Heegner Divisors and Nonholomorphic Modular Forms

We consider an embedded modular curve in a locally symmetric space M attached to an orthogonal group of signature (p, 2) and associate to it a nonholomorphic elliptic modular form by integrating a certain theta function over the modular curve. We compute the Fourier expansion and identify the generating series of the (suitably defined) intersection numbers of the Heegner divisors in M with the modular curve as the holomorphic part of the modular form. This recovers and generalizes parts of work of Hirzebruch and Zagier.     

[FeFe]‐Hydrogenase with Chalcogenide Substitutions at the H‐Cluster Maintains Full H2 Evolution Activity

The [FeFe]‐hydrogenase HYDA1 from Chlamydomonas reinhardtii is particularly amenable to biochemical and biophysical characterization because the H‐cluster in the active site is the only inorganic cofactor present. Herein, we present the complete chemical incorporation of the H‐cluster into the HYDA1‐apoprotein scaffold and, furthermore, the successful replacement of sulfur in the native [4Fe_H] cluster with selenium. The crystal structure of the reconstituted pre‐mature HYDA1[4Fe4Se]_H protein was determined, and a catalytically intact artificial H‐cluster variant was generated upon in vitro maturation. Full hydrogen evolution activity as well as native‐like composition and behavior of the redesigned enzyme were verified through kinetic assays, FTIR spectroscopy, and X‐ray structure analysis. These findings reveal that even a bioinorganic active site with exceptional complexity can exhibit a surprising level of compositional plasticity.     

An improved pixel-based approach for analyzing images in two-dimensional gel electrophoresis

An improved pixel-based approach for analyzing 2-DE images is presented. The key feature of the method is to create a mask based on all gels in the experiment using image morphology, followed by multivariate analysis on the pixel level. The method reduces the impact of noise and background by identifying regions in the image where protein spots are present, but make no assumption on individual spot boundaries for isolated spots. This makes it possible to detect significant changes in complex regions, and visualize these changes over multiple gels in an easy way. False missing values and spot volumes caused by imposing erroneous spot boundaries are thus circumvented. The approach presented gives improved pixel-based information from the gels, and is also an alternative to existing methods for data-reduction, significance testing and visualization of 2-DE data. Results are compared with software using a common spot boundary approach on an experiment consisting of 35 full size gel images. Gel alignment is required before analysis.     

The nature of the active site in heterogeneous metal catalysis

This tutorial review, of relevance for the surface science and heterogeneous catalysis communities, provides a molecular-level discussion of the nature of the active sites in metal catalysis. Fundamental concepts such as "Br?nsted-Evans-Polanyi relations" and "volcano curves" are introduced, and are used to establish a strict partitioning between the so-called "electronic" and "geometrical" effects. This partitioning is subsequently employed as the basis for defining the concept "degree of structure sensitivity" which can be used when analyzing the structure sensitivity of catalytic reactions.     

Bridging across length scales: multi-scale ordering of supported lipid bilayers via lipoprotein self-assembly and surface patterning

We show that a two-step process, involving spontaneous self-assembly of lipids and apolipoproteins and surface patterning, produces single, supported lipid bilayers over two discrete and independently adjustable length scales. Specifically, an aqueous phase incubation of DMPC vesicles with purified apolipoprotein A-I results in the reconstitution of high density lipoprotein (rHDL), wherein nanoscale clusters of single lipid bilayers are corralled by the protein. Adsorption of these discoidal particles to clean hydrophilic glass (or silicon) followed by direct exposure to a spatial pattern of short-wavelength UV radiation directly produces microscopic patterns of nanostructured bilayers. Alternatively, simple incubation of aqueous phase rHDL with a chemically patterned hydrophilic/hydrophobic surface produces a novel compositional pattern, caused by an increased affinity for adsorption onto hydrophilic regions relative to the surrounding hydrophobic regions. Further, by simple chemical denaturation of the boundary protein, nanoscale compartmentalization can be selectively erased, thus producing patterns of laterally fluid, lipid bilayers structured solely at the mesoscopic length scale. Since these aqueous phase microarrays of nanostructured lipid bilayers allow for membrane proteins to be embedded within single nanoscale bilayer compartments, they present a viable means of generating high-density membrane protein arrays. Such a system would permit in-depth elucidation of membrane protein structure-function relationships and the consequences of membrane compartmentalization on lipid dynamics.     

