The number of open paths in an oriented rho-percolation model

We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.

Rho Signaling Pathway and Apical Constriction in the Early Lens Placode

Epithelial invagination in many model systems is driven by apical cell constriction, mediated by actin and myosin II contraction regulated by GTPase activity. Here we investigate apical constriction during chick lens placode invagination. Inhibition of actin polymerization and myosin II activity by cytochalasin D or blebbistatin prevents lens invagination. To further verify if lens placode invaginate through apical constriction, we analyzed the role of Rho-ROCK pathway. Rho GTPases expression at the apical portion of the lens placode occurs with the same dynamics as that of the cytoskeleton. Overexpression of the pan-Rho inhibitor C3 exotoxin abolished invagination and had a strong effect on apical myosin II enrichment and a mild effect on apical actin localization. In contrast, pharmacological inhibition of ROCK activity interfered significantly with apical enrichment of both actin and myosin. These results suggest that apical constriction in lens invagination involves ROCK but apical concentration of actin and myosin are regulated through different pathways upstream of ROCK. genesis 49: 368-379, 2011. (C) 2011 Wiley-Liss, Inc.

Distribution of small Rho GTPases in the developing rat submandibular gland

During the rat submandibular gland (SMG) development, organogenesis and cytodifferentiation depend on the actin cytoskeleton, which is regulated by small Rho GTPases. These proteins link cell surface receptors to pathways that regulate cell motility, polarity, gene expression, vesicular trafficking, proliferation and apoptosis. The aim of this study was to evaluate, by immunohistochemistry, the distribution pattern of RhoA, RhoB, RhoC, Rac1 and Cdc42 during cytodifferentiation of the rat SMG and in male adults. All GTPases were found in epithelial and mesenchymal tissues throughout gland development. Rac1 appeared to be important for parenchyma expansion at the beginning of cytodifferentiation, while RhoC, Cdc42 and the inactive phosphorylated form of Rac1 seemed associated with lumen formation and cell polarization in terminal tubules. RhoA and RhoB labeling was evident throughout development. All GTPases were differentially expressed in the adult gland, suggesting that they play specific roles during differentiation and function of the rat SMG.

O-GlcNAcylation contributes to the vascular effects of ET-1 via activation of the RhoA/Rho-kinase pathway

Aims Glycosylation with beta-N-acetylglucosamine (O-GlcNAcylation) is one of the most complex post-translational modifications. The cycling of O-GlcNAc is controlled by two enzymes: UDP-NAc transferase (OGT) and O-GlcNAcase (OGA). We recently reported that endothelin-1 (ET-1) augments vascular levels of O-GlcNAcylated proteins. Here we tested the hypothesis that O-GlcNAcylation contributes to the vascular effects of ET-1 via activation of the RhoA/Rho-kinase pathway. Methods and results Incubation of vascular smooth muscle cells (VSMCs) with ET-1 (0.1 mu M) produces a time-dependent increase in O-GlcNAc levels. ET-1-induced O-GlcNAcylation is not observed when VSMCs are previously transfected with OGT siRNA, treated with ST045849 (OGT inhibitor) or atrasentan (ET(A) antagonist). ET-1 as well as PugNAc (OGA inhibitor) augmented contractions to phenylephrine in endothelium-denuded rat aortas, an effect that was abolished by the Rho kinase inhibitor Y-27632. Incubation of VSMCs with ET-1 increased expression of the phosphorylated forms of myosin phosphatase target subunit 1 (MYPT-1), protein kinase C-potentiated protein phosphatase 1 inhibitor protein (protein kinase C-potentiated phosphatase inhibitor-17), and myosin light chain (MLC) and RhoA expression and activity, and this effect was abolished by both OGT siRNA transfection or OGT inhibition and atrasentan. ET-1 also augmented expression of PDZ-Rho GEF (guanine nucleotide exchange factor) and p115-Rho GEF in VSMCs and this was prevented by OGT siRNA, ST045849, and atrasentan. Conclusion We suggest that ET-1 augments O-GlcNAcylation and this modification contributes to increased vascular contractile responses via activation of the RhoA/Rho-kinase pathway.

Catalase-peroxidase activity is decreased in a Caulobacter crescentus rho mutant

A Caulobacter crescentus rho:Tn5 mutant strain presenting a partially functional transcription termination factor Rho is highly sensitive to hydrogen peroxide in both exponential and stationary phases. The mutant was shown to be permanently under oxidative stress, based on fluorophore oxidation, and also to be sensitive to tert-butyl hydroperoxide and paraquat. However, the results showed that the activities of superoxide dismutases CuZnSOD and FeSOD and the alkylhydroperoxide reductase ahpC mRNA levels in the rho mutant were comparable to the wild-type control in the exponential and stationary phases. In contrast, the KatG catalase activity of the rho mutant strain was drastically decreased and did not show the expected increase in the stationary phase compared with the exponential phase. Transcription of the katG gene was increased in the rho mutant and the levels of the immunoreactive KatG protein do not differ considerably compared with the wild type in the stationary phase, suggesting that KatG activity is affected in a translational or a post-translational step.

D*D rho vertex from QCD sum rules

We calculate the form factors and the coupling constant in the D*D rho vertex in the framework of QCD sum rules. We evaluate the three-point correlation functions of the vertex considering D, rho and D* mesons off-shell. The form factors obtained are very different but give the same coupling constant: g(D*D rho) = 4.3 +/- 0.9 GeV(-1). (C) 2011 Elsevier B.V. All rights reserved.

rho D*D* vertex from QCD sum rules

We calculate the form factors and the coupling constant in the rho D*D* vertex in the framework of QCD sum rules. We evaluate the three point correlation functions of the vertex considering both rho and D* mesons off-shell. The form factors obtained are very different but give the same coupling constant: g rho D*D* = 6.60 +/- 0.31. This number is 50% larger than what we would expect from SU(4) estimates. (c) 2007 Elsevier B.V. All rights reserved.

