Consensus over Random Graph Processes: Network Borel-Cantelli Lemmas for Almost Sure Convergence

Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step, every node updates its state based on a Bernoulli trial, independent in time and among different nodes: either averaging among the neighbor set generated by the random graph, or sticking with its current state. Connectivity-independence and arc-independence are introduced to capture the fundamental influence of the random graphs on the consensus convergence. Necessary and/or sufficient conditions are presented on the success probabilities of the Bernoulli trials for the network to reach a global almost sure consensus, with some sharp threshold established revealing a consensus zero-one law. Convergence rates are established by lower and upper bounds of the $\epsilon$-computation time. We also generalize the concepts of connectivity/arc independence to their analogues from the $*$-mixing point of view, so that our results apply to a very wide class of graphical models, including the majority of random graph models in the literature, e.g., Erd\H{o}s-R\'{e}nyi, gossiping, and Markovian random graphs. We show that under $*$-mixing, our convergence analysis continues to hold and the corresponding almost sure consensus conditions are established. Finally, we further investigate almost sure finite-time convergence of random gossiping algorithms, and prove that the Bernoulli trials play a key role in ensuring finite-time convergence. These results add to the understanding of the interplay between random graphs, random computations, and convergence probability for distributed information processing.Comment: IEEE Transactions on Information Theory, In Pres

Caffeine as a tool for investigating the integration of Cdc25 phosphorylation, activity and ubiquitin-dependent degradation in Schizosaccharomyces pombe

The evolutionarily conserved Cdc25 phosphatase is an essential protein that removes inhibitory phosphorylation moieties on the mitotic regulator Cdc2. Together with the Wee1 kinase, a negative regulator of Cdc2 activity, Cdc25 is thus a central regulator of cell cycle progression in Schizosaccharomyces pombe. The expression and activity of Cdc25 is dependent on the activity of the Target of Rapamycin Complex 1 (TORC1). TORC1 inhibition leads to the activation of Cdc25 and repression of Wee1, leading to advanced entry into mitosis. Withdrawal of nitrogen leads to rapid Cdc25 degradation via the ubiquitin- dependent degradation pathway by the Pub1 E3- ligase. Caffeine is believed to mediate the override of DNA damage checkpoint signalling, by inhibiting the activity of the ataxia telangiectasia mutated (ATM)/Rad3 homologues. This model remains controversial, as TORC1 appears to be the preferred target of caffeine in vivo. Recent studies suggest that caffeine induces DNA damage checkpoint override by inducing the nuclear accumulation of Cdc25 in S. pombe. Caffeine may thus modulate Cdc25 activity and stability via inhibition of TORC1. A clearer understanding of the mechanisms by which caffeine stabilises Cdc25, may provide novel insights into how TORC1 and DNA damage signalling is integrated

Redundant Mechanisms Prevent Mitotic Entry Following Replication Arrest in the Absence of Cdc25 Hyper-Phosphorylation in Fission Yeast

Following replication arrest the Cdc25 phosphatase is phosphorylated and inhibited by Cds1. It has previously been reported that expressing Cdc25 where 9 putative amino-terminal Cds1 phosphorylation sites have been substituted to alanine results in bypass of the DNA replication checkpoint. However, these results were acquired by expression of the phosphorylation mutant using a multicopy expression vector in a genetic background where the DNA replication checkpoint is intact. In order to clarify these results we constructed a Cdc25(9A)-GFP native promoter integrant and examined its effect on the replication checkpoint at endogenous expression levels. In this strain the replication checkpoint operates normally, conditional on the presence of the Mik1 kinase. In response to replication arrest the Cdc25(9A)-GFP protein is degraded, suggesting the presence of a backup mechanism to eliminate the phosphatase when it cannot be inhibited through phosphorylation

