Computations on Sofic S-gap Shifts

Let $S=\{s_{n}\}$ be an increasing finite or infinite subset of $\mathbb N \bigcup \{0\}$ and $X(S)$ the $S$-gap shift associated to $S$. Let $f_{S}(x)=1-\sum\frac{1}{x^{s_{n}+1}}$ be the entropy function which will be vanished at $2^{h(X(S))}$ where $h(X(S))$ is the entropy of the system. Suppose $X(S)$ is sofic with adjacency matrix $A$ and the characteristic polynomial $\chi_{A}$. Then for some rational function $Q_{S}$, $\chi_{A}(x)=Q_{S}(x)f_{S}(x)$. This $Q_{S}$ will be explicitly determined. We will show that $\zeta(t)=\frac{1}{f_{S}(t^{-1})}$ or $\zeta(t)=\frac{1}{(1-t)f_{S}(t^{-1})}$ when $|S|<\infty$ or $|S|=\infty$ respectively. Here $\zeta$ is the zeta function of $X(S)$. We will also compute the Bowen-Franks groups of a sofic $S$-gap shift.Comment: This paper has been withdrawn due to extending results about SFT shifts to sofic shifts (Theorem 2.3). This forces to apply some minor changes in the organization of the paper. This paper has been withdrawn due to a flaw in the description of the adjacency matrix (2.3

Computability and dynamical systems

In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler task of proving mathematical results. Nevertheless, there have been some recent developments in the latter direction. Here we introduce some of the ideas and techniques used so far, and suggest some lines of research for further work on this fascinating topic

Unprecedented staining of polar lipids by a luminescent rhenium complex revealed by FTIR microspectroscopy in adipocytes.

Fourier transform infrared (FTIR) microspectroscopy and confocal imaging have been used to demonstrate that the neutral rhenium(i) tricarbonyl 1,10-phenanthroline complex bound to 4-cyanophenyltetrazolate as the ancillary ligand is able to localise in regions with high concentrations of polar lipids such as phosphatidylethanolamine (PE), sphingomyelin, sphingosphine and lysophosphatidic acid (LPA) in mammalian adipocytes

Exogenous Ether Lipids Predominantly Target Mitochondria

Ether lipids are ubiquitous constituents of cellular membranes with no discrete cell biological function assigned yet. Using fluorescent polyene-ether lipids we analyzed their intracellular distribution in living cells by microscopy. Mitochondria and the endoplasmic reticulum accumulated high amounts of ether-phosphatidylcholine and ether-phosphatidylethanolamine. Both lipids were specifically labeled using the corresponding lyso-ether lipids, which we established as supreme precursors for lipid tagging. Polyfosine, a fluorescent analogue of the anti-neoplastic ether lipid edelfosine, accumulated to mitochondria and induced morphological changes and cellular apoptosis. These data indicate that edelfosine could exert its pro-apoptotic power by targeting and damaging mitochondria and thereby inducing cellular apoptosis. In general, this study implies an important role of mitochondria in ether lipid metabolism and intracellular ether lipid trafficking

Loss of the interferon-γ-inducible regulatory immunity-related GTPase (IRG), Irgm1, causes activation of effector IRG proteins on lysosomes, damaging lysosomal function and predicting the dramatic susceptibility of Irgm1-deficient mice to infection

The interferon-γ (IFN-γ)-inducible immunity-related GTPase (IRG), Irgm1, plays an essential role in restraining activation of the IRG pathogen resistance system. However, the loss of Irgm1 in mice also causes a dramatic but unexplained susceptibility phenotype upon infection with a variety of pathogens, including many not normally controlled by the IRG system. This phenotype is associated with lymphopenia, hemopoietic collapse, and death of the mouse.Deutscher Akademischer Austausch Dienst (DAAD); International Graduate School in Development Health and Disease (IGS-DHD); Deutsche For-schungsgemeinschaft (SFBs 635, 670, 680); Max-Planck-Gesellschaft (Max Planck Fellowship)

Cell biology of lipid droplets

Lipid storage has attracted much attention in the past years, both by the broader public and the biomedical scientific community. Driven by concerns about the obesity epidemic that affects most industrialized countries and even substantial parts of the population in less and least developed countries, work from researchers of many disciplines has shed light on the genetics, the physiology, and the cellular mechanisms of fat accumulation. This review focuses on the actual organelle of fat deposition, the lipid droplet (LD), and on the recent progress in mechanistic understanding of processes like LD biogenesis, LD growth and degradation, protein targeting to LDs and LD fusion

Live cell multicolor imaging of lipid droplets with a new dye, LD540

A lipophilic dye based on the Bodipy fluorophore, LD540, was developed for microscopic imaging of lipid droplets. In contrast to previous lipid droplet dyes, it can spectrally be resolved from both green and red fluorophores allowing multicolor imaging in both fixed and living cells. Its improved specificity, brightness and photostability support live cell imaging, which was used to demonstrate by two-color imaging lipid droplet motility along microtubules

Tracing fatty acid metabolism by click chemistry.

Fatty acids are abundant constituents of all biological systems, and their metabolism is important for normal function at all levels of an organism. Aberrations in fatty acid metabolism are associated with pathological states and have become a focus of current research, particularly due to the interest in metabolic overload diseases. Here we present a click-chemistry-based method that allows tracing of fatty acid metabolism in virtually any biological system. It combines high sensitivity with excellent linearity and fast sample turnover. Since it is free of radioactivity, it can be combined with any other modern analysis technology and can be used in high-throughput applications. Using the new method, we provide for the first time an analysis of cellular fatty metabolism with high time resolution and a comprehensive comparison of utilization of a broad spectrum of fatty acids in hepatoma and adipose cell lines