Oriented Percolation in One-dimensional 1/vertical bar x-y vertical bar(2) Percolation Models

We consider independent edge percolation models on Z, with edge occupation probabilities. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104: 547, 1986). The proof is based on multi-scale analysis.

Percolation in a network with long-range connections: Implications for cytoskeletal structure and function

Cell shape, signaling, and integrity depend on cytoskeletal organization. In this study we describe the cytoskeleton as a simple network of filamentary proteins (links) anchored by complex protein structures (nodes). The structure of this network is regulated by a distance-dependent probability of link formation as P = p/d(s), where p regulates the network density and s controls how fast the probability for link formation decays with node distance (d). It was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells. Here we examined the ability of the two-dimensional network to percolate (i.e. to have end-to-end connectivity), and found that the percolation threshold depends strongly on s. The system undergoes a transition around s = 2. The percolation threshold of networks with s < 2 decreases with increasing system size L, while the percolation threshold for networks with s > 2 converges to a finite value. We speculate that s < 2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity. Additionally, we measured the length distribution of F-actin filaments from publicly available images of a variety of cell types. In agreement with model predictions, cells originating from more deformable tissues show longer F-actin cytoskeletal filaments. (C) 2008 Elsevier B.V. All rights reserved.

Collapse of rho (xx) Ringlike Structures in 2DEGs Under Tilted Magnetic Fields

In the quantum Hall regime, the longitudinal resistivity rho (xx) plotted as a density-magnetic-field (n (2D) -B) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [see, e.g., Zhang et al., in Phys. Rev. Lett. 95:216801, 2005. For tilted magnetic fields, some of these ringlike structures ""shrink"" as the tilt angle is increased and fully collapse at theta (c) a parts per thousand 6A degrees. Here we theoretically investigate the topology of these structures via a non-interacting model for the 2DEG. We account for the inter Landau-level coupling induced by the tilted magnetic field via perturbation theory. This coupling results in anticrossings of Landau levels with parallel spins. With the new energy spectrum, we calculate the corresponding n (2D) -B diagram of the density of states (DOS) near the Fermi level. We argue that the DOS displays the same topology as rho (xx) in the n (2D) -B diagram. For the ring with filling factor nu=4, we find that the anticrossings make it shrink for increasing tilt angles and collapse at a large enough angle. Using effective parameters to fit the theta=0A degrees data, we find a collapsing angle theta (c) a parts per thousand 3.6A degrees. Despite this factor-of-two discrepancy with the experimental data, our model captures the essential mechanism underlying the ring collapse.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

On phantom thermodynamics

The thermodynamic properties of dark energy fluids described by an equation of state parameter omega = p/rho are rediscussed in the context of FRW type geometries. Contrarily to previous claims, it is argued here that the phantom regime omega < -1 is not physically possible since that both the temperature and the entropy of every physical fluids must be always positive definite. This means that one cannot appeal to negative temperature in order to save the phantom dark energy hypothesis as has been recently done in the literature. Such a result remains true as long as the chemical potential is zero. However, if the phantom fluid is endowed with a non-null chemical potential, the phantom field hypothesis becomes thermodynamically consistent, that is, there are macroscopic equilibrium states with T > 0 and S > 0 in the course of the Universe expansion. (C) 2008 Elsevier B.V. All rights reserved.

Uranium series disequilibria in ground waters from a fractured bedrock aquifer (Morungaba Granitoids-Southern Brazil): Implications to the hydrochemical behavior of dissolved U and Ra

Activity concentrations of dissolved U-234, U-238, Ra-226 and Ra-228 were determined in ground waters fromtwo deep wells drilled in Morungaba Granitoids (Southern Brazil). Sampling was done monthly for little longer than 1 year. Significant disequilibrium between U-238, U-234 and Ra-226 were observed in all samples. The variation of U-238 and U-234 activity concentrations and U-234/U-238 activity ratios is related to seasonal changes. Although the distance between the two wells is short (about 900m), systematic differences of activity concentrations of U isotopes, as well as of U-234/U-238, Ra-226/U-234 and Ra-228/Ra-226 activity ratios were noticed, indicating distinct host rock-water interactions. Slightly acidic ground water percolation through heterogeneous host rock, associated with different recharge processes, may explain uranium and radium isotope behavior. (c) 2008 Elsevier Ltd. All rights reserved.

Segregation effects according to the evolutionary stage of galaxy groups

We study segregation phenomena in 57 groups selected from the 2dF Percolation-Inferred Galaxy Groups (2PIGG) catalogue of galaxy groups. The sample corresponds to those systems located in areas of at least 80 per cent redshift coverage out to 10 times the radius of the groups. The dynamical state of the galaxy systems was determined after studying their velocity distributions. We have used the Anderson-Darling test to distinguish relaxed and non-relaxed systems. This analysis indicates that 84 per cent of groups have galaxy velocities consistent with the normal distribution, while 16 per cent of them have more complex underlying distributions. Properties of the member galaxies are investigated taking into account this classification. Our results indicate that galaxies in Gaussian groups are significantly more evolved than galaxies in non-relaxed systems out to distances of similar to 4R(200), presenting significantly redder (B - R) colours. We also find evidence that galaxies with M(R) <= -21.5 in Gaussian groups are closer to the condition of energy equipartition.