Topological structure preserving numerical simulations of dynamical models

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined application.     

Contributions to the mathematics of the nonstandard finite difference method and applications

We formalize the transfer of essential properties of the solution of a differential equation to the solution of a discrete scheme as qualitative stability with respect to the properties. This permits us to motivate some rules (viz. on the order of the difference equation, on the renormalization of the denominator of the discrete derivative, and on nonlocal approximation of nonlinear terms) used in the design of nonstandard finite difference schemes. Extensions of some models are considered, and numerical examples confirming the efficiency of the nonstandard approach are provided. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 518–543, 2001     

Ferroelectric phase transitions near ionic liquid/vacuum interfaces

A simple theoretical model is developed describing ionic liquids as regular solutions. The separation of these ionic mixtures is studied on the base of the Cahn-Hilliard theory coupled with electrostatics. It is shown that the ionic liquids decompose to thin layers of oppositely charged liquids at low temperatures. At larger temperatures the separation occurs only near the ionic liquid/vacuum surface, thus explaining the oscillatory-decaying structure of the electric double layer observed via computer simulations. In contrast to noncharged liquids the ionic ones exhibit two critical temperatures, where the temperature coefficients of all characteristic lengths possess singularities. These second order ferroelectric phase transitions are possible explanations of the experimentally measured via light scattering peculiar temperature dependence of the interfacial dipole moment density on several ionic liquid/vacuum interfaces.     

Structural organization of plasma membrane lipids isolated from cells cultured as a monolayer and in tissue-like conditions

In this paper, folate conjugated poly(ε-caprolactone-co-4-maleate-ε-caprolactone) (P(CL-co-MCL)-folate) was prepared by a carbodiimide coupling reaction, i.e., the vitamin folic acid (FA) was covalently linked to the main chain of the maleate-functionalized polymer, poly(ε-caprolactone-co-4-maleate-ε-caprolactone) (P(CL-co-MCL)). Then the 5-Fluorouracil (5-FU) loaded nanoparticles of P(CL-co-MCL)-folate were achieved by solvent-evaporation method. Their properties were extensively studied by dynamic light scattering (DLS) and scan electron microscopy (SEM). DLS and SEM showed that the nanoparticles were in a well-defined spherical shape with a uniform size distribution. We also investigated the entrapment and in vitro release behavior, which indicated that the release speed of 5-FU could be well controlled and the release half-life period could reach 16.86h, which was 26.4 times longer than that of pure 5-FU. The in vitro targeting test displayed that the 5-FU loaded P(CL-co-MCL)-folate nanoparticles exhibited an enhanced cell inhibition because folate targeting increased the concentration of 5-FU loaded P(CL-co-MCL)-folate nanoparticles in the tumor cells with folate receptor overexpressed. Meanwhile, the tumor inhibition of 5-FU loaded P(CL-co-MCL)-folate nanoparticles was much higher than that of pure 5-FU and that of 5-FU loaded P(CL-co-MCL) nanoparticles. Therefore, P(CL-co-MCL)-folate nanoparticles would be highly beneficial for biomedical and pharmaceutical applications.     

Application of a ligand-based theoretical approach to derive conversion paths and ligand conformations in CYP11B2-mediated aldosterone formation

The biosynthesis of the mineralocorticoid hormone aldosterone involves a multistep hydroxylation of 11-deoxycorticosterone at the 11- and 18-positions, resulting in the formation of corticosterone and 18-hydroxycorticosterone, the final precursor of aldosterone. Two members of the cytochrome P450 11B family, CYP11B1 and CYP11B2, are known to catalyze these 11- and 18-hydroxylations, however, only CYP11B2 can oxidize 18-hydroxycorticosterone to aldosterone. It is unknown what sequence of hydroxylations leads to the formation of 18-hydroxycorticosterone. In this study we have investigated which of the possible conversion paths towards formation of 18-hydroxycorticosterone and aldosterone are most likely from the ligand perspective. Therefore, we combined quantum mechanical investigations on the steroid conformations of 11-deoxycorticosterone and its ensuing reaction intermediates with Fukui indices calculations to predict the reactivity of their carbon atoms for an attack by the iron-oxygen species. Both F(-) and F(0) were calculated to account for different mechanisms of substrate conversion. We show which particular initial conformations of 11-deoxycorticosterone and which conversion paths are likely to result in the successful synthesis of aldosterone, and thereby may be representative for the mechanism of aldosterone biosynthesis by CYP11B2. Moreover, we found that the most likely path for aldosterone synthesis coincides with the substrate conformation proposed in an earlier publication. To summarize, we show that on a theoretical and strictly ligand-directed basis only a limited number of reaction paths in the conversion of 11-deoxycorticosterone to aldosterone is possible. Despite its theoretical nature, this knowledge may help to understand the catalytic function of CYP11B1 and CYP11B2.     

