A Feynman-Kac formula for the quantum Heisenberg ferromagnet. I

The Hamiltonian of the (anisotropic) quantum Heisenberg (anti-) ferromagnet on an arbitrary finite lattice is lifted to a Hamiltonian acting on sections of the bundle obtained by twisting a certain line bundle over the classical spin configuration space (which is a Kähler manifold) with the Dolbeault complex. This procedure is extended fromSU(2) to arbitrary compact semi-simple Lie groups and arbitrary irreducible representations. The Bott-Borel-Weil theorem gives a heat kernel representation for the original partition function in an external magnetic field. TheU(1)-gauged local Hamiltonian is the sum of the free, supersymmetric, twisted Dolbeault Laplace operator (multiplied by the inverse of an arbitrary small mass parameter) plus the lifted Hamiltonian.The resulting (Euclidean) Lagrangian is nonlocal and describes bosons which do and fermions which do not propagate through the lattice. All fields couple to the external magnetic field. The Lagrangian contains Yukawa and Luttinger type interactions.     

Synthesis of 2,3-benzoxepins by sequential cyclopropanation/ring-enlargement reactions of benzopyrylium triflates with diazoesters

Functionalized 2,3-benzoxepins were prepared by cyclopropanation of benzopyrylium triflates with diazoesters and subsequent TFA-mediated ring enlargement.     

Engineering Rieske Non‐Heme Iron Oxygenases for the Asymmetric Dihydroxylation of Alkenes

The asymmetric dihydroxylation of olefins is of special interest due to the facile transformation of the chiral diol products into valuable derivatives. Rieske non‐heme iron oxygenases (ROs) represent promising biocatalysts for this reaction as they can be engineered to efficiently catalyze the selective mono‐ and dihydroxylation of various olefins. The introduction of a single point mutation improved selectivities (≥95 %) and conversions (>99 %) towards selected alkenes. By modifying the size of one active site amino acid side chain, we were able to modulate the regio‐ and stereoselectivity of these enzymes. For distinct substrates, mutants displayed altered regioselectivities or even favored opposite enantiomers compared to the wild‐type ROs, offering a sustainable approach for the oxyfunctionalization of a wide variety of structurally different olefins.     

Identifying Mixtures of Mixtures Using Bayesian Estimation

The use of a finite mixture of normal distributions in model-based clustering allows us to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows us to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semiparametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark datasets. Supplementary materials for this article are available online.     

Interaction between inner and outer layer in drag-reduced turbulent flows

Effects of wall-based skin-friction drag reduction strategies on the statistical properties of large-scale motions in moderate Reynolds number turbulent flows have been investigated by exploiting Direct Numerical Simulation of turbulent channels. To educe large scales, a new efficient parallel distributed memory algorithm has been implemented which delivers data-driven modes of increasing characteristic lengthscales: the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD). The influence of wall-based skin friction reduction on large scales is studied by comparing single point statistics, such as r.m.s. fluctuations, and two-point statistics, as cross-correlation functions in controlled and uncontrolled channel flow fields at constant friction Reynolds number. The traditional way of observing large-scale footprinting at the wall, as cross-correlation of the streamwise velocity components at different wall distances, has been found to be unreliable when comparing drag-reduced flows, due to the arbitrary choice of a reference plane in the logarithmic layer. A more sound way of observing the footprinting via the correlation of the streamwise velocity with the friction velocity is addressed and shows an increase of the footprinting in drag-reduced flows. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Immobilization of histidine-tagged proteins on electrodes

The development of new enzyme immobilization techniques that do not affect catalytic activity or conformation of a protein is an important research task in biotechnology including biosensor applications and heterogeneous reaction systems. One of the most promising approaches for controlled protein immobilization is based on the immobilized metal ion affinity chromatography (IMAC) principle originally developed for protein purification. Here we describe the current status and future perspectives of immobilization of His-tagged proteins on electrode surfaces. Recombinant proteins comprising histidine-tags or histidine rich native proteins have a strong affinity to transition metal ions. For metal ion immobilization at the electrode surface different matrices can be used such as self-assembled monolayers or conductive polymers. This specific technique allows a reversible immobilization of histidine-tagged proteins at electrodes in a defined orientation which is an important prerequisite for efficient electron transfer between the electrode and the biomolecule. Any application requiring immobilized biocatalysts on electrodes can make use of this immobilization approach, making future biosensors and biocatalytic technologies more sensitive, simpler, reusable and less expensive while only requiring mild enzyme modifications.     

The influence of SO2 and NO2 impurities on CO2 gas hydrate formation and stability

The sequestration of industrially emitted CO(2) in gas hydrate reservoirs has been recently discussed as an option to reduce atmospheric greenhouse gas. This CO(2) contains, despite much effort to clean it, traces of impurities such as SO(2) and NO(2) . Here, we present results of a pilot study on CO(2) hydrates contaminated with 1% SO(2) or 1% NO(2) and show the impact on hydrate formation and stability. Microscopic observations show similar hydrate formation rates, but an increase in hydrate stability in the presence of SO(2). Laser Raman spectroscopy indicates a strong enrichment of SO(2) in the liquid and hydrate phase and its incorporation in both large and small cages of the hydrate lattice. NO(2) is not verifiable by laser Raman spectroscopy, only the presence of nitrate ions could be confirmed. Differential scanning calorimetry analyses show that hydrate stability and dissociation enthalpy of mixed CO(2)-SO(2) hydrates increase, but that only negligible changes arise in the presence of NO(2) impurities. X-ray diffraction data reveal the formation of sI hydrate in all experiments. The conversion rates of ice+gas to hydrate increase in the presence of SO(2), but decrease in the presence of NO(2). After hydrate dissociation, SO(2) and NO(2) dissolved in water and form strong acids.     

Accurate distance determination of nucleic acids via Förster resonance energy transfer: implications of dye linker length and rigidity

In Fo?rster resonance energy transfer (FRET) experiments, the donor (D) and acceptor (A) fluorophores are usually attached to the macromolecule of interest via long flexible linkers of up to 15 ? in length. This causes significant uncertainties in quantitative distance measurements and prevents experiments with short distances between the attachment points of the dyes due to possible dye-dye interactions. We present two approaches to overcome the above problems as demonstrated by FRET measurements for a series of dsDNA and dsRNA internally labeled with Alexa488 and Cy5 as D and A dye, respectively. First, we characterize the influence of linker length and flexibility on FRET for different dye linker types (long, intermediate, short) by analyzing fluorescence lifetime and anisotropy decays. For long linkers, we describe a straightforward procedure that allows for very high accuracy of FRET-based structure determination through proper consideration of the position distribution of the dye and of linker dynamics. The position distribution can be quickly calculated with geometric accessible volume (AV) simulations, provided that the local structure of RNA or DNA in the proximity of the dye is known and that the dye diffuses freely in the sterically allowed space. The AV approach provides results similar to molecular dynamics simulations (MD) and is fully consistent with experimental FRET data. In a benchmark study for ds A-RNA, an rmsd value of 1.3 ? is achieved. Considering the case of undefined dye environments or very short DA distances, we introduce short linkers with a propargyl or alkenyl unit for internal labeling of nucleic acids to minimize position uncertainties. Studies by ensemble time correlated single photon counting and single-molecule detection show that the nature of the linker strongly affects the radius of the dye's accessible volume (6-16 ?). For short propargyl linkers, heterogeneous dye environments are observed on the millisecond time scale. A detailed analysis of possible orientation effects (κ(2) problem) indicates that, for short linkers and unknown local environments, additional κ(2)-related uncertainties are clearly outweighed by better defined dye positions.