Higher order shock waves

Shock waves and the relevant Rankine-Hugoniot conditions may be inadequate even in simple cases. As an example, the electromagnetic field generated by a point charge, whose velocity jumps from0 to a constant value, not only jumps across a spherical surface expanding at light speed, but also includes a-distribution term. This suggests that the concept of higher order shock waves be introduced, the associated compatibility conditions being also deduced.

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Sommario Il concetto di onda d'urto può rivelarsi inadeguato per descrivere situazioni anche semplici. A titolo di esempio, si determina esplicitamente l'espressione del campo elettromagnetico generato da una carica puntiforme la cui velocità passa istantaneamente da0 a un valore costante. Il campo elettromagnetico non solo è discontinuo attraverso una superficie sferica che si espande alla velocità della luce, ma include anche un termine che coinvolge la distribuzione. Ciò suggerisce di definire le onde d'urto di ordine superiore, per le quali si determinano le corrispondenti condizioni di compatibilità.

     

Polynuclear manganese grids and clusters—A magnetic perspective

High nuclearity paramagnetic, spin-coupled transition metal clusters and grids are fascinating chemists and physicists partly because of their structural beauty, and the challenge of creating them, but also because of their novel physical properties. Magnetic interactions between the spin centers are a primary focus. This review will examine a selection of Mn(II) polynuclear grids and clusters, with nuclearities in the range Mn₄ to Mn₉. Theoretical treatments of the magnetic properties are discussed, and approaches to solving the exchange problem for ‘large’ spin systems related to computational difficulties. A freely available software package (MAGMUN4.1) is presented as a means of dealing simply with spin-coupled clusters in general, and symmetry reduction methods are discussed briefly as a means of dealing with ‘large’ spin systems.     

Asymmetric Synthesis of the Nakijiquinones-Selective Inhibitors of the Her-2/Neu Protooncogene

A Wieland-Miescher type ketone and a tetramethoxyaryl derivative are the key building blocks for the enantioselective total synthesis of nakijiquinone C (1). The nakijiquinones are the only natural products known that selectively inhibit the Her-2/Neu tyrosine kinase, a protooncogene product that is vastly overexpressed in about 30 % of primary breast, ovary, and gastric carcinomas.     

Synthesis of lipidated eNOS peptides by combining enzymatic, noble metal- and acid-mediated protecting group techniques with solid phase peptide synthesis and fragment condensation in solution

Lipid-modified proteins play decisive roles in important biological processes such as signal transduction, organization of the cytoskeleton, and vesicular transport. Lipidated peptides embodying the characteristic partial structures of their parent lipidated proteins and semisynthetic proteins synthesized from such peptides are valuable tools for the study of these biological phenomena. We have developed an efficient synthesis strategy that allows for the synthesis of long multiply lipidated peptides embodying various side chain functional groups. The strategy was successfully applied in the synthesis of the N-terminal undetrigintapeptide of endothelial NO-synthase and related lipopeptides. Key elements of the synthesis strategy are the combined use of the enzyme-labile para-phenylacetoxybenzyloxycarbonyl (PhAcOZ) urethane as N-terminal blocking group, the Pd0-sensitive allyl ester as C-terminal protecting function and acid-labile side chain protecting groups for solution-phase synthesis of labile S-palmitoylated building blocks under the mildest conditions with solid-phase techniques and solution-phase fragment condensations. The successful synthesis of the triply lipidated 29-mer eNOS peptide convincingly demonstrates the full capacity of the protecting group methods.     

An enzyme-labile safety catch linker for synthesis on a soluble polymeric support

The development of new and broadly applicable linker groups which are stable under a variety of reaction conditions and allow release of the desired products from the solid support under very mild conditions is of great interest in organic synthesis and combinatorial chemistry. We describe an enzyme-labile safety-catch linker which releases alcohols and amines through i) enzymatic cleavage of an amino group and ii) subsequent lactam formation. The linker group was investigated on different polymeric supports: TentaGel. PEGA, CPG-beads and the soluble polymer POE-6000. From these linker-polymer conjugates 2-methoxy-5-nitrobenzyl alcohol was released by penicillin G acylase catalysed cleavage of a phenylacetamide and attack of the liberated benzylamine on the neighbouring ester group in ortho position. The model study revealed that only in the case of soluble POE-6000 conjugate high yields for the cleavage could be achieved. In the case of the other solid supports the enzyme does not have access to the interior of the polymer matrix. The application of the POE-6000 linker conjugate was investigated for various esters in Pd0-catalysed Heck-, Suzuki- and Sonogashira reactions as well as in a Mitsunobu reaction and cycloadditions. These studies proved that the linker is stable under a broad variety of reaction conditions and that the enzymatic method allows for release of the desired product alcohols under extremely mild conditions at pH 7 and 37 degrees C. In addition, the enzymatic reaction proceeds with complete chemoselectivity, that is other esters or amides are not attacked by the biocatalyst. In addition to alcohols amines can also be cleaved by means of the enzyme-initiated two-step process. In these cases the higher stability of amides as compared to esters requires warming to 60 degrees C to induce cyclization and release of the desired product.     

