Spectroscopic analysis of small organic molecules: a comprehensive near-edge x-ray-absorption fine-structure study of C6-ring-containing molecules

We report high-resolution C 1s near-edge x-ray-absorption fine-structure (NEXAFS) spectra of the C6-ring-containing molecules benzene (C6H6), 1,3- and 1,4-cyclohexadiene (C6H8), cyclohexene (C6H10), cyclohexane (C6H12), styrene (C8H8), and ethylbenzene (C8H10) which allow us to examine the gradual development of delocalization of the corresponding pi electron systems. Due to the high experimental resolution, vibrational progressions can be partly resolved in the spectra. The experimental spectra are compared with theoretical NEXAFS spectra obtained from density-functional theory calculations where electronic final-state relaxation is accounted for. The comparison yields very good agreement between theoretical spectra and experimental results. In all cases, the spectra can be described by excitations to pi*- and sigma*-type final-state orbitals with valence character, while final-state orbitals of Rydberg character make only minor contributions. The lowest C 1s-->1pi* excitation energy is found to agree in the (experimental and theoretical) spectra of all molecules except for 1,3-cyclohexadiene (C6H8) where an energy smaller by about 0.6 eV is obtained. The theoretical analysis can explain this result by different binding properties of this molecule compared to the others.     

Synthesis of star-shaped poly(epsilon-caprolactone) via'click' chemistry and 'supramolecular click' chemistry

The synthesis of star-shaped poly(epsilon-caprolactone) is described via azide-alkyne cycloaddition ('click' chemistry) and via self-assembly of polymeric ligands into [2 x 2] grid-like metal complexes ('supramolecular click' chemistry).     

Predicting substrates by docking high-energy intermediates to enzyme structures

With the emergence of sequences and even structures for proteins of unknown function, structure-based prediction of enzyme activity has become a pragmatic as well as an interesting question. Here we investigate a method to predict substrates for enzymes of known structure by docking high-energy intermediate forms of the potential substrates. A database of such high-energy transition-state analogues was created from the KEGG metabolites. To reduce the number of possible reactions to consider, we restricted ourselves to enzymes of the amidohydrolase superfamily. We docked each metabolite into seven different amidohydrolases in both the ground-state and the high-energy intermediate forms. Docking the high-energy intermediates improved the discrimination between decoys and substrates significantly over the corresponding standard ground-state database, both by enrichment of the true substrates and by geometric fidelity. To test this method prospectively, we attempted to predict the enantioselectivity of a set of chiral substrates for phosphotriesterase, for both wild-type and mutant forms of this enzyme. The stereoselectivity ratios of the six enzymes considered for those four substrate enantiomer pairs differed over a range of 10- to 10,000-fold and underwent 20 switches in stereoselectivities for favored enantiomers, compared to the wild type. The docking of the high-energy intermediates correctly predicted the stereoselectivities for 18 of the 20 substrate/enzyme combinations when compared to subsequent experimental synthesis and testing. The possible applications of this approach to other enzymes are considered.     

Unambiguous determination of the ionization state of a glycoside hydrolase active site lysine by 1H-15N heteronuclear correlation spectroscopy

We have investigated the lysine side chain amines in the 34 kDa catalytic domain from Cellulomonas fimi beta-(1,4)-glycosidase Cex (or CfXyn10A) using 1H-detected 15N heteronuclear correlation NMR spectroscopy. Signals from the 1Hzeta ( approximately 8 ppm) and 15Nzeta ( approximately 35 ppm) of Lys302 in the unmodified enzyme and Lys47 in a trapped cellobiosyl-enzyme intermediate were detected in a 1H-15N HMQC spectrum (pH 6.5 and 30 degrees C). The amine of Lys302 forms a buried ion pair, and that of Lys47 is hydrogen bonded to the cellobioside. Both lysines are positively charged, as unambiguously demonstrated by the splitting of their 15Nzeta signals into quartets (|1JNH| approximately 75 Hz) in a 1H-15N HSQC spectrum recorded without 1H decoupling during 15N evolution. Qualitative insights into the dynamic properties of these lysines are also provided by the deviations of their quartet intensity ratios from that of approximately 3:1:1:3 expected for a highly mobile amine. On the basis of the observed ratios of approximately 1:1:1:1 for the quartet of Lys302 and approximately 0.5:1:1:0.5 for Lys47, the amine of the latter active site residue is most rigidly positioned. Signals from at least 8 and 10 additional positively charged, mobile amines in Cex were observed at 10 degrees C and pH 6.5 and 5.6, respectively. By using conditions of reduced temperature, slightly acidic pH, and low general base concentrations, as well as water flipback pulses to minimize the effects of hydrogen exchange, 1H-15N correlation experiments provide a sensitive route to directly investigate the charge states and dynamic properties of the N-terminal and side chain amines in proteins and protein complexes.     

Upper Bounds on the Rate of Quantum Ergodicity

We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation of an upper bound of order on the rate of quantum ergodicity if the classical system is ergodic with a certain rate. In addition we obtain a similar bound on transition amplitudes if the classical system is weak mixing. Both results generalise previous ones by Zelditch. Communicated by Jens Marklof Submitted: March 16, 2005 Accepted: February 2, 2006     

Defect chaos and bursts: hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non-Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscillations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.     

Very low-refractive-index optical thin films consisting of an array of SiO2 nanorods

The refractive-index contrast in dielectric multilayer structures, optical resonators, and photonic crystals is an important figure of merit that creates a strong demand for high-quality thin films with a low refractive index. A SiO2 nanorod layer with low refractive index of n = 1.08, to our knowledge the lowest ever reported in thin-film materials, is grown by oblique-angle electron-beam deposition of SiO2. A single-pair distributed Bragg reflector employing a SiO2 nanorod layer is demonstrated to have enhanced reflectivity, showing the great potential of low-refractive-index films for applications in photonic structures and devices.     

The chain rule as a functional equation

We consider operators T from C¹(R) to C(R) satisfying the “chain rule”

     

Fitting cores and supersolvable groups

Let A be a group. What can be said about the group B to ensure that A and the normal product AB belong to the same prescribed class of groups? Results in this direction are given for the classes of supersolvable groups, absolutely solvable groups and Lagrange groups.     

Answer set programming in intuitionistic logic

As a demonstration of the flexibility of constructive mathematics, we propose an interpretation of propositional answer set programming (ASP) in terms of intuitionistic proof theory, in particular in terms of simply typed lambda calculus. While connections between ASP and intuitionistic logic are well-known, they usually take the form of characterizations of stable models with the help of some intuitionistic theories represented by specific classes of Kripke models. As such the known results are model-theoretic rather than proof-theoretic. In contrast, we offer an explanation of ASP using constructive proofs.