On the holonomy of connections with skew-symmetric torsion

We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated 2-form or any spinor. Suitable integral formulas allow us to prove similar properties in case of a compact Riemannian manifold equipped with a metric connection of skew-symmetric torsion. On the Aloff-Wallach space N(1,1) we construct families of connections admitting parallel spinors. Furthermore, we investigate the geometry of these connections as well as the geometry of the underlying Riemannian metric. Finally, we prove that any 7-dimensional 3-Sasakian manifold admits ²-parameter families of linear metric connections and spinorial connections defined by 4-forms with parallel spinors.Mathematics Subject Classification (2000):53 C 25, 81 T 30We thank Andrzej Trautman for drawing our attention to these papers by Cartan – see [27].     

Distorted Molecules: Perturbation Design,Preparation and Structures

The structure of a molecule can change considerably as its energy and thus its electron distribution within the time-domain of dynamic relaxation varies. Based on comparison of approriate measured data of related compounds and supported by quantum chemical calculations, therefore, charge-perturbed and/or sterically overcrowded molecules can be designed. Their preparation, handling, and structural characterization, frequently under extreme and especially largely aprotic conditions, provides some surprises. New structural principles become evident and old-fashioned ones are confirmed. Thus the contact-ion aggregates that form on ultrasonically supported reduction of unsaturated hydrocarbons with sodium metal partly contain dibenzene sodium sandwiches. Vicinal dimethylamino substituents or isoelectronic isopropyl groups cause steric overcrowding and facilitate oxidation to molecular cations by energetically favorable delocalization of the generated positive charge. Molecules and molecular ions in which an even number of π electrons are distributed over a σ skeleton containing an odd number of centers preferentially form cyanine subunits. This is demonstrated by the novel ethene dication and dianion salts with central C? C single bonds and molecular halves twisted relative to each other. Altogether in two years well over 50 structures have been determined. Much has been learned from them, especially about electron transfer and contact ion-pair formation in aprotic solvents. Nevertheless, we had to realize that answers to many questions, above all “what crystallizes, how, and why”, are still out of reach.     

Double-chip protein arrays: force-based multiplex sandwich immunoassays with increased specificity

Protein assays provide direct access to biologically and pharmacologically relevant information. To obtain a maximum of information from the very smallest amounts of complex biological samples, highly multiplexed protein assays are needed. However, at present, cross-reactions of binding reagents restrict the use of such assays to selected cases and severely limit the potential for up-scaling the technology. Here we describe a double-chip format, which can effectively overcome this specificity problem for sandwich immunoassays. This format consists of a capture array and a reference array with fluorescent labeled detection antibodies coupled to the reference array via DNA duplexes. This format allows for the local application of the labeled detection antibodies onto their corresponding specific spots on the capture array. Here we show that this double-chip format allows for the use of cross-reactive antibodies without generating false positive signals, and an assay for the parallel detection of seven different cytokines was set up. Even without further optimization, the dynamic range and the limit of detection for interleukin 8 were found to be comparable to those obtained with other types of multiplexed sandwich immunoassays.     

40 Years of Research on Polybrominated Diphenyl Ethers (PBDEs)—A Historical Overview and Newest Data of a Promising Anticancer Drug

Polybrominated diphenyl ethers (PBDEs) are a group of molecules with an ambiguous background in literature. PBDEs were first isolated from marine sponges of Dysidea species in 1981 and have been under continuous research to the present day. This article summarizes the two research aspects, (i) the marine compound chemistry research dealing with naturally produced PBDEs and (ii) the environmental toxicology research dealing with synthetically-produced brominated flame-retardant PBDEs. The different bioactivity patterns are set in relation to the structural similarities and dissimilarities between both groups. In addition, this article gives a first structure–activity relationship analysis comparing both groups of PBDEs. Moreover, we provide novel data of a promising anticancer therapeutic PBDE (i.e., 4,5,6-tribromo-2-(2′,4′-dibromophenoxy)phenol; termed P01F08). It has been known since 1995 that P01F08 exhibits anticancer activity, but the detailed mechanism remains poorly understood. Only recently, Mayer and colleagues identified a therapeutic window for P01F08, specifically targeting primary malignant cells in a low µM range. To elucidate the mechanistic pathway of cell death induction, we verified and compared its cytotoxicity and apoptosis induction capacity in Ramos and Jurkat lymphoma cells. Moreover, using Jurkat cells overexpressing antiapoptotic Bcl-2, we were able to show that P01F08 induces apoptosis mainly through the intrinsic mitochondrial pathway.     

