Weakly Lefschetz symplectic manifolds

The harmonic cohomology of a Donaldson symplectic submanifold and of an Auroux symplectic submanifold are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the $s$-Lefschetz propery. In particular, we consider the symplectic blow-ups of the complex projective space along weakly Lefschetz symplectic submanifolds. As an application we construct, for each even integer $s\geq 2$, compact symplectic manifolds which are $s$-Lefschetz but not $(s+1)$-Lefschetz.Comment: 22 pages; many improvements from previous versio

Tangential projections and secant defective varieties

Going one step further in Zak's classification of Scorza varieties with secant defect equal to one, we characterize the Veronese embedding of $\P^n$ given by the complete linear system of quadrics and its smooth projections from a point as the only smooth irreducible complex and non-degenerate projective subvarieties of $\P^N$ that can be projected isomorphically into $\P^{2n}$ when $N\geq\binom{n+2}{2}-2$.Comment: To appear in Bulletin of the London Mathematical Societ

Cellular Responses of the Retina to West Nile Virus Infection

Age-related macular degeneration (AMD) is the leading cause of blindness in the developing world in people aged over 60 years, manifested as a loss of central vision in one or both eyes, with significant morbidity including loss of mobility and depression. This condition involves the degeneration of the macula, and although the exact aetiology of this disease is unknown, various epidemiological studies have shown it to be multifactorial. Current research points towards the involvement of a dysregulated immune system in the pathogenesis and progression of the disease: as the body ages, the immune system increasingly adopts a more inflammatory basal state. However, not all of the aged population develops AMD and it is highly likely that an additional stimulus or stimuli is/are needed to exploit this dysregulated immune environment to initiate this disease. Given the range of pathogens that can infect the retina, we hypothesize that this breaking point could manifest as a chronic inflammation as a result of a low-level infection. West Nile Virus (WNV) is a flavivirus that has come into international prominence ever since its spread into previously WNV-free regions following the 1999 New York outbreak. As several case reports have shown that WNV is capable of infecting the retina, and given its immunopathogenic properties, we believe the virus is a useful tool to model key immune pathways and responses that may be involved in the development and progression of AMD. Of significant interest are the processes involved in the breakdown of the outer blood-retinal barrier (BRB), which is an important step in the progression of AMD from an early stage to a more severe one. Additionally, deciphering and understanding the profile and populations of leukocytes that are recruited during an immunopathic infection in an organ regarded as being immunoprivileged is of great appeal. With this in mind, we set out to investigate the effects of WNV infection on the retinal pigment epithelium (RPE), which comprises the outer BRB. Previously, our laboratory established the WNV BRB model by quantitating various parameters, such as level of infectivity, viral output by WNV-infected RPE and effects of WNV infection on RPE proliferation/migration. The effect of WNV on the extracellular matrix (ECM) production by RPE was also investigated and increases in collagen I, IV and fibronectin were noted. Global ECM production induced a lowered rate of proliferation of RPE seeded on WNV-infected RPE ECM as opposed to mock-infected ECM. A full genome microarray was also undertaken on WNV-infected RPE to analyse differentially regulated gene mRNA production, and increases in several immune genes, as well as genes involved in the stress-response pathway and the TGFβ pathway were found. This current investigation expanded upon these results, and found that WNV infection produces a predominantly CCL5 chemokine response rather than a CCL2 response. Additionally, a lack of TNF production was noted, despite a high initial upregulation of the TNF gene in WNV-infected cells. WNV attenuation was found to be predominantly IFNβ-1-driven, while induction of indoleamine 2,3 dioxygenase activity was induced in part by IFNλ-1 and -2. The effects of WNV infection on RPE barrier integrity was investigated, and an initial increase in infected cells of barrier integrity was observed. Several investigations resulted in a conclusion of a soluble-mediator as the likely mechanism behind this initial increase, and while none of the chemokines tested appeared to contribute to this change, the results suggest that it may be TLR3/RIG-I independent. Finally, establishment of a murine WNV intravitreal model was also undertaken, and several key parameters were determined, including confirmation of WNV-infection of the murine retina, effect of WNV titre on mortality, and histological analysis of the effects of WNV infection on the murine retina. Quantification of the leukocyte profile recruited into the WNV-infected murine retina and choroid revealed significant increases in inflammatory Ly6Chi monocytes, as well as significant differences between immune mice and naïve mice intravitreally infected with WNV, and differences between 2 month old and 5 month old mice. Collectively, these results highlight the importance of the interferon response in both direct and indirect anti-WNV activities and immunomodulation, the changes in outer BRB integrity and possible contributors to its degradation, and the establishment of the murine intravitreal WNV model along with identification of several key leukocytes that are recruited at the peak of infection. These results will help guide further research and highlight possible immune pathways that may contribute to dysregulated inflammatory processes that may occur during the pathogenesis of AMD

Antigenic Variation and Telomere Structure in Trypanosoma brucei

Trypanosoma brucei survives immune attack in its mammalian hosts by periodically changing the variant surface glycoprotein (VSG). From the -1000 VSG genes (VSGs) scattered throughout the genome, a few are located at telomere loci called expression sites (ESs) one is expressed at any time, suggesting a stringent regulatory mechanism. Here, it is demonstrated that trypanosomes engineered to express two VSGs simultaneously from the same ES can multiply in cultures and infect animals normally. Mechanisms involved in the control ES-associated gene expression are thought to involve some kind of telomere position effect. Telomeres typically contain simple DNA repeats (TTAGGG in animals and trypanosomatids) that are the binding sites for telomeric proteins, and end in 3\u27 protrusions known as overhangs. In mammals, telomeres fold back in structures known as t-loops, in which the overhang is intercalated in the duplex DNA. The length of the TTAGGG tracts was measured (-15 kb) and the presence of 3\u27 overhangs was established in trypanosome telomeric DNA. EM studies revealed the presence of t-loops in trypanosome telomeric DNA and at both ends of minichromosomes. Therefore, trypanosome telomeres have conserved features and probably contain proteins with conserved functions. Binding of the human protein TRFI to telomeres procyclic trypanosomes caused transient cell cycle arrest and abrupt telomere shortening, indicating that TRFI is interfering with a presumed trypanosome telomere complex. Trypanosome protein extracts did not exhibit a detectable TRFI-like DNA-binding activity. A yeast one-hybrid screen was developed to detect trypanosome proteins with the ability to TTAGGG. However, this screen was interfered by the presence of an endogenous TTAGGG binding activity and by the trypanosome nucleosome assembly protein NAP1

Symplectic structure of equilibrium thermodynamics

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a Lagrange submanifold of the corresponding tangent bundle, if the fundamental equation is known explicitly. As a consequence, Hamiltonians can be defined that describe thermodynamic processes.Comment: New sections, comments and references added. Final version to appear in IJGMM