Generalized impedance boundary conditions with vanishing or sign-changing impedance

We consider a Laplace type problem with a generalized impedance boundary condition of the form $\partial_\nu u=-\partial_x(g\partial_xu)$ on a flat part $\Gamma$ of the boundary. Here $\nu$ is the outward unit normal vector to $\partial\Omega$, $g$ is the impedance parameter and $x$ is the coordinate along $\Gamma$. Such problems appear for example in the modelling of small perturbations of the boundary. In the literature, the cases $g=1$ or $g=-1$ have been investigated. In this work, we address situations where $\Gamma$ contains the origin and $g(x)=\mathbb{1}_{x>0}(x)x^\alpha$ or g(x)=-\mbox{sign}(x)|x|^\alpha with $\alpha\ge0$. In other words, we study cases where $g$ vanishes at the origin and changes its sign. The main message is that the well-posedness in the Fredholm sense of the corresponding problems depends on the value of $\alpha$. For $\alpha\in[0,1)$, we show that the associated operators are Fredholm of index zero while it is not the case when $\alpha=1$. The proof of the first results is based on the reformulation as 1D problems combined with the derivation of compact embedding results for the functional spaces involved in the analysis. The proof of the second results relies on the computation of singularities and the construction of Weyl's sequences. We also discuss the equivalence between the strong and weak formulations, which is not straightforward. Finally, we provide simple numerical experiments which seem to corroborate the theorems

Effects of Surotomycin on Clostridium difficile Viability and Toxin Production In Vitro

The increasing incidence and severity of infection by Clostridium difficile have stimulated attempts to develop new antimicrobial therapies. We report here the relative abilities of two antibiotics (metronidazole and vancomycin) in current use for treating C. difficile infection and of a third antimicrobial, surotomycin, to kill C. difficile cells at various stages of development and to inhibit the production of the toxin proteins that are the major virulence factors. The results indicate that none of the drugs affects the viability of spores at 8× MIC or 80× MIC and that all of the drugs kill exponential-phase cells when provided at 8× MIC. In contrast, none of the drugs killed stationary-phase cells or inhibited toxin production when provided at 8× MIC and neither vancomycin nor metronidazole killed stationary-phase cells when provided at 80× MIC. Surotomycin, on the other hand, did kill stationary-phase cells when provided at 80× MIC but did so without inducing lysis

Temporal regulation of embryonic M-phases.

Temporal regulation of M-phases of the cell cycle requires precise molecular mechanisms that differ among different cells. This variable regulation is particularly clear during embryonic divisions. The first embryonic mitosis in the mouse lasts twice as long as the second one. In other species studied so far (C. elegans, Sphaerechinus granularis, Xenopus laevis), the first mitosis is also longer than the second, yet the prolongation is less pronounced than in the mouse. We have found recently that the mechanisms prolonging the first embryonic M-phase differ in the mouse and in Xenopus embryos. In the mouse, the metaphase of the first mitosis is specifically prolonged by the unknown mechanism acting similarly to the CSF present in oocytes arrested in the second meiotic division. In Xenopus, higher levels of cyclins B participate in the M-phase prolongation, however, without any cell cycle arrest. In Xenopus embryo cell-free extracts, the inactivation of the major M-phase factor, MPF, depends directly on dissociation of cyclin B from CDK1 subunit and not on cyclin B degradation as was thought before. In search for other mitotic proteins behaving in a similar way as cyclins B we made two complementary proteomic screens dedicated to identifying proteins ubiquitinated and degraded by the proteasome upon the first embryonic mitosis in Xenopus laevis. The first screen yielded 175 proteins. To validate our strategy we are verifying now which of them are really ubiquitinated. In the second one, we identified 9 novel proteins potentially degraded via the proteasome. Among them, TCTP (Translationally Controlled Tumor Protein), a 23-kDa protein, was shown to be partially degraded during mitosis (as well as during meiotic exit). We characterized the expression and the role of this protein in Xenopus, mouse and human somatic cells, Xenopus and mouse oocytes and embryos. TCTP is a mitotic spindle protein positively regulating cellular proliferation. Analysis of other candidates is in progress

Mode of Action and Bactericidal Properties of Surotomycin against Growing and Nongrowing Clostridium difficile

Surotomycin (CB-183,315), a cyclic lipopeptide, is in phase 3 clinical development for the treatment of Clostridium difficile infection. We report here the further characterization of the in vitro mode of action of surotomycin, including its activity against growing and nongrowing C. difficile. This was assessed through time-kill kinetics, allowing a determination of the effects on the membrane potential and permeability and macromolecular synthesis in C. difficile. Against representative strains of C. difficile, surotomycin displayed concentration-dependent killing of both logarithmic-phase and stationary-phase cultures at a concentration that was ≤16× the MIC. Exposure resulted in the inhibition of macromolecular synthesis (in DNA, RNA, proteins, and cell wall). At bactericidal concentrations, surotomycin dissipated the membrane potential of C. difficile without changes to the permeability of propidium iodide. These observations are consistent with surotomycin acting as a membrane-active antibiotic, exhibiting rapid bactericidal activities against growing and nongrowing C. difficile

