Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties

Given a degenerate Calabi-Yau variety $X$ equipped with local deformation data, we construct an almost differential graded Batalin-Vilkovisky (dgBV) algebra $PV^{*,*}(X)$, producing a singular version of the extended Kodaira-Spencer differential graded Lie algebra (dgLa) in the Calabi-Yau setting. Assuming Hodge-to-de Rham degeneracy and a local condition that guarantees freeness of the Hodge bundle, we prove a Bogomolov-Tian-Todorov--type unobstructedness theorem for smoothing of singular Calabi-Yau varieties. In particular, this provides a unified proof for the existence of smoothing of both $d$-semistable log smooth Calabi-Yau varieties (as studied by Friedman and Kawamata-Namikawa and maximally degenerate Calabi-Yau varieties (as studied by Kontsevich-Soibelman and Gross-Siebert). We also demonstrate how our construction yields a logarithmic Frobenius manifold structure on a formal neighborhood of $X$ in the extended moduli space by applying the technique of Barannikov-Kontsevich.Comment: 64 pages; v5: final version to appear in JD

Mice Lacking NKT Cells but with a Complete Complement of CD8+ T-Cells Are Not Protected against the Metabolic Abnormalities of Diet-Induced Obesity

The contribution of natural killer T (NKT) cells to the pathogenesis of metabolic abnormalities of obesity is controversial. While the combined genetic deletion of NKT and CD8+ T-cells improves glucose tolerance and reduces inflammation, interpretation of these data have been complicated by the recent observation that the deletion of CD8+ T-cells alone reduces obesity-induced inflammation and metabolic dysregulation, leaving the issue of the metabolic effects of NKT cell depletion unresolved. To address this question, CD1d null mice (CD1d−/−), which lack NKT cells but have a full complement of CD8+ T-cells, and littermate wild type controls (WT) on a pure C57BL/6J background were exposed to a high fat diet, and glucose intolerance, insulin resistance, dyslipidemia, inflammation, and obesity were assessed. Food intake (15.5±4.3 vs 15.3±1.8 kcal/mouse/day), weight gain (21.8±1.8 vs 22.8±1.4 g) and fat mass (18.6±1.9 vs 19.5±2.1 g) were similar in CD1d−/− and WT, respectively. As would be expected from these data, metabolic rate (3.0±0.1 vs 2.9±0.2 ml O2/g/h) and activity (21.6±4.3 vs 18.5±2.6 beam breaks/min) were unchanged by NKT cell depletion. Furthermore, the degree of insulin resistance, glucose intolerance, liver steatosis, and adipose and liver inflammatory marker expression (TNFα, IL-6, IL-10, IFN-γ, MCP-1, MIP1α) induced by high fat feeding in CD1d−/− were not different from WT. We conclude that deletion of NKT cells, in the absence of alterations in the CD8+ T-cell population, is insufficient to protect against the development of the metabolic abnormalities of diet-induced obesity

Phocid Seal Leptin: Tertiary Structure and Hydrophobic Receptor Binding Site Preservation during Distinct Leptin Gene Evolution

The cytokine hormone leptin is a key signalling molecule in many pathways that control physiological functions. Although leptin demonstrates structural conservation in mammals, there is evidence of positive selection in primates, lagomorphs and chiropterans. We previously reported that the leptin genes of the grey and harbour seals (phocids) have significantly diverged from other mammals. Therefore we further investigated the diversification of leptin in phocids, other marine mammals and terrestrial taxa by sequencing the leptin genes of representative species. Phylogenetic reconstruction revealed that leptin diversification was pronounced within the phocid seals with a high dN/dS ratio of 2.8, indicating positive selection. We found significant evidence of positive selection along the branch leading to the phocids, within the phocid clade, but not over the dataset as a whole. Structural predictions indicate that the individual residues under selection are away from the leptin receptor (LEPR) binding site. Predictions of the surface electrostatic potential indicate that phocid seal leptin is notably different to other mammalian leptins, including the otariids. Cloning the grey seal leptin binding domain of LEPR confirmed that this was structurally conserved. These data, viewed in toto, support a hypothesis that phocid leptin divergence is unlikely to have arisen by random mutation. Based upon these phylogenetic and structural assessments, and considering the comparative physiology and varying life histories among species, we postulate that the unique phocid diving behaviour has produced this selection pressure. The Phocidae includes some of the deepest diving species, yet have the least modified lung structure to cope with pressure and volume changes experienced at depth. Therefore, greater surfactant production is required to facilitate rapid lung re-inflation upon surfacing, while maintaining patent airways. We suggest that this additional surfactant requirement is met by the leptin pulmonary surfactant production pathway which normally appears only to function in the mammalian foetus