Knots and links in lens spaces

The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.

Fibered knots and links in lens spaces

La tesi propone alcuni esempi di link fibrati in spazi lenticolari. Sfruttando la compatibilità fra le mosse di chirurgia intera e la nozione di open book decomposition, si ricava un esempio di link fibrato prima in L(p,1), per poi generalizzarlo a L(p,q). Si conclude determinando una struttura di contatto equivalente alla open book relativa agli spazi del tipo L(p,1).

Caenorhabditis elegans Heterochromatin protein 1 (HPL-2) links developmental plasticity, longevity and lipid metabolism

Background Heterochromatin protein 1 (HP1) family proteins have a well-characterized role in heterochromatin packaging and gene regulation. Their function in organismal development, however, is less well understood. Here we used genome-wide expression profiling to assess novel functions of the Caenorhabditis elegans HP1 homolog HPL-2 at specific developmental stages. Results We show that HPL-2 regulates the expression of germline genes, extracellular matrix components and genes involved in lipid metabolism. Comparison of our expression data with HPL-2 ChIP-on-chip profiles reveals that a significant number of genes up- and down-regulated in the absence of HPL-2 are bound by HPL-2. Germline genes are specifically up-regulated in hpl-2 mutants, consistent with the function of HPL-2 as a repressor of ectopic germ cell fate. In addition, microarray results and phenotypic analysis suggest that HPL-2 regulates the dauer developmental decision, a striking example of phenotypic plasticity in which environmental conditions determine developmental fate. HPL-2 acts in dauer at least partly through modulation of daf-2/IIS and TGF-β signaling pathways, major determinants of the dauer program. hpl-2 mutants also show increased longevity and altered lipid metabolism, hallmarks of the long-lived, stress resistant dauers. Conclusions Our results suggest that the worm HP1 homologue HPL-2 may coordinately regulate dauer diapause, longevity and lipid metabolism, three processes dependent on developmental input and environmental conditions. Our findings are of general interest as a paradigm of how chromatin factors can both stabilize development by buffering environmental variation, and guide the organism through remodeling events that require plasticity of cell fate regulation.

Exovesicles from human activated dendritic cells fuse with resting dendritic cells, allowing them to present alloantigens

Dendritic cells (DCs) can release microvesicles, but the latter's numbers, size, and fate are unclear. Fluorescently labeled DCs were visualized by laser-scanning microscopy. Using a Surpass algorithm, we were able to identify and quantify per cell several hundred microvesicles released from the surface of stimulated DCs. We show that most of these microvesicles are not of endocytic origin but result from budding of the plasma membrane, hence their name, exovesicle. Using a double vital staining, we show that exovesicles isolated from activated DCs can fuse with the membrane of resting DCs, thereby allowing them to present alloantigens to lymphocytes. We concluded that, within a few hours from their release, exovesicles may amplify local or distant adaptive immunological response.

Sitosterolaemia in Switzerland: molecular genetics links the US Amish-Mennonites to their European roots

Sitosterolaemia is a rare autosomal recessive disease characterized by increased intestinal absorption of plant sterols, decreased hepatic excretion into bile and elevated concentrations in plasma phytosterols. Homozygous or compound heterozygous loss of function mutations in either of the ATP-binding cassette (ABC) proteins ABCG5 and ABCG8 explain the increased absorption of plant sterols. Here we report a Swiss index patient with sitosterolaemia, who presented with the classical symptoms of xanthomas, but also had mitral and aortic valvular heart disease. Her management over the last 20 years included a novel therapeutic approach of high-dose cholesterol feeding that was semi-effective. Mutational and extended haplotype analyses showed that our patient shared this haplotype with that of the Amish-Mennonite sitosterolaemia patients, indicating they are related ancestrally.