Stability of weak numerical schemes for stochastic differential equations.

The paper considers numerical stability and convergence of weak schemes solving stochastic differential equations. A relatively strong notion of stability for a special type of test equations is proposed. These are stochastic differential equations with multiplicative noise. For different explicit and implicit schemes the regions of stability are also examined

Option pricing under incompleteness and stochastic volatility.

We consider a very general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities. Since this model typically yields an incomplete market, we show that for the purpose of pricing options, a small investor should use the minimal equivalent martingale measure associated to the underlying stock price process. Then we present stochastic numerical methods permitting the explicit computation of option prices and hedging strategies, and we illustrate our approach by specific examples

Metal-Enhanced Fluorescence of Chlorophylls in Light-Harvesting Complexes Coupled to Silver Nanowires

We investigate metal-enhanced fluorescence of peridinin-chlorophyll protein coupled to silver nanowires using optical microscopy combined with spectrally and time-resolved fluorescence techniques. In particular we study two different sample geometries: first, in which the light-harvesting complexes are deposited onto silver nanowires, and second, where solution of both nanostructures are mixed prior deposition on a substrate. The results indicate that for the peridinin-chlorophyll complexes placed in the vicinity of the silver nanowires we observe higher intensities of fluorescence emission as compared to the reference sample, where no nanowires are present. Enhancement factors estimated for the sample where the light-harvesting complexes are mixed together with the silver nanowires prior deposition on a substrate are generally larger in comparison to the other geometry of a hybrid nanostructure. While fluorescence spectra are identical both in terms of overall shape and maximum wavelength for peridinin-chlorophyll-protein complexes both isolated and coupled to metallic nanostructures, we conclude that interaction with plasmon excitations in the latter remains neutral to the functionality of the biological system. Fluorescence transients measured for the PCP complexes coupled to the silver nanowires indicate shortening of the fluorescence lifetime pointing towards modifications of radiative rate due to plasmonic interactions. Our results can be applied for developing ways to plasmonically control the light-harvesting capability of photosynthetic complexes

The Geometry of the Catalytic Active Site in [FeFe]-hydrogenases is Determined by Hydrogen Bonding and Proton Transfer

[FeFe]-hydrogenases are efficient metalloenzymes that catalyze the oxidation and evolution of molecular hydrogen, H2. They serve as a blueprint for the design of synthetic H2-forming catalysts. [FeFe]-hydrogenases harbor a six-iron cofactor that comprises a [4Fe-4S] cluster and a unique diiron site with cyanide, carbonyl, and hydride ligands. To address the ligand dynamics in catalytic turnover and upon carbon monoxide (CO) inhibition, we replaced the native aminodithiolate group of the diiron site by synthetic dithiolates, inserted into wild-type and amino acid variants of the [FeFe]-hydrogenase HYDA1 from Chlamydomonas reinhardtii. The reactivity with H2 and CO was characterized using in situ and transient infrared spectroscopy, protein crystallography, quantum chemical calculations, and kinetic simulations. All cofactor variants adopted characteristic populations of reduced species in the presence of H2 and showed significant changes in CO inhibition and reactivation kinetics. Differences were attributed to varying interactions between polar ligands and the dithiolate head group and/or the environment of the cofactor (i.e., amino acid residues and water molecules). The presented results show how catalytically relevant intermediates are stabilized by inner-sphere hydrogen bonding suggesting that the role of the aminodithiolate group must not be restricted to proton transfer. These concepts may inspire the design of improved enzymes and biomimetic H2-forming catalysts

Cyanide Binding to [FeFe]-Hydrogenase Stabilizes the Alternative Configuration of the Proton Transfer Pathway

Hydrogenases are H2 converting enzymes that harbor catalytic cofactors in which iron (Fe) ions are coordinated by biologically unusual carbon monoxide (CO) and cyanide (CN−) ligands. Extrinsic CO and CN−, however, inhibit hydrogenases. The mechanism by which CN− binds to [FeFe]-hydrogenases is not known. Here, we obtained crystal structures of the CN−-treated [FeFe]-hydrogenase CpI from Clostridium pasteurianum. The high resolution of 1.39 Å allowed us to distinguish intrinsic CN− and CO ligands and to show that extrinsic CN− binds to the open coordination site of the cofactor where CO is known to bind. In contrast to other inhibitors, CN− treated crystals show conformational changes of conserved residues within the proton transfer pathway which could allow a direct proton transfer between E279 and S319. This configuration has been proposed to be vital for efficient proton transfer, but has never been observed structurally

Accumulating the hydride state in the catalytic cycle of [FeFe]-hydrogenases

H2 turnover at the [FeFe]-hydrogenase cofactor (H-cluster) is assumed to follow a reversible heterolytic mechanism, first yielding a proton and a hydrido-species which again is double-oxidized to release another proton. Three of the four presumed catalytic intermediates (Hox, Hred/Hred and Hsred) were characterized, using various spectroscopic techniques. However, in catalytically active enzyme, the state containing the hydrido-species, which is eponymous for the proposed heterolytic mechanism, has yet only been speculated about. We use different strategies to trap and spectroscopically characterize this transient hydride state (Hhyd) for three wild-type [FeFe]-hydrogenases. Applying a novel set-up for real-time attenuated total- reflection Fourier-transform infrared spectroscopy, we monitor compositional changes in the state-specific infrared signatures of [FeFe]-hydrogenases, varying buffer pH and gas composition. We selectively enrich the equilibrium concentration of Hhyd, applying Le Chatelier’s principle by simultaneously increasing substrate and product concentrations (H2/H+). Site-directed manipulation, targeting either the proton-transfer pathway or the adt ligand, significantly enhances Hhyd accumulation independent of pH

