Local limits and harmonic functions for nonisotropic random walks on free groups

Summary Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2s) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits.     

Integer points on hypersurfaces

Very general hypersurfaces in ⁴ contain r ^2+(4/9) integer points in any ball of radiusr>1. As a consequence, an irreducible algebraic hypersurface in ⁿ (wheren4) which is not a cylinder and is of degreed, contains c(d, n)r ^{n–1–(5/9)} integer points in a ball of radiusr. This improves on the known boundc(d, n)r ^n–(3/2).Meinem verehrten Lehrer Professor E. Hlawka zum siebzigsten Geburtstag gewidmetWritten with partial support from NSF-MCS-8211461.     

Dynamic Fourier transform infrared spectroscopy in polymer research

The rapid-scanning capability of FTIR instrumentation has revitalized the field of vibrational spectroscopy in polymer research and will be discussed with reference to the study of polyurethane kinetics, the temperature dependence of hydrogen bonding in polyamide 6 and strain-induced crystallization in a polydimethylsiloxane elastomer.     

Anion substitution effects on structure and magnetism in the chromium chalcogenide Cr5Te8—Part I: Cluster glass behavior in trigonal Cr(1+x)Q2 with basic cell (Q=Te, Se; Te:Se=7:1)

The effect of substitution of the anion Te by Se in non-stoichiometric Cr₅Te₈ has been investigated with respect to its crystal structure, magnetic properties, and electronic structure. The compounds Cr_(1+x)Q₂ (Q=Te, Se; Te:Se=7:1; (1+x)=1.234(6), 1.264(6), 1.300(7)) were synthesized at elevated temperatures followed by quenching the samples to room temperature. The crystal structures have been refined with X-ray powder diffraction data with the Rietveld method in the trigonal space group with lattice parameters a=3.8651(1)-3.8831(1) Å and c=5.9917(2)-6.0528(2) Å. The structure is related to the NiAs structure with full and deficient metal layers stacking alternatively along the c-axis. The irreversibility in the field-cooled/zero-field-cooled magnetization suggests that the substitution effects of one Te by one Se is strong enough to cause cluster-glass behavior, from ferromagnetic Cr₅Te₈ to cluster-glass Cr_(1+x)Q₂. Non-saturation magnetizations at 5.5 T and the magnetic relaxation results further support the existence of cluster-glass behavior. Accompanying SPR-KKR (spin-polarized relativistic Korringa-Kohn-Rostoker) band structure calculations strongly support the observation that the Cr(1) sites are preferentially occupied by Cr atoms and predict that these compounds are metallic. Results for the spin-resolved DOS and magnetic moments on each crystallographic sites are presented.     

π-Bindungsbeitrag in Boranen, 2. Mitt.:Ab initio- und Kraftfeld-Rechnungen von Vinyldifluorboran

Ab initio calculations on vinyldifluoroborane yield a -contribution of 23 kJ/mol (5.5 kcal/mol) mainly due to the C=C bond and not to the lone pairs of the fluorine atoms. The rotational barrier was also determined. The force field calculations favour the interpretation of the bond structure derived from the theab initio results.

     

Biosynthesis of isoprenoids. purification and properties of IspG protein from Escherichia coli

[Structure: see text]. The IspG protein is known to catalyze the transformation of 2-C-methyl-d-erythritol 2,4-cyclodiphosphate into 1-hydroxy-2-methyl-2-(E)-butenyl 4-diphosphate in the nonmevalonate pathway of isoprenoid biosynthesis. We have found that the apparent IspG activity in the cell extracts of recombinant Escherichia coli cells as observed by a radiochemical assay can be enhanced severalfold by coexpression of the isc operon which is involved in the assembly of iron-sulfur clusters. The recombinant protein was isolated by affinity chromatography under anaerobic conditions. With a mixture of flavodoxin, flavodoxin reductase, and NADPH as the reducing agent, stringent assay methods based on photometry or on 13C NMR detection of multiply 13C-labeled substrate/product ratios afforded catalytic activities greater than 60 nmol mg(-1) min(-1) for the protein "as isolated" (i.e., without reconstitution of any kind). Lower apparent activities were found using photoreduced deazaflavin as an artifactual electron donor, whereas dithionite was unable to serve as an artificial electron donor. The apparent Michaelis constant for 2-C-methyl-D-erythritol 2,4-cyclodiphosphate was 700 microM. The enzyme was inactivated by EDTA and could be reactivated by Mn2+. The pH optimum was at 9.0. The protein contained 2.4 iron ions and 4.4 sulfide ions per subunit. The replacement of any of the three conserved cysteine residues afforded mutant proteins which were devoid of catalytic activity and contained less than 6% of Fe2+ and less than 23% of S2- as compared to the wild-type protein. Sequence comparison indicates that putative IspG proteins of plants, the apicomplexan protozoan Plasmodium falciparum, and bacteria from the Bacteroidetes/Chlorobi group contain an insert of about 170-320 amino acid residues as compared with eubacterial enzymes.     

Microarray-based in vitro evaluation of DNA oligomer libraries designed in silico.