Solid-phase synthesis of lipidated peptides

Characteristic partial structures of lipidated proteins embodying different lipid groups as well as additional fluorescent tags or a maleimide for coupling to proteins can be synthesized readily by means of a new solid-phase technique employing the oxidative cleavage of the hydrazide linker as well as on-resin farnesylation and palmitoylation after appropriate deprotection of cysteine thiol groups as the key steps.     

Enantiospecific synthesis of the (9S,18R)-diastereomer of the leukocyte adhesion inhibitor cyclamenol A

Cyclamenol A is one of the very few non-carbohydrate and non-peptide natural products that inhibit leukocyte adhesion to endothelial cells. We report on the first enantioselective total synthesis of the (9S, 18R)-diastereomer of this macrocyclic polyene lactam. Key elements of the synthesis are i) the synthesis of the required chiral building blocks by employing readily accessible building blocks from the chiral pool, that is, (S)-malic acid and (R)-hydroxyisobutyric acid, ii) assembly of a linear polyene precursor by means of Wittig and Horner olefination reactions as key C-C bond-forming transformations, iii) ring closure by means of a vanadium-mediated pinacolisation reaction and iv) conversion of the generated cis-diol into a (Z)-olefin to complete the entire polyene system of the natural product. Attempts to close the macrocyclic ring by a macrolactamisation, a double Stille coupling or direct olefination in a McMurry reaction failed. Crucial to the successful completion of the synthesis was the correct orchestration of the final steps. It was necessary to first deprotect the intermediate formed after macrocycle formation and to generate the sensitive heptaene system in the last step by means of a Corey-Hopkins sequence.     

Solid-phase synthesis and biological evaluation of a teleocidin library--discovery of a selective PKCdelta down regulator

Protein kinaseC (PKC) is linked to the signal-induced modulation of a wide variety of cellular processes, such as growth, differentiation, secretion, apoptosis, and tumor development. The design and synthesis of small molecules that regulate these different cellular signaling systems is at the forefront of modern drug design. Herein we report a) an efficient method for the synthesis of indolactamV (6), a PKC activator, and its N13-des(methyl) analogues (19) using a regioselective organometallic transformation, a convenient aminomalonate derivative (10) to introduce the appropriate functionality and an enantiospecific enzymic hydrolysis as key steps; b) the use of this method in the first solid-phase synthesis of a teleocidin library modifying the N-13, C-12 and C-7 alkyl chains, and, therefore, producing a library of potential activators and/or inhibitors of PKC of the general structure (32); c) the activation of PKC by selected members of the library using a MARCKS translocation in vivo assay system; d) the observation that some of these analogues are nearly as effective as the natural PKC activators phorbol dibutyrate and (-)-indolactam V (6), and e) the observation that some of these analogues have different potential to induce down-regulation of members of the PKC gene family after chronic stimulation.     

Approximations of inventory models

Summary A general procedure is presented for constructing approximations of discrete review single product dynamic inventory models. Bounds are derived for the approximations and compared with the ones ofHinderer [1978],Whitt [1978] for the approximation of a general dynamic program. Good order-policies are constructed. Finally, conditions are given under which the sequence of bounds associated with a sequence of approximating models converges to zero.

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Zusammenfassung Es wird ein allgemeines Verfahren zur Approximation periodisch inspizierter dynamischer Ein-Produkt-Lagerhaltungsmodelle betrachtet. Dazu werden Fehlerschranken gegeben. Diese werden verglichen mit denen vonHinderer [1978],Whitt [1978] für ein allgemeines dynamisches Entscheidungsmodell. Außerdem werden gute Bestellpolitiken konstruiert und hinreichende Bedingungen gegeben, unter denen die Fehlerschranken einer Folge von approximierenden Modellen gegen Null konvergiert.