A solid-state 39K and 13C NMR study of polymeric potassium metallocenes

The quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) and double frequency sweep (DFS)/QCPMG pulse sequences are applied in order to acquire the first solid-state 39K NMR spectra of organometallic complexes, the polymeric main group metallocenes cyclopentadienyl potassium (CpK) and pentamethylcyclopentadienyl potassium (Cp*K). Piecewise QCPMG NMR techniques are used to acquire a high S/N 39K spectrum of the broad central transition of Cp*K, which is ca. 200 kHz in breadth. Analytical and numerical simulations indicate that there is a significant quadrupolar interaction present at both potassium nuclei (C(Q)(39K) = 2.55(6)/2.67(8) MHz and 4.69(8) MHz for CpK (static/MAS) and Cp*K, respectively). Experimental quadrupolar asymmetry parameters suggest that both structures are bent about the potassium atoms (eta(Q)(39K) = 0.28(3)/0.29(3) for CpK (static/MAS) and eta(Q)(39K) = 0.30(3) for Cp*K). Variable-temperature (VT) 39K NMR experiments on CpK elucidate temperature-dependent changes in quadrupolar parameters which can be rationalized in terms of alterations of bond distances and angles with temperature. 13C CP/MAS NMR experiments are conducted upon both samples to quantify the carbon chemical shielding anisotropy (CSA) at the Cp' ring carbon atoms. Ab initio carbon CSA and 39K electric-field gradient (EFG) and CSA calculations are conducted and discussed for the CpK complex, in order to correlate the experimental NMR parameters with molecular structure in CpK and Cp*K. 39K DFS/QCPMG and 13C CP/MAS experiments prove invaluable for probing molecular structure, temperature-dependent structural changes, and the presence of impurities in these systems.     

Noniterative biexponential fluorescence lifetime imaging in the investigation of cellular metabolism by means of NAD(P)H autofluorescence.

The cofactors NADH and NADPH, hereafter NAD(P)H [NAD(P)= nicotinamide adenine dinucleotide (phosphate)], belong to the principal endogenous indicators of energetic cellular metabolism. Since the metabolic activity of cells is given by the ratio between the concentrations of free and protein-bound NAD(P)H, the development of autofluorescence techniques which accurately measure the modifications to this ratio is particularly significant. Hitherto the methods applied in the monitoring of cellular metabolism have provided either imprecise results, due to interference of the NAD(P)H signal by perturbing factors, or they have required a complicated internal calibration. We employ biexponential fluorescence lifetime imaging (FLIM) in order to discriminate between the free and protein-bound NAD(P)H without any previous calibration. Thus, we have obtained directly, and for the first time, a high-resolution map of cellular metabolism, that is, an image of the contribution of the protein-bound NAD(P)H to the cumulative NAD(P)H fluorescence signal. Moreover, we demonstrate that protein-NAD(P)H complexes characterised by different fluorescence lifetimes are not uniformly distributed all over the cell, as assumed until now, but are concentrated in certain cellular regions. The different fluorescence lifetimes indicate either different protein-NAD(P)H complexes or different bond strengths between NAD(P)H and the protein in these complexes. Since an important aspect in biological applications is to monitor the dynamics of the relevant processes (such as cellular metabolism), rapid dynamical techniques, for example, rapid biexponential fluorescence lifetime imaging, are needed. Furthermore, it is necessary to reduce the evaluation effort as much as possible. Most of the evaluation techniques in multiexponential FLIM are time-expensive iterative methods. The few exceptions are connected with a loss of information, for example, global analysis; or a loss in accuracy, for example, the rapid evaluation technique (RLD). We implement for the first time in FLIM a noniterative, nonrestrictive method originally developed by Prony for approximations of multiexponential decays. The accuracy of this method is verified in biexponential FLIM experiments in time-domain on mixtures of two chromophores both in homogenous and in heterogeneous media. The resulting fluorescence lifetimes agree (within error margins) with the lifetimes of the pure substances determined in monoexponential FLIM experiments. The rapidity of our evaluation method as compared to iterative pixel-by-pixel methods is evidenced by a reduction of the evaluation time by more than one order of magnitude. Furthermore, the applicability of this method for the biosciences is demonstrated in the investigation of cellular metabolism by means of NAD(P)H endogenous fluorescence.     

Rapid high-pressure liquid chromatographic analysis of verapamil in blood and plasma

A high-pressure liquid chromatographic assay procedure has been developed for verapamil in blood or plasma. A paired-ion solvent system with a reversed-phase column is employed. The procedure is specific for verapamil and the retention times of the major metabolites are identified. This procedure is sensitive to a lower blood concentration of 1 ng/ml and standard curves were found to be linear up to the highest concentration tested, 500 ng/ml. Several drugs were tested for interference with the assay, but none were found to cause any problems. The procedure is simple, rapid and permits the analysis of up to 25 samples per day.     

van der Waals corrections to density functional theory calculations: Methane,ethane, ethylene,benzene, formaldehyde,ammonia, water,PBE, and CPMD

Parameters are developed for a practical application of the empirical van der Waals (vdW) correction infrastructure available in the CPMD density functional theory (DFT) code. The binding energy, geometry, and potential energy surface (PES) are examined for methane, ethane, ethylene, formaldehyde, ammonia, three benzene dimer geometries, and three benzene–water geometries. The vdW corrected results compare favorably with MP2 and CCSD(T) calculations near the complete basis set limits, and with experimental results where they are available.     