Importance of a C-Terminal Conserved Region of Chk1 for Checkpoint Function

BACKGROUND: The protein kinase Chk1 is an essential component of the DNA damage checkpoint pathway. Chk1 is phosphorylated and activated in the fission yeast Schizosaccharomyces pombe when cells are exposed to agents that damage DNA. Phosphorylation, kinase activation, and nuclear accumulation are events critical to the ability of Chk1 to induce a transient delay in cell cycle progression. The catalytic domain of Chk1 is well-conserved amongst all species, while there are only a few regions of homology within the C-terminus. A potential pseudosubstrate domain exists in the C-terminus of S. pombe Chk1, raising the possibility that the C-terminus acts to inhibit the catalytic domain through interaction of this domain with the substrate binding site. METHODOLOGY/PRINCIPAL FINDINGS: To evaluate this hypothesis, we characterized mutations in the pseudosubstrate region. Mutation of a conserved aspartic acid at position 469 to alanine or glycine compromises Chk1 function when the mutants are integrated as single copies, demonstrating that this domain of Chk1 is critical for function. Our data does not support, however, the hypothesis that the domain acts to inhibit Chk1 function as other mutations in the amino acids predicted to comprise the pseudosubstrate do not result in constitutive activation of the protein. When expressed in multi-copy, Chk1D469A remains non-functional. In contrast, multi-copy Chk1D469G confers cell survival and imposes a checkpoint delay in response to some, though not all forms of DNA damage. CONCLUSIONS/SIGNIFICANCE: Thus, we conclude that this C-terminal region of Chk1 is important for checkpoint function and predict that a limiting factor capable of associating with Chk1D469G, but not Chk1D469A, interacts with Chk1 to elicit checkpoint activation in response to a subset of DNA lesions

Parvovirus Minute Virus of Mice Induces a DNA Damage Response That Facilitates Viral Replication

Infection by DNA viruses can elicit DNA damage responses (DDRs) in host cells. In some cases the DDR presents a block to viral replication that must be overcome, and in other cases the infecting agent exploits the DDR to facilitate replication. We find that low multiplicity infection with the autonomous parvovirus minute virus of mice (MVM) results in the activation of a DDR, characterized by the phosphorylation of H2AX, Nbs1, RPA32, Chk2 and p53. These proteins are recruited to MVM replication centers, where they co-localize with the main viral replication protein, NS1. The response is seen in both human and murine cell lines following infection with either the MVMp or MVMi strains. Replication of the virus is required for DNA damage signaling. Damage response proteins, including the ATM kinase, accumulate in viral-induced replication centers. Using mutant cell lines and specific kinase inhibitors, we show that ATM is the main transducer of the signaling events in the normal murine host. ATM inhibitors restrict MVM replication and ameliorate virus-induced cell cycle arrest, suggesting that DNA damage signaling facilitates virus replication, perhaps in part by promoting cell cycle arrest. Thus it appears that MVM exploits the cellular DNA damage response machinery early in infection to enhance its replication in host cells

Comparative analysis of rosaceous genomes and the reconstruction of a putative ancestral genome for the family

Abstract Background Comparative genome mapping studies in Rosaceae have been conducted until now by aligning genetic maps within the same genus, or closely related genera and using a limited number of common markers. The growing body of genomics resources and sequence data for both Prunus and Fragaria permits detailed comparisons between these genera and the recently released Malus × domestica genome sequence. Results We generated a comparative analysis using 806 molecular markers that are anchored genetically to the Prunus and/or Fragaria reference maps, and physically to the Malus genome sequence. Markers in common for Malus and Prunus, and Malus and Fragaria, respectively were 784 and 148. The correspondence between marker positions was high and conserved syntenic blocks were identified among the three genera in the Rosaceae. We reconstructed a proposed ancestral genome for the Rosaceae. Conclusions A genome containing nine chromosomes is the most likely candidate for the ancestral Rosaceae progenitor. The number of chromosomal translocations observed between the three genera investigated was low. However, the number of inversions identified among Malus and Prunus was much higher than any reported genome comparisons in plants, suggesting that small inversions have played an important role in the evolution of these two genera or of the Rosaceae.Apple genome research at FEM is supported by the research office of the Provincia autonoma di Trento. DJS and ELG acknowledge a grant from the East Malling Trust. Fragaria genomics at EMR is funded by the BBSRC. JMB is supported by a grant by Plant & Food Research's Excellence Programme. Apple genomics at Plant & Food Research is partially supported by the New Zealand Foundation for Research Science and Technology project C06X0812 "Exploiting Opportunities from Horticultural Genomics". Research conducted at IRTA was partly funded by the CONSOLIDER-INGENIO 2010 Program (CSD2007-00036) and project INIA-RTA2007-00063-00-00, both from the Spanish Ministry of Science and Innovation. RosCOS development at OSU/MSU was funded by the National Research Initiative Competitive Grant 2005-35300-15454 of USDA's National Institute of Food and Agriculture.Peer Reviewe

