Role of carboxylate bridges in modulating nonheme diiron(II)/O(2) reactivity

A series of diiron(II) complexes of the dinucleating ligand HPTP (N,N,N',N'-tetrakis(2-pyridylmethyl)-2-hydroxy-1,3-diaminopropane) with one or two supporting carboxylate bridges has been synthesized and characterized. The crystal structure of one member of each subset has been obtained to reveal for subset A a (micro-alkoxo)(micro-carboxylato)diiron(II) center with one five- and one six-coordinate metal ion and for subset B a coordinatively saturated (micro-alkoxo)bis(micro-carboxylato)diiron(II) center. These complexes react with O(2) in second-order processes to form adducts characterized as (micro-1,2-peroxo)diiron(III) complexes. Stopped-flow kinetic studies show that the oxygenation step is sensitive to the availability of an O(2) binding site on the diiron(II) center, as subset B reacts more slowly by an order of magnitude. The lifetimes of the O(2) adducts are also distinct and can be modulated by the addition of oxygen donor ligands. The O(2) adduct of a monocarboxylate complex decays by a fast second-order process that must be monitored by stopped-flow methods, but becomes stabilized in CH(2)Cl(2)/DMSO (9:1 v/v) and decomposes by a much slower first-order process. The O(2) adduct of a dicarboxylate complex is even more stable in pure CH(2)Cl(2) and decays by a first-order process. These differences in adduct stability are reflected in the observation that only the O(2) adducts of monocarboxylate complexes can oxidize substrates, and only those substrates that can bind to the diiron center. Thus, the much greater stability of the O(2) adducts of dicarboxylate complexes can be rationalized by the formation of a (micro-alkoxo)(micro-1,2-peroxo)diiron(III) complex wherein the carboxylate bridges in the diiron(II) complex become terminal ligands in the O(2) adduct, occupy the remaining coordination sites on the diiron center, and prevent binding of potential substrates. Implications for the oxidation mechanisms of nonheme diiron enzymes are discussed.     

A short elementary proof of Grothendieck's theorem on algebraic vectorbundles over the projective line

Let E be an algebraic (or holomorphic) vectorbundle over the Riemann sphere $\text{P}$¹($\text{C}$). Then Grothendieck proved that E splits into a sum of line bundles E = ⊕L_i and the isomorphism classes of the L_i are (up to order) uniquely determined by E. The L_i in turn are classified by an integer (their Chern numbers) so that m-dimensional vectorbundles over $\text{P}$¹$\text{C}$ are classified by an m-tuple of integers

$\text{κ(E) = (κ}{}_1\text{(E),…,κ}{}_{\mathrm{m}}\text{(E)), κ}{}_1\text{(E)≥?≥κ}{}_{\mathrm{m}}\text{(E), κ}{}_{\mathrm{i}}\text{(E)∈}\text{Z}$

.In this short note we present a completely elementary proof of these facts which, as it turns out, works over any field k.     

Upper and lower bounds for recurrent and recursively decomposable parallel processor-networks

A “recursively decomposable network” can be partitioned into a finite number of subnetworks that are smaller “versions of itself,” where the subnetworks are themselves recursively decomposable. Several interesting notions of such networks emerge depending on the collections of parameters chosen to model the relative behavioral characteristics that make a subnetwork a version of another. Examples of such parameters are permutation time, bandwidth, latency, topology, wires, degree, and size. This paper introduces and studies the class of networks that are recursively decomposable relative to bandwidth limitations, and the subclass of “recurrent networks” that are recursively decomposable relative to topology limitations. We show that an N-node recursively decomposable into halves network with bandwidth-inefficiency function β(x) must be at least $\frac{N}{2}\sum\nolimits_{i = l}^{\lg N}{\frac{1}{{\beta(2^i)}}}$ wires. This implies that the linear array, hypercube, and completely connected networks are all exactly optimal. The above lower bound is generalized to networks that are recursively decomposable, but not necessarily into halves. We show that the bound is tight up to a constant factor by exhibiting recurrent networks matching the above lower bounds. Our lower bound results both tighten and generalize a result of Meertens: no recurrent, fixed degree network can permute in O(log N) time. © 1996 John Wiley & Sons, Inc. ©1996 John Wiley & Sons, Inc.     