Synthesis and Structures of β‐Diketoiminate Complexes of Magnesium

The reaction of the β‐diketoiminate lithium complex (dipp)NacNacLi · OEt₂ ((dipp)NacNac = 2‐((2,6‐diisopropylphenyl)amino)‐4‐((2,6‐diisopropylphenyl)imino)‐pent‐2‐enyl) with iPrMgCl and MgI₂ yield the corresponding (dipp)NacNacMgiPr · OEt₂ ( 1 ) and (dipp)NacNacMgI · OEt₂ ( 2 ). The reaction of 2 with NaBH₄ in diethylether gives (dipp)NacNacMg(μ‐H)₃BH · OEt₂ ( 3 ). The core element of compounds 1 – 3 is a six‐membered ring formed by N(1)–C(1)–C(2)–C(3)–N(2) and magnesium. The structures of 1 and 2 show the β‐diketoiminate backbone in a boat‐conformation with the tetrahedrally coordinated metal center at the prow and the opposing carbon atom at the stern. The magnesium atom in 3 is octahedrally coordinated and out of the β‐diketoiminate plane.     

Homogeneous non-degenerate 3-(α,δ)-Sasaki manifolds and submersions over quaternionic Kähler spaces

Annals of Global Analysis and Geometry - We show that every 3- $$(\alpha ,\delta )$$ -Sasaki manifold of dimension $$4n + 3$$ admits a locally defined Riemannian submersion over a quaternionic...     

On the topology and the geometry of SO(3)-manifolds

Consider the non-standard embedding of SO(3) into SO(5) given by the five-dimensional irreducible representation of SO(3), henceforth called SO(3)_ir. In this note, we study the topology and the differential geometry of five-dimensional Riemannian manifolds carrying such an SO(3)_ir structure, i.e., with a reduction of the frame bundle to SO(3)_ir.     

Biosynthesis of riboflavin. Single turnover kinetic analysis of 6,7-dimethyl-8-ribityllumazine synthase

6,7-dimethyl-8-ribityllumazine synthase (lumazine synthase) catalyzes the condensation of 5-amino-6-ribitylamino-2,4-(1H,3H)-pyrimidinedione with 3,4-dihydroxy-2-butanone 4-phosphate, affording the riboflavin precursor, 6,7-dimethyl-8-ribityllumazine. Single turnover experiments monitored by multiwavelength photometry were performed with the recombinant lumazine synthase of Bacillus subtilis. Mixing of the enzyme with the pyrimidine type substrate is conducive to a hypsochromic shift as well as a decrease in absorbance of the heterocyclic substrate; the rate constant for that reaction is 0.02 s(-1) microM(-1). Rapid mixing of the complex between enzyme and pyrimidine type substrate with the second substrate, 3,4-dihydroxy-2-butanone 4-phosphate, is followed by the appearance of an early optical transient characterized by an absorption maxima at 330 nm of low intensity which was tentatively assigned as a Schiff base intermediate. The subsequent elimination of phosphate affords a transient with intense absorption maxima at 455 and 282 nm, suggesting an intermediate with an extended system of conjugated double bonds. The subsequent formation of the enzyme product, 6,7-dimethyl-8-ribityllumazine, is the rate-determining step.