Shimalactone Biosynthesis Involves Spontaneous Double Bicyclo-Ring Formation with 8π-6π Electrocyclization

Shimalactones A and B are neuritogenic polyketides possessing characteristic oxabicyclo[2.2.1]heptane and bicyclo[4.2.0]octadiene ring systems that are produced by the marine fungus Emericella variecolor GF10. We identified a candidate biosynthetic gene cluster and conducted heterologous expression analysis. Expression of ShmA polyketide synthase in Aspergillus oryzae resulted in the production of preshimalactone. Aspergillus oryzae and Saccharomyces cerevisiae transformants expressing ShmA and ShmB produced shimalactones A and B, thus suggesting that the double bicyclo-ring formation reactions proceed non-enzymatically from preshimalactone epoxide. DFT calculations strongly support the idea that oxabicyclo-ring formation and 8π-6π electrocyclization proceed spontaneously after opening of the preshimalactone epoxide ring through protonation. We confirmed the formation of preshimalactone epoxide in vitro, followed by its non-enzymatic conversion to shimalactones in the dark.     

On localizations of the characteristic classes of ℓ-adic sheaves and conductor formula in characteristic p > 0

Abbes, Kato and Saito generalize the Grothendieck-Ogg-Shafarevich formula to an arbitrary dimension (Kato and Saito in Ann. Math. 168:33–96, 2008; Abbes and Saito in Invent. Math. 168:567–612, 2007). In this paper, assuming the strong resolution of singularities, we prove a localized version of a formula proved using the characteristic class of an ?-adic sheaf by Abbes and Saito (Invent Math 168:567–612, 2007). We prove a localized version of the Lefschetz-Verdier trace formula proved in Grothendieck (Formule de Lefschetz, exposé III, SGA 5, Lect. Notes Math., vol 589, pp 372–406, Exp. X, Springer, Berlin, 1977 [Théorème 4.4]). As an application, we prove a conductor formula in an arbitrary dimension in the equal characteristic case.     

Kaon condensation and lambda–nucleon loop in the relativistic mean-field approach

The possibility of kaon condensation in high-density symmetric nuclear matter is investigated including both s- and p-wave kaon–baryon interactions within the relativistic mean-field (RMF) theory. Above a certain density, we have a collective state carrying the same quantum numbers as the antikaon. The appearance of the state is caused by the time component of the axial-vector interaction between kaons and baryons. It is shown that the system becomes unstable with respect to condensation of K– pairs. We consider how the effective baryon masses affect the kaon self-energy coming from the time component of the axial-vector interaction. Also, the role of the spatial component of the axial-vector interaction on the possible existence of the collective kaonic states is discussed in connection with Λ-mixing effects in the ground state of high-density matter. Implications of condensation for high-energy heavy-ion collisions are briefly mentioned.