Functional Models for the Oxygen-Evolving Complex of Photosystem II

In the last ten years, a number of advances have been made in the study of the oxygen-evolving complex (OEC) of photosystem II (PSII). Along with this new understanding of the natural system has come rapid advance in chemical models of this system. The advance of PSII model chemistry is seen most strikingly in the area of functional models where the few known systems available when this topic was last reviewed has grown into two families of model systems. In concert with this work, numerous mechanistic proposals for photosynthetic water oxidation have been proposed. Here, we review the recent efforts in functional model chemistry of the oxygen-evolving complex of photosystem II.     

The Sedimentation of Colloidal Nanoparticles in Solution and Its Study Using Quantitative Digital Photography

Sedimentation and diffusion are important aspects of the behavior of colloidal nanoparticles in solution, and merit attention during the synthesis, characterization, and application of nanoparticles. Here, the sedimentation of nanoparticles is studied quantitatively using digital photography and a simple model based on the Mason–Weaver equation. Good agreement between experimental time‐lapse photography and numerical solutions of the model is found for a series of gold nanoparticles. The new method is extended to study for the first time the gravitational sedimentation of DNA‐linked gold nanoparticle dimers as a model system of a higher complexity structure. Additionally, simple formulas are derived for estimating suitable parameters for the preparative centrifugation of nanoparticle solutions.     

Random Walks on Wreath Products of Groups

We bound the rate of convergence to uniformity for a certain random walk on the complete monomial groups GS _n for any group G. Specifically, we determine that n log n+ n log (|G|–1|) steps are both necessary and sufficient for ² distance to become small. We also determine that n log n steps are both necessary and sufficient for total variation distance to become small. These results provide rates of convergence for random walks on a number of groups of interest: the hyperoctahedral group ₂S _n , the generalized symmetric group _m S _n , and S _m S _n . In the special case of the hyperoctahedral group, our random walk exhibits the cutoff phenomenon.     

Enantioselective separation of rivastigmine by capillary electrophoresis with cyclodextrines

Different beta-cyclodextrines (beta-cyclodextrin, heptakis (2,3,6-tri-O-methyl)-beta-cyclodextrin, hydroxypropyl-beta-cyclodextrin, and sulfated beta-cyclodextrin) were investigated as additives for the enantioselective separation of the R-form from rivastigmine ((S)-N-ethyl-3-[(1-dimethylamino) ethyl]-N-methyl-phenyl carbamate), contained as impurity in this drug, which is used for the treatment of Alzheimer's disease. Electrophoresis was performed in an acidic background electrolyte (triethanolammonium phosphate, 75 mM, pH 2.5) with various concentrations of the additives. The electrophoretic mobilities measured are typical functions of the additive concentrations, with complex constants (obtained by fitting the appropriate binding curve on the data) ranging between about 180 and 770 M(-1). Best separation was obtained with 7.5 mM beta-cyclodextrin, with the R-enantiomer as impurity migrating before the main S-compound. Intra- and interday reproducibility (n = 6 and 18, respectively) of migration time and peak area was in the low percentage range, linearity of the calibration line for the quantitation of the impurity in the range between 2.3 and 50 microg/ml, expressed by the linear correlation coefficient, was 0.9998. The limits of detection and quantitation, respectively, were 0.7 and 2.3 microg/ml, corresponding to 0.05 and 0.15%, m/m of the R- relative to the S-compound. Analysis can be carried out at 18 degrees C in less than 19 min.     

