Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

Theory of laser-induced ultrafast structural changes in solids

The present thesis is a contribution to the study of laser-solid interaction. Despite the numerous applications resulting from the recent use of laser technology, there is still a lack of satisfactory answers to theoretical questions regarding the mechanism leading to the structural changes induced by femtosecond lasers in materials. We provide here theoretical approaches for the description of the structural response of different solids (cerium, samarium sulfide, bismuth and germanium) to femtosecond laser excitation. Particular interest is given to the description of the effects of the laser pulse on the electronic systems and changes of the potential energy surface for the ions. Although the general approach of laser-excited solids remains the same, the potential energy surface which drives the structural changes is calculated with different theoretical models for each material. This is due to the difference of the electronic properties of the studied systems. We use the Falicov model combined with an hydrodynamic method to study photoinduced phase changes in cerium. The local density approximation (LDA) together with the Hubbard-type Hamiltonian (LDA+U) in the framework of density functional theory (DFT) is used to describe the structural properties of samarium sulfide. We parametrize the time-dependent potential energy surface (calculated using DFT+ LDA) of bismuth on which we perform quantum dynamical simulations to study the experimentally observed amplitude collapse and revival of coherent $A_{1g}$ phonons. On the basis of a time-dependent potential energy surface calculated from a non-orthogonal tight binding Hamiltonian, we perform molecular dynamics simulation to analyze the time evolution (coherent phonons, ultrafast nonthermal melting) of germanium under laser excitation. The thermodynamic equilibrium properties of germanium are also reported. With the obtained results we are able to give many clarifications and interpretations of experimental results and also make predictions.

Predicting overall service quality: a structural equation modelling approach

In this article, the results of a modified SERVQUAL questionnaire (Parasuraman et al., 1991) are reported. The modifications consisted in substituting questionnaire items particularly suited to a specific service (banking) and context (county of Girona, Spain) for the original rather general and abstract items. These modifications led to more interpretable factors which accounted for a higher percentage of item variance. The data were submitted to various structural equation models which made it possible to conclude that the questionnaire contains items with a high measurement quality with respect to five identified dimensions of service quality which differ from those specified by Parasuraman et al. And are specific to the banking service. The two dimensions relating to the behaviour of employees have the greatest predictive power on overall quality and satisfaction ratings, which enables managers to use a low-cost reduced version of the questionnaire to monitor quality on a regular basis. It was also found that satisfaction and overall quality were perfectly correlated thus showing that customers do not perceive these concepts as being distinct

The genetic basis of resistance to anticoagulants in rodents

Anticoagulant compounds, i.e., derivatives of either 4-hydroxycoumarin (e.g., warfarin, bromadiolone) or indane-1,3-dione (e.g., diphacinone, chlorophacinone), have been in worldwide use as rodenticides for > 50 years. These compounds inhibit blood coagulation by repression of the vitamin K reductase reaction (VKOR). Anticoagulant-resistant rodent populations have been reported from many countries and pose a considerable problem for pest control. Resistance is transmitted as an autosomal dominant trait although, until recently, the basic genetic mutation was unknown. Here, we report on the identification of eight different mutations in the VKORC1 gene in resistant laboratory strains of brown rats and house mice and in wild-caught brown rats from various locations in Europe with five of these mutations affecting only two amino acids (Tyr139Cys, Tyr139Ser, Tyr139Phe and Leu128Gln, Leu128Ser). By recombinant expression of VKORC1 constructs in HEK293 cells we demonstrate that mutations at Tyr139 confer resistance to warlarin at variable degrees while the other mutations, in addition, dramatically reduce VKOR activity. Our data strongly argue for at least seven independent mutation events in brown rats and two in mice. They suggest that mutations in VKORC1 are the genetic basis of anticoagulant resistance in wild populations of rodents, although the mutations alone do not explain all aspects of resistance that have been reported. We hypothesize that these mutations, apart from generating structural changes in the VKORC1 protein, may induce compensatory mechanisms to maintain blood clotting. Our findings provide the basis for a DNA-based field monitoring of anticoagulant resistance in rodents.

The molecular basis of HIV capsid assembly - five years of progress

The assembly of HIV is relatively poorly investigated when compared with the process of virus entry. Yet a detailed understanding of the mechanism of assembly is fundamental to our knowledge of the complete life cycle of this virus and also has the potential to inform the development of new antiviral strategies. The repeated multiple interaction of the basic structural unit, Gag, might first appear to be little more than concentration dependent self-assembly but the precise mechanisms emerging for HIV are far from simple. Gag interacts not only with itself but also with host cell lipids and proteins in an ordered and stepwise manner. It binds both the genomic RNA and the virus envelope protein and must do this at an appropriate time and place within the infected cell. The assembled virus particle must successfully release from the cell surface and, whilst being robust enough for transmission between hosts, must nonetheless be primed for rapid disassembly when infection occurs. Our current understanding of these processes and the domains of Gag involved at each stage is the subject of this review. Copyright (C) 2004 John Wiley Sons, Ltd.