M e t hylsi lyl hyd roxylami nes: Preparative, Spectroscopic and Ab initio Studiest

Methylsilylhydroxylamines [ (MeH,Si),NOMe, (MeH,Si) MeNOMe, Me,NOSiH,Me] have been prepared from bromo(methy1)silane and the corresponding methylhydroxylamines in the presence of an auxiliary base (triethylamine or N,N,N',N'-tetramethylethylenediamine). The compounds were studied by N M R spectroscopy of all elements present ( l H , 13C, 15N, 170, 29Si). The magnitude of the one-bond coupling constants 1J('5N29Si) is interpreted in terms of the hybridization associated with the pyramidal co-ordination of nitrogen, a unique structural feature in Si/N chemistry. Ab initiu studies confirmed these structural predictions. Singly silylated hydroxylamines have been shown to be more strongly pyramidal than doubly silylated ones. Calculations on the model compound (H,Si),NOMe gave a barrier to inversion at nitrogen of 9.7 kcal mol-'. This inversion is accompanied by a partial rotation around the N-0 bond. The has a planar co-ordination at the nitrogen atom, has been maintained ever since, and during the last 40 years the structures of a large number of silylamines have been determined.2 As a general rule it was derived from these results that all compounds with doubly and triply silylated nitrogen atoms exhibit a planar geometry at n i t r~g e n .~ Only for a few monosilylated amines deviations from a planar arrangement of the nitrogen substituents occur, but with significant variations for the gas phase and the solid state. p,d, B~n d i n g ,~ formerly the most widespread hypothesis to explain this and other unique properties of silylamines, like low basicity at nitrogen and short Si-N bonds, was shown to be rather insignificant, and p,. interactions (negative hyperconjugation, anomeric effect) and an electrostatic repulsion model ' have since been introduced as more meaningful approaches. Compounds with a wide variety of substituents at the silicon part of the molecules have been structurally studied, but the variations of nitrogen substituents have been limited to silylated hydrazines some of which were presented in previous papers from this laboratory.8 For this class of Si/N compounds with nitrogen in its oxidation state -11, planarity at nitrogen induced by silyl substituents appears to be also well established.' As a continuation of these studies we have now investigated silylated hydroxylamines bearing oxygen as a very electronegative substituent at nitrogen in its oxidation state -I. In this context we recently reported the unique structure of 0-methyl-N,N-bis(ptolylsily1)hydroxylamine 1, oneofonly a few doubly N-silylated compounds with a pyramidal co-ordination sphere at nitrogen. ' ' t Non-SI unit employed: cal = 4.184 J. 1 As a follow-up to this work, and as a part of our current search for new single-source feedstock precursors for chemical vapour deposition ' (CVD) of silicon nitride and oxynitride films, ' we are now examining low-molecular-weight silylhydroxylamines with low carbon contents and high volatilities. These small molecules should also allow a direct comparison of experimental data with the results of more sophisticated theoretical calculations of structure and bonding. Results and Discussion Preparation of Methylsilylhydroxy1amines.-Since compounds with silyl groups H,Si are generally pyrophoric, methylsilyl groups, the organosilyl groups with the lowest carbon content, were chosen for this study. Bromo(methy1)silane is a powerful silylating agent for N H and OH functions and reacts with 0-methyl, N,O-dimethyl-and N,N-dimethylhydroxylamine in the presence of triethylamine to give the silylated hydroxylamines 2,3 and 4, respectively (Scheme 1). The compounds have low boiling points (97, 61 and 58 "C, respectively), and separation from the solvents and from the excess of triethylamine is difficult. These complications can be overcome by a solvent-free reaction mode and by using N,N,N',N'-tetramethylethylenediamine (tmen) as the dehydrohalogenating agent. The advantage of tmen is its dibasic nature. Since both di-and mono-protonated tmen salts are non-volatile

Unbiased analysis of obesity related, fat depot specific changes of adipocyte volumes and numbers using light sheet fluorescence microscopy

In translational obesity research, objective assessment of adipocyte sizes and numbers is essential to characterize histomorphological alterations linked to obesity, and to evaluate the efficacies of experimental medicinal or dietetic interventions. Design-based quantitative stereological techniques based on the analysis of 2D-histological sections provide unbiased estimates of relevant 3D-parameters of adipocyte morphology, but often involve complex and time-consuming tissue processing and analysis steps. Here we report the application of direct 3D light sheet fluorescence microscopy (LSFM) for effective and accurate analysis of adipocyte volumes and numbers in optically cleared adipose tissue samples from a porcine model of diet-induced obesity (DIO). Subcutaneous and visceral adipose tissue samples from DIO-minipigs and lean controls were systematically randomly sampled, optically cleared with 3DISCO (3-dimensional imaging of solvent cleared organs), stained with eosin, and subjected to LSFM for detection of adipocyte cell membrane autofluorescence. Individual adipocytes were unbiasedly sampled in digital 3D reconstructions of the adipose tissue samples, and their individual cell volumes were directly measured by automated digital image analysis. Adipocyte numbers and mean volumes obtained by LSFM analysis did not significantly differ from the corresponding values obtained by unbiased quantitative stereological analysis techniques performed on the same samples, thus proving the applicability of LSFM for efficient analysis of relevant morphological adipocyte parameters. The results of the present study demonstrate an adipose tissue depot specific plasticity of adipocyte growth responses to nutrient oversupply. This was characterized by an exclusively hypertrophic growth of visceral adipocytes, whereas adipocytes in subcutaneous fat tissue depots also displayed a marked (hyperplastic) increase in cell number. LSFM allows for accurate and efficient determination of relevant quantitative morphological adipocyte parameters. The applied stereological methods and LSFM protocols are described in detail and can serve as a guideline for unbiased quantitative morphological analyses of adipocytes in other studies and species