The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differential-geometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of the method for the case of affine pencils of differential operators is suggested.Comment: 12 page

Formality theorems for Hochschild chains in the Lie algebroid setting

In this paper we prove Lie algebroid versions of Tsygan's formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies a version of Tsygan's formality conjecture for Hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary Poisson Lie algebroid. The proofs are based on the use of Kontsevich's quasi-isomorphism for Hochschild cochains of R[[y_1,...,y_d]], Shoikhet's quasi-isomorphism for Hochschild chains of R[[y_1,...,y_d]], and Fedosov's resolutions of the natural analogues of Hochschild (co)chain complexes associated with a Lie algebroid.Comment: 40 pages, no figure

Affine su(2) fusion rules from gerbe 2-isomorphisms

We give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The fusion-rule coefficients are related to the existence of a 2-isomorphism between pullbacks of these 1-isomorphisms to a submanifold of SU(2) x SU(2) determined by the corresponding three conjugacy classes. This construction is motivated by its application in the description of junctions of maximally symmetric defect lines in the Wess-Zumino-Witten model.Comment: 41 pages, 1 figure (the published version

Conformational changes of calmodulin upon Ca2+ binding studied with a microfluidic mixer

A microfluidic mixer is applied to study the kinetics of calmodulin conformational changes upon Ca2+ binding. The device facilitates rapid, uniform mixing by decoupling hydrodynamic focusing from diffusive mixing and accesses time scales of tens of microseconds. The mixer is used in conjunction with multiphoton microscopy to examine the fast Ca2+-induced transitions of acrylodan-labeled calmodulin. We find that the kinetic rates of the conformational changes in two homologous globular domains differ by more than an order of magnitude. The characteristic time constants are ≈490 μs for the transitions in the C-terminal domain and ≈20 ms for those in the N-terminal domain of the protein. We discuss possible mechanisms for the two distinct events and the biological role of the stable intermediate, half-saturated calmodulin

Cohomological aspects on complex and symplectic manifolds

We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent useful tools in studying non K\"ahler geometry. We give an overview on the comparisons among the dimensions of the cohomology groups that can be defined and we show how we reach the $\partial\overline\partial$-lemma in complex geometry and the Hard-Lefschetz condition in symplectic geometry. For more details we refer to [6] and [29].Comment: The present paper is a proceeding written on the occasion of the "INdAM Meeting Complex and Symplectic Geometry" held in Cortona. It is going to be published on the "Springer INdAM Series

Adverse effects of anti-tuberculosis drugs on HepG2 cell bioenergetics

Tuberculosis (TB) is an intractable chronic infection. Disease treatment with anti-TB drugs remains challenging due to drug-induced hepatotoxicity. The toxicity of the anti-TB drugs rifampicin (RIF), isoniazid (INH) and pyrazinamide (PZA) either alone or in combination was investigated in HepG2 cells. Assays of intracellular adenosine triphosphate (ATP) levels at 4-, 24- and 48-h post-exposure to gradient concentrations of RIF, INH and PZA were conducted. Drug-induced effects on mitochondrial membrane potential (MMP), mitochondrial complex I and complex III activity, nicotinamide adenine dinucleotide (NAD+) levels and cellular lactate production were assessed. Decreased ATP levels were dose-dependent and correlated with drug exposure duration. Approximate 24-h IC50s were 0.5 mM, 70 mM and 84 mM for RIF, INH and PZA, respectively. Twenty-four hours post-drug treatment, reductions of MMP (p = 0.0005), mitochondrial complex I and III activities (p = 0.0001 and p = 0.0003, respectively), NAD+ levels (p = 0.0057) and increased lactate production (p < 0.0001) were observed. Drug combinations used to mimic cumulative drug treatments induced a synergistic inhibition of mitochondrial complex I activity. An assessment of cellular ultrastructure using transmission electron microscopy indicated drug-induced mitophagy. Collectively, our study suggests that hepatotoxicity of commonly employed anti-TB drugs is mediated by their curtailment of mitochondrial function

Virasoro constraints in Drinfeld-Sokolov hierarchies

We describe a geometric theory of Virasoro constraints in generalized Drinfeld-Sokolov hierarchies. Solutions of Drinfeld-Sokolov hierarchies are succinctly described by giving a principal bundle on a complex curve together with the data of a Higgs field near infinity. String solutions for these hierarchies are defined as points having a big stabilizer under a certain Lie algebra action. We characterize principal bundles coming from string solutions as those possessing connections compatible with the Higgs field near infinity. We show that tau-functions of string solutions satisfy second-order differential equations generalizing the Virasoro constraints of 2d quantum gravity.Comment: 28 page

Insulin-Like Peptides and the Target of Rapamycin Pathway Coordinately Regulate Blood Digestion and Egg Maturation in the Mosquito Aedes aegypti

Mosquitoes are insects that vector many serious pathogens to humans and other vertebrates. Most mosquitoes must feed on the blood of a vertebrate host to produce eggs. In turn, multiple cycles of blood feeding promote frequent contacts with hosts and make mosquitoes ideal disease vectors. Both hormonal and nutritional factors are involved in regulating egg development in the mosquito, Aedes aegypti. However, the processes that regulate digestion of the blood meal remain unclear.Here we report that insulin peptide 3 (ILP3) directly stimulated late phase trypsin-like gene expression in blood fed females. In vivo knockdown of the mosquito insulin receptor (MIR) by RNA interference (RNAi) delayed but did not fully inhibit trypsin-like gene expression in the midgut, ecdysteroid (ECD) production by ovaries, and vitellogenin (Vg) expression by the fat body. In contrast, in vivo treatment with double-stranded MIR RNA and rapamycin completely blocked egg production. In vitro experiments showed that amino acids did not simulate late phase trypsin-like gene expression in the midgut or ECD production by the ovaries. However, amino acids did enhance ILP3-mediated stimulation of trypsin-like gene expression and ECD production.Overall, our results indicate that ILPs from the brain synchronize blood meal digestion and amino acid availability with ovarian ECD production to maximize Vg expression by the fat body. The activation of digestion by ILPs may also underlie the growth promoting effects of insulin and TOR signaling in other species

Drosophila Insulin Pathway Mutants Affect Visual Physiology and Brain Function Besides Growth, Lipid, and Carbohydrate Metabolism

OBJECTIVE—Type 2 diabetes is the most common form of diabetes worldwide. Some of its complications, such as retinop-athy and neuropathy, are long-term and protracted, with an un-clear etiology. Given this problem, genetic model systems, such as in flies where type 2 diabetes can be modeled and studied, offer distinct advantages. RESEARCH DESIGN AND METHODS—We used individual flies, control, and mutant individuals with partial loss-of-function insulin pathway genes. We measured wing size and tested body weight for growth phenotypes, the latter by means of a microbal-ance. We studied total lipid and carbohydrate content, lipids by a reaction in single fly homogenates with vanillin-phosphoric acid, and carbohydrates with an anthrone-sulfuric acid reaction. Cholinesterase activity was measured using the Ellman method in head homogenates from pooled fly heads, and electroretinogram