Twisted K-Theory and K-Theory of Bundle Gerbes

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of K-brane charges in nontrivial backgrounds are briefly discussed. Received: 29 June 2001 / Accepted: 15 October 2001     

Molecularly Designed Stabilized Asymmetric Hollow Fiber Membranes for Aggressive Natural Gas Separation

New rigid polyimides with bulky CF₃ groups were synthesized and engineered into high‐performance hollow fiber membranes. The enhanced rotational barrier provided by properly positioned CF₃ side groups prohibited fiber transition layer collapse during cross‐linking, thereby greatly improving CO₂/CH₄ separation performance compared to conventional materials for aggressive natural gas feeds.     

Diastereoselective Friedel-Crafts alkylation of indoles with chiral alpha-phenyl benzylic cations. Asymmetric synthesis of anti-1,1,2-triarylalkanes

The reactions of chiral benzyl carbocations bearing alpha-phenyl substituents with N-sulfonylated indoles afford 1,1,2-triarylalkanes with anti-selectivities. This outcome is a reversal of facial diastereoselectivity relative to Bach's alpha-alkyl-bearing benzyl cations. The reactions are promoted by either a Br?nsted acid (TFA) or Lewis acid (BF3.OEt2), offering differential diastereoselectivities and reactivities. The electronic properties of both reacting partners strongly influence the reaction rates and the product diastereoselectivities and appear to operate under kinetic control. This chemistry provides an efficient access to sterically congested tetrasubstituted ethanes.     

Constructing the Spectrum of Packings and Coverings for the Complete Graph with Stars with up to Five Edges

The packing and covering problems have been considered for several classes of graphs. For instance, Bryant et. al. have investigated the packing problem for paths and cycles, and the packing and covering problems for 3-cubes. The packing and covering problems were settled for stars with up to six edges by Roditty. In this paper, for every possible leave graph (excess graph), we find a corresponding maximum packing (minimum covering) of the complete graph with stars with up to five edges.     

Effects of As(III) binding on beta-hairpin structure

While arsenic(III) compounds can exert profound toxicological and pharmacological effects, their modes of action and, in particular, the structural consequences of their binding to cysteinyl side chains in proteins, remain poorly understood. To gain an understanding of how arsenic binding influences beta-structure, pairs of cysteines were introduced into a model monomeric beta-hairpin to yield a family of peptides such that coordination occurs either across the strands or within the same strand of the beta-hairpin. Circular dichroism, NMR, UV-vis spectroscopy, and rapid-reaction studies were used to characterize the binding of monomethylarsonous acid or p-succinylamidephenyl arsenoxide (PSAO) to these peptides. Placement of cysteines at non-hydrogen bond (NHB) positions across the beta-hairpin, such that they occupy the same face of the sheet, was found to enhance the structure as assessed by CD. Cross-strand cysteine residues that project on opposite faces close to the termini of the hairpin can still bind arsenic tightly and show modestly increased beta-sheet content. NMR and modeling studies suggest that arsenic can be accommodated at this locus without disrupting the core interactions stabilizing the turn. However, As(III) binding to nonopposed cysteines, or to cysteines at HB and NHB positions along one strand of the hairpin, caused loss of structure. UV-vis titrations show that all these hairpin peptides bind PSAO stoichiometrically with K(d) values from 13 to 106 nM. Further, binding is moderately rapid, with second-order rate constants for association of 10,000-22,000 M(-1) s(-)1 irrespective of the placement of the cysteines within the hairpin and the consequent extent of structural reorganization required as a result of binding. These studies complement recent work with alpha-helices and further demonstrate that capture of a pair of thiols by As(III) may result in significant changes in local secondary structure in the protein targets of these potent bioactive agents.     

Numerical study of the gel transition in reversible associating polymers

Four temperatures to characterize the gel transition in reversible associating polymers have been calculated in a novel mixed molecular dynamics/Monte Carlo model. (1) The temperature below which relaxation times no longer show Arrhenius dependence on temperature; (2) the Vogel-Fulcher temperature at which the structural relaxation time extrapolates to infinity; (3) the micelle formation temperature at which the number of reversible bonds sharply increases; and (4) a crossover temperature at which the viscosity exhibits a power law divergence as predicted by mode coupling theory. These specific temperatures are obtained from measurements of diffusivity, specific heat, and network topology.     

Breaking Symmetry Relaxes Structural and Magnetic Restraints,Suppressing QTM in Enantiopure Butterfly Fe2Dy2 SMMs**

The {Fe₂Dy₂} butterfly systems can show single molecule magnet (SMM) behaviour, the nature of which depends on details of the electronic structure, as previously demonstrated for the [Fe₂Dy₂(μ₃-OH)₂(Me-teaH)₂(O₂CPh)₆] compound, where the [N,N-bis-(2-hydroxyethyl)-amino]-2-propanol (Me-teaH₃) ligand is usually used in its racemic form. Here, we describe the consequences for the SMM properties by using enantiopure versions of this ligand and present the first homochiral 3d/4 f SMM, which could only be obtained for the S enantiomer of the ligand for [Fe₂Dy₂(μ₃-OH)₂(Me-teaH)₂(O₂CPh)₆] since the R enantiomer underwent significant racemisation. To investigate this further, we prepared the [Fe₂Dy₂(μ₃-OH)₂(Me-teaH)₂(O₂CPh)₄(NO₃)₂] version, which could be obtained as the RS-, R- and S-compounds. Remarkably, the enantiopure versions show enhanced slow relaxation of magnetisation. The use of the enantiomerically pure ligand suppresses QTM, leading to the conclusion that use of enantiopure ligands is a “gamechanger” by breaking the cluster symmetry and altering the intimate details of the coordination cluster's molecular structure.