Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing in Economics and Finance in Montreal, 14-16 June 2007; at the conference "Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March 2008; et

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

Association of Calcineurin with the COPI Protein Sec28 and the COPII Protein Sec13 Revealed by Quantitative Proteomics

Calcineurin is a calcium-calmodulin-dependent serine/threonine specific protein phosphatase operating in key cellular processes governing responses to extracellular cues. Calcineurin is essential for growth at high temperature and virulence of the human fungal pathogen Cryptococcus neoformans but the underlying mechanism is unknown. We performed a mass spectrometry analysis to identify proteins that associate with the calcineurin A catalytic subunit (Cna1) in C. neoformans cells grown under non-stress and high temperature stress conditions. A novel prioritization strategy for mass spectrometry data from immunoprecipitation experiments identified putative substrates and proteins potentially operating with calcineurin in common pathways. Cna1 co-purified with proteins involved in membrane trafficking including the COPI component Sec28 and the COPII component Sec13. The association of Cna1 with Sec28 and Sec13 was confirmed by co-immunoprecipitation. Cna1 exhibited a dramatic change in subcellular localization during high temperature stress from diffuse cytoplasmic to ER-associated puncta and the mother-bud neck and co-localized with Sec28 and Sec13

De Novo Growth Zone Formation from Fission Yeast Spheroplasts

Eukaryotic cells often form polarized growth zones in response to internal or external cues. To understand the establishment of growth zones with specific dimensions we used fission yeast, which grows as a rod-shaped cell of near-constant width from growth zones located at the cell tips. Removing the cell wall creates a round spheroplast with a disorganized cytoskeleton and depolarized growth proteins. As spheroplasts recover, new growth zones form that resemble normal growing cell tips in shape and width, and polarized growth resumes. Regulators of the GTPase Cdc42, which control width in exponentially growing cells, also control spheroplast growth zone width. During recovery the Cdc42 scaffold Scd2 forms a polarized patch in the rounded spheroplast, demonstrating that a growth zone protein can organize independent of cell shape. Rga4, a Cdc42 GTPase activating protein (GAP) that is excluded from cell tips, is initially distributed throughout the spheroplast membrane, but is excluded from the growth zone after a stable patch of Scd2 forms. These results provide evidence that growth zones with normal width and protein localization can form de novo through sequential organization of cellular domains, and that the size of these growth zones is genetically controlled, independent of preexisting cell shape

Spatial control of Cdc42 signalling by a GM130-RasGRF complex regulates polarity and tumorigenesis

The small GTPase Cdc42 is a key regulator of polarity, but little is known in mammals about its spatial regulation and the relevance of spatial Cdc42 pools for polarity. Here we report the identification of a GM130-RasGRF complex as a regulator of Cdc42 at the Golgi. Silencing GM130 results in RasGRF-dependent inhibition of the Golgi pool of Cdc42, but does not affect Cdc42 at the cell surface. Furthermore, active Cdc42 at the Golgi is important to sustain asymmetric front-rear Cdc42-GTP distribution in directionally migrating cells. Concurrent to Cdc42 inhibition, silencing GM130 also results in RasGRF-dependent Ras-ERK pathway activation. Moreover, depletion of GM130 is sufficient to induce E-cadherin downregulation, indicative of a loss in cell polarity and epithelial identity. Accordingly, GM130 expression is frequently lost in colorectal and breast cancer patients. These findings establish a previously unrecognized role for a GM130-RasGRF-Cdc42 connection in regulating polarity and tumorigenesis

Identification of an Amphipathic Helix Important for the Formation of Ectopic Septin Spirals and Axial Budding in Yeast Axial Landmark Protein Bud3p

Correct positioning of polarity axis in response to internal or external cues is central to cellular morphogenesis and cell fate determination. In the budding yeast Saccharomyces cerevisiae, Bud3p plays a key role in the axial bud-site selection (axial budding) process in which cells assemble the new bud next to the preceding cell division site. Bud3p is thought to act as a component of a spatial landmark. However, it is not clear how Bud3p interacts with other components of the landmark, such as the septins, to control axial budding. Here, we report that overexpression of Bud3p causes the formation of small septin rings (∼1 µm in diameter) and arcs aside from previously reported spiral-like septin structures. Bud3p closely associates with the septins in vivo as Bud3p colocalizes with these aberrant septin structures and forms a complex with two septins, Cdc10p and Cdc11p. The interaction of Bud3p with the septins may involve multiple regions of Bud3p including 1–858, 850–1220, and 1221–1636 a.a. since they all target to the bud neck but exhibit different effects on septin organization when overexpressed. In addition, our study reveals that the axial budding function of Bud3p is mediated by the N-terminal region 1–858. This region shares an amphipathic helix (850–858) crucial for bud neck targeting with the middle portion 850–1103 involved in the formation of ectopic septin spirals and rings. Interestingly, the Dbl-homology domain located in 1–858 is dispensable for axial bud-site selection. Our findings suggest that multiple regions of Bud3p ensure efficient targeting of Bud3p to the bud neck in the assembly of the axial landmark and distinct domains of Bud3p are involved in axial bud-site selection and other cellular processes

Pleiotropic Effects of Deubiquitinating Enzyme Ubp5 on Growth and Pathogenesis of Cryptococcus neoformans

Ubiquitination is a reversible protein modification that influences various cellular processes in eukaryotic cells. Deubiquitinating enzymes remove ubiquitin, maintain ubiquitin homeostasis and regulate protein degradation via the ubiquitination pathway. Cryptococcus neoformans is an important basidiomycete pathogen that causes life-threatening meningoencephalitis primarily in the immunocompromised population. In order to understand the possible influence deubiquitinases have on growth and virulence of the model pathogenic yeast Cryptococcus neoformans, we generated deletion mutants of seven putative deubiquitinase genes. Compared to other deubiquitinating enzyme mutants, a ubp5Δ mutant exhibited severely attenuated virulence and many distinct phenotypes, including decreased capsule formation, hypomelanization, defective sporulation, and elevated sensitivity to several external stressors (such as high temperature, oxidative and nitrosative stresses, high salts, and antifungal agents). Ubp5 is likely the major deubiquitinating enzyme for stress responses in C. neoformans, which further delineates the evolutionary divergence of Cryptococcus from the model yeast S. cerevisiae, and provides an important paradigm for understanding the potential role of deubiquitination in virulence by other pathogenic fungi. Other putative deubiquitinase mutants (doa4Δ and ubp13Δ) share some phenotypes with the ubp5Δ mutant, illustrating functional overlap among deubiquitinating enzymes in C. neoformans. Therefore, deubiquitinating enzymes (especially Ubp5) are essential for the virulence composite of C. neoformans and provide an additional yeast survival and propagation advantage in the host