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     

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).     

Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas

A theoretical model of the evaporation of a pure liquid layer is developed. We focus on the influence of an inert gaseous component, in addition to vapor, on surface-tension-driven Bénard instabilities. It is assumed that the gas phase is perfectly mixed at some distance from the liquid-gas interface (given composition, pressure, and temperature). If this distance is not much larger than the liquid layer thickness, it is shown that a reduction of the full two-layer problem to a one-layer problem is possible, provided the evaporation rate is not too large. An analytical expression is given for the corresponding dimensionless heat transfer coefficient (a generalized, wavenumber-dependent Biot number) at the evaporating interface. The approach is validated through a comparison with a direct numerical resolution of the full two-layer problem.     

Molecular dynamics study of hydration in ethanol-water mixtures using a polarizable force field

The abnormal physicochemical characteristics of ethanol solvation in water are commonly attributed to the phenomenon of hydrophobic hydration. To investigate the structural organization of hydrophobic hydration in water-ethanol mixtures, we use molecular dynamics simulations based on detailed atomic models. Induced polarization is incorporated into the potential function on the basis of the classical Drude oscillator model. Water-ethanol mixtures are simulated at 11 ethanol molar fractions, from 0.05 to 0.9. Although the water and ethanol models are parametrized separately to reproduce the vaporization enthalpy, static dielectric constant, and self-diffusion constant of neat liquids at ambient conditions, they also reproduce the energetic and dynamical properties of the mixtures accurately. Furthermore, the calculated dielectric constant for the various water-alcohol mixtures is in excellent agreement with experimental data. The simulations provide a detailed structural characterization of the mixtures. A depletion of water-water hydrogen bonding in the first hydration shell of ethanol is compensated by an enhancement in the second hydration shell. The structuring effect from the second solvation shell gives rise to a net positive hydrogen-bonding excess for ethanol molar fractions up to approximately 0.5. For larger molar fractions, the second hydration shell is not sufficiently populated to overcome the net H-bond depletion from the first shell.     

Cross-coupling reactions of phenylmagnesium halides with fluoroazines and fluorodiazines

The first nickel-catalyzed cross-coupling reactions between fluoroarenes and aryl organometallics using commercially available ligands are described. The nickel-catalyzed cross-coupling reactions between aryl Grignard reagents and fluoroazines and -diazines occurred in THF at room temperature using commercially available 1,2-bis(diphenylphosphino)ethane, 1,3-bis(diphenylphosphino)propane, or 1,1'-bis(diphenylphosphino)ferrocene as ligand. Various fluoro substrates such as pyridines, diazines (pyrazine, pyridazine), benzodiazines (quinoxaline), and quinolines were successfully involved in the reaction with phenylmagnesium halides (phenylmagnesium chloride, 2-methoxyphenylmagnesium bromide, and 4-methoxyphenylmagnesium bromide). The conditions used also allowed the cross-coupling of 4-fluorotoluene with arylmagnesium reagents.