Finite groups and geometries: a view on the present state and on the future

The model: groups of Lie-Chevalley type and buildingsThis paper is not the presentation of a completed theory but rather a report on a search progressing as in the natural sciences in order to better understand the relationship between groups and incidence geometry, in some future sought-after theory Τ. The search is based on assumptions and on wishes some of which are time-dependent, variations being forced, in particular, by the search itself.A major historical reference for this subject is, needless to say, Klein's Erlangen Programme. Klein's views were raised to a powerful theory thanks to the geometric interpretation of the simple Lie groups due to Tits (see for instance), particularly his theory of buildings and of groups with a BN-pair (or Tits systems). Let us briefly recall some striking features of this.Let G be a group of Lie-Chevalley type of rank r, denned over GF(q), q = pn, p prime. Let Xr denote the Dynkin diagram of G. To these data corresponds a unique thick building B(G) of rank r over the Coxeter diagram Xr (assuming we forget arrows provided by the Dynkin diagram). It turns out that B(G) can be constructed in a uniform way for all G, from a fixed p-Sylow subgroup U of G, its normalizer NG(U) and the r maximal subgroups of G containing NG(U).

SO2 depletion in tropospheric volcanic plumes

Ground based remote sensing techniques are used to measure volcanic SO2 fluxes in efforts to characterise volcanic activity. As these measurements are made several km from source there is the potential for in-plume chemical transformation of SO2 to sulphate aerosol (conversion rates are dependent on meteorological conditions), complicating interpretation of observed SO2 flux trends. In contrast to anthropogenic plumes, SO2 lifetimes are poorly constrained for tropospheric volcanic plumes, where the few previous loss rate estimates vary widely (from ≪1 to >99% per hour .We report experiments conducted on the boundary layer plume of Masaya volcano, Nicaragua during the dry season. We found that SO2 fluxes showed negligible variation with plume age or diurnal variations in temperature, relative humidity and insolation, providing confirmation that remote SO2 flux measurements (typically of ≈500-2000 s old plumes) are reliable proxies for source emissions for ash free tropospheric plumes not emitted into cloud or fog. Copyright 2004 by the American Geophysical Union.

Solution structure of the N-terminal transactivation domain of ERM modified by SUMO-1.

ERM is a member of the PEA3 group of the Ets transcription factor family that plays important roles in development and tumorigenesis. The PEA3s share an N-terminal transactivation domain (TADn) whose activity is inhibited by small ubiquitin-like modifier (SUMO). However, the consequences of sumoylation and its underlying molecular mechanism remain unclear. The domain structure of ERM TADn alone or modified by SUMO-1 was analyzed using small-angle X-ray scattering (SAXS). Low resolution shapes determined ab initio from the scattering data indicated an elongated shape and an unstructured conformation of TADn in solution. Covalent attachment of SUMO-1 does not perturb the structure of TADn as indicated by the linear arrangement of the SUMO moiety with respect to TADn. Thus, ERM belongs to the growing family of proteins that contain intrinsically unstructured regions. The flexible nature of TADn may be instrumental for ERM recognition and binding to diverse molecular partners.

Ectopic expression of the Ets transcription factor ER81 in transgenic mouse mammary gland enhances both urokinase plasminogen activator and stromelysin-1 transcription

The PEA3 group members PEA3, ER81 and ERM, which are highly conserved transcription factors from the Ets family, are over-expressed in metastatic mammary tumors. In the current study, we present the characterization of a transgenic mouse strain which over-expresses ER81 in the mammary gland via the long terminal repeat of the mouse mammary tumor virus (LTR-MMTV). Although six genotypically positive transgenic lines were identified, only one expressed the ectopic transcript with an exclusive expression in the lactating and late-pregnancy (18th day) mammary glands. No mammary tumor or mammary deregulation appeared after 2 years of ectopic ER81 expression following lactation. We then sought to identify ER81 target genes, and the urokinase plasminogen activator (uPA) and the stromelysin-1, two enzymes involved in extracellular matrix degradation, were found to be transcriptionally upregulated in lactating mammary glands over-expressing ER81. Since these enzymes are involved in metastasis, this murine model could be further used to enhance mammary cancer metastatic process by crossing these animals with mice carrying non-metastatic mammary tumors. We thus created a transgenic mouse model permitting the over-expression of a functionally active Ets transcription factor in the mammary gland without perturbing its development.