Toeplitz operators on symplectic manifolds

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.Comment: 40 page

A local families index formula for d-bar operators on punctured Riemann surfaces

Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of d-bar operators on the Teichmuller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space M{g,n} in the sense of orbifolds where it can be written in terms of Mumford-Morita-Miller classes. The degree two part of the formula gives the curvature of the corresponding determinant line bundle equipped with the Quillen connection, a result originally obtained by Takhtajan and Zograf.Comment: 47 page

Pellino-1 regulates the responses of the airway to viral infection

Exposure to respiratory pathogens is a leading cause of exacerbations of airway diseases such as asthma and chronic obstructive pulmonary disease (COPD). Pellino-1 is an E3 ubiquitin ligase known to regulate virally-induced inflammation. We wished to determine the role of Pellino-1 in the host response to respiratory viruses in health and disease. Pellino-1 expression was examined in bronchial sections from patients with GOLD stage two COPD and healthy controls. Primary bronchial epithelial cells (PBECs) in which Pellino-1 expression had been knocked down were extracellularly challenged with the TLR3 agonist poly(I:C). C57BL/6 Peli1−/− mice and wild type littermates were subjected to intranasal infection with clinically-relevant respiratory viruses: rhinovirus (RV1B) and influenza A. We found that Pellino-1 is expressed in the airways of normal subjects and those with COPD, and that Pellino-1 regulates TLR3 signaling and responses to airways viruses. In particular we observed that knockout of Pellino-1 in the murine lung resulted in increased production of proinflammatory cytokines IL-6 and TNFα upon viral infection, accompanied by enhanced recruitment of immune cells to the airways, without any change in viral replication. Pellino-1 therefore regulates inflammatory airway responses without altering replication of respiratory viruses

Is CFTR-delF508 Really Absent from the Apical Membrane of the Airway Epithelium?

Background Understanding where mutant CFTR is localised in airway epithelia is essential in guiding the best therapeutic approach to correct the dysfunction of the CFTR protein. The widely held paradigm is that CF patients harbouring the commonest mutation, CFTR-delF508, trap CFTR within the endoplasmic reticulum and target it for degradation. However there are conflicting reports concerning expression and localisation of CFTR-delF508 in lung tissue. To attempt to resolve this fundamental issue we developed a novel approach to measure CFTR-delF508 in the lower airways of patients who have undergone lung transplantation for advanced CF. By sampling CF and non-CF epithelium simultaneously from the same individual, confounding factors of different airway microenvironments which may have influenced previous observations can be overcome. Methods Epithelia sampled by bronchial brushing above (CF) and below (non-CF) the bronchial anastomosis were stained for CFTR and the localisation and level of expression assessed (n = 12). Results There was no significant difference in the proportion of tall columnar cells showing CFTR immunostaining as a discrete band at the apical membrane in cells harbouring the CFTR-delF508 mutation compared to non-CF cells (p = 0.21, n = 12). However, the amount of CFTR expressed at the apical surface was reduced by ~50% in CF cells compared to non-CF cells (p = 0.04, n = 5). Conclusions Our novel observation challenges the prevailing paradigm that CFTR is essentially absent from the apical membrane of respiratory cells harbouring the CFTR-delF508 mutation. Moreover, it raises the possibility that the new generation of CFTR potentiators may offer a realistic therapeutic option for CF patients