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

Variability in the Dynamics of Mortality and Immobility Responses of Freshwater Arthropods Exposed to Chlorpyrifos

The species sensitivity distribution (SSD) concept is an important probabilistic tool for environmental risk assessment (ERA) and accounts for differences in species sensitivity to different chemicals. The SSD model assumes that the sensitivity of the species included is randomly distributed. If this assumption is violated, indicator values, such as the 50% hazardous concentration, can potentially change dramatically. Fundamental research, however, has discovered and described specific mechanisms and factors influencing toxicity and sensitivity for several model species and chemical combinations. Further knowledge on how these mechanisms and factors relate to toxicologic standard end points would be beneficial for ERA. For instance, little is known about how the processes of toxicity relate to the dynamics of standard toxicity end points and how these may vary across species. In this article, we discuss the relevance of immobilization and mortality as end points for effects of the organophosphate insecticide chlorpyrifos on 14 freshwater arthropods in the context of ERA. For this, we compared the differences in response dynamics during 96 h of exposure with the two end points across species using dose response models and SSDs. The investigated freshwater arthropods vary less in their immobility than in their mortality response. However, differences in observed immobility and mortality were surprisingly large for some species even after 96 h of exposure. As expected immobility was consistently the more sensitive end point and less variable across the tested species and may therefore be considered as the relevant end point for population of SSDs and ERA, although an immobile animal may still potentially recover. This is even more relevant because an immobile animal is unlikely to survive for long periods under field conditions. This and other such considerations relevant to the decision-making process for a particular end point are discussed

SUMO-Targeted Ubiquitin Ligase, Rad60, and Nse2 SUMO Ligase Suppress Spontaneous Top1–Mediated DNA Damage and Genome Instability

Through as yet undefined proteins and pathways, the SUMO-targeted ubiquitin ligase (STUbL) suppresses genomic instability by ubiquitinating SUMO conjugated proteins and driving their proteasomal destruction. Here, we identify a critical function for fission yeast STUbL in suppressing spontaneous and chemically induced topoisomerase I (Top1)–mediated DNA damage. Strikingly, cells with reduced STUbL activity are dependent on tyrosyl–DNA phosphodiesterase 1 (Tdp1). This is notable, as cells lacking Tdp1 are largely aphenotypic in the vegetative cell cycle due to the existence of alternative pathways for the removal of covalent Top1–DNA adducts (Top1cc). We further identify Rad60, a SUMO mimetic and STUbL-interacting protein, and the SUMO E3 ligase Nse2 as critical Top1cc repair factors in cells lacking Tdp1. Detection of Top1ccs using chromatin immunoprecipitation and quantitative PCR shows that they are elevated in cells lacking Tdp1 and STUbL, Rad60, or Nse2 SUMO ligase activity. These unrepaired Top1ccs are shown to cause DNA damage, hyper-recombination, and checkpoint-mediated cell cycle arrest. We further determine that Tdp1 and the nucleotide excision repair endonuclease Rad16-Swi10 initiate the major Top1cc repair pathways of fission yeast. Tdp1-based repair is the predominant activity outside S phase, likely acting on transcription-coupled Top1cc. Epistasis analyses suggest that STUbL, Rad60, and Nse2 facilitate the Rad16-Swi10 pathway, parallel to Tdp1. Collectively, these results reveal a unified role for STUbL, Rad60, and Nse2 in protecting genome stability against spontaneous Top1-mediated DNA damage

Healthy ageing of cloned sheep

The health of cloned animals generated by somatic-cell nuclear transfer (SCNT) has been of concern since its inception; however, there are no detailed assessments of late-onset, non-communicable diseases. Here we report that SCNT has no obvious detrimental longterm health effects in a cohort of 13 cloned sheep. We perform musculoskeletal assessments, metabolic tests and blood pressure measurements in 13 aged (7–9 years old) cloned sheep, including four derived from the cell line that gave rise to Dolly. We also perform radiological examinations of all main joints, including the knees, the joint most affected by osteoarthritis in Dolly, and compare all health parameters to groups of 5- and 6-year-old sheep, and published reference ranges. Despite their advanced age, these clones are euglycaemic, insulin sensitive and normotensive. Importantly, we observe no clinical signs of degenerative joint disease apart from mild, or in one case moderate, osteoarthritis in some animals. Our study is the first to assess the long-term health outcomes of SCNT in large animals

Correlation of LNCR rasiRNAs Expression with Heterochromatin Formation during Development of the Holocentric Insect Spodoptera frugiperda

Repeat-associated small interfering RNAs (rasiRNAs) are derived from various genomic repetitive elements and ensure genomic stability by silencing endogenous transposable elements. Here we describe a novel subset of 46 rasiRNAs named LNCR rasiRNAs due to their homology with one long non-coding RNA (LNCR) of Spodoptera frugiperda. LNCR operates as the intermediate of an unclassified transposable element (TE-LNCR). TE-LNCR is a very invasive transposable element, present in high copy numbers in the S. frugiperda genome. LNCR rasiRNAs are single-stranded RNAs without a prominent nucleotide motif, which are organized in two distinct, strand-specific clusters. The expression of LNCