Numerical solution of the time-dependent incompressible Navier-Stokes equations in the stream function and vorticity formulation

In this work we study the time-dependent incompressible Navier-Stokes problem. We introduce a suitable technique based on the splitting of the vorticity into two components. Then we discretize in space the resulting uncoupled system by means of continuous Lagrange finite elements. This is achieved by first performing the semi-discretization in time of these equations by a classical characteristics method for the advective term. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of cellular structures for soft tissue modelling

The aim of the paper is to show how the method of homogenization can be applied in modelling of soft tissue undergoing large deformation. Simplified microstructures are considered, which consist of hyperelastic porous matrix and periodic array of fluid‐filled cells. At the microscopic level diffusion processes are described by the Darcy law, permeability of the cellular membrane is introduced. Although at the macroscopic scale the tissue is incompressible, the flow inside microscopic volumes induces viscous relaxation effects. The homogenized problem is formulated.     

Synthesis of New Triazolopyrazine Antimalarial Compounds

A radical approach to late-stage functionalization using photoredox and Diversinate^™ chemistry on the Open Source Malaria (OSM) triazolopyrazine scaffold (Series 4) resulted in the synthesis of 12 new analogues, which were characterized by NMR, UV, and MS data analysis. The structures of four triazolopyrazines were confirmed by X-ray crystal structure analysis. Several minor and unexpected side products were generated during these studies, including two resulting from a possible disproportionation reaction. All compounds were tested for their ability to inhibit the growth of the malaria parasite Plasmodium falciparum (3D7 and Dd2 strains) and for cytotoxicity against a human embryonic kidney (HEK293) cell line. Moderate antimalarial activity was observed for some of the compounds, with IC₅₀ values ranging from 0.3 to >20 µM; none of the compounds displayed any toxicity against HEK293 at 80 µM.     

1H and 13C NMR assignments for two new xanthones from the endophytic fungus Xylaria sp. FRR 5657

The complete 1H and 13C NMR assignments are reported for the new natural products, 7-hydroxy-3-(hydroxymethyl)-1-methoxy-9H-xanthen-9-one (1) and 2,5-dihydroxy-8-methoxy-6-methyl-9-oxo-9H-xanthene -1-carboxylic acid (2). Both of these secondary metabolites were isolated from the fermentation culture of the endophytic fungus Xylaria sp. FRR 5657. 1D and 2D NMR experiments that included 1H, gCOSY, gHSQC and gHMBC were used for the determination of the structure and assignment of these xanthones.     

Catalytic asymmetric reactions for organic synthesis: the combined C-H activation/siloxy-cope rearrangement

Tetrakis(N-[4-dodecylbenzenesulfonyl]-(L)-prolinate) dirhodium [Rh(2)(S-DOSP)(4)]-catalyzed decomposition of vinyldiazoacetates in the presence of allyl silyl ethers results in the formation of the direct C-H insertion product and the product derived from a combined C-H activation/siloxy-Cope rearrangement. Both products are formed with very high diastereoselectivity (>94% de) and high enantioselectvity (78-93% ee). Under thermal or microwave conditions, the direct C-H insertion product undergoes a siloxy-Cope rearrangement in a stereoselective manner.     

Thermo-biolithography: a technique for patterning nucleic acids and proteins

We describe a "biolithographic" technique in which the unique properties of biopolymeric materials and the selective catalytic activities of enzymes are exploited for patterning surfaces under simple and bio-friendly conditions. We begin by coating a reactive film of the polysaccharide chitosan onto an inorganic surface (glass or silicon wafer). Chitosan's pH-responsive solubility facilitates film deposition, while the nucleophilic properties of this polysaccharide allow simple chemistries or biochemistries to be used to covalently attach species to the film. The thermally responsive protein gelatin is then cast on top of the chitosan film, and the gelatin gel serves as a sacrificial "thermoresist". Pattern transfer is accomplished by applying a heated stamp to melt specific regions of the gelatin thermoresist and selectively expose the underlying chitosan. Finally, molecules are conjugated to the exposed chitosan sublayer and the sacrificial gelatin layer is removed (either by treating with warm water or protease). To demonstrate the concept, we patterned a reactive dye (NHS-fluorescein), a model 20-base oligonucleotide (using standard glutaraldehyde coupling chemistries), and a model green fluorescent protein (using tyrosinase-initiated conjugation). Because gelatin can be applied and removed under mild conditions, sequential thermo-biolithographic steps can be performed without destroying previously patterned biomacromolecules. These studies represent the first step toward exploiting nature's exquisite specificity for lithographic patterning.     

Homogenization approach to the multi-compartment model of perfusion

The paper deals with modelling of the coupled diffusion-deformation processes in biological tissues with potential applications in describing the blood perfusion, or fluid filtration phenomena in general. The micromodel to be homogenized is based on the Biot type model for the incompressible medium. Due to the strong heterogeneity in the permeability coefficients associated with three compartments of the representative microstructural cell (RMC), the homogenization of the model leads to the double diffusion phenomena. The resulting homogenized equations, involving the stress-equilibrium equation and other two equations governing the mass redistribution, describe the parallel diffusion in two high-conducting compartments (arterial and venous sectors) separated by the low conducting matrix which represents the perfused tissue. To obtain the homogenized model, the method of two scale convergence is applied. The homogenized coefficients are defined in terms of the characteristic response of the RMC. It is possible to identify the instantaneous and fading memory viscoelastic coefficients; other effective parameters, controlling the fluid redistribution between the compartments, are involved also in time convolutions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of Naturally Occurring Pyranonaphthoquinones: (±) 9-Demethoxyeleutherin, (±) 9-Demethoxyisoeleutherin,and Pentalongin via Nef Reaction

The article describes alternative method for the synthesis of (±) 9-demethoxyeleutherin and (±) 9-demethoxyisoeleutherin, the analogs of naturally occurring pyranonaphthoquinones antibiotics eleutherin and isoeleutherin. This methodology has provided the target molecules using a shorter route involving five simple chemical transformations with Nef reaction as a key step. All the intermediates and target molecules were completely characterized by spectral techniques and confirmed by comparison with literature data. Further we have extended Nef protocol toward formal synthesis of naturally occuring pyranonaphthoquinone pentalongin. We accomplished synthesis of of 2-(1,4-dimethoxynaphthalen-2-yl)acetic acid devoid of very toxic cyanide intermediates, which has been converted into pentalongin.     

Chemoenzymatic asymmetric synthesis of fluoxetine,atomoxetine, nisoxetine,and duloxetine

The asymmetric synthesis of two well-known anti-depressant drugs, fluoxetine and duloxetine has been accomplished in a chemoenzymatic manner. The main highlight of the synthesis is the enantioselective cyanohydrin formation by a plant (R)-HNL (hydroxynitrile lyase). The enantiopure cyanohydrins are then synthetically manipulated into the above two drug molecules and two of their structural analogues, atomoxetine and nisoxetine.