Motivic Serre invariants, ramification, and the analytic Milnor fiber

We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce the so-called analytic Milnor fiber associated to the germ of a morphism f from a smooth complex algebraic variety X to the affine line. This analytic Milnor fiber is a smooth rigid variety over the field of Laurent series C((t)). Its etale cohomology coincides with the singular cohomology of the classical topological Milnor fiber of f; the monodromy transformation is given by the Galois action. Moreover, the points on the analytic Milnor fiber are closely related to the motivic zeta function of f, and the arc space of X. We show how the motivic zeta function can be recovered as some kind of Weil zeta function of the formal completion of X along the special fiber of f, and we establish a corresponding Grothendieck trace formula, which relates, in particular, the rational points on the analytic Milnor fiber over finite extensions of C((t)), to the Galois action on its etale cohomology. The general observation is that the arithmetic properties of the analytic Milnor fiber reflect the structure of the singularity of the germ f.Comment: Some minor errors corrected. The original publication is available at http://www.springerlink.co

Singular Support of a Vertex Algebra and the Arc Space of Its Associated Scheme

Book Subtitle: In Honour of the 75th Birthday of Tony JosephSeries Title: Progress in Mathematics (vol. 330)Attached to a vertex algebra V are two geometric objects. The associated scheme of V isthespectrum of Zhu's Poisson algebra Rv.Thesingular support of V is the spectrum of the associated graded algebra gr(V) with respect to Li's canonical decreasing filtration. There is a closed embedding from the singular support to the arc space of the associated scheme, which is an isomorphism in many interesting cases. In this note we give an example of a non-quasi-lisse vertex algebra whose associated scheme is reduced, for which the isomorphism is not true as schemes but true as varieties

Artificial Intelligence, Machine Learning and Modeling for Understanding the Oceans and Climate Change

International audienceThe ongoing transformation of climate and biodiversity will have a drastic impact on almost all forms of life in the ocean with further consequences on food security, ecosystem services in coastal and inland communities. Despite these impacts, scientific data and infrastructures are still lacking to understand and quantify the consequences of these perturbations on the marine ecosystem. Understanding this phenomenon is not only an urgent but also a scientifically demanding task. Consequently, it is a problem that must be addressed with a tific cohort approach, where multi-disciplinary teams collaborate to bring the best of different scientific areas. In this proposal paper, we describe our newly launched four-years project focusedon developing new artificial intelligence, machine learning, and mathematical modeling tools to contribute to the understanding of the structure, functioning, and underlying mechanisms and dynamics of the global ocean symbiome and its relation with climate change. These actions should enable the understanding of our oceans and predict and mitigate the consequences of climate and biodiversity changes

Ciblage thérapeutique des récepteurs couplés aux protéines G

Les récepteurs couplés aux protéines G (RCPG) constituent une famille de cibles thérapeutiques incontournables associées à un large spectre de fonctions. Les molécules actuellement sur le marché du type agoniste ou antagoniste agissent via le site actif du récepteur ou site orthostérique. Plus récemment, des composés se liant à des sites distincts, dits sites allostériques, ont été décrits dans différentes classes de RCPG. Ces composés, nommés modulateurs allostériques, sont généralement dotés d’une meilleure sélectivité entre les récepteurs d’une même famille et sont capables de moduler spécifiquement la signalisation endogène du récepteur, ce qui les distingue des composés orthostériques conventionnels. L’objectif de cette revue est de souligner le potentiel thérapeutique de cette nouvelle classe de composés, en décrivant les propriétés pharmacologiques associées aux modulateurs allostériques, leur stratégie d’identification et les défis liés à leur développement

Structure of the Melanocortin-2 Receptor Accessory Protein MRAP and its Roles in the Regulation of Melanocortin Receptors Trafficking and Signaling