An asymptotic definition of K-groups of automorphisms and a non-Bernoullian counter-example

Summary Let GZⁿ be a group of measure preserving transformations of a Lebesgue space. J. P. Conze [1] has developed an entropy theory for such groups and described a class of groups obeying a form of the Kolmogorov zero-one law called K-groups. A Bernoulli group is a group isomorphic to the group of translates (shifts) of elements of the space with product measure where X _g =X is a probability space. Bernoulli groups are also K-groups. Katznelson and Weiss [3] have shown entropy is a complete invariant for isomorphism classes of Bernoulli groups. We give an asymptotic definition of K-groups in terms of finite -algebras and justify this definition in terms of entropy and Conze's formulation. This definition s used to help us construct a K-group GZ ⁿ that is completely non-Bernoulli, that is one that contains no Bernoulli subgroup.     

Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion

Summary Conventional numerical methods, when applied to the ordinary differential equations of motion of classical mechanics, conserve the total energy and angular momentum only to the order of the truncation error. Since these constants of the motion play a central role in mechanics, it is a great advantage to be able to conserve them exactly. A new numerical method is developed, which is a generalization to arbitrary order of the discrete mechanics described in earlier work, and which conserves the energy and angular momentum to all orders. This new method can be applied much like a corrector as a modification to conventional numerical approximations, such as those obtained via Taylor series, Runge-Kutta, or predictor-corrector formulae. The theory is extended to a system of particles in Part II of this work.     

Zur Minimalität trigonometrischer Polynomoperatoren

Cheney and others [2] have shown that, with respect to the norm of uniform convergence, the Fourier operator F_n:C₂p_n is the only minimal projection. For a more detailed study of operators A:C₂P_n we investigate the evaluation functionals respectively the mean of their norms . We give a complete characterization of polynomial operators which minimize this quantity. As an application we can simplify the proof in [2]. Moreover, we show that the trigonometric interpolation operators, having the above minimal-property,are exactly those with equidistant nodes.

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Diese Arbeit enthält die wesentlichen Resultate einer Diplomarbeit, die der Verfasser an der Eberhard-Karls-Universität Tübingen unter der Anleitung von A.Schönhage angefertigt hat.     

über die Striktionslinien von einparametrigen Scharen linearer Räume

A generalisation of a ruled surface in n-dimensional euclidean space may be generated by euclidean motion of a s-plane A_s. For this one-parametric family {A_s} the curve of striction is defined and the following theorems are proved:

1. The generators A_s are parallel along the curve of striction, i.e. the multivectors representing A_s form a parallel vector field along the curve of striction.
2. If the curve of striction is geodesic on {A_s}, it is also an isogonal trajectory of the family of generators {A_s}.

     

Mathematical Models of Death Signaling Networks

This review provides an overview of the progress made by computational and systems biologists in characterizing different cell death regulatory mechanisms that constitute the cell death network. We define the cell death network as a comprehensive decision-making mechanism that controls multiple death execution molecular circuits. This network involves multiple feedback and feed-forward loops and crosstalk among different cell death-regulating pathways. While substantial progress has been made in characterizing individual cell death execution pathways, the cell death decision network is poorly defined and understood. Certainly, understanding the dynamic behavior of such complex regulatory mechanisms can be only achieved by applying mathematical modeling and system-oriented approaches. Here, we provide an overview of mathematical models that have been developed to characterize different cell death mechanisms and intend to identify future research directions in this field.     

Zika Virus Inhibitors Based on a 1,3-Disubstituted 1H-Pyrazolo[3,4-d]pyrimidine-amine Scaffold

To search for Zika virus (ZIKV) antivirals, we have further explored previously reported 7H-pyrrolo[2,3-d]pyrimidines by examining an alternative substitution pattern of their central scaffold, leading to compound 5 with low micromolar antiviral activity. To circumvent the synthetic difficulties associated with compound 5, we have exploited a 1H-pyrazolo[3,4-d]pyrimidine scaffold and performed structure-activity relationship studies on its peripheral rings A and B. While ring B is less sensitive to structural modifications, an electron-withdrawing group at the para position of ring A is preferred for enhanced antiviral activity. Overall, we have not only discovered an alternative substitution pattern centered on a 1H-pyrazolo[3,4-d]pyrimidine scaffold but also generated anti-ZIKV compounds including 6 and 13, which possess low micromolar antiviral activity and relatively low cytotoxicity. These compounds represent new chemotypes that will be further optimized in our continued efforts to discover anti-ZIKV agents.