Adsorptive Stripping Voltammetric Determination of 2,4-Dichlorophenol by Laponite Modified Carbon Paste Electrode

A laponite modified carbon paste electrode was prepared, characterized and applied for the 2,4-dichlorophenol (2,4-DCP) voltammetric determination. It takes advantage of the ability of laponite to adsorb phenols, as well as of its availability and very low cost. Kinetic and equilibrium data for 2,4-DCP adsorption by laponite in aqueous dispersions demonstrated that the adsorption process obeyed a pseudo first order kinetic model and was consistent with the formation of adsorbed multilayers on a surface with heterogeneous pore distribution. The composite paste electrode exhibited a heterogeneous surface with 65 % increased surface area and 27 % enhanced catalytic activity compared to the unmodified one. The adsorptive stripping voltammetric determination of 2,4-DCP at an electrode with an optimized graphite:laponite ratio of 55 : 15 w% using a 3 min accumulation time at pH 5.5 was found to be suitable for its quantification in the linear concentration range extended up to 50 μmol L⁻¹ with a sensitivity of 0.56 μA L μmol⁻¹ and a LOD of 0.2 μmol L⁻¹ (S/N=3).The 2,4-DCP electrochemical response was not affected by the presence of some structurally similar phenols, like catechol and p-nitrophenol, while resorcinol, 2-chlorophenol, and 4-chlorophenol presented interferences. The results were validated by 2,4-DCP determination in spiked tap water.     

Oscillatory wetting instability induced by liquid-liquid decomposition in a Ga--Pb alloy

We present the first experimental investigation and pertinent theoretical modeling of an interfacial oscillatory instability in a binary fluid alloy, the Ga-Pb system. It is characterized by spinodal decomposition at elevated temperatures and by a complete wetting transition at liquid-liquid coexistence. For the alloy Ga(0.95)Pb(0.05) the fluid interface has been probed by second harmonic generation (SHG) under UHV conditions at temperatures between 740 and 550 K. At conditions inside the miscibility gap clear oscillations of the SHG-intensity with a period of approximately 30 min are found for different cooling cycles and also at constant temperatures. These interfacial oscillatory instabilities simultaneously induce temperature oscillations in the bulk fluid with the same period. This phenomenon can be explained by a periodic variation of the fluid interfacial emissivity. A model has been developed which describes the wetting-dewetting dynamics by hydrodynamic equations within the Reynolds approximation. It is found that the interfacial oscillatory instability is determined by capillary-gravitation instability. The model quantitatively describes the time evolution of the interfacial and temperature oscillations and gives the correct value of the oscillation period. A detailed comparison of the experimental and model results is given.     

Detection of tetracysteine-tagged proteins using a biarsenical fluorescein derivative through dry microplate array gel electrophoresis

The design of an extended-run 96-well sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) system and the development of protein detection technology based upon fluorescein derivatives that bind to peptide epitope tags, allows the creation of a truly high-throughput analysis of protein expression, where less than 20 min are needed to separate proteins and analyze results. We demonstrate the overall capabilities of such a method combination in a complex cell lysate background, while comparing the specific results obtained using a biarsenical fluorescein-derivative and tetracysteine epitope-tagged proteins with total protein staining using a fluorescent gel stain and with Western blotting where an anti-oligohistidine (His) tag antibody has been employed. When applied on purified target proteins without extraneous protein background, the demonstrated sensitivity of the assay on the extended-run 96-array precast SDS-PAGE system allows detection of quantities of tagged protein as low as 1 pmol per band.     

Chemical composition of propolis from Canada, its antiradical activity and plant origin

The chemical composition of propolis from two regions in Canada was studied: Boreal forest and the Pacific coastal forest that lie outside the area of distribution of Aigeiros poplars, the usual propolis source plants. In the sample from Victoria, p-hydroxyacetophenone, benzyl hydroxybenzoate and cinnamic acid were the major components, accompanied by significant amounts of dihydrochalcones, which allowed the identification of its plant source: Populus trichocarpa of section Tacamahaca. Three dihydrochalcones were new for propolis. The sample from Richmond was characterized by large amounts of p-coumaric and cinnamic acid, typical for poplars of section Leuce, subsection Trepidae, its plant source was identified as P. tremuloides. Both samples showed a good radical scavenging activity against DPPH. Obviously, the Northern type propolis is a promising potential source of biologically active substances and deserves further investigation.