Stationary Solutions and Connecting Orbits for <Emphasis Type="Italic">p</Emphasis>-Laplace Equation

We deal with one dimensional p-Laplace equation of the form

$$\begin{aligned} u_t = (|u_x|^{p-2} u_x )_x + f(x,u), \ x\in (0,l), \ t>0, \end{aligned}$$

under Dirichlet boundary condition, where \(p>2\) and \(f:[0,l]\times {\mathbb {R}}\rightarrow {\mathbb {R}}\) is a continuous function with \(f(x,0)=0\). We will prove that if there is at least one eigenvalue of the p-Laplace operator between \(\lim _{u\rightarrow 0} f(x,u)/|u|^{p-2}u\) and \(\lim _{|u|\rightarrow +\infty } f(x,u)/|u|^{p-2}u\), then there exists a nontrivial stationary solution. Moreover we show the existence of a connecting orbit between stationary solutions. The results are based on Conley index and detect stationary states even when those based on fixed point theory do not apply. In order to compute the Conley index for nonlinear semiflows deformation along p is used.

     

MicroRNA Delivery by Graphene-Based Complexes into Glioblastoma Cells

Glioblastoma (GBM) is the most common primary and aggressive tumour in brain cancer. Novel therapies, despite achievements in chemotherapy, radiation and surgical techniques, are needed to improve the treatment of GBM tumours and extend patients’ survival. Gene delivery therapy mostly uses the viral vector, which causes serious adverse events in gene therapy. Graphene-based complexes can reduce the potential side effect of viral carries, with high efficiency of microRNA (miRNA) or antisense miRNA delivery to GBM cells. The objective of this study was to use graphene-based complexes to induce deregulation of miRNA level in GBM cancer cells and to regulate the selected gene expression involved in apoptosis. The complexes were characterised by Fourier transform infrared spectroscopy (FTIR), scanning transmission electron microscopy and zeta potential. The efficiency of miRNA delivery to the cancer cells was analysed by flow cytometry. The effect of the anticancer activity of graphene-based complexes functionalised by the miRNA sequence was analysed using 2,3-bis-(2-methoxy-4-nitro-5-sulfophenyl)-2H-tetrazolium-5-carboxyanilide salt (XTT) assays at the gene expression level. The results partly explain the mechanisms of miRNA deregulation stress, which is affected by graphene-based complexes together with the forced transport of mimic miR-124, miR-137 and antisense miR-21, -221 and -222 as an anticancer supportive therapy.     

Photoreactivity of an Exemplary Anthracene Mixture Revealed by NMR Studies,including a Kinetic Approach

Anthracenes are an important class of acenes. They are being utilized more and more often in chemistry and materials sciences, due to their unique rigid molecular structure and photoreactivity. In particular, photodimerization can be harnessed for the fabrication of novel photoresponsive materials. Photodimerization between the same anthracenes have been investigated and utilized in various fields, while reactions between varying anthracenes have barely been investigated. Here, Nuclear Magnetic Resonance (NMR) spectroscopy is employed for the investigation of the photodimerization of two exemplary anthracenes: anthracene (A) and 9-bromoanthracene (B), in the solutions with only A or B, and in the mixture of A and B. Estimated k values, derived from the presented kinetic model, showed that the dimerization of A was 10 times faster in comparison with B when compounds were investigated in separate samples, and 2 times faster when compounds were prepared in the mixture. Notably, the photoreaction in the mixture, apart from AA and BB, additionally yielded a large amount of the AB mixdimer. Another important advantage of investigating a mixture with different anthracenes is the ability to estimate the relative reactivity for all the reactions under the same experimental conditions. This results in a better understanding of the photodimerization processes. Thus, the rational photofabrication of mix-anthracene-based materials can be facilitated, which is of crucial importance in the field of polymer and material sciences.     

Decoding the Fucose Migration Product during Mass-Spectrometric analysis of Blood Group Epitopes

Fucose is a signaling carbohydrate that is attached at the end of glycan processing. It is involved in a range of processes, such as the selectin-dependent leukocyte adhesion or pathogen-receptor interactions. Mass-spectrometric techniques, which are commonly used to determine the structure of glycans, frequently show fucose-containing chimeric fragments that obfuscate the analysis. The rearrangement leading to these fragments—often referred to as fucose migration—has been known for more than 25 years, but the chemical identity of the rearrangement product remains unclear. In this work, we combine ion-mobility spectrometry, radical-directed dissociation mass spectrometry, cryogenic IR spectroscopy of ions, and density-functional theory calculations to deduce the product of the rearrangement in the model trisaccharides Lewis x and blood group H2. The structural search yields the fucose moiety attached to the galactose with an α(1→6) glycosidic bond as the most likely product.