Thesis (Ph.D.)--University of Rochester. School of Medicine and Dentistry. Dept. of Pharmacology and Physiology, 2008.The melanocortin-2 receptor or adrenocorticotropic hormone (ACTH) receptor is the main regulator of glucocorticoid synthesis. Loss of function of MC2 receptors causes a severe glucocorticoid deficiency that, if not treated, results in death. Interestingly, the MC2 receptor requires the MC2 receptor accessory protein (MRAP) for proper trafficking to the plasma membrane. These studies were performed to better understand the structure of the single transmembrane spanning protein MRAP and how it regulates melanocortin receptor trafficking and function. We show that MRAP displays a previously uncharacterized topology. Epitopes on both the N- and C-terminal ends of MRAP were localized on the external face of CHO cells at comparable levels. Using antibodies raised against N- and C-terminal MRAP peptides, we demonstrated that both ends of endogenous MRAP face the outside in adrenal cells. Nearly half of MRAP was glycosylated at the single endogenous N-terminal glycosylation site, and over half was glycosylated when the natural glycosylation site was replaced by one in the C-terminal domain. Coimmunoprecipitation of differentially tagged MRAPs established that MRAP is a dimer. By selectively immunoprecipitating cell surface MRAP in one or the other orientation, we showed that MRAP homodimers are antiparallel and form a stable complex with MC2 receptor. In the absence of MRAP, MC2 receptor was trapped in the endoplasmic reticulum, but with MRAP, the MC2 receptor was glycosylated and localized on the plasma membrane, where it signaled in response to ACTH. MRAP is the first eukaryotic membrane protein identified with an antiparallel homodimeric structure. We also showed that an epitope-tagged chaperone for odorant and taste receptors, Receptor Transporting Protein-1S (RTP-1S), also displayed dual topology, suggesting that this unusual structure may be common to several GPCR accessory proteins. We used bimolecular fluorescence complementation to ask where MRAP achieves dual topology. Fragments of yellow fluorescent protein (YFP) were fused to the N- or C-terminus of MRAP such that YFP fluorescence could occur only in antiparallel homodimers; fluorescence was present in the endoplasmic reticulum. MRAP retained dual topology after deletion of most of the amino-terminus. In contrast, deletion of residues 31-37, just N-terminal to the transmembrane domain, forced MRAP into a single Nexoplasmic/Ccytoplasmic (Nexo/Ccyt) orientation and blocked its ability to promote MC2 receptor trafficking and homodimerization. When the transmembrane domain of MRAP was replaced with the corresponding region from receptor activity modifying protein 3 (RAMP3), dual topology was retained but MRAP was inactive. Insertion of MRAP residues 29-37 conferred dual topology to RAMP3, normally in an Nexo/Ccyt orientation. When expressed with MRAPΔ1-30, MRAPΔ10-20, or MRAPΔ21-30, MC2 receptor was localized on the plasma membrane but unable to respond to ACTH. Residues 18-21 of MRAP were critical; MC2 receptor expressed with MRAP(18-21A) localized to the plasma membrane but did not bind [125I]ACTH or increase cAMP in response to ACTH. A newly identified MRAP homolog, MRAP2, lacks amino acids 18-21(LDYI) of MRAP and, like MRAP(18-21A), allows MC2 receptor trafficking but not signaling. MRAP2 with an LDYI insertion functions like MRAP. These results demonstrate that MRAP not only facilitates MC2 receptor trafficking but also allows properly localized receptor to bind ACTH and consequently signal. Because MC2 receptor, MC5 receptor and MRAP are expressed together in several tissues including adrenal glands and adipocytes, we studied how MRAP regulates MC5 receptor trafficking and signaling. MRAP dramatically decreased MC5 receptor concentration at the plasma membrane of CHO cells in a dose-dependent manner. In the absence of MRAP, MC5 receptor fused to a red fluorescent protein was localized at the plasma membrane. In contrast, when MRAP was present, MC5 receptor was retained in intracellular compartments. Co-immunoprecipitation experiments determined that MC5 receptor and MRAP were present in the same complex, while bimolecular fluorescence complementation established that these complexes are localized in the ER and possibly in the Golgi. MC2 receptor and MC5 receptor formed homo- and heterodimers. However, whereas MC2 receptor homodimer formation was not altered by MRAP, the formation of MC2-MC5 receptor heterodimers as well as MC5 receptor homodimers was almost completely prevented by MRAP. The N-terminus, but not the transmembrane domain or the C-terminus of MRAP, was necessary to retain the MC5 receptor in intracellular compartments. Together these results suggest that a single protein, MRAP, is capable of regulating the trafficking and dimerization of two closely related receptors, MC2 and MC5 receptor, in two completely opposite ways

Artificial Intelligence, Machine Learning and Modeling for Understanding the Oceans and Climate Change

International audienceThe ongoing transformation of climate and biodiversity will have a drastic impact on almost all forms of life in the ocean with further consequences on food security, ecosystem services in coastal and inland communities. Despite these impacts, scientific data and infrastructures are still lacking to understand and quantify the consequences of these perturbations on the marine ecosystem. Understanding this phenomenon is not only an urgent but also a scientifically demanding task. Consequently, it is a problem that must be addressed with a tific cohort approach, where multi-disciplinary teams collaborate to bring the best of different scientific areas. In this proposal paper, we describe our newly launched four-years project focusedon developing new artificial intelligence, machine learning, and mathematical modeling tools to contribute to the understanding of the structure, functioning, and underlying mechanisms and dynamics of the global ocean symbiome and its relation with climate change. These actions should enable the understanding of our oceans and predict and mitigate the consequences of climate and biodiversity changes

Artificial Intelligence, Machine Learning and Modeling for Understanding the Oceans and Climate Change

International audienceThe ongoing transformation of climate and biodiversity will have a drastic impact on almost all forms of life in the ocean with further consequences on food security, ecosystem services in coastal and inland communities. Despite these impacts, scientific data and infrastructures are still lacking to understand and quantify the consequences of these perturbations on the marine ecosystem. Understanding this phenomenon is not only an urgent but also a scientifically demanding task. Consequently, it is a problem that must be addressed with a tific cohort approach, where multi-disciplinary teams collaborate to bring the best of different scientific areas. In this proposal paper, we describe our newly launched four-years project focusedon developing new artificial intelligence, machine learning, and mathematical modeling tools to contribute to the understanding of the structure, functioning, and underlying mechanisms and dynamics of the global ocean symbiome and its relation with climate change. These actions should enable the understanding of our oceans and predict and mitigate the consequences of climate and biodiversity changes