Differences in regulation of the first two M-phases in Xenopus laevis embryo cell-free extracts

AbstractThe first embryonic M-phase is special, being the time when paternal and maternal chromosomes mix together for the first time. Reports from a variety of species suggest that the regulation of first M-phase has many particularities; however, no systematic comparative study of the biochemical aspects of first and the following M-phases has been previously undertaken. Here, we ask whether the regulation of the first embryonic M-phase is modified, using Xenopus cell-free extracts. We developed new types of extract specific for the first and the second M-phase obtained either from parthenogenetic or from in vitro fertilized embryos. Analyses of these extracts confirmed that the amplitude of histone H1 kinase activity reflecting CDK1/cyclin B (or MPF for M-phase Promoting Factor) activity is higher and persists longer than during the second M-phase, and that levels of cyclins B1 and B2 are correspondingly higher during the first than the second embryonic M-phase. Inhibition of protein synthesis shortly before M-phase entry reduced mitotic histone H1 kinase amplitude, shortened the period of mitotic phosphorylation of chosen marker proteins, and reduced cyclin B1 and B2 levels, suggesting a role of B-type cyclins in regulating the duration of mitotic events. Moreover, addition of exogenous cyclin B to the extract prior the second mitosis brought forward the activation of mitotic histone H1 kinase but prolonged the duration of this activity. We also confirmed that the inhibitory phosphorylation of CDK1 on tyrosine 15 oscillates between the first two embryonic M-phases, but is clearly more pronounced before the first than the second mitosis, while the MAP kinase ERK2 tended to show greater activation during the first embryonic M-phase but with a similar duration of activation. We conclude that discrete differences exist between the first two M-phases in Xenopus embryo and that higher CDK1/cyclin B activity and B-type cyclin levels could account for the different characteristics of these M-phases

Electron Capture in Collisions of Slow Highly Charged Ions with an Atom and a Molecule: Processes and Fragmentation Dynamics

International audienceProcesses involved in slow collisions between highly charged ions (HCI) and neutral targets are presented. First, the mechanisms responsible for double electron capture are discussed. We show that, while the electron-nucleus interaction is expected to be dominant at projectile velocities of about 0.5 a.u., the electron-electron interaction plays a decisive role during the collision and gains importance when the projectile velocity decreases. This interaction has also to be invoked in the capture of core electrons by HCI. Finally, the molecular fragmentation of H2 following the impact of HCI is studied

Oocyte-somatic cells interactions, lessons from evolution

BACKGROUND: Despite the known importance of somatic cells for oocyte developmental competence acquisition, the overall mechanisms underlying the acquisition of full developmental competence are far from being understood, especially in non-mammalian species. The present work aimed at identifying key molecular signals from somatic origin that would be shared by vertebrates. RESULTS: Using a parallel transcriptomic analysis in 4 vertebrate species - a teleost fish, an amphibian, and two mammals - at similar key steps of developmental competence acquisition, we identified a large number of species-specific differentially expressed genes and a surprisingly high number of orthologous genes exhibiting similar expression profiles in the 3 tetrapods and in the 4 vertebrates. Among the evolutionary conserved players participating in developmental competence acquisition are genes involved in key processes such as cellular energy metabolism, cell-to-cell communications, and meiosis control. In addition, we report many novel molecular actors from somatic origin that have never been studied in the vertebrate ovary. Interestingly, a significant number of these new players actively participate in Drosophila oogenesis. CONCLUSIONS: Our study provides a comprehensive overview of evolutionary-conserved mechanisms from somatic origin participating in oocyte developmental competence acquisition in 4 vertebrates. Together our results indicate that despite major differences in ovarian follicular structure, some of the key players from somatic origin involved in oocyte developmental competence acquisition would be shared, not only by vertebrates, but also by metazoans. The conservation of these mechanisms during vertebrate evolution further emphasizes the important contribution of the somatic compartment to oocyte quality and paves the way for future investigations aiming at better understanding what makes a good egg

On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates

International audienceWe are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a small parameter ε > 0. In this context, in order to prove convergence of finite elements methods, it is necessary to get regularity results of the solutions to these regularized problems which hold uniformly in ε. In the present work, we obtain these results in smooth domains and in 2D polygonal geometries. In presence of corners, due to the particular structure of the regularized problems, classical techniques à la Grisvard do not work and instead, we apply the Kondratiev approach. We describe the procedure in detail to keep track of the dependence in ε in all the estimates. The main originality of this study lies in the fact that the limit problem is ill-posed in any framework