The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate

We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation and we establish its nondegeneracy. For the corresponding three-dimensional problem, the nondegeneracy property of the positive ground state to the Choquard equation was proved by E. Lenzmann (2009)

Desingularization of vortices for the Euler equation

We study the existence of stationary classical solutions of the incompressible Euler equation in the plane that approximate singular stationnary solutions of this equation. The construction is performed by studying the asymptotics of equation -\eps^2 \Delta u^\eps=(u^\eps-q-\frac{\kappa}{2\pi} \log \frac{1}{\eps})_+^p with Dirichlet boundary conditions and $q$ a given function. We also study the desingularization of pairs of vortices by minimal energy nodal solutions and the desingularization of rotating vortices.Comment: 40 page

Vortex density models for superconductivity and superfluidity

We study some functionals that describe the density of vortex lines in superconductors subject to an applied magnetic field, and in Bose-Einstein condensates subject to rotational forcing, in quite general domains in 3 dimensions. These functionals are derived from more basic models via Gamma-convergence, here and in a companion paper. In our main results, we use these functionals to obtain descriptions of the critical applied magnetic field (for superconductors) and forcing (for Bose-Einstein), above which ground states exhibit nontrivial vorticity, as well as a characterization of the vortex density in terms of a non local vector-valued generalization of the classical obstacle problem.Comment: 34 page

Associations of common polymorphisms in GCKR with type 2 diabetes and related traits in a Han Chinese population: a case-control study

<p>Abstract</p> <p>Background</p> <p>Several studies have shown that variants in the glucokinase regulatory protein gene (<it>GCKR</it>) were associated with type 2 diabetes and dyslipidemia. The purpose of this study was to examine whether tag single nucleotide polymorphisms (SNPs) in the <it>GCKR </it>region were associated with type 2 diabetes and related traits in a Han Chinese population and to identify the potential mechanisms underlying these associations.</p> <p>Methods</p> <p>We investigated the association of polymorphisms in the <it>GCKR </it>gene with type 2 diabetes by employing a case-control study design (1118 cases and 1161 controls). Four tag SNPs (rs8179206, rs2293572, rs3817588 and rs780094) with pairwise r²> 0.8 and minor allele frequency > 0.05 across the <it>GCKR </it>gene and its flanking regions were studied and haplotypes were constructed. Genotyping was performed by matrix-assisted laser desorption/ionization time-of-flight mass spectroscopy using a MassARRAY platform.</p> <p>Results</p> <p>The G alleles of <it>GCKR </it>rs3817588 and rs780094 were associated with an increased risk of type 2 diabetes after adjustment for year of birth, sex and BMI (OR = 1.24, 95% CI 1.08-1.43, p = 0.002 and OR = 1.22, 95% CI 1.07-1.38, p = 0.002, respectively). In the non-diabetic controls, the GG carriers of rs3817588 and rs780094 were nominally associated with a lower plasma triglyceride level compared to the AA carriers after adjustment for year of birth, sex and BMI (p for trend = 0.00004 and 0.03, respectively). Furthermore, the association of rs3817588 with plasma triglyceride level was still significant after correcting for multiple testing.</p> <p>Conclusions</p> <p>The rs3817588 A/G polymorphism of the <it>GCKR </it>gene was associated with type 2 diabetes and plasma triglyceride level in the Han Chinese population.</p

Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials

We study the existence of stationnary positive solutions for a class of nonlinear Schroedinger equations with a nonnegative continuous potential V. Amongst other results, we prove that if V has a positive local minimum, and if the exponent of the nonlinearity satisfies N/(N-2)<p<(N+2)/(N-2), then for small epsilon the problem admits positive solutions which concentrate as epsilon goes to 0 around the local minimum point of V. The novelty is that no restriction is imposed on the rate of decay of V. In particular, we cover the case where V is compactly supported.Comment: 22 page

Structure-Based Development of Small Molecule PFKFB3 Inhibitors: A Framework for Potential Cancer Therapeutic Agents Targeting the Warburg Effect

Cancer cells adopt glycolysis as the major source of metabolic energy production for fast cell growth. The HIF-1-induced PFKFB3 plays a key role in this adaptation by elevating the concentration of Fru-2,6-BP, the most potent glycolysis stimulator. As this metabolic conversion has been suggested to be a hallmark of cancer, PFKFB3 has emerged as a novel target for cancer chemotherapy. Here, we report that a small molecular inhibitor, N4A, was identified as an initial lead compound for PFKFB3 inhibitor with therapeutic potential. In an attempt to improve its potency, we determined the crystal structure of the PFKFB3•N4A complex to 2.4 Å resolution and, exploiting the resulting molecular information, attained the more potent YN1. When tested on cultured cancer cells, both N4A and YN1 inhibited PFKFB3, suppressing the Fru-2,6-BP level, which in turn suppressed glycolysis and, ultimately, led to cell death. This study validates PFKFB3 as a target for new cancer therapies and provides a framework for future development efforts

