Enantiodivergent synthesis of D- and L-erythro-sphingosines through Mannich-type reactions of N-benzyl-2,3-O-isopropylidene-D-glyceraldehyde nitrone

The addition of a 2-silyloxy silylketene acetal to N-benzyl-2,3-O-isopropylidene-D-glyceraldehyde nitrone (Mannich-type reaction) can be stereocontrolled to give 2S,3S,4S and 2R,3R,4S adducts as major compounds, depending on whether the reaction is activated with zinc(II) triflate or tin(IV) chloride, respectively. The corresponding major adducts were used for preparing diastereomeric polyhydroxy-beta-aminoesters that were further converted into suitable orthogonally protected enantiomeric D- and L-erythro-sphingosines.     

Radical ring expansion reactions of methylenecyclopropane derivatives: a theoretical study

The evolution of the primary radicals from 1-(3-bromopropyl)-2-ethyl-3-methylenecyclopropane, 1-(3-bromopropyl)-1-trimethylsilyl-2-methylenecyclopropane, 1-(3-bromobutyl)-2-ethyl-3-methylenecyclopropane, and 1-(3-bromobutyl)-1-trimethylsilyl-2-methylenecyclopropane was theoretically studied at the ROMP2/6-311++G(d,p)//UB3LYP/6-31G(d,p) theory level taking into account the effect of solvent through a PCM-UAHF model. For the propyl-substituted radicals, the attack of the radical center on the double bond takes place most favorably in an exo fashion. The subsequent ring expansions yield the product corresponding to the rupture of the endo C-C bond as the most favorable one in accordance with the experimental results. In the case of 1-(3-bromobutyl)-2-ethyl-3-methylenecyclopropane, the Gibbs energy barriers for the endo and exo attacks are the same, and the subsequent reversible evolution yields the product corresponding to the rupture of the exo C-C bond as the most favorable one through thermodynamic control in agreement with experiment. Finally, for 1-(3-bromobutyl)-1-trimethylsilyl-2-methylenecyclopropane, our calculations predict that the endo attack is 0.8 kcal/mol more favorable than the exo one. In the subsequent reversible ring expansion, the product corresponding to the rupture of the endo C-C bond is kinetically the most favored one in reasonable agreement with the experimental observations.     

Analysis of monoamine oxidase enzymatic activity by reversed-phase high performance liquid chromatography and inhibition by beta-carboline alkaloids occurring in foods and plants

Monoamine oxidase (MAO) is a flavin adenine dinucleotide (FAD)-containing enzyme located at the outer membranes of mitochondria that catalyzes the oxidative deamination of biogenic and xenobiotic amines. We have used a chromatographic method to measure MAO-enzymatic activity by using kynuramine as a non-selective substrate with its MAO-oxidation product subsequently analyzed by RP-HPLC-DAD and HPLC-mass spectrometry (MS). This method was applied to study the kinetic parameters, inhibition and reaction products of MAO recombinant enzymes in presence of tetrahydro-beta-carboline and beta-carboline alkaloids occurring in foods, plants and mammals. Analysis by HPLC showed that tetrahydro-beta-carbolines or beta-carbolines were not modified by MAO. Several beta-carbolines such as tryptoline (1,2,3,4-tetrahydro-beta-carboline) and 1-methyltryptoline (1-methyl-1,2,3,4-tetrahydro-beta-carboline) were inhibitors of MAO-A; instead their corresponding 6-hydroxy-derivatives (6-hydroxytryptoline and 6-hydroxy-1-methyltryptoline) lacked this activity. Tetrahydro-beta-carboline-3-carboxylic acids were unable to inhibit MAO enzymes. In contrast, their oxidation products, i.e. the fully aromatic beta-carbolines (norharman and harman), acted as good inhibitors of MAO. Two tetrahydro-beta-carbolines (i.e. tryptoline and 1-methyltryptoline) occurring in foods were isolated by solid-phase extraction (SPE) and RP-HPLC from selected samples of sausages and the corresponding extracts exhibited good inhibition properties over MAO-A. These results suggest that beta-carbolines from foods, plants, and mammals may exert inhibitory actions on MAO enzymes.     

