On Liénard's equation and the uniqueness of limit cycles in predator-prey systems

We study a system of ODE's modelling the interaction of one predator and one prey dx/dt = xg(x) - yp(x), dy/dt = gamma y[- delta - nu y - alpha y2 + h(x)]. This system defines a two-species community which incorporates competition among prey in the absence of any predators as well as a density-dependent predator specific death rate. This system is investigated under ecologically natural regularity conditions and assumptions on g, p and h to ensure the existence and uniqueness of limit cycles. The proof uses the standard Hopf-Andronov bifurcation theory and the technique of Liénard's equation.     

Synthesis and characterization of hydroxy-functionalized models for the active site in Fe-only-hydrogenases

The reactions of DL-1,4-disulfanylbutane-2,3-diol and 1,3-disulfanylpropan-2-ol with dodecacarbonyltriiron have been investigated. As main products, the iron complexes 1 and 2 were isolated and characterized by spectroscopic methods, as well as single crystal X-ray analysis. Additionally, the unusually large bond angles in the dithiolato bridge was investigated via density-functional theory (DFT) calculations. Moreover, the electrochemical features have been studied by cyclic voltammetry.     

Dibenzazecine scaffold rebuilding—Is the flexibility always essential for high dopamine receptor affinities?

The moderately flexible 7-methyl-5,6,7,8,9,14-hexahydrodibenz[d,g]azecines are known to be potent dopamine receptor antagonists, whereas the corresponding rigid dibenzo[d,g]quinolizines are inactive. We built the scaffolds of dibenzo[c,g], [c,f] and [d,f]azecines and together with their ring closed, more rigid precursors, evaluated the affinities for the human D₁–D₅ receptors (radioligand binding) as well as the functionalities (calcium assay) and thus investigated the influence of annelation and conformative flexibility of these compounds on their affinity for human cloned dopamine receptors.     

Investigation of amino acid containing [FeFe] hydrogenase models concerning pendant base effects

The present investigations deal with the modeling of the peptide surrounding of [FeFe] hydrogenase using amine containing disulphides to simulate possible influences of the amino acid lysine (K237) on the electrochemical and electrocatalytic properties of biomimetic compounds based on [Fe2S2] moieties. Fe₃(CO)₁₂ was reacted with Boc-4-amino-1,2-dithiolane, Boc-Adt-OMe (Adt = 4-amino-1,2-dithiolane-4-carboxylic acid, Boc = tert-butoxycarbonyl) and Boc-Adp tert-butyl ester (Adp = (S)-2-amino-3-(1,2-dithiolan-4-yl)propionic acid) to elongate the FeN distance in comparison to the well known [Fe₂{(SCH₂)₂NR}(CO)₆] model complexes. Efforts to deprotect the complexes containing Boc-4-amino-1,2-dithiolane with trifluoroacetic acid result in the formation of [Fe₃(μ³-O)(μ-O₂C₂F₃)₆(OC₄H₈)₂(H₂O)]. The novel [2Fe2S] complexes are characterized using spectroscopic, electrochemical techniques and X-ray diffraction studies.     

Erythropoietin ameliorates rat experimental autoimmune neuritis by inducing transforming growth factor-β in macrophages

Erythropoietin (EPO) is a pleiotropic cytokine originally identified for its role in erythropoiesis. In addition, in various preclinical models EPO exhibited protective activity against tissue injury. There is an urgent need for potent treatments of autoimmune driven disorders of the peripheral nervous system (PNS), such as the Guillain-Barré syndrome (GBS), a disabling autoimmune disease associated with relevant morbidity and mortality. To test the therapeutic potential of EPO in experimental autoimmune neuritis (EAN) - an animal model of human GBS--immunological and clinical effects were investigated in a preventive and a therapeutic paradigm. Treatment with EPO reduced clinical disease severity and if given therapeutically also shortened the recovery phase of EAN. Clinical findings were mirrored by decreased inflammation within the peripheral nerve, and myelin was well maintained in treated animals. In contrast, EPO increased the number of macrophages especially in later stages of the experimental disease phase. Furthermore, the anti-inflammatory cytokine transforming growth factor (TGF)-beta was upregulated in the treated cohorts. In vitro experiments revealed less proliferation of T cells in the presence of EPO and TGF-beta was moderately induced, while the secretion of other cytokines was almost not altered by EPO. Our data suggest that EPO revealed its beneficial properties by the induction of beneficial macrophages and the modulation of the immune system towards anti-inflammatory responses in the PNS. Further studies are warranted to elaborate the clinical usefulness of EPO for treating immune-mediated neuropathies in affected patients.     