Identification of conical structures in small aluminum oxide clusters: infrared spectroscopy of (Al2O3)1-4(AlO)+

The vibrational spectroscopy of the electronically closed-shell (Al 2O 3) n (AlO) (+) cations with n = 1-4 is studied in the 530-1200 cm (-1) range by infrared predissociation spectroscopy of the corresponding ion-He atom complexes in combination with quantum chemical calculations. In all cases we find, assisted by a genetic algorithm, global minimum structures that differ considerably from those derived from known modifications of bulk alumina. The n = 1 and n = 4 clusters exhibit an exceptionally stable conical structure of C 3 v symmetry, whereas for n = 2 and n = 3, multiple isomers of lower symmetry and similar energy may contribute to the recorded spectra. A blue shift of the highest energy absorption band is observed with increasing cluster size and attributed to a shortening of Al-O bonds in the larger clusters. This intense band is assigned to vibrational modes localized on the rim of the conical structures for n = 1 and n = 4 and may aid in identifying similar, highly symmetric structures in larger ions.     

Syntheses, reactivity and DFT studies of group 2 and group 12 metal complexes of tris(pyrazolyl)methanides featuring "free" pyramidal carbanions

Reactions of HC(Me2pz)3 with Grignard reagents, dialkyl magnesium compounds and dimethylzinc are reported, together with a DFT study on some of the aspects of this chemistry. Reactions of HC(Me2pz)3 with MeMgX (X=Cl or Br) gave the half-sandwich zwitterionic compounds [Mg((Me)Tpmd)X] (X=Cl (2) or Br (3); (Me)Tpmd(-)=[C(Me2pz)3](-)). Addition of HCl to 2 gave the structurally characterised half-sandwich compound [Mg{HC(Me2pz)3}Cl2(thf)] (4). The zwitterionic sandwich compound [Mg(MeTpmd)2] (5) formed in low yields in the reaction of MeMgX with HC(Me2pz)3 but was readily prepared from HC(Me2pz)3 and either MgnBu2 or MgPh2. The structurally characterised compound 5 contains two "naked" sp3-hybridised carbanions fully separated from the dicationic metal centre. Only by using MgPh2 as starting material could the half-sandwich compound [Mg(MeTpmd)Ph(thf)] (6) be isolated. The zwitterionic sandwich compound 5 reacted with HOTf (OTf(-)=[O3SCF3](-)) to form the dication [Mg{HC(Me2pz)3}2]2+ (7(2+)), which was structurally characterised. Pulsed field gradient spin-echo (PGSE) diffusion NMR spectroscopy revealed both compounds to be intact in solution. In contrast to the magnesium counterparts, HC(Me2pz)3 reacted only slowly with ZnMe2 (and not at all with ZnPh2) to form the half-sandwich zwitterion [Zn(MeTpmd)Me] (8), which contains a cationic methylzinc moiety separated from a single sp3-hybridised carbanion. Density functional calculations on the zwitterions [M(MeTpmd)Me] and [M(MeTpmd)2] (M=Mg, Zn) revealed that the HOMO in each case is a (Me)Tpmd-based carbanion lone pair. The kappa 1C isomers of [M(MeTpmd)Me] were calculated to be considerably less stable than their kappa 3N-bound counterparts, with the largest gain in energy for Mg due to the greater ease of electron transfer from metal to the (Me)Tpmd apical carbon atom on formation of the zwitterion. Moreover, the computed M-C bond dissociation enthalpies of the kappa 1C isomers of [M(MeTpmd)Me] are considerably higher than expected by simple extrapolation from the corresponding computed H-C bond dissociation enthalpy.     

A new fluorescent calix crown ether: synthesis and complex formation with alkali metal ions

We synthesised a new N-benzylaza-21-crown-7 ether 5 with a dihydroxy coumarin as a fluorescence sensor and investigated the binding behaviour towards alkali metal cations in methanol by fluorescence titrations. The association constants are within one order of magnitude, with the exception of sodium. Potassium is the preferred binding partner (K(Na)=330 M(-1); K(K)=8600 M(-1); K(Rb)=8200 M(-1); K(Cs)=4400 M(-1)). The corresponding aza-21-crown-7 ether (6) was attached by a methylene unit to a resorcarene to give fluorescent calix crown ether 12. The binding abilities of the calix crown ether towards alkali metal ions in methanol have also been investigated, and an increasing complex stability, distinct for potassium and rubidium in comparison with 5, was found: K(Na)=440 M(-1); K(K)=110,000 M(-1); K(Rb)=63,000 M(-1); K(Cs)=20,000 M(-1). Like bis(crown ether)s, a cooperative complexation of the crown ether and the cavitand scaffold can be assumed. The proposed complex geometry is supported by Kohn-Sham DFT calculations for the potassium and caesium complexes.