New regularity theorems for non-autonomous variational integrals with (p, q)-growth

One prominent problem in the calculus of variations is minimizing anisotropic integrals with a (p, q)-elliptic density F depending on the gradient of a function ${w : \Omega \rightarrow \mathbb{R}^N}$ with ${\Omega \subset \mathbb{R}^n}$ . The best known sufficient bound for regularity of solutions is q <?p (n?+?2)/n. On the other hand, if we allow an additional x-dependence of the density we have the much weaker result q <?p (n + 1)/n. If one additionally imposes the local boundedness of the minimizer, then these bounds can be improved to q <?p?+?2 and q <?p?+?1. In this paper we give natural assumptions for F closing the gap between the autonomous and non-autonomous situation.     

Fleetamine (3-O-α-d-glucopyranosyl-swainsonine): the synthesis of a hypothetical inhibitor of endo-α-mannosidase

3-O-α-d-Glucopyranosyl-swainsonine was originally proposed¹⁷ as a potential inhibitor of the mammalian enzyme endo-α-mannosidase, but its synthesis has not been reported. Herein we report the total synthesis of this enigmatic compound, utilizing a halide-ion catalysed glycosylation of a swainsonine lactam with a glucosyl iodide donor as the key step. The resulting inhibitor was evaluated as an inhibitor of human endo-α-mannosidase, and as a ligand for bacterial orthologs from Bacteroides thetaiotaomicron and Bacteroides xylanisolvens, including active-centre variants, although no evidence for binding or inhibition was observed. The surprising lack of binding was rationalized by using structural alignment with an endo-α-mannosidase inhibitor complex, which identified deleterious interactions with the swainsonine piperidine ring and an essential active site residue.     

Short-chain polyphosphates: Extraction effects on migration and size estimation of Saccharomyces cerevisiae extracts with polyacrylamide gel electrophoresis

Polyacrylamide gel electrophoresis is commonly used to characterize the chain length of polyphosphates (polyP), more generally called condensed phosphates. After separation, nonradioactive, optical polyP staining is limited to chain lengths greater than 15 ${\mathrm{PO}}_3^{-}$monomers with toluidine blue or 4′,6-diamidino-2-phenylindole. PolyP chain lengths longer than 62${\mathrm{PO}}_3^{-}$monomers were correlated to the shortest DNA ladders. In this study, synthetic linear polyPs (Sigma-Aldrich “Type 45”, estimated mean length of 45 ${\mathrm{PO}}_3^{-}$ monomers), trimetaphosphate (trimetaP: 3 ${\mathrm{PO}}_3^{-}$ ring), tripolyphosphate (tripolyP), pyrophosphate (PP_i), and inorganic orthophosphate (o-P_i) were visualized after separation by an in situ hydrolytic degradation process to o-P_i that was subsequently stained with methyl green. Statistically insignificant migration reduction of synthetic short-chain polyP after perchloric acid or phenol–chloroform extraction was confirmed with the Friedman test. ³¹P diffusion–ordered NMR spectroscopy confirmed that extraction also reduced PP_i diffusivity by <10%. Linear regression between the R_f peak migration value and the logarithm of synthetic polyP molecular weights enabled estimation of extracted polyP chain lengths from 2 to 45 ${\mathrm{PO}}_3^{-}$monomers. Linear polyP extracts from Saccharomyces cerevisiae grown in aerobic conditions were generally shorter than extracts cultured in anaerobic conditions. Extractions from both aerobic and anaerobic S. cerevisiae included tripolyP and o-P_i, but no PP_i.