ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Global Gene Expression Analysis during Germination in the Chytridiomycete Blastocladiella emersonii

Blastocladiella emersonii is an aquatic fungus of the Chytridiomycete class. During germination, the zoospore, a motile nongrowing cell, goes through a cascade of morphological changes that culminates with its differentiation into the germling cell, capable of coenocytic vegetative growth. Transcriptome analyses of B. emersonii cells were carried out during germination induced under various environmental conditions. Microarray data analyzing 3,563 distinct B. emersonii genes revealed that 26% of them are differentially expressed during germination in nutrient medium at at least one of the time points investigated. Over 500 genes are upregulated during the time course of germination under those conditions, most being related to cell growth, including genes involved in protein biosynthesis, DNA transcription, energetic metabolism, carbohydrate and oligopeptide transport, and cell cycle control. On the other hand, several transcripts stored in the zoospores are downregulated during germination in nutrient medium, such as genes involved in signal transduction, amino acid transport, and chromosome organization. In addition, germination induced in the presence of nutrients was compared with that triggered either by adenine or potassium ions in inorganic salt solution. Several genes involved in cell growth, induced during germination in nutrient medium, do not show increased expression when B. emersonii zoospores germinate in inorganic solution, suggesting that nutrients exert a positive effect on gene transcription. The transcriptome data also revealed that most genes involved in cell signaling show the same expression pattern irrespective of the initial germination stimulus.

Metabolic oxidative stress elicited by the copper(II) complex [Cu(isaepy)(2)] triggers apoptosis in SH-SY5Y cells through the induction of the AMP-activated protein kinase/p38(MAPK)/p53 signalling axis: evidence for a combined use with 3-bromopyruvate in neuroblastoma treatment

We have demonstrated previously that the complex bis[(2-oxindol-3-ylimino)-2-(2-aminoethyl)pyridine-N,N`]copper(II), named [Cu(isaepy)(2)], induces AMPK (AMP-activated protein kinase)-dependent/p53-mediated apoptosis in tumour cells by targeting mitochondria. In the present study, we found that p38(MAPK) (p38 mitogen-activated protein kinase) is the molecular link in the phosphorylation cascade connecting AMPK to p53. Transfection of SH-SY5Y cells with a dominant-negative mutant of AMPK resulted in a decrease in apoptosis and a significant reduction in phospho-active p38(MAPK) and p53. Similarly, reverse genetics of p38(MAPK) yielded a reduction in p53 and a decrease in the extent of apoptosis, confirming an exclusive hierarchy of activation that proceeds via AMPK/p38(MAPK)/p53. Fuel supplies counteracted [Cu(isaepy)(2)]-induced apoptosis and AMPK/p38(MAPK)/p53 activation, with glucose being the most effective, suggesting a role for energetic imbalance in [Cu(isaepy)(2)] toxicity. Co-administration of 3BrPA (3-bromopyruvate), a well-known inhibitor of glycolysis, and succinate dehydrogenase, enhanced apoptosis and AMPK/p38(MAPK)/p53 signalling pathway activation. Under these conditions, no toxic effect was observed in SOD (superoxide dismutase)-overexpressing SH-SY5Y cells or in PCNs (primary cortical neurons), which are, conversely, sensitized to the combined treatment with [Cu(isaepy)(2)] and 3BrPA only if grown in low-glucose medium or incubated with the glucose-6-phosphate dehydrogenase inhibitor dehydroepiandrosterone. Overall, the results suggest that NADPH deriving from the pentose phosphate pathway contributes to PCN resistance to [Cu(isaepy)(2)] toxicity and propose its employment in combination with 3BrPA as possible tool for cancer treatment.