Geometric gradient-flow dynamics with singular solutions

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy’s Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We identify singular solutions of these equations corresponding to collapsed (clumped) states and discuss their evolution.     

Multifunctional Cationic PeptoStars as siRNA Carrier: Influence of Architecture and Histidine Modification on Knockdown Potential

RNA interference provides enormous potential for the treatment of several diseases, including cancer. Nevertheless, successful therapies based on siRNA require overcoming various challenges, such as poor pharmacokinetic characteristics of the small RNA molecule and inefficient cytosolic accumulation. In this respect, the development of functional siRNA carrier systems is a major task in biomedical research. To provide such a desired system, the synthesis of 3‐arm and 6‐arm PeptoStars is aimed for. The different branched polypept(o)idic architectures share a stealth‐like polysarcosine corona for efficient shielding and a multifunctional polylysine core, which can be independently varied in size and functionality for siRNA complexation‐, transport and intra cellular release. The special feature of star‐like polypept(o)ides is in their uniform small size (<20 nm) and a core–shell structure, which implies a high stability and stealth‐like properties and thus, they may combine long circulation times and a deep penetration of cancerous tissue. Initial toxicity and complement studies demonstrate well tolerated cationic PeptoStars with high complexation capability toward siRNA (N/P ratio up to 3:1), which can lead to potent RNAi for optimized systems. Here, the synthetic development of 3‐arm and 6‐arm polypept(o)idic star polymers, their modification with endosomolytic moieties, and first in vitro insights on RNA interference are reported on.     

The retro Grignard addition reaction revisited: the reversible addition of benzyl reagents to ketones

The Grignard addition reaction is known to be a reversible process with allylic reagents, but so far the reversibility has not been demonstrated with other alkylmagnesium halides. By using crossover experiments it has been established that the benzyl addition reaction is also a reversible transformation. The retro benzyl reaction was shown by the addition of benzylmagnesium chloride to di-tert-butyl ketone followed by exchange of both the benzyl and the ketone moiety with another substrate. Similar experiments were performed with phenylmagnesium bromide and tert-butylmagnesium chloride, but in these two cases the Grignard addition reaction did not show any sign of a reverse transformation.     

Torsion and Abelianization in Equivariant Cohomology

Let X be a topological space upon which a compact connected Lie group G acts. It is well known that the equivariant cohomology H ^* _G (X; Q) is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology H ^* _T (X; Q), where T is a maximal torus of G. This relationship breaks down for coefficient rings k other than Q. Instead, we prove that under a mild condition on k the algebra H ^* _G (X; k) is isomorphic to the subalgebra of H ^* _T (X; k) annihilated by the divided difference operators.     

Stabilization of fully reduced iron-sulfur clusters by carbene ligation: the [FenSn]0 oxidation levels (n = 4, 8)

The all-ferrous [Fe4S4](0) state has been demonstrated in the fully reduced Fe protein of the Azotobacter vinelandii nitrogenase complex. We seek synthetic analogues of this state more tractable than the recently prepared but highly unstable cluster [Fe4S4(CN)4](4-) (Scott, Berlinguette, Holm, and Zhou, Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9741). The N-heterocyclic carbene 1,3-diisopropyl-4,5-dimethylimidazol-2-ylidene (Pr(i)2NHCMe2) has been found to stabilize the fully reduced clusters [Fe8S8(Pr(i)2NHCMe2)6] (4) and [Fe4S4(Pr(i)2NHCMe2)4] (5), which are prepared by cluster assembly or phosphine substitution of FenSn (n = 8, 16) clusters. Cluster 4 is also obtained by reaction of the carbene with all-ferrous [Fe7S6(PEt3)5Cl2] (3) and cluster 5 by carbene cleavage of 4. Detailed structures of 3 (monocapped prismatic), 4, and 5 are described; the latter two are the first iron-sulfur clusters with Fe-C sigma bonds. Cluster 4 possesses the [Fe8(mu3-S) 6(mu4-S)2] edge-bridged double cubane structure and 5 the cubane-type [Fe4(mu3-S)4] stereochemistry. The all-ferrous formulations of the clusters are confirmed by X-ray structure parameters and (57)Fe isomer shifts. Both clusters are stable under conventional aprotic anaerobic conditions, enabling further study of reactivity. The collective properties of 5 indicate that it is a meaningful synthetic analogue of the core of the fully reduced protein-bound cluster.     

VFe3S4 single and double cubane clusters: synthesis, structures, and dependence of redox potentials and electron distribution on ligation and heterometal

Both vanadium and molybdenum cofactor clusters are found in nitrogenase. In biomimetic research, many fewer heterometal MFe3S4 cubane-type clusters have been synthesized with M = V than with M = Mo because of the well-established structural relationship of the latter to the molybdenum coordination unit in the enzyme. In this work, a series of single cubane and edge-bridged double cubane clusters containing the cores [VFe3(mu3-S)4]2+ and [V2Fe6(mu3-S)6(mu4-S)2]2+ have been prepared by ligand substitution of the phosphine clusters [(Tp)VFe3S4(PEt3)3]1+ and [(Tp)2V2Fe6S8(PEt3)4]. The single cubanes [(Tp)VFe3S4L3]2- and double cubanes [(Tp)2V2Fe6S8L4]4- (L= F-, N3-, CN-, PhS-) are shown by X-ray structures to have trigonal symmetry and centrosymmetry, respectively. Single cubanes form the three-member electron transfer series [(Tp)VFe3S4L3]3-,2-,1-. The ligand dependence of redox potentials and electron distribution in cluster cores as sensed by 57Fe isomer shifts (delta) have been determined. Comparison of these results with those previously determined for the analogous molybdenum clusters (Pesavento, Berlinguette, and Holm Inorg. Chem. 2007, 46, 510) allows detection of the influence of heterometal M on the properties. At constant M and variable L, redox potentials are lowest for pi-donor ligands and largest for cyanide and relate approximately with decreasing ferrous character in clusters with constant charge z = 2-. At constant L and z and variable M, EV > E(Mo) and delta(av)V < delta(av)Mo, demonstrating that M = Mo clusters are more readily oxidized and suggesting a qualitative relation between lower potentials (greater ease of oxidation) and ferrous character.