A note on determinants,minors and a boundary map

We give an explicit formula for the first non-trivial boundary map of the Akin–Buchsbaum–Weyman resolution (Schur functors and Schur complexes, Adv. Math 1982;44:207-278). The role of the Laplace expansion formula is emphasized.     

Counting BPS States on the Enriques Calabi-Yau

We study topological string amplitudes for the FHSV model using various techniques. This model has a type II realization involving a Calabi-Yau threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By applying heterotic/type IIA duality, we compute the topological amplitudes in the fibre to all genera. It turns out that there are two different ways to do the computation that lead to topological couplings with different BPS content. One of them gives the standard D0-D2 counting amplitudes, and from the other one we obtain information about bound states of D0-D4-D2 branes on the Enriques fibre. We also study the model using mirror symmetry and the holomorphic anomaly equations. We verify in this way the heterotic results for the D0-D2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms, and up to genus three. This model turns out to be much simpler than the generic B-model and might be exactly solvable.     

Synthesis of C12-Keto Saxitoxin Derivatives with Unusual Inhibitory Activity Against Voltage-Gated Sodium Channels

A novel series of C12-keto-type saxitoxin (STX) derivatives bearing an unusual nonhydrated form of the ketone at C12 has been synthesized, and their Na_V-inhibitory activity has been evaluated in a cell-based assay as well as whole-cell patch-clamp recording. Among these compounds, 11-benzylidene STX ( 3 a ) showed potent inhibitory activity against neuroblastoma Neuro 2A in both cell-based and electrophysiological analyses, with EC₅₀ and IC₅₀ values of 8.5 and 30.7 nm , respectively. Interestingly, the compound showed potent inhibitory activity against tetrodotoxin-resistant subtype of Na_V1.5, with an IC₅₀ value of 94.1 nm . Derivatives 3 a – d and 3 f showed low recovery rates from Na_V1.2 subtype (ca 45–79 %) compared to natural dcSTX ( 2 ), strongly suggesting an irreversible mode of interaction. We propose an interaction model for the C12-keto derivatives with Na_V in which the enone moiety in the STX derivatives 3 works as Michael acceptor for the carboxylate of Asp¹⁷¹⁷.     

Biopolymer Skeleton Produced by Rhizobium radiobacter: Stoichiometric Alternation of Glycosidic and Amidic Bonds in the Lipopolysaccharide O‐Antigen

The lipopolysaccharide (LPS) O‐antigen structure of the plant pathogen Rhizobium radiobacter strain TT9 and its possible role in a plant‐microbe interaction was investigated. The analyses disclosed the presence of two O‐antigens, named Poly1 and Poly2. The repetitive unit of Poly2 constitutes a 4‐α‐l ‐rhamnose linked to a 3‐α‐d ‐fucose residue. Surprisingly, Poly1 turned out to be a novel type of biopolymer in which the repeating unit is formed by a monosaccharide and an amino‐acid derivative, so that the polymer has alternating glycosidic and amidic bonds joining the two units: 4‐amino‐4‐deoxy‐3‐O‐methyl‐d ‐fucose and (2′R,3′R,4′S)‐N‐methyl‐3′,4′‐dihydroxy‐3′‐methyl‐5′‐oxoproline). Differently from the O‐antigens of LPSs from other pathogenic Gram‐negative bacteria, these two O‐antigens do not activate the oxidative burst, an early innate immune response in the model plant Arabidopsis thaliana, explaining at least in part the ability of this R. radiobacter strain to avoid host defenses during a plant infection process.     

Hydrogenation of poly(myrcene) and poly(farnesene) using diimide reduction at ambient pressure

Ambient pressure chemical hydrogenation using p-toluene sulfonyl hydrazide (TSH) via thermal diimide formation (N₂H₂) permitted reduction of double bonds of poly(myrcene) (poly[Myr]) and poly(farnesene) (poly[Far]). Both pendent and backbone double bonds in poly(Myr) (M_n = 56 kg/mol) and poly(Far) (M_n = 62 kg/mol) synthesized by conventional free radical polymerization were hydrogenated to almost completion. Furthermore, TSH semi-batch addition efficiently hydrogenated double bonds, while avoiding undesired autohydrogenation of diimides that occurred in batch mode. Thermal stability improved for hydrogenated poly(Myr) and poly(Far), where temperature at 10% weight loss (T_10%) increased from 188 to 404°C for poly(Myr) and from 310 to 379°C for poly(Far). T_gs of poly(Myr) and poly(Far) also increased by about 10–25°C, indicating increased stiffness after hydrogenation. Finally, viscosities of poly(Myr) and poly(Far) were also increased after hydrogenation, and a greater increase was observed for poly(Myr) (by two orders of magnitude from 10² to 10⁴ Pa s) due to its M_n being much higher than its entanglement molecular weight. Poly(Far) viscosity only increased by 1.5 times after hydrogenation (~10⁴ Pa s), comparable to the poly(Myr) after hydrogenation, suggesting unsaturated poly(Far) was more entangled than unsaturated poly(Myr) because of its longer side chains.     

A new method of using supercritical carbon dioxide as a green solvent for synthesis and purification of 5,5‴-bis(tridecafluorohexyl)-2,2′:5′,2″:5″,2‴-quaterthiophene,which is one of n-type organic semiconducting materials

We have investigated synthesis as well as purification of 5,5?-bis(tridecafluorohexyl)-2,2′:5′,2″:5″,2?-quaterthiophene (BFH-4?T, n-type organic semiconducting material) using supercritical carbon dioxide (scCO₂) as a green solvent. BFH-4T was obtained in good selectivity and high yield by TDAE/PdCl₂-catalyzed reductive coupling reaction of 5-bromo-5′-(tridecafluorohexyl)-2,2′-bithiophene in scCO₂. We have also successfully established purification of the reaction mixture by passing scCO₂ in the reaction vessel. The product was yellow powder of BFH-4T with purity of more than 99% and Pd catalyst was not contained.     

Biphenyl ether and biphenyl quinolizidine lactone alkaloids from Heimia salicifolia

Three new biphenyl ether quinolizidine lactone alkaloids (1–3) and 13 new biphenyl quinolizidine lactone alkaloids (4–16) were isolated from Heimia salicifolia (Lythraceae) together with seven known alkaloids. Their structures were determined by spectroscopic analyses and chemical conversions.