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

Signal processing with Levy information

Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a "message", then under the transformed measure the original Levy process takes on the character of an "information process". In this paper we develop a theory of such Levy information processes. The underlying Levy process, which we call the fiducial process, represents the "noise type". Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian, and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London

The \u3ci\u3eCryptococcus neoformans\u3c/i\u3e Flc1 Homologue Controls Calcium Homeostasis and Confers Fungal Pathogenicity in the Infected Hosts

Cryptococcus neoformans, an opportunistic yeast pathogen, relies on a complex network of stress response pathways that allow for proliferation in the host. In Saccharomyces cerevisiae, stress responses are regulated by integral membrane proteins containing a transient receptor potential (TRP) domain, including the flavin carrier protein 1 (Flc1), which regulates calcium homeostasis and flavin transport. Here, we report that deletion of C. neoformans FLC1 results in cytosolic calcium elevation and increased nuclear content of calcineurin-dependent transcription factor Crz1, which is associated with an aberrant cell wall chitin overaccumulation observed in the flc1Δ mutant. Absence of Flc1 or inhibition of calcineurin with cyclosporine A prevents vacuolar fusion under conditions of combined osmotic and temperature stress, which is reversed in the flc1Δ mutant by the inhibition of TORC1 kinase with rapamycin. Flc1-deficient yeasts exhibit compromised vacuolar fusion under starvation conditions, including conditions that stimulate formation of carbohydrate capsule. Consequently, the flc1Δ mutant fails to proliferate under low nutrient conditions and displays a defect in capsule formation. Consistent with the previously uncharacterized role of Flc1 in vacuolar biogenesis, we find that Flc1 localizes to the vacuole. The flc1Δ mutant presents a survival defect in J774A.1 macrophage cell-line and profound virulence attenuation in both the Galleria mellonella and mouse pulmonary infection models, demonstrating that Flc1 is essential for pathogenicity. Thus, cryptococcal Flc1 functions in calcium homeostasis and links calcineurin and TOR signaling with vacuolar biogenesis to promote survival under conditions associated with vacuolar fusion required for this pathogen’s fitness and virulence

Simulating High-Dimensional Multivariate Data using the bigsimr R Package

It is critical to accurately simulate data when employing Monte Carlo techniques and evaluating statistical methodology. Measurements are often correlated and high dimensional in this era of big data, such as data obtained in high-throughput biomedical experiments. Due to the computational complexity and a lack of user-friendly software available to simulate these massive multivariate constructions, researchers resort to simulation designs that posit independence or perform arbitrary data transformations. To close this gap, we developed the Bigsimr Julia package with R and Python interfaces. This paper focuses on the R interface. These packages empower high-dimensional random vector simulation with arbitrary marginal distributions and dependency via a Pearson, Spearman, or Kendall correlation matrix. bigsimr contains high-performance features, including multi-core and graphical-processing-unit-accelerated algorithms to estimate correlation and compute the nearest correlation matrix. Monte Carlo studies quantify the accuracy and scalability of our approach, up to $d=10,000$. We describe example workflows and apply to a high-dimensional data set -- RNA-sequencing data obtained from breast cancer tumor samples.Comment: 22 pages, 10 figures, https://cran.r-project.org/web/packages/bigsimr/index.htm

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

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

Multisite Phosphorylation of the Guanine Nucleotide Exchange Factor Cdc24 during Yeast Cell Polarization

BACKGROUND:Cell polarization is essential for processes such as cell migration and asymmetric cell division. A common regulator of cell polarization in most eukaryotic cells is the conserved Rho GTPase, Cdc42. In budding yeast, Cdc42 is activated by a single guanine nucleotide exchange factor, Cdc24. The mechanistic details of Cdc24 activation at the onset of yeast cell polarization are unclear. Previous studies have suggested an important role for phosphorylation of Cdc24, which may regulate activity or function of the protein, representing a key step in the symmetry breaking process. METHODOLOGY/PRINCIPAL FINDINGS:Here, we directly ask whether multisite phosphorylation of Cdc24 plays a role in its regulation. We identify through mass spectrometry analysis over thirty putative in vivo phosphorylation sites. We first focus on sites matching consensus sequences for cyclin-dependent and p21-activated kinases, two kinase families that have been previously shown to phosphorylate Cdc24. Through site-directed mutagenesis, yeast genetics, and light and fluorescence microscopy, we show that nonphosphorylatable mutations of these consensus sites do not lead to any detectable consequences on growth rate, morphology, kinetics of polarization, or localization of the mutant protein. We do, however, observe a change in the mobility shift of mutant Cdc24 proteins on SDS-PAGE, suggesting that we have indeed perturbed its phosphorylation. Finally, we show that mutation of all identified phosphorylation sites does not cause observable defects in growth rate or morphology. CONCLUSIONS/SIGNIFICANCE:We conclude that lack of phosphorylation on Cdc24 has no overt functional consequences in budding yeast. Yeast cell polarization may be more tightly regulated by inactivation of Cdc42 by GTPase activating proteins or by alternative methods of Cdc24 regulation, such as conformational changes or oligomerization