Dirac-Fock models for atoms and molecules and related topics

An overview on various results concerning the Dirac-Fock model, the various variational characterization of its solutions and its nonrelativistic limit. A notion of ground state for this totally unbounded is also defined.Comment: To appear in Proc. ICMP2003. World Scientif

The hardwiring of development: Organization and function of genomic regulatory systems

The gene regulatory apparatus that directs development is encoded in the DNA, in the form of organized arrays of transcription factor target sites. Genes are regulated by interactions with multiple transcription factors and the target sites for the transcription factors required for the control of each gene constitute its cis-regulatory system. These systems are remarkably complex. Their hardwired internal organization enables them to behave as genomic information processing systems. Developmental gene regulatory networks consist of the cis-regulatory systems of all the relevant genes and the regulatory linkages amongst them. Though there is yet little explicit information, some general properties of genomic regulatory networks have become apparent. The key to understanding how genomic regulatory networks are organized, and how they work, lies in experimental analysis of cis-regulatory systems at all levels of the regulatory network

General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

This paper is concerned with {an extension and reinterpretation} of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. {We state} two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then, these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states

Variational methods in relativistic quantum mechanics

This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded from below. This has two main consequences. First, the energy functional is strongly indefinite. Second, the Euler-Lagrange equations are linear or nonlinear eigenvalue problems with eigenvalues lying in a spectral gap (between the negative and positive continuous spectra). Moreover, since we work in the space domain R^3, the Palais-Smale condition is not satisfied. For these reasons, the problems discussed in this review pose a challenge in the Calculus of Variations. The existence proofs involve sophisticated tools from nonlinear analysis and have required new variational methods which are now applied to other problems

Some connections between Dirac-Fock and Electron-Positron Hartree-Fock

We study the ground state solutions of the Dirac-Fock model in the case of weak electronic repulsion, using bifurcation theory. They are solutions of a min-max problem. Then we investigate a max-min problem coming from the electron-positron field theory of Bach-Barbaroux-Helffer-Siedentop. We show that given a radially symmetric nuclear charge, the ground state of Dirac-Fock solves this max-min problem for certain numbers of electrons. But we also exhibit a situation in which the max-min level does not correspond to a solution of the Dirac-Fock equations together with its associated self-consistent projector

Bordetella parapertussis Survives inside Human Macrophages in Lipid Raft-Enriched Phagosomes

Bordetella parapertussis is a human pathogen that causes whooping cough. The increasing incidence of B. parapertussis has been attributed to the lack of cross protection induced by pertussis vaccines. It was previously shown that B. parapertussis is able to avoid bacterial killing by polymorphonuclear leukocytes (PMN) if specific opsonic antibodies are not present at the site of interaction. Here, we evaluated the outcome of B. parapertussis innate interaction with human macrophages, a less aggressive type of cell and a known reservoir of many persistent pathogens. The results showed that in the absence of opsonins, O antigen allows B. parapertussis to inhibit phagolysosomal fusion and to remain alive inside macrophages. The O antigen targets B. parapertussis to lipid rafts that are retained in the membrane of phagosomes that do not undergo lysosomal maturation. Forty-eight hours after infection, wild-type B. parapertussis bacteria but not the O antigen-deficient mutants were found colocalizing with lipid rafts and alive in nonacidic compartments. Taken together, our data suggest that in the absence of opsonic antibodies, B. parapertussis survives inside macrophages by preventing phagolysosomal maturation in a lipid raft- and O antigen-dependent manner. Two days after infection, about 15% of macrophages were found loaded with live bacteria inside flotillin-enriched phagosomes that had access to nutrients provided by the host cell recycling pathway, suggesting the development of an intracellular infection. IgG opsonization drastically changed this interaction, inducing efficient bacterial killing. These results highlight the need for B. parapertussis opsonic antibodies to induce bacterial clearance and prevent the eventual establishment of cellular reservoirs of this pathogen.Fil: Gorgojo, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigación y Desarrollo en Fermentaciones Industriales. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Centro de Investigación y Desarrollo en Fermentaciones Industriales; ArgentinaFil: Harvill, Eric. State University of Pennsylvania; Estados UnidosFil: Rodriguez, Maria Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigación y Desarrollo en Fermentaciones Industriales. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Centro de Investigación y Desarrollo en Fermentaciones Industriales; Argentin