On Fermat Diophantine functional equations,little Picard theorem and beyond

Aequationes mathematicae - We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$ with integers $$m,n\ge...     

Wimp searches with gamma rays in the Fermi era: Challenges,methods and results

The launch of the gamma-ray telescope Fermi Large Area Telescope (Fermi-LAT) started a pivotal period in indirect detection of dark matter. By outperforming expectations, for the first time a robust and stringent test of the paradigm of weakly interacting massive particles (WIMPs) is within reach. In this paper, we discuss astrophysical targets for WIMP detection and the challenges they present, review the analysis tools which have been employed to tackle these challenges, and summarize the status of constraints on and the claimed detections in the WIMP parameter space. Methods and results will be discussed in comparison to Imaging Air Cherenkov Telescopes. We also provide an outlook on short term and longer term developments.     

Crosslinked poly(ethylene oxide) containing siloxanes fabricated through thiol‐ene photochemistry

Homogenous amphiphilic crosslinked polymer films comprising of poly(ethylene oxide) and polysiloxane were synthesized utilizing thiol‐ene “ click ” photochemistry. A systematic variation in polymer composition was Carried out to obtain high quality films with varied amount of siloxane and poly(ethylene oxide). These films showed improved gas separation performance with high gas permeabilities with good CO₂/N₂ selectivity. Furthermore, the resulting films were also tested for its biocompatibility, as a carrier media which allow human adult mesenchymal stem cells to retain their capacity for osteoblastic differentiation after transplantation. The obtained crosslinked films were characterized using differential scanning calorimetry, dynamic mechanical analysis, thermogravimetric analysis, FTIR, Raman‐IR , and small angle X‐ray scattering. The synthesis ease and commercial availability of the starting materials suggests that these new crosslinked polymer networks could find applications in wide range of applications. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1548–1557     

Azasugar inhibitors as pharmacological chaperones for Krabbe disease

Krabbe disease is a devastating neurodegenerative disorder characterized by rapid demyelination of nerve fibers. This disease is caused by defects in the lysosomal enzyme β-galactocerebrosidase (GALC), which hydrolyzes the terminal galactose from glycosphingolipids. These lipids are essential components of eukaryotic cell membranes: substrates of GALC include galactocerebroside, the primary lipid component of myelin, and psychosine, a cytotoxic metabolite. Mutations of GALC that cause misfolding of the protein may be responsive to pharmacological chaperone therapy (PCT), whereby small molecules are used to stabilize these mutant proteins, thus correcting trafficking defects and increasing residual catabolic activity in cells. Here we describe a new approach for the synthesis of galacto-configured azasugars and the characterization of their interaction with GALC using biophysical, biochemical and crystallographic methods. We identify that the global stabilization of GALC conferred by azasugar derivatives, measured by fluorescence-based thermal shift assays, is directly related to their binding affinity, measured by enzyme inhibition. X-ray crystal structures of these molecules bound in the GALC active site reveal which residues participate in stabilizing interactions, show how potency is achieved and illustrate the penalties of aza/iminosugar ring distortion. The structure–activity relationships described here identify the key physical properties required of pharmacological chaperones for Krabbe disease and highlight the potential of azasugars as stabilizing agents for future enzyme replacement therapies. This work lays the foundation for new drug-based treatments of Krabbe disease.     

Chromatography-Free Multicomponent Synthesis of Thioureas Enabled by Aqueous Solution of Elemental Sulfur

The development of a new three-component chromatography-free reaction of isocyanides, amines and elemental sulfur allowed us the straightforward synthesis of thioureas in water. Considering a large pool of organic and inorganic bases, we first optimized the preparation of aqueous polysulfide solution from elemental sulfur. Using polysulfide solution, we were able to omit the otherwise mandatory chromatography, and to isolate the crystalline products directly from the reaction mixture by a simple filtration, retaining the sulfur in the solution phase. A wide range of thioureas synthesized in this way confirmed the reasonable substrate and functional group tolerance of our protocol.