Accurate length control of supramolecular oligomerization: Vernier assemblies

Linear oligomeric supramolecular assemblies of defined length have been generated using the Vernier principle. Two molecules, containing a different number (n and m) of mutually complementary binding sites, separated by the same distance, interact with each other to form an assembly of length (n x m). The assembly grows in the same way as simple supramolecular polymers, but at a molecular stop signal, when the binding sites come into register, the assembly terminates giving an oligomer of defined length. This strategy has been realized using tin and zinc porphyrin oligomers as the molecular building blocks. In the presence of isonicotinic acid, a zinc porphyrin trimer and a tin porphyrin dimer form a 3:4 triple stranded Vernier assembly six porphyrins long. The triple strand Vernier architecture introduced here adds an additional level of cooperativity, yielding a stability and selectivity that cannot be achieved via a simple Vernier approach. The assembly properties of the system were characterized using fluorescence titrations and size-exclusion chromatography (SEC). Assembly of the Vernier complex is efficient at micromolar concentrations in nonpolar solvents, and under more competitive conditions, a variety of fragmentation assemblies can be detected, allowing determination of the stability constants for this system and detailed speciation profiles to be constructed.     

Stabilization of charge-separated states in phthalocyanine-fullerene ensembles through supramolecular donor-acceptor interactions

A novel ZnPc-C60 dyad (3), in which two photoactive units are brought together by a phenylenevinylene spacer has been synthesized. The synthetic strategy en route toward 3 involves a Heck reaction to attach 4-vinylbenzaldehyde to a monoiodophthalocyanine precursor, followed by standard cycloaddition of azomethine ylides (generated from the formylPc derivative and N-methylglycine) to one of the double bonds of C60. Electrochemical studies reveal that in 3 the ZnPc is about 39 mV more difficult to oxidize than in the corresponding ZnPc reference, which points to appreciable electronic communication between ZnPc and C60 in the ground state. In the excited state, photoexcitation leads to the formation of a charge-separated ZnPc*+-C60*- state, for which a lifetime of 130 ns was determined in THF. Hetero-association between complementary Pcs (1 and 2 or 3 and 2), which carry different peripheral functionalities (i.e., either electron-donating alkoxy groups or electron-deficient alkylsulfonyl chains) was assessed by different techniques. They provided evidence for donor-acceptor 1:1 complex formation with a stability constant of ca. 10(5) M(-1) in CHCl3. Interestingly, hetero-association of ZnPc-C60 dyad 3 with an electron-deficient PdPc (2) allowed the construction of supramolecular triads, in which a substantial stabilization of the radical pair is seen relative to that of the covalently linked dyad ZnPc-C60 (3).     

Photoinduced charge-transfer states in subphthalocyanine-ferrocene dyads

Very efficient stabilization of the photoinduced charge-transfer state was achieved in simple subphthalocyanine-ferrocene dyads, reaching radical pair lifetimes of about 0.2 ms.     

Guaranteed and locally computable a posteriori error estimate

^** Email: vejchod{at}math.cas.cz A new approach, based on the combination of the equilibratedresidual method and the method of hypercircle, is proposed fora posteriori error estimation. Computer implementation of theequilibrated residual method is fast, but it does not produceguaranteed estimates. On the other hand, the method of hypercircledelivers guaranteed estimates, but it is not fast because itinvolves solving a global linear algebraic system. The combinationof these two methods leads to guaranteed and locally computablea posteriori error estimator. This combined method is appliedto linear elliptic problem in two dimensions with mixed boundaryconditions and non-negative absolute terms.     

The pluripolar hull of a graph and fine analytic continuation

We show that if the graph of an analytic function in the unit disk D is not complete pluripolar in C² then the projection of its pluripolar hull contains a fine neighborhood of a point . Moreover the projection of the pluripolar hull is always finely open. On the other hand we show that if an analytic function f in D extends to a function ℱ which is defined on a fine neighborhood of a point and is finely analytic at p then the pluripolar hull of the graph of f contains the graph of ℱ over a smaller fine neighborhood of p. We give several examples of functions with this property of fine analytic continuation. As a corollary we obtain new classes of analytic functions in the disk which have non-trivial pluripolar hulls, among them C^∞ functions on the closed unit disk which are nowhere analytically extendible and have infinitely-sheeted pluripolar hulls. Previous examples of functions with non-trivial pluripolar hull of the graph have fine analytic continuation.     

On the asymptotic behavior of the principal eigenvalues of some elliptic problems

This paper is concerned with nonself-adjoint elliptic problems involving indefinite weights and boundary conditions of the Dirichlet, Neumann or Robin type. We study the asymptotic behavior of the principal eigenvalues, when the first order term (drift term) becomes larger and larger. The basic results of Berestycki et al. (Commun. Math. Phys., 253:451–480, 2005) are extended to the present context. Moreover, answers are provided to some open problems raised in Berestycki et al. (Commun. Math. Phys., 253:451–480, 2005).     

Distortion Varieties

The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter distortions. These are based on Chow polytopes and Gröbner bases. Multi-parameter distortions are studied using tropical geometry. The motivation for distortion varieties comes from multi-view geometry in computer vision. Our theory furnishes a new framework for formulating and solving minimal problems for camera models with image distortion.