Determination of Copper(II) Ion Concentration by Lifetime Measurements of Green Fluorescent Protein

The understanding of cellular processes and functions and the elucidation of their physiological mechanisms is an important aim in the life sciences. One important aspect is the uptake and the release of essential substances as well as their interactions with the cellular environment. As green fluorescent protein (GFP) can be genetically encoded in cells it can be used as an internal sensor giving a deeper insight into biochemical pathways. Here we report that the presence of copper(II) ions leads to a decrease of the fluorescence lifetime (τ _fl) of GFP and provide evidence for Förster resonance energy transfer (FRET) as the responsible quenching mechanism. We identify the His₆-tag as the responsible binding site for Cu^2?+? with a dissociation constant K _d ?=?9 ±2 μM and a Förster radius R ₀?=?2.1 ±0.1 nm. The extent of the lifetime quenching depends on [Cu^2?+?] which is comprehended by a mathematical titration model. We envision that Cu^2?+? can be quantified noninvasively and in real-time by measuring τ _fl of GFP.     

Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers

For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.     

Electrochemotherapy of Mycosis fungoides by interferon-alpha

Eight patients with 29 lesions of histologically verified 1st stage of Mycosis fungoides were successfully treated by electrochemotherapy with interferon-alpha. For this purpose 8 biphasic pulses were used, each of 50+50 micros duration with 900 micros interpulse intervals, resulting in a burst of 7.1 ms total duration. Compared to the traditional monoimmunotherapy with interferon-alpha applied three times weekly for a total of 4 weeks, the electrochemotherapy was very efficient. Complete response (CR) was observed in 25 (86%) of the 29 treated lesions by single-act electrochemotherapy with interferon-alpha. At the end of the 12-month period, all 29 lesions showed 100% complete response (CR). New lesions for a period of 12 months were not observed. The expected mechanism involved in multiple cytotoxic action of interferon-alpha could be the local increased concentration in the tumour and prolongation of the time of its action after the application of pulses.     

A hybrid algorithm for the unbounded knapsack problem

This paper presents a new approach for exactly solving the Unbounded Knapsack Problem (UKP) and proposes a new bound that was proved to dominate the previous bounds on a special class of UKP instances. Integrating bounds within the framework of sparse dynamic programming led to the creation of an efficient and robust hybrid algorithm, called EDUK2. This algorithm takes advantage of the majority of the known properties of UKP, particularly the diverse dominance relations and the important periodicity property. Extensive computational results show that, in all but a very few cases, EDUK2 significantly outperforms both MTU2 and EDUK, the currently available UKP solvers, as well the well-known general purpose mathematical programming optimizer CPLEX of ILOG. These experimental results demonstrate that the class of hard UKP instances needs to be redefined, and the authors offer their insights into the creation of such instances.     

Smoothing of Radon projections type of data by bivariate polynomials

Given information about a function in two variables, consisting of a finite number of Radon projections, we study the problem of smoothing this data by a bivariate polynomial. It turns out that the smoothing problem is closely connected with the interpolation problem. We propose several schemes consisting of sets of parallel chords in the unit disk which ensure uniqueness of the bivariate polynomial having prescribed Radon projections along these chords. Regular schemes play an important role in both interpolation and smoothing of such kind of data. We prove that the existence and uniqueness of the best smoothing polynomial relies on a regularity property of the scheme of chords. Results of some numerical experiments are presented too.     

Convergence of the method of chords for solving generalized equations

In this article, we study an iterative procedure of the following form

Quasimaximality and principal filters isomorphism between

Let I be a quasimaximal subset of a computable basis of the fully efective vector space V . We give a necessary and sufficient condition for the existence of an isomorphism between the principal filter respectivelly. We construct both quasimaximal sets that satisfy and quasimaximal sets that do not satisfy this condition. With the latter we obtain a negative answer to Question 5.4 posed by Downey and Remmel in [3].Based on the authors Ph.D. dissertation.Mathematics Subject Classification (2000): 03D25, 03C57     

Stability of various silicone oil/water emulsion films as a function of surfactant and salt concentration

There have been reports, originally by the Bristol group, and subsequently by others, of the preparation and properties of emulsions of stable, nearly monodisperse droplets of poly(dimethylsiloxane) (PDMS) in water, where no added surfactant is used. It has been assumed that their stability is due to the high density of surface-ionized hydroxyl groups, similar in fact to the closely related St?ber silica particles. In this study we confirm, from droplet lifetime studies, that droplets, prepared from such synthesized PDMS, are significantly more stable to coalescence than similar-sized droplets prepared from three types of commercially available PDMS, containing HO-, MeO-, or Me3-terminated chains, respectively. It is shown, however, that the zeta potentials of the synthesized PDMS and of the various commercial oils are all very similar (as indeed are their Hamaker constants). So some other explanation must be inferred for the enhanced stability to coalescence of the synthesized PDMS droplets compared to the commercial PDMS droplets. It is shown, for droplets formed from n-hexane and the synthesized oil, that stability to coalescence is conferred at PDMS volume fractions (phiPDMS) around 0.2 in the mixture. The synthesized PDMS is known to consist of mixtures of cyclic PDMS and short-chain linear species, with terminal -OH groups. There is some (indirect) evidence that in the interval 0.25 < phiPDMS < 0.35, the linear PDMS chains may be adsorbed close to a monolayer at the mixed oil/water interface, possibly conferring some enhanced Gibbs elasticity to the interface. This underpins the possibility that, in the synthesized oil droplets themselves, there is also preferential adsorption of the linear chains at the PDMS/water interface, and this leads to a value of the Gibbs elasticity, sufficient to significantly reduce coalescence. Unfortunately, the Gibbs elasticity could not be measured in this case. However, such preferential adsorption is unlikely to occur with the commercial PDMS oils, which are not so heterogeneous. Finally, it is shown that droplets of the three commercial PDMS oils could be stabilized against coalescence, if a sufficient, minimum amount of sodium dodecyl sulfate (SDS) is added. Gibbs elasticity values have been estimated in these cases, from plots of interfacial tension against ln(SDS concentration).