Anharmonic effects and the lattice dynamics of insulators

Anharmonic effects manifest themselves in everyday properties of solids. Two of the more obvious examples are thermal expansion and heat conductivity. More sophisticated examples anharmonicity are provided by the direct measurement of the lifetimes and of the pressure and temperature dependence of modes of vibration solids by infrared, Raman, Brillouin, or neutron spectroscopy. The present article reviews current status of the theory of anharmonic effects in insulators. We will draw our examples almost exclusively from the simplest insulators, namely the fcc rare gas solids (RGS) and alkali-halides (AH) mostly of the rocksalt structure. Much what we have to say is applicable to other kinds solids also, but we shall not dwell on this aspect. We shall arbitrarily exclude perhaps the two most interesting classes of anharmonic solids, that ferroelectrics and quantum solids. These subjects are sufficiently developed as to warrant reviews their own and it would be impossible to do them justice in the space avdable here. No mention will be made of the vast subject of impurity modes which especially in the case of alkali-halides has developed into an autonomous branch of solidstate physics. For similar reasons we have chosen to exclude thermal conductivity attenuation sound and second sound. We are then left with what we feel to be a more manageable task reviewing the basic anharmonic properties of the simplest classes of perfect insulators. Our selection of material reflects our own biased and peculiar interests. Examples wdl be illustrative rather than exhaustive. Previous reviews and basic articles dealing with anharmonic effects are listed separately in the references at the end of this article.     

Broadband optimization of a pentamode-layered spherical acoustic waveguide

Transformational acoustics offers the theoretical possibility of cloaking obstacles within fluids, provided metamaterials having continuously varying bulk moduli and densities can be found or constructed. Realistically, materials with the proper, continuously varying anisotropies do not presently exist. Discretely layered cloaks having constant material parameters within each layer are a viable alternative, but due to their discrete nature, may become ineffective outside of narrow frequency ranges. Because of such limitations, there is interest in finding discretely layered systems that can be effective in as wide as possible bandwidth without the need for unrealizable material properties within each layer. The present work introduces a novel methodology for finding optimal material parameters for use in such layered cloaks. In principle, the technique could be applied to any acoustic or electromagnetic scattering problem, but for purposes of demonstration, this paper considers a fluid-loaded acoustically hard sphere with a cloak that comprised layered pentamodes, whose material properties are constrained to lie within reasonable ranges relative to the density and bulk modulus of water.     

Photodamage of a Mn(III/IV)-oxo mixed-valence compound and photosystem II: evidence that a high-valent manganese species is responsible for UV-induced photodamage of the oxygen-evolving complex in photosystem II

The Mn cluster in photosystem II (PS II) is believed to play an important role in the UV photoinhibition of green plants, but the mechanism is still not clear at a molecular level. In this work, the photochemical stability of [Mn(III)(O)(2)Mn(IV)(H(2)O)(2)(Terpy)(2)](NO(3))(3) (Terpy=2,2':6',2'-terpyridine), designated as Mn-oxo mixed-valence dimer, a well characterized functional model of the oxygen-evolving complex in PS II, was examined in aqueous solution by exposing the complex to excess light irradiation at six different wavelengths in the range of 250 to 700 nm. The photodamage of the Mn-oxo mixed-valence dimer was confirmed by the decrease of its oxygen-evolution activity measured in the presence of the chemical oxidant oxone. Ultraviolet light irradiation induced a new absorption peak at around 400-440 nm of the Mn-oxo mixed-valence dimer. Visible light did not have the same effect on the Mn-oxo mixed-valence dimer. We speculate that the spectral change may be caused by conversion of the Mn(III)O(2)Mn(IV) dimer into a new structure--Mn(IV)O(2)Mn(IV). In the processes, the appearance of a 514 nm fluorescence peak was observed in the solution and may be linked to the hydration or protonation of Terpy ligand in the Mn-oxo dimer. In comparing the response of the PS II functional model compound and the PS II complex to excess light radiation, our results support the idea that UV photoinhibition is triggered at the Mn(4)Ca center of the oxygen-evolution complex in PS II by forming a modified structure, possibly a Mn(IV) species, and that the reaction of Mn ions is likely the initial step.