Design and Evaluation of a Hybrid Radiofrequency Applicator for Magnetic Resonance Imaging and RF Induced Hyperthermia: Electromagnetic Field Simulations up to 14.0 Tesla and Proof-of-Concept at 7.0 Tesla

This work demonstrates the feasibility of a hybrid radiofrequency (RF) applicator that supports magnetic resonance (MR) imaging and MR controlled targeted RF heating at ultrahigh magnetic fields (B₀≥7.0T). For this purpose a virtual and an experimental configuration of an 8-channel transmit/receive (TX/RX) hybrid RF applicator was designed. For TX/RX bow tie antenna electric dipoles were employed. Electromagnetic field simulations (EMF) were performed to study RF heating versus RF wavelength (frequency range: 64 MHz (1.5T) to 600 MHz (14.0T)). The experimental version of the applicator was implemented at B₀ = 7.0T. The applicators feasibility for targeted RF heating was evaluated in EMF simulations and in phantom studies. Temperature co-simulations were conducted in phantoms and in a human voxel model. Our results demonstrate that higher frequencies afford a reduction in the size of specific absorption rate (SAR) hotspots. At 7T (298 MHz) the hybrid applicator yielded a 50% iso-contour SAR (iso-SAR-50%) hotspot with a diameter of 43 mm. At 600 MHz an iso-SAR-50% hotspot of 26 mm in diameter was observed. RF power deposition per RF input power was found to increase with B₀ which makes targeted RF heating more efficient at higher frequencies. The applicator was capable of generating deep-seated temperature hotspots in phantoms. The feasibility of 2D steering of a SAR/temperature hotspot to a target location was demonstrated by the induction of a focal temperature increase (ΔT = 8.1 K) in an off-center region of the phantom. Temperature simulations in the human brain performed at 298 MHz showed a maximum temperature increase to 48.6C for a deep-seated hotspot in the brain with a size of (19×23×32)mm³ iso-temperature-90%. The hybrid applicator provided imaging capabilities that facilitate high spatial resolution brain MRI. To conclude, this study outlines the technical underpinnings and demonstrates the basic feasibility of an 8-channel hybrid TX/RX applicator that supports MR imaging, MR thermometry and targeted RF heating in one device.     

O-Alkylthio- and O-alkylselenooxalate iron complexes: Structures of CpFe(CO)2ECOCO2Me and [CpFe(CO)2ECO]2

When the iron sulfide complexes (μ-S_x)[CpFe(CO)₂]₂ (x = 2, 3) are treated with O-alkyl oxalyl chlorides ROCOCOCl the complexes CpFe(CO)₂SCOCO₂R (1) [R = Me (a), Et (b)] are obtained. Similarly, the complexes CpFe(CO)₂SeCOCO₂R (2) are obtained from the analogous iron selenide (μ-Se)[CpFe(CO)₂]₂ reaction with the same reagents. Treatment of the iron selenide with half equivalent of oxalyl chloride produces the dimeric complex [CpFe(CO)₂SeCO]₂ (3). The new complexes, 1, 2 and 3, have been characterized by elemental analyses, IR and ¹H NMR spectroscopy. The solid state structures of 1a, 2a, 3 and [CpFe(CO)₂SCO]₂ (4) were determined by an X-ray crystal structure analysis.     

Nickel(II) complexes with Schiff-base ligands derived from epimeric pyranose backbones as 2,3-chelators: modeling the coordination chemistry of chitosan

Two mononuclear nickel(II) complexes with Schiff-base ligands derived from the epimeric sugars glucosamine and mannosamine have been synthesized. The X-ray crystal structure reveals a distorted octahedral geometry at the nickel(II) ions with an N4O2 donor set and the rare 2,3-chelation of the donor atoms of the carbohydrate backbone. Upon complexation only the glucopyranose ring maintains the 4C1 chair conformation, whereas the mannopyranose ring adopts the OS5 screw-boat conformation. Dimeric units of complex cations are formed by intermolecular hydrogen bonding which are further assembled by pi-stacking affording one-dimensional chains with a twofold screw symmetry.     

Stochastic Hierarchical Systems: Excitable Dynamics

We present a discrete model of stochastic excitability by a low-dimensional set of delayed integral equations governing the probability in the rest state, the excited state, and the refractory state. The process is a random walk with discrete states and nonexponential waiting time distributions, which lead to the incorporation of memory kernels in the integral equations. We extend the equations of a single unit to the system of equations for an ensemble of globally coupled oscillators, derive the mean field equations, and investigate bifurcations of steady states. Conditions of destabilization are found, which imply oscillations of the mean fields in the stochastic ensemble. The relation between the mean field equations and the paradigmatic Kuramoto model is shown.