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Dioxygenated cyclopentenones are versatile building blocks for the synthesis of several natural products. Herein we report a direct asymmetric synthesis of trans-4,5-dioxygenated cyclopentenone derivatives through base-catalyzed rearrangement of pyranones followed by dynamic kinetic resolution. Milder conditions than previously reported for this rearrangement have been found regarding amine base catalysis, solvent and temperature effects. All data supports a mechanism involving cyclization of an intermediate formed by electrocyclic ring opening of a pyranone-derived enol. We have developed conditions for asymmetric synthesis of trans-4-tert-butoxy-5-hydroxycyclopent-2-enone, in 81% yield and 95% ee, and analogous dioxygenated cyclopentenones, via a lipase induced dynamic kinetic resolution.

We study the dependence of geometric quantization of the standard symplectic torus on the choice of invariant polarization. Real and mixed polarizations are interpreted as degenerate complex structures. Using a weak version of the equations of covariant constancy, and the Weil-Brezin expansion to describe distributional sections, we give a unified analytical description of the quantization spaces for all nonnegative polarizations. The Blattner-Kostant-Sternberg (BKS) pairing maps between half-form corrected quantization spaces for different polarizations are shown to be transitive and related to an action of $Sp(2g,\R)$. Moreover, these maps are shown to be unitary., 24 pages; revised version, to appear in JFA

Two new TTF-based donors that are dithiolene ligand precursors, 3-{5-[(2-cyanoethyl)thio]-2-(5,6-dihydrothieno[2,3-d][1,3]dithiol-2ylidene-1,3-dithiol-4-yl)thio}propanenitrile, dtdt (1) and 3-({5-[(2-cyanoethyl)thio]-2-thieno[2,3-d][1,3]dithiol-2-ylidene-1,3-dithiol-4yl)thio}propanenitrile, a-tdt (2), were synthesized and characterized. The electrochemical properties of these compounds were studied by cyclic voltammetry (CV) in acetonitrile. Compound 1 shows two reversible oxidation process at 1 E1/2 = 0.639 V and 2 E1/2 = 0.997 V versus Ag/AgCl. This same processes occurs at 1 E1/2 = 0.612 V and 2 E1/2 = 0.906 V in the case of 2. The crystal structures con

We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift k -> k+n appears in a natural way in this finite-dimensional framework., small misprints corrected

We extend the coherent state transform (CST) of Hall to the context of abelian varieties by considering them as quotients of the complexification of the abelian group K=U(1)g. We show that this transform, applied to appropriate distributions on K, gives all classical theta functions, and that, by defining on this space of theta functions an inner product related to the K-averaged heat kernel, the unitarity of the CST transform is still preserved.

A direct asymmetric synthesis of a trans-4,5-difunctionalised cyclopentenone derivative has been achieved in 55% yield and 80% ee by organocatalysed rearrangement of a pyranone in tert-butanol by DABCO with simultaneous enzymatic resolution.

P2X receptors are trimeric membrane ion channels activated by extracellular ATP. Elucidation of their physiological roles has been handicapped by a lack of specific tools. In the present work, the P2X2 receptor was engineered to open and close with different wavelengths of light. We synthesized a photoswitchable crosslinker, bis(maleimido)azobenzene, of molecular dimensions appropriate to bridge cysteines introduced at different subunits at the outer pore (P329C). This produced a P2X2 receptor that was opened within milliseconds at 440 nm light and closed rapidly at 360 nm light, as measured by the ionic currents. When the P329C mutation was combined with the ATP-binding site mutation, K69A, ATP had no effect while light-induced currents were still present. The light-gated receptor displayed similar unitary currents, inward rectification and calcium permeability (PCa/PNa = 2.6), as the P2X2 receptors activated by ATP. P2X3 receptors with an equivalent mutation (P320C) could be controlled with light, displaying typical rapid desensitization. P2X3[P320C] subunits also co-assembled with native P2X2 subunits in pheochromocytoma 12 cells to form light-gated heteromeric P2X2/3 receptors. We extended this approach to acid-sensing ion channels (ASICs), which are also trimers but are unrelated in sequence to P2X receptors. The structurally equivalent mutation in human ASIC1 (G430C) was readily opened and closed by brief applications of light following modification with bis(maleimido)azobenzene. This provides functional evidence that P2X receptors and ASICs can open by a similar mechanism at the level of the pore. The generation of these engineered receptors should facilitate investigation of the functional roles of P2X receptors and ASICs in the cell, tissue and intact organism.

A new method to obtain the Picard-Fuchs equations of effective, N=2 supersymmetric gauge theories with massive matter hypermultiplets in the fundamental representation is presented. It generalises a previously described method to derive the Picard-Fuchs equations of both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. The techniques developed are well suited to symbolic computer calculations., Comment: 29 pages, uses phyzzx.tex

A new method to obtain the Picard-Fuchs equations of effective $N = 2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding $N = 2$ theory., Latex version, 43 pages, a few cosmetic changes and some references added