Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

Energy properness and Sasakian-Einstein metrics

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page

Obstructions to the Existence of Sasaki-Einstein Metrics

We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructed, including 3-fold and 4-fold singularities of ADE type that have been studied previously in the physics literature. We show that the AdS/CFT dual of one obstruction is that the R-charge of a gauge invariant chiral primary operator violates the unitarity bound.Comment: 35 pages, 1 figure; references and a footnote adde

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

Dynamic Measurements of Membrane Insertion Potential of Synthetic Cell Penetrating Peptides

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Langmuir, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://doi.org/10.1021/la403370p.Cell penetrating peptides (CPPs) have been established as excellent candidates for mediating drug delivery into cells. When designing synthetic CPPs for drug delivery applications, it is important to understand their ability to penetrate the cell membrane. In this paper, anionic or zwitterionic phospholipid monolayers at the air-water interface are used as model cell membranes to monitor the membrane insertion potential of synthetic CPPs. The insertion potential of CPPs having different cationic and hydrophobic amino acids were recorded using a Langmuir monolayer approach that records peptide adsorption to model membranes. Fluorescence microscopy was used to visualize alterations in phospholipid packing due to peptide insertion. All CPPs had the highest penetration potential in the presence of anionic phospholipids. In addition, two of three amphiphilic CPPs inserted into zwitterionic phospholipids, but none of the hydrophilic CPPs did. All the CPPs studied induced disruptions in phospholipid packing and domain morphology, which were most pronounced for amphiphilic CPPs. Overall, small changes to amino acids and peptide sequences resulted in dramatically different insertion potentials and membrane reorganization. Designers of synthetic CPPs for efficient intracellular drug delivery should consider small nuances in CPP electrostatic and hydrophobic properties

Small Changes in the Primary Structure of Transportan 10 Alter the Thermodynamics and Kinetics of its Interaction with Phospholipid Vesicles

ABSTRACT: The kinetics and thermodynamics of binding of transportan 10 (tp10) and four of its variants to phospholipid vesicles, and the kinetics of peptide-induced dye efflux, were compared. Tp10 is a 21-residue, amphipathic, cationic, cell-penetrating peptide similar to helical antimicrobial peptides. The tp10 variants examined include amidated and free peptides, and replacements of tyrosine by tryptophan. Carboxy-terminal amidation or substitution of tryptophan for tyrosine enhance binding and activity. The Gibbs energies of peptide binding to membranes determined experimentally and calculated from the interfacial hydrophobicity scale are in good agreement. The Gibbs energy for insertion into the bilayer core was calculated using hydrophobicity scales of residue transfer from water to octanol and to the membrane/ water interface. Peptide-induced efflux becomes faster as the Gibbs energies for binding and insertion of the tp10 variants decrease. If anionic lipids are included, binding and efflux rate increase, as expected because all tp10 variants are cationic and an electrostatic component is added. Whether the most important effect of peptide amidation is the change in charge or an enhancement of helical structure, however, still needs to be established. Nevertheless, it is clear that the changes in efflux rate reflect the differences in the thermodynamics of binding and insertion of the free and amidated peptide groups. We have recently reported a detailed investigation (1) o

Calabi-Yau Volumes and Reflexive Polytopes

We study various geometrical quantities for Calabi–Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the Sasaki–Einstein base of the corresponding Calabi–Yau cone are calculated. By doing so, we conjecture new bounds for the Sasaki–Einstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence

Inhibition of cyclooxygenase-2 decreases breast cancer cell motility, invasion and matrix metalloproteinase expression

BACKGROUND: Cyclooxygenase (COX) is the rate-limiting enzyme that catalyzes the formation of prostaglandins. The inducible isoform of COX (COX-2) is highly expressed in aggressive metastatic breast cancers and may play a critical role in cancer progression (i.e. growth and metastasis). However, the exact mechanism(s) for COX-2-enhanced metastasis has yet to be clearly defined. It is well established that one of the direct results of COX-2 action is increased prostaglandin production, especially prostaglandin E(2 )(PGE(2)). Here, we correlate the inhibition of COX-2 activity with decreased breast cancer cell proliferation, migration, invasion and matrix metalloproteinase (MMP) expression. METHODS: Breast cancer cells (Hs578T, MDA-MB-231 and MCF-7) were treated with selective COX-2 inhibitors (NS-398 and Niflumic acid, NA). Cell proliferation was measured by staining with erythrosin B and counting the viable cells using a hemacytometer. Cell migration and invasion were measured using migration and invasion chamber systems. MMP expression was determined by enzyme immunoassay (secreted protein) and real-time quantitative polymerase chain reaction (mRNA). RESULTS: Our results show that there is a decline in proliferation, migration and invasion by the Hs578T and MDA-MB-231 breast cancer cell lines in the presence of either low concentrations (1 μM or lower) NA or NS-398. We also report that MMP mRNA and protein expression by Hs578T cells is inhibited by NS-398; there was a 50% decrease by 100 μM NS-398. PGE(2 )completely reversed the inhibitory effect of NS-398 on MMP mRNA expression. CONCLUSION: Our data suggests that COX-2-dependent activity is a necessary component for cellular and molecular mechanisms of breast cancer cell motility and invasion. COX-2 activity also modulates the expression of MMPs, which may be a part of the molecular mechanism by which COX-2 promotes cell invasion and migration. The studies suggest that COX-2 assists in determining and defining the metastatic signaling pathways that promote the breast cancer progression to metastasis

TTF-1 Action on the Transcriptional Regulation of Cyclooxygenase-2 Gene in the Rat Brain

We have recently found that thyroid transcription factor-1 (TTF-1), a homeodomain-containing transcription factor, is postnatally expressed in discrete areas of the hypothalamus and closely involved in neuroendocrine functions. We now report that transcription of cyclooxygenase-2 (COX-2), the rate limiting enzyme in prostaglandin biosynthesis, was inhibited by TTF-1. Double immunohistochemistry demonstrated that TTF-1 was expressed in the astrocytes and endothelial cells of blood vessel in the hypothalamus. Promoter assays and electrophoretic mobility shift assays showed that TTF-1 inhibited COX-2 transcription by binding to specific binding domains in the COX-2 promoter. Furthermore, blocking TTF-1 synthesis by intracerebroventricular injection of an antisense oligomer induced an increase of COX-2 synthesis in non-neuronal cells of the rat hypothalamus, and resulted in animals' hyperthermia. These results suggest that TTF-1 is physiologically involved in the control of thermogenesis by regulating COX-2 transcription in the brain