Methylene spacer-regulated structural variation in cobalt(II/III) complexes with bridging acetate and Salen- or Salpn-type Schiff-base ligands

Two linear, trinuclear mixed-valence complexes, [Co-II{(mu-L-1)(mu-OAc)Co-III (OAc)}(2)] (1) and [Co-II(mu-L-2) (mu-OAc)Co-III(OAc)}(2)] (2) and two mononuclear Con' complexes [Co-III{L-3)(OAc)] (3), and [Co-III {L-4}(OAc)] (4) were prepared and the molecular structures of 1, 2 and 4 elucidated on the basis of X-ray crystallography [OAc = Acetate ion, H2L1 = H(2)Salen 1,6-bis(2-hydroxyphenyl)-2,5-diazahexa-1,5-diene, H2L2 H2Me2-Salen = 2,7-bis(2-hydroxyphenyl)-2,6-diazaocta-2,6-diene, H2L3 = H(2)Salpn = 1,7-bis(2-hydroxyphenyl)-2,6-diazahepta1,6-diene, H2L4 = H(2)Me(2)Salpn = 2,8-bis(2-hydroxyphenyl)3,7-diazanona-2,7-dienel. In complexes I and 2, the acetate groups show both monodentate and bridging bidentate coordination modes, whereas chelating bidentate acetate is present in 4. The terminal (CoN2O4)-N-III centres in 1 and 2 exhibit uniform facial arrangements of both non-bridged N2O and bridging O-3 donor sets and the Co-II centre is coordinated to six (four phenoxo and two acetato) oxygen atoms of the bridging ligands. The effective magnetic moment at room temperature corresponds to the presence of high-spin Coll in both 1 and 2. The complexes 1 and 2 are thus Co-III(S = 0)Co-II(S = 3/2)-Co-II(S = 0) trimers. Complexes 3 and 4 are monomeric and diamagnetic containing low-spin Co-III(S = 0) with chelating tetradentate Schiff base and bidentate acetate. Calculations based on DFT rationalise the formation of trinuclear or monomiclear complexes. (C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

Metal complexes of cyclen and cyclam derivatives useful for medical applications: a discussion based on thermodynamic stability constants and structural data

A series of the most common chelators used in magnetic resonance imaging ( MRI) and in radiopharmaceuticals for medical diagnosis and tumour therapy, H(4)dota, H(4)teta, H(8)dotp and H(8)tetp, is examined from a chemical point of view. Differences between 12- and 14-membered tetraazamacrocyclic derivatives with methylcarboxylate and methylphosphonate pendant arms and their chelates with divalent first-series transition metal and trivalent lanthanide ions are discussed on the basis of their thermodynamic stability constants, X- ray structures and theoretical studies.

GRID and docking analyses reveal a molecular basis for flavonoid inhibition of src-family kinase activity

Flavonoids reduce cardiovascular disease risk through anti-inflammatory, anti-coagulant and anti-platelet actions. One key flavonoid inhibitory mechanism is blocking kinase activity that drives these processes. Flavonoids attenuate activities of kinases including phosphoinositide-3-kinase (PI3K), Fyn, Lyn, Src, Syk, PKC, PIM1/2, ERK, JNK, and PKA. X-ray crystallographic analyses of kinase-flavonoid complexes show that flavonoid ring systems and their hydroxyl substitutions are important structural features for their binding to kinases. A clearer understanding of structural interactions of flavonoids with kinases is necessary to allow construction of more potent and selective counterparts. We examined flavonoid (quercetin, apigenin and catechin) interactions with Src-family kinases (Lyn, Fyn and Hck) applying the Sybyl docking algorithm and GRID. A homology model (Lyn) was used in our analyses to demonstrate that high quality predicted kinase structures are suitable for flavonoid computational studies. Our docking results revealed potential hydrogen bond contacts between flavonoid hydroxyls and kinase catalytic site residues. Identification of plausible contacts indicated that quercetin formed the most energetically stable interactions, apigenin lacked hydroxyl groups necessary for important contacts, and the non-planar structure of catechin could not support predicted hydrogen bonding patterns. GRID analysis using a hydroxyl functional group supported docking results. Based on these findings, we predicted that quercetin would inhibit activities of Src-family kinases with greater potency than apigenin and catechin. We validated this prediction using in vitro kinase assays. We conclude that our study can be used as a basis to construct virtual flavonoid interaction libraries to guide drug discovery using these compounds as molecular templates.