Gene expression patterns associated with blood-feeding in the malaria mosquito Anopheles gambiae

BACKGROUND: Blood feeding, or hematophagy, is a behavior exhibited by female mosquitoes required both for reproduction and for transmission of pathogens. We determined the expression patterns of 3,068 ESTs, representing ~2,000 unique gene transcripts using cDNA microarrays in adult female Anopheles gambiae at selected times during the first two days following blood ingestion, at 5 and 30 min during a 40 minute blood meal and at 0, 1, 3, 5, 12, 16, 24 and 48 hours after completion of the blood meal and compared their expression to transcript levels in mosquitoes with access only to a sugar solution. RESULTS: In blood-fed mosquitoes, 413 unique transcripts, approximately 25% of the total, were expressed at least two-fold above or below their levels in the sugar-fed mosquitoes, at one or more time points. These differentially expressed gene products were clustered using k-means clustering into Early Genes, Middle Genes, and Late Genes, containing 144, 130, and 139 unique transcripts, respectively. Several genes from each group were analyzed by quantitative real-time PCR in order to validate the microarray results. CONCLUSION: The expression patterns and annotation of the genes in these three groups (Early, Middle, and Late genes) are discussed in the context of female mosquitoes' physiological responses to blood feeding, including blood digestion, peritrophic matrix formation, egg development, and immunity

Gaia Data Release 2 Mapping the Milky Way disc kinematics

Context. The second Gaia data release (Gaia DR2) contains high-precision positions, parallaxes, and proper motions for 1.3 billion sources as well as line-of-sight velocities for 7.2 million stars brighter than G(RVS) = 12 mag. Both samples provide a full sky coverage. Aims. To illustrate the potential of Gaia DR2, we provide a first look at the kinematics of the Milky Way disc, within a radius of several kiloparsecs around the Sun. Methods. We benefit for the first time from a sample of 6.4 million F-G-K stars with full 6D phase-space coordinates, precise parallaxes (sigma((omega) over bar)/(omega) over bar Results. Gaia DR2 allows us to draw 3D maps of the Galactocentric median velocities and velocity dispersions with unprecedented accuracy, precision, and spatial resolution. The maps show the complexity and richness of the velocity field of the galactic disc. We observe streaming motions in all the components of the velocities as well as patterns in the velocity dispersions. For example, we confirm the previously reported negative and positive galactocentric radial velocity gradients in the inner and outer disc, respectively. Here, we see them as part of a non-axisymmetric kinematic oscillation, and we map its azimuthal and vertical behaviour. We also witness a new global arrangement of stars in the velocity plane of the solar neighbourhood and in distant regions in which stars are organised in thin substructures with the shape of circular arches that are oriented approximately along the horizontal direction in the U - V plane. Moreover, in distant regions, we see variations in the velocity substructures more clearly than ever before, in particular, variations in the velocity of the Hercules stream. Conclusions. Gaia DR2 provides the largest existing full 6D phase-space coordinates catalogue. It also vastly increases the number of available distances and transverse velocities with respect to Gaia DR1. Gaia DR2 offers a great wealth of information on the Milky Way and reveals clear non-axisymmetric kinematic signatures within the Galactic disc, for instance. It is now up to the astronomical community to explore its full potential.Peer reviewe