Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.     

Qualitative behaviour of a ratio-dependent predator–prey system

This paper deals with the qualitative properties of an autonomous system of differential equations, modeling ratio-dependent predator–prey interactions.This model differs from traditional ratio dependent models essentially in the predator mortality term, the death rate of the predator is not constant but instead increases when there is overcrowding.We incorporate delay(s) into the system. The most important observation is that as the delay(s) is (are) increased the originally asymptotic stable interior equilibrium loses its stability. Furthermore at a certain critical value a Hopf bifurcation takes place: small amplitude periodic solutions arise.     

Accurate measurement of long-range heteronuclear coupling constants from undistorted multiplets of an enhanced CPMG-HSQMBC experiment

Here, we present a modified CPMG-HSQMBC experiment which is capable to reduce the detrimental phase twists in the "long-range" connectivity multiplets caused by proton-proton couplings. We demonstrate that concerted CPMG pulse trains applied on both nuclei in the starting CPMG-INEPT transfer step can considerably be improved by composite pi pulses that compensate for pulse imperfections and off-resonance effects. Experimental optimization of the interpulse delay within the CPMG cycle was found to be crucial in order to achieve the best possible "decoupling" of homonuclear coupling modulation.     

Quantitative Comparison of Tandem Mass Spectra Obtained on Various Instruments

The similarity between two tandem mass spectra, which were measured on different instruments, was compared quantitatively using the similarity index (SI), defined as the dot product of the square root of peak intensities in the respective spectra. This function was found to be useful for comparing energy-dependent tandem mass spectra obtained on various instruments. Spectral comparisons show the similarity index in a 2D “heat map”, indicating which collision energy combinations result in similar spectra, and how good this agreement is. The results and methodology can be used in the pharma industry to design experiments and equipment well suited for good reproducibility. We suggest that to get good long-term reproducibility, it is best to adjust the collision energy to yield a spectrum very similar to a reference spectrum. It is likely to yield better results than using the same tuning file, which, for example, does not take into account that contamination of the ion source due to extended use may influence instrument tuning. The methodology may be used to characterize energy dependence on various instrument types, to optimize instrumentation, and to study the influence or correlation between various experimental parameters.

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The Synthesis of 3‐Phosphabicyclo[3.1.0]‐ hexane 3‐Oxides and 1,2‐Dihydrophosphinine 1‐Oxides with Lipophilic P‐Alkoxy Substituents by Ring Enlargement

A series of 1‐alkoxy‐3‐phospholene 1‐oxides available from the microwave‐assisted direct esterification of 1‐hydroxy‐3‐phospholene oxide was converted to the two diastereomers of 6,6‐dichloro‐3‐phosphabicyclo[3.1.0]hexane 3‐oxides by the addition of dichlorocarbene to the double bond. Thermolysis of the 3‐phospholene oxide–dichlorocarbene adducts afforded the corresponding 1,2‐dihydrophosphinine 1‐oxides as a ca. 3:1 mixture of two double bond isomers. Relative stability of the isomers of the intermediates and the products and their stereostructures were evaluated by B3LYP/6‐31G(d,p) calculations.     

Histidine-rich branched peptides as Cu(II) and Zn(II) chelators with potential therapeutic application in Alzheimer's disease

Two histidine-rich branched peptides with one lysine as a branching unit have been designed and synthesized by solid-phase peptide synthesis. Their complex formation with Cu(II) and Zn(II) as well as their ability to attenuate the metal-ion induced amyloid aggregation has been characterized. Both peptides can keep Cu(II) and Zn(II) in complexed forms at pH 7.4 and can bind two equivalents of metal ions in solutions with excess metal. The stoichiometry, stability and structure of the complexes formed have been determined by pH potentiometry, UV-Vis spectrophotometry, circular dichroism, EPR and NMR spectroscopy and ESI-MS. Both mono- and bimetallic species have been detected over the whole pH range studied. The basic binding mode is either a tridentate {N(amino), N(amide), N(im)} or a histamine-type of coordination which is complemented by the binding of far imidazole or amino groups leading to macrochelate formation. The peptides were able to prevent Cu(II)-induced Aβ(1-40) aggregation but could not effectively compete for Zn(II) in vitro. Our results suggest that branched peptides containing potential metal-binding sites may be suitable metal chelators for reducing the risk of amyloid plaque formation in Alzheimer's disease.     

A 3D mammalian cell separator biochip

The dissimilar cytoskeletal architecture in diverse cell types induces a difference in their deformability that presents a viable approach to separate cells in a non-invasive manner. We report on the design and fabrication of a robust and scalable device capable of separating a heterogeneous population of cells with variable degree of deformability into enriched populations with deformability above a certain threshold. The three dimensional device was fabricated in fused silica by femtosecond laser direct writing combined with selective chemical etching. The separator device was evaluated using promyelocytic HL60 cells. Using flow rates as large as 167 μL min(-1), throughputs of up to 2800 cells min(-1) were achieved at the device output. A fluorescence-activated cell sorting (FACS) viability analysis on the cells revealed 81% of the population maintain cellular integrity after passage through the device.