycol) (PEG2,000)/poly(d,l-lactide) (PLA50) mixture, or a PEG2,000-PLA50 copolymer, to prevent adsorption of a model protein, the hen egg-white lysozyme (HEWL), at the air-water interface. This was achieved by analyzing the surface pressure/surface area curves, and the X-ray reflectivity data of the polymer films spread on a Langmuir trough, obtained in absence or in presence of the protein. For both the mixture and the copolymer, the amount of protein adsorbed at the air-water interface decreases when the density of the polymer surface coverage increases. It was shown that even in a condensed state, the polymer film made by the mixture can not totally prevent HEWL molecules to adsorb and penetrate the polymer mixed film, but however, protein molecules would not be directly exposed to the more hydrophobic phase, i.e. the air phase. It was also shown that the configuration adopted by the copolymer at the interface in its condensed state would prevent adsorption of HEWL molecules for several hours; this would be due in particular to the presence of PEG segments in the interfacial film.     

Computerized, comprehensive databases of cellular and secreted proteins from normal human embryonic lung MRC-5 fibroblasts: identification of transformation and/or proliferation sensitive proteins

Databases of protein information from human embryonal lung fibroblasts (MRC-5) have been established using computer analyzed two-dimensional gel electrophoresis. One thousand four hundred and eighty-two cellular proteins (1060 with isoelectric focusing and 422 with nonequilibrium pH gradient electrophoresis, in the first dimension) ranging in molecular mass between 8 and 234 kDa were separated and numbered. Information entered in the database (in most cases for major proteins) includes: protein name, HeLa protein catalog number, mouse protein catalog number, proteins matched in transformed human epithelial amnion cells (AMA) and peripheral blood mononuclear cells (PBMC), transformation and/or proliferation sensitive proteins, synthesis in quiescent cells, cell cycle regulated proteins, mitochondrial and heat shock proteins, cytoskeletal proteins and proteins whose synthesis is affected by interferons. Additional information entered for a few transformation-sensitive proteins that have been selected for future studies includes levels of synthesis and amounts in fetal human tissues. A total of four hundred and seventy-six [35S]methionine labeled polypeptides (258 isoelectric focusing; 218, nonequilibrium pH gradient electrophoresis) secreted by MRC-5 fibroblasts were separated and recorded (J. E. Celis et al., Leukemia 1987, 1, 707-717). Information entered in this database includes molecular weight and transformation sensitive proteins. These databases, as well as those of epithelial and lymphoid cell proteins (J. E. Celis et al., Leukemia 1988, 9, 561-601), represent the initial stages of a systematic effort to establish comprehensive databases of human protein information. In the long run, these databases are expected to offer a useful framework in which to focus the human genome sequencing effort.