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     

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

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.     

Electroenzymatic reactions. Investigation of a reductive dehalogenase by means of electrogenerated redox cosubstrates

As an illustration of how cyclic voltammetry can be used to unravel the mechanisms and kinetics of redox enzymes, the reductive dechlorination of trichloroethylene and tetrachloroethylene by a typical reductive dehalogenase, the tetrachloroethene reductive dehalogenase of Sulfurospirillum multivorans (formerly called Dehalospirillum multivorans), was investigated by means of several electrochemically generated cosubstrates. They comprised the monocation and the neutral form of methylviologen, the neutral form of benzylviologen, and cobaltocene. Cyclic voltammetry is used to produce the active form of the cosubstrate under controlled potential conditions. It shows large plateau-shaped catalytic responses, which are used to measure the kinetics of the enzymatic reaction as a function of the substrate and cosubstrate concentrations. The variation of the rate constant for the cosubstrate reaction with its standard potential shows the transition between two asymptotic behaviors, one in which the reaction is under diffusion control and the other in which it is under counter-diffusion control. Simple fitting of this plot allows an estimation of the standard potential of the electron acceptor center in the enzyme (E degrees = -0.57 V vs NHE).