Spectroscopic and structural studies of bis[isopropoxy(thiocarbonyl)]sulfide, [(CH(3))(2)CHOC(S)](2)S

Structural and conformational properties of the molecule bis[isopropoxy(thiocarbonyl)]sulfide, [(CH(3))(2)CHOC(S)](2)S, have been studied by vibrational spectroscopy (IR and Raman) and quantum chemical calculations (HF and B3LYP with 6-31+G* basis sets). The crystal and molecular structure of the title compound was determined by X-ray diffraction methods. It crystallizes in the monoclinic C2/c space group with a = 8.4007(4), b = 13.5936(5), c = 10.3648(5) angstrom, beta = 106.024(4)degrees and Z = 4 molecules per unit cell. The molecules are sited on a crystallographic twofold axis passing through the sulphide atom and arranged in layers perpendicular to the b-axis. The solid state IR and Raman spectra of the compound give no sign of any other rotamer. (C) 2009 Elsevier B.V. All rights reserved.

Structural role of fluoride in the ion-conducting glass system B(2)O(3)-PbO-LiF studied by single- and double-resonance NMR

The local structure of an ion-conducting glass with nominal composition 50B(2)O(3)-10PbO-40LiF has been investigated by complementary (7)Li, (11)B, (19)F, and (207)Pb single- and double-resonance experiments. The results give insight into the structural role of the lithium fluoride additive in borate glasses: (1) LiF is seen to actively participate in the network transformation process contributing to the conversion of three- into four-coordinate boron units, as shown by (11)B single-resonance as well as by (11)B{(19)F} and (19)F{(11)B} double-resonance experiments. (2) (19)F signal quantification experiments suggest substantial fluoride loss, presumably caused by formation of volatile BF(3). A part of the fluoride remains in the dopant role, possibly in the form of small LiF-like cluster domains, which serve as a mobile ion supply. (3) The extent of lithium-fluorine and lead-fluorine interactions has been characterized by (7)Li{(19)F} and (207)Pb{(19)F} REDOR and SEDOR experiments. On the basis of these results, a quantitative structural description of this system has been developed.

The binding of synthetic triiodo L-thyronine analogs to human transthyretin: Molecular basis of cooperative and non-cooperative ligand recognition

Transthyretin (TTR) is a tetrameric beta-sheet-rich transporter protein directly involved in human amyloid diseases. Several classes of small molecules can bind to TTR delaying its amyloid fibril formation, thus being promising drug candidates to treat TTR amyloidoses. In the present study, we characterized the interactions of the synthetic triiodo L-thyronine analogs and thyroid hormone nuclear receptor TR beta-selecfive agonists GC-1 and GC-24 with the wild type and V30M variant of human transthyretin (TTR). To achieve this aim, we conducted in vitro TTR acid-mediated aggregation and isothermal titration calorimetry experiments and determined the TTR:GC-1 and TTR:GC-24 crystal structures. Our data indicate that both GC-1 and GC-24 bind to TTR in a non-cooperative manner and are good inhibitors of TTR aggregation, with dissociation constants for both hormone binding sites (HBS) in the low micromolar range. Analysis of the crystal structures of TTRwt:GC-1(24) complexes and their comparison with the TTRwt X-ray structure bound to its natural ligand thyroxine (T4) suggests, at the molecular level, the basis for the cooperative process displayed by T4 and the non-cooperative process provoked by both GC-1 and GC-24 during binding to TTR. (C) 2010 Elsevier Inc. All rights reserved.

Structural modeling of high-affinity thyroid receptor-ligand complexes

Understanding the molecular basis of the binding modes of natural and synthetic ligands to nuclear receptors is fundamental to our comprehension of the activation mechanism of this important class of hormone regulated transcription factors and to the development of new ligands. Thyroid hormone receptors (TR) are particularly important targets for pharmaceuticals development because TRs are associated with the regulation of metabolic rates, body weight, and circulating levels of cholesterol and triglycerides in humans. While several high-affinity ligands are known, structural information is only partially available. In this work we obtain structural models of several TR-ligand complexes with unknown structure by docking high affinity ligands to the receptors` ligand binding domain with subsequent relaxation by molecular dynamics simulations. The binding modes of these ligands are discussed providing novel insights into the development of TR ligands. The experimental binding free energies are reasonably well-reproduced from the proposed models using a simple linear interaction energy free-energy calculation scheme.

Cyclocreatine, an anticancer and neuroprotective agent. Spectroscopic, structural and theoretical study

The structural, spectroscopic and theoretical study of cyclocreatine (1-carboxymethyl-2-iminoimidazolidine, CyCre) has been performed prompted by the biological relevance of the molecule and its potential role as a ligand in biometalic compounds. The crystal structure of CyCre has been determined by X-ray diffraction methods. The compound crystallizes as a zwitterion in the monoclinic system, space group P2(1)/c. The crystal is further stabilized by a network of N-H center dot center dot center dot O bonds. Infrared and Raman spectra of the solid, electronic spectra of aqueous solutions at different pH values and (1)H and (13)C NMR spectra have been recorded and analyzed. Band assignments were accomplished with the help of theoretical calculations. Optimized molecular geometries, harmonic vibrational frequencies and molecular electrostatic potentials were calculated using methods based on the density functional theory. (C) 2010 Elsevier B.V. All rights reserved.

Molecular Basis of the Thermostability and Thermophilicity of Laminarinases: X-ray Structure of the Hyperthermostable Laminarinase from Rhodothermus marinus and Molecular Dynamics Simulations

Glycosyl hydrolases are enzymes capable of breaking the glycosidic linkage of polysaccharides and have considerable industrial and biotechnological applications. Driven by the later applications, it is frequently desirable that glycosyl hydrolases display stability and activity under extreme environment conditions, such as high temperatures and extreme pHs. Here, we present X-ray structure of the hyperthermophilic laminarinase from Rhodothermus marinus (RmLamR) determined at 1.95 angstrom resolution and molecular dynamics simulation studies aimed to comprehend the molecular basis, for the thermal stability of this class of enzymes. As most thermostable proteins, RmLamR contains a relatively large number of salt bridges, which are not randomly distributed on the structure. On the contrary, they form clusters interconnecting beta-sheets of the catalytic domain. Not all salt bridges, however, are beneficial for the protein thermostability: the existence of charge-charge interactions permeating the hydrophobic core of the enzymes actually contributes to destabilize the structure by facilitating water penetration into hydrophobic cavities, as can be seen in the case of mesophilic enzymes. Furthermore, we demonstrate that the mobility of the side-chains is perturbed differently in each class of enzymes. The side-chains of loop residues surrounding the catalytic cleft in the mesophilic laminarinase gain mobility and obstruct the active site at high temperature. By contrast, thermophilic laminarinases preserve their active site flexibility, and the active-site cleft remains accessible for recognition of polysaccharide substrates even at high temperatures. The present results provide structural insights into the role played by salt-bridges and active site flexibility on protein thermal stability and may be relevant for other classes of proteins, particularly glycosyl hydrolases.

Structural and spectroscopic properties of the diazocarbene radical (CNN) and its ions CNN(+) and CNN(-): a high-level theoretical investigation

The diazocarbene radical, CNN, and the ions CNN(+) and CNN(-) were investigated at a high level of theory. Very accurate structural parameters for the states X(3)Sigma(-) and A(3)Pi of CNN, and X(2)Pi of both CNN(+) and CNN(-) were obtained with the UCCSD(T) method using correlated-consistent basis functions with extrapolations to the complete basis set limit, with valence only and also with all electrons correlated. Harmonic and anharmonic frequencies were obtained for all species and the Renner parameter and average frequencies evaluated for the Pi states. At the UCCSD(T)/CBS(T-5) level of theory, Delta(f)H(0 K) = 138.89 kcal/mol and Delta(f)H(298 K) = 139.65 kcal/mol were obtained for diazocarbene; for the ionization potential and the electron affinity of CNN, 10.969 eV (252.95 kcal/mol), and 1.743 eV (40.19 kcal/mol), respectively, are predicted. Geometry optimization was also carried out with the CASSCF/MRCI/CBS(T-5) approach for the states X(3)Sigma(-) A(3)Pi, and a(1)Delta of CNN, and with the CASSCF/MRSDCI/aug-cc-pVTZ approach for the states b(1)Sigma(+), c(1)Pi, d(1)Sigma(-), and B(3)Sigma(-), and excitation energies (T(e)) evaluated. Vertical energies were calculated for 15 electronic states, thus improving on the accuracy of the five transitions already described, and allowing for a reliable overview of a manifold of other states, which is expected to guide future spectroscopic experiments. This study corroborates the experimental assignment for the vertical transition X (3)Sigma(-) <- E (3)Pi.