Quadratically Hyponormal Weighted Shifts with Recursive Tail

We characterize positive quadratic hyponormality of the weighted shift W-alpha(x) associated to the weight sequence alpha(x) : 1, 1, root x, (root u, root v, root w)(Lambda) with Stampfli recursive tail, and produce an interval in x with non-empty interior in the positive real line for quadratic hyponormality but not positive quadratic hyponormality for such a shift. (C) 2013 Elsevier Inc. All rights reserved.

Synthesis Of Linoleate Analogs With Longer Alkyl Termini To Test For Proposed "Tail-First" Binding In SBLO-1

Lipoxygenases are nonheme-iron proteins that catalyze the oxygenation of polyunsaturated fatty acids to give conjugated diene hydroperoxides. For example, soybean lipoxygenase-1 (SBLO-1) converts linoleate into 13-(S)-hydroperoxy-9(Z),11(E)-octadecadienoate (13(S)-HPOD). Although the crystal structure of SBLO-1 has been determined, it is still unclear how the substrate binds at the active site. This absence of knowledge makes it difficult to understand the role of the enzyme during catalysis of the reaction. We hypothesize that SBLO-1 binds linoleate ¿tail-first¿, so that the methyl terminus is within a hydrophobic pocket deep within the enzyme. It is believed that the hydrophobic residue phenylalanine-557 at this site has stabilizing interactions with the terminal methyl group on linoleate. To test this hypothesis, we have developed a synthetic pathway that will yield linoleate analogs with longer fatty acid chains by 1 and 2 more carbons at the alkyl terminus. These substrates will be analyzed through kinetic assays done in combination with wild type SBLO-1 and mutants in which we have replaced phenylalanine-557 with valine.