The length and depth of algebraic groups

Mathematische Zeitschrift - Let G be a connected algebraic group. An unrefinable chain of G is a chain of subgroups $$G = G_0> G_1> \cdots > G_t = 1$$ , where each $$G_i$$ is a...     

Intermediates of N-Heterocyclic Carbene (NHC) Dimerization Probed in the Gas Phase by Ion Mobility Mass Spectrometry: C−H⋅⋅⋅:C Hydrogen Bonding Versus Covalent Dimer Formation

N-Heterocyclic carbenes (NHCs, :C ) can interact with azolium salts ( C−H⁺ ) by either forming a hydrogen-bonded aggregate ( CHC⁺ ) or a covalent C−C bond ( CCH⁺ ). In this study, the intramolecular NHC–azolium salt interactions of aromatic imidazolin-2-ylidenes and saturated imidazolidin-2-ylidenes have been investigated in the gas phase by traveling wave ion mobility mass spectrometry (TW IMS) and DFT calculations. The TW IMS experiments provided evidence for the formation of these important intermediates in the gas phase, and they identified the predominant aggregation mode (hydrogen bond vs. covalent C−C) as a function of the nature of the interacting carbene–azolium pairs.     

Strategies Towards Capturing Nitrogenase Substrates and Intermediates via Controlled Alteration of Electron Fluxes

Nitrogenase utilizes an ATP-dependent reductase to deliver electrons to its catalytic component to enable two important reactions: the reduction of N₂ to NH₄⁺, and the reduction of CO to hydrocarbons. The two nitrogenase-based reactions parallel the industrial Haber–Bosch and Fischer–Tropsch processes, yet they occur under ambient conditions. As such, understanding the enzymatic mechanism of nitrogenase is crucial for the future development of biomimetic strategies for energy-efficient production of valuable chemical commodities. Mechanistic investigations of nitrogenase has long been hampered by the difficulty to trap substrates and intermediates relevant to the nitrogenase reactions. Recently, we have successfully captured CO on the Azotobacter vinelandii V-nitrogenase via two approaches that alter the electron fluxes in a controlled manner: one approach utilizes an artificial electron donor to trap CO on the catalytic component of V-nitrogenase in the resting state; whereas the other employs a mismatched reductase component to reduce the electron flux through the system and consequently accumulate CO on the catalytic component of V-nitrogenase. Here we summarize the major outcome of these recent studies, which not only clarified the catalytic relevance of the one-CO (lo-CO) and multi-CO (hi-CO) bound states of nitrogenase, but also pointed to a potential competition between N₂ and CO for binding to the same pair of reactive Fe sites across the sulfur belt of the cofactor. Together, these results highlight the utility of these strategies in poising the cofactor at a well-defined state for substrate- or intermediate-trapping via controlled alteration of electron fluxes, which could prove beneficial for further elucidation of the mechanistic details of nitrogenase-catalyzed reactions.     

A design of experiments concept for the minimization of nonspecific peptide adsorption in the mass spectrometric determination of substance P and related hemokinin‐1

Substance P and hemokinin‐1 were predominantly examined by immunoassays with their limitation to differentiate appropriately between both peptides. The use of liquid chromatography coupled with tandem mass spectrometry is a promising, highly selective alternative. Adsorption processes have been identified in preliminary experiments to play a crucial role in the loss of mass spectrometry intensity of both peptides. Therefore, a design of experiments concept was created to minimize nonspecific peptide adsorption. For this purpose, the most critical influencing parameters—(1) the composition of the injection solvent as well as (2) the most suitable container material—were systematically and concordantly investigated. The addition of modifiers, such as formic acid, dimethyl sulfoxide, and organic solvents, to the injection solvent led to a substantial gain of intensity of substance P and hemokinin‐1 compared to the start gradient as an injection solvent. Furthermore, the systematic investigation underlined the high impact of the container material, demonstrating polypropylene as the most favorable material. A conjoint injection solvent optimum was found to determine both peptides simultaneously by the conduction of a sweet‐spot analysis. The experimental design substantially reduced nonspecific peptide adsorption and enabled the simultaneous and selective determination of endogenous substance P and hemokinin‐1 plasma levels.     

Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples.