Non-characteristic approximate roots of polynomials

AbstractWe generalize Abhyankar–Mohʼs theory of approximate roots of polynomials to the case of approximate roots of non-characteristic degrees of an irreducible element of K((X))[Y]

The Łojasiewicz exponent over a field of arbitrary characteristic

Let K be an algebraically closed field and let K((XQ)) denote the field of generalized series with coefficients in K. We propose definitions of the local Łojasiewicz exponent of F = ( f1, . . . , fm) ∈ K[[X, Y ]]m as well as of the Łojasiewicz exponent at infinity of F = ( f1, . . . , fm) ∈ K[X, Y ]m, which generalize the familiar case of K = C and F ∈ C{X, Y }m (resp. F ∈ C[X, Y ]m), see Cha˛dzy´nski and Krasi´nski (In: Singularities, 1988; In: Singularities, 1988; Ann Polon Math 67(3):297–301, 1997; Ann Polon Math 67(2):191–197, 1997), and prove some basic properties of such numbers. Namely, we show that in both cases the exponent is attained on a parametrization of a component of F (Theorems 6 and 7), thus being a rational number. To this end, we define the notion of the Łojasiewicz pseudoexponent of F ∈ (K((XQ))[Y ])m for which we give a description of all the generalized series that extract the pseudoexponent, in terms of their jets. In particular, we show that there exist only finitely many jets of generalized series giving the pseudoexponent of F (Theorem 5). The main tool in the proofs is the algebraic version of Newton’s Polygon Method. The results are illustrated with some explicit examples

Deletion of Plasmodium falciparum Protein RON3 Affects the Functional Translocation of Exported Proteins and Glucose Uptake.

The survival of Plasmodium spp. within the host red blood cell (RBC) depends on the function of a membrane protein complex, termed the Plasmodium translocon of exported proteins (PTEX), that exports certain parasite proteins, collectively referred to as the exportome, across the parasitophorous vacuolar membrane (PVM) that encases the parasite in the host RBC cytoplasm. The core of PTEX consists of three proteins: EXP2, PTEX150, and the HSP101 ATPase; of these three proteins, only EXP2 is a membrane protein. Studying the PTEX-dependent transport of members of the exportome, we discovered that exported proteins, such as ring-infected erythrocyte surface antigen (RESA), failed to be transported in parasites in which the parasite rhoptry protein RON3 was conditionally disrupted. RON3-deficient parasites also failed to develop beyond the ring stage, and glucose uptake was significantly decreased. These findings provide evidence that RON3 influences two translocation functions, namely, transport of the parasite exportome through PTEX and the transport of glucose from the RBC cytoplasm to the parasitophorous vacuolar (PV) space where it can enter the parasite via the hexose transporter (HT) in the parasite plasma membrane.IMPORTANCE The malarial parasite within the erythrocyte is surrounded by two membranes. Plasmodium translocon of exported proteins (PTEX) in the parasite vacuolar membrane critically transports proteins from the parasite to the erythrocytic cytosol and membrane to create protein infrastructure important for virulence. The components of PTEX are stored within the dense granule, which is secreted from the parasite during invasion. We now describe a protein, RON3, from another invasion organelle, the rhoptry, that is also secreted during invasion. We find that RON3 is required for the protein transport function of the PTEX and for glucose transport from the RBC cytoplasm to the parasite, a function thought to be mediated by PTEX component EXP2

A proteomic approach based on peptide affinity chromatography, 2-dimensional electrophoresis and mass spectrometry to identify multiprotein complexes interacting with membrane-bound receptors

There is accumulating evidence that membrane-bound receptors interact with many intracellular proteins. Multiprotein complexes associated with ionotropic receptors have been extensively characterized, but the identification of proteins interacting with G protein-coupled receptors (GPCRs) has so far only been achieved in a piecemeal fashion, focusing on one or two protein species. We describe a method based on peptide affinity chromatography, two-dimensional electrophoresis, mass spectrometry and immunoblotting to identify the components of multiprotein complexes interacting directly or indirectly with intracellular domains of GPCRs or, more generally, any other membrane-bound receptor. Using this global approach, we have characterized multiprotein complexes that bind to the carboxy-terminal tail of the 5-hydroxytryptamine type 2C receptor and are important for its subcellular localization in CNS cells (Bécamel et al., EMBO J., 21(10): 2332, 2002)

Distinct External Signals Trigger Sequential Release of Apical Organelles during Erythrocyte Invasion by Malaria Parasites

The invasion of erythrocytes by Plasmodium merozoites requires specific interactions between host receptors and parasite ligands. Parasite proteins that bind erythrocyte receptors during invasion are localized in apical organelles called micronemes and rhoptries. The regulated secretion of microneme and rhoptry proteins to the merozoite surface to enable receptor binding is a critical step in the invasion process. The sequence of these secretion events and the external signals that trigger release are not known. We have used time-lapse video microscopy to study changes in intracellular calcium levels in Plasmodium falciparum merozoites during erythrocyte invasion. In addition, we have developed flow cytometry based methods to measure relative levels of cytosolic calcium and study surface expression of apical organelle proteins in P. falciparum merozoites in response to different external signals. We demonstrate that exposure of P. falciparum merozoites to low potassium ion concentrations as found in blood plasma leads to a rise in cytosolic calcium levels through a phospholipase C mediated pathway. Rise in cytosolic calcium triggers secretion of microneme proteins such as the 175 kD erythrocyte binding antigen (EBA175) and apical membrane antigen-1 (AMA-1) to the merozoite surface. Subsequently, interaction of EBA175 with glycophorin A (glyA), its receptor on erythrocytes, restores basal cytosolic calcium levels and triggers release of rhoptry proteins. Our results identify for the first time the external signals responsible for the sequential release of microneme and rhoptry proteins during erythrocyte invasion and provide a starting point for the dissection of signal transduction pathways involved in regulated exocytosis of these key apical organelles. Signaling pathway components involved in apical organelle discharge may serve as novel targets for drug development since inhibition of microneme and rhoptry secretion can block invasion and limit blood-stage parasite growth

Deficiency of Huntingtin Has Pleiotropic Effects in the Social Amoeba Dictyostelium discoideum

Huntingtin is a large HEAT repeat protein first identified in humans, where a polyglutamine tract expansion near the amino terminus causes a gain-of-function mechanism that leads to selective neuronal loss in Huntington's disease (HD). Genetic evidence in humans and knock-in mouse models suggests that this gain-of-function involves an increase or deregulation of some aspect of huntingtin's normal function(s), which remains poorly understood. As huntingtin shows evolutionary conservation, a powerful approach to discovering its normal biochemical role(s) is to study the effects caused by its deficiency in a model organism with a short life-cycle that comprises both cellular and multicellular developmental stages. To facilitate studies aimed at detailed knowledge of huntingtin's normal function(s), we generated a null mutant of hd, the HD ortholog in Dictyostelium discoideum. Dictyostelium cells lacking endogenous huntingtin were viable but during development did not exhibit the typical polarized morphology of Dictyostelium cells, streamed poorly to form aggregates by accretion rather than chemotaxis, showed disorganized F-actin staining, exhibited extreme sensitivity to hypoosmotic stress, and failed to form EDTA-resistant cell–cell contacts. Surprisingly, chemotactic streaming could be rescued in the presence of the bivalent cations Ca2+ or Mg2+ but not pulses of cAMP. Although hd− cells completed development, it was delayed and proceeded asynchronously, producing small fruiting bodies with round, defective spores that germinated spontaneously within a glassy sorus. When developed as chimeras with wild-type cells, hd− cells failed to populate the pre-spore region of the slug. In Dictyostelium, huntingtin deficiency is compatible with survival of the organism but renders cells sensitive to low osmolarity, which produces pleiotropic cell autonomous defects that affect cAMP signaling and as a consequence development. Thus, Dictyostelium provides a novel haploid organism model for genetic, cell biological, and biochemical studies to delineate the functions of the HD protein

Mutations of the Mouse ELMO Domain Containing 1 Gene (Elmod1) Link Small GTPase Signaling to Actin Cytoskeleton Dynamics in Hair Cell Stereocilia

Stereocilia, the modified microvilli projecting from the apical surfaces of the sensory hair cells of the inner ear, are essential to the mechanoelectrical transduction process underlying hearing and balance. The actin-filled stereocilia on each hair cell are tethered together by fibrous links to form a highly patterned hair bundle. Although many structural components of hair bundles have been identified, little is known about the signaling mechanisms that regulate their development, morphology, and maintenance. Here, we describe two naturally occurring, allelic mutations that result in hearing and balance deficits in mice, named roundabout (rda) and roundabout-2J (rda2J). Positional cloning identified both as mutations of the mouse ELMO domain containing 1 gene (Elmod1), a poorly characterized gene with no previously reported mutant phenotypes. The rda mutation is a 138 kb deletion that includes exons 1–5 of Elmod1, and rda2J is an intragenic duplication of exons 3–8 of Elmod1. The deafness associated with these mutations is caused by cochlear hair cell dysfunction, as indicated by conspicuous elongations and fusions of inner hair cell stereocilia and progressive degeneration of outer hair cell stereocilia. Mammalian ELMO-family proteins are known to be involved in complexes that activate small GTPases to regulate the actin cytoskeleton during phagocytosis and cell migration. ELMOD1 and ELMOD2 recently were shown to function as GTPase-activating proteins (GAPs) for the Arf family of small G proteins. Our finding connecting ELMOD1 deficiencies with stereocilia dysmorphologies thus establishes a link between the Ras superfamily of small regulatory GTPases and the actin cytoskeleton dynamics of hair cell stereocilia