The P446L variant in GCKR associated with fasting plasma glucose and triglyceride levels exerts its effect through increased glucokinase activity in liver

Genome-wide association studies have identified a number of signals for both Type 2 Diabetes and related quantitative traits. For the majority of loci, the transition from association signal to mutational mechanism has been difficult to establish. Glucokinase (GCK) regulates glucose storage and disposal in the liver where its activity is regulated by glucokinase regulatory protein (GKRP; gene name GCKR). Fructose-6 and fructose-1 phosphate (F6P and F1P) enhance or reduce GKRP-mediated inhibition, respectively. A common GCKR variant (P446L) is reproducibly associated with triglyceride and fasting plasma glucose levels in the general population. The aim of this study was to determine the mutational mechanism responsible for this genetic association. Recombinant human GCK and both human wild-type (WT) and P446L-GKRP proteins were generated. GCK kinetic activity was observed spectrophotometrically using an NADP+-coupled assay. WT and P446L-GKRP-mediated inhibition of GCK activity and subsequent regulation by phosphate esters were determined. Assays matched for GKRP activity demonstrated no difference in dose-dependent inhibition of GCK activity or F1P-mediated regulation. However, the response to physiologically relevant F6P levels was significantly attenuated with P446L-GKRP (n = 18; P ≤ 0.03). Experiments using equimolar concentrations of both regulatory proteins confirmed these findings (n = 9; P < 0.001). In conclusion, P446L-GKRP has reduced regulation by physiological concentrations of F6P, resulting indirectly in increased GCK activity. Altered GCK regulation in liver is predicted to enhance glycolytic flux, promoting hepatic glucose metabolism and elevating concentrations of malonyl-CoA, a substrate for de novo lipogenesis, providing a mutational mechanism for the reported association of this variant with raised triglycerides and lower glucose levels

Cellular characterisation of the GCKR P446L variant associated with type 2 diabetes risk

Aims/hypothesis Translation of genetic association signals into molecular mechanisms for diabetes has been slow. The glucokinase regulatory protein (GKRP; gene symbol GCKR) P446L variant, associated with inverse modulation of glucose- and lipid-related traits, has been shown to alter the kinetics of glucokinase (GCK) inhibition. As GCK inhibition is associated with nuclear sequestration, we aimed to determine whether this variant also alters the direct interaction between GKRP and GCK and their intracellular localisation. Methods Fluorescently tagged rat and human wild-type (WT)- or P446L-GCKR and GCK were transiently transfected into HeLa cells and mouse primary hepatocytes. Whole-cell and nuclear fluorescence was quantified in individual cells exposed to low- or high-glucose conditions (5.5 or 25 mmol/l glucose, respectively). Interaction between GCK and GKRP was measured by sensitised emission-based fluorescence resonance energy transfer (FRET) efficiency

Functional Characterization of MODY2 Mutations Highlights the Importance of the Fine-Tuning of Glucokinase and Its Role in Glucose Sensing

Glucokinase (GK) acts as a glucose sensor in the pancreatic beta-cell and regulates insulin secretion. Heterozygous mutations in the human GK-encoding GCK gene that reduce the activity index increase the glucose-stimulated insulin secretion threshold and cause familial, mild fasting hyperglycaemia, also known as Maturity Onset Diabetes of the Young type 2 (MODY2). Here we describe the biochemical characterization of five missense GK mutations: p.Ile130Thr, p.Asp205His, p.Gly223Ser, p.His416Arg and p.Ala449Thr. The enzymatic analysis of the corresponding bacterially expressed GST-GK mutant proteins show that all of them impair the kinetic characteristics of the enzyme. In keeping with their position within the protein, mutations p.Ile130Thr, p.Asp205His, p.Gly223Ser, and p.His416Arg strongly decrease the activity index of GK, affecting to one or more kinetic parameters. In contrast, the p.Ala449Thr mutation, which is located in the allosteric activator site, does not affect significantly the activity index of GK, but dramatically modifies the main kinetic parameters responsible for the function of this enzyme as a glucose sensor. The reduced Kcat of the mutant (3.21±0.28 s−1 vs 47.86±2.78 s−1) is balanced by an increased glucose affinity (S0.5 = 1.33±0.08 mM vs 7.86±0.09 mM) and loss of cooperativity for this substrate. We further studied the mechanism by which this mutation impaired GK kinetics by measuring the differential effects of several competitive inhibitors and one allosteric activator on the mutant protein. Our results suggest that this mutation alters the equilibrium between the conformational states of glucokinase and highlights the importance of the fine-tuning of GK and its role in glucose sensing