We report on the microarray-based in vitro evaluation of two libraries of DNA oligonucleotide sequences, designed in silico for applications in supramolecular self-assembly, such as DNA computing and DNA-based nanosciences. In this first study which is devoted to the comparison of sequence motif properties theoretically predicted with their performance in real-life, the DNA-directed immobilization (DDI) of proteins was used as an example of DNA-based self-assembly. Since DDI technologies, DNA computing, and DNA nanoconstruction essentially depend on similar prereguisites, in particular, large and uniform hybridization efficiencies combined with low nonspecific cross-reactivity between individual sequences, we anticipate that the microarray approach demonstrated here will enable rapid evaluation of other DNA sequence libraries.     

Transition metal methylene complexes : III. Methylene (CH2), a carbonyl analogous ligand; crystal structure of μ-methylenebis(carbonyl-η5-cyclopentadienylrhodium)(Rh—Rh

μ-Carbonylbis(carbonyl-ν⁵-cycopentadienylrhodium)(Rh—Rh) reacts with N-methyl-and N-ethyl-N-nitrosourea in boiling benzene to yield the dinuclear, diamagnetic, neutral rhodium complexes μ-methylene- (A) and μ-ethylidenebis(carbonyl-η⁵-cyclopentadienylrhodium)(Rh—Rh) (B), respectively. Deuterium labelled experiments prove the origin of the metal-stabilized methylene ligand to be the alkyl group of the organic precursor. This new method of preparation of transition metal—methylene complexes may be used as an alternative to the commonly used diazo method; the latter method was shown to work with diazodiethylmalonate and dicarbonyl-η⁵-cyclopentadienylrhodium, the reaction yielding μ-bis(ethoxycarbonyl)methylenebis(carbonyl-η⁵-cyclopentadienylrhodium)(Rh—Rh).Compound A crystallizes in the triclinic system, P$\text{1}$, and with cell constants of a 803.42(5), b 909.98(6), c 938.81(2) pm, α 74.402(3), β81.923(3), and γ 83.685(6)°. The unit cell volume and the calculated density are 651.6 ų and 2.069 g cm^-3, for one molecule in the asymmetric unit. The molecular geometry of μ-CH₂[η⁵-C₅H₅Rh(CO)]₂ was established from 2718 unique reflections collected with a computer-controlled diffractometer and refined to a final R(F) = 0.0379. The molecular parameters derived from the single-crystal X-ray study conform to a remarkable degree with those found for μ-CO[η⁵-C₅H₅Rh(CO)]₂. Thus, the bridging ligands CH₂ and CO seem to be analogous in their effects on the structural characteristics of the molecular framework of the two molecules.     

New features in the catalytic cycle of cytochrome P450 during the formation of compound I from compound 0

Density functional theory (DFT) is applied to the dark section of the catalytic cycle of the enzyme cytochrome P450, namely, the formation of the active species, Compound I (Cpd I), from the ferric-hydroperoxide species (Cpd 0) by a protonation-assisted mechanism. The chosen 96-atom model includes the key functionalities deduced from experiment: Asp(251), Thr(252), Glu(366), and the water channels that relay the protons. The DFT model calculations show that (a) Cpd I is not formed spontaneously from Cpd 0 by direct protonation, nor is the process very exothermic. The process is virtually thermoneutral and involves a significant barrier such that formation of Cpd I is not facile on this route. (b) Along the protonation pathway, there exists an intermediate, a protonated Cpd 0, which is a potent oxidant since it is a ferric complex of water oxide. Preliminary quantum mechanical/molecular mechanical calculations confirm that Cpd 0 and Cpd I are of similar energy for the chosen model and that protonated Cpd 0 may exist as an unstable intermediate. The paper also addresses the essential role of Thr(252) as a hydrogen-bond acceptor (in accord with mutation studies of the OH group to OMe).     

Competition between van der Waals and hydrogen bonding interactions: structure of the trans-1-naphthol/N(2) cluster

The excitation energy in the multiphoton ionization spectrum of the trans-1-naphthol/N(2) cluster shows only a small red shift with respect to isolated naphthol, indicating a van der Waals pi-bound structure rather than a hydrogen-bonded one. To confirm this interpretation, high-level electronic structure calculations were performed for several pi- and hydrogen-bonded isomers of this cluster. The calculations were carried out at the second order M?ller-Plesset (MP2) level of perturbation theory with the family of correlation consistent basis sets up to quintuple-zeta quality including corrections for the basis set superposition error and extrapolation to the MP2 complete basis set (CBS) limit. We report the optimal geometries, vibrational frequencies, and binding energies (D(e)), also corrected for harmonic zero-point energies (D(0)), for three energetically low-lying isomers. In all calculations the lowest energy structure was found to be an isomer with the N(2) molecule bound to the pi-system of the naphthol ring carrying the OH group. In the CBS limit its dissociation energy was computed to be D(0) = 2.67 kcal/mol (934 cm(-1)) as compared to D(0) = 1.28 kcal/mol (448 cm(-1)) for the H-bound structure. The electronic structure calculations therefore confirm the assignment of the experimental electronic spectrum corresponding to a van der Waals pi-bound structure. The energetic stabilization of the pi-bound isomer with respect to the hydrogen-bonded one is rather unexpected when compared with previous findings in related systems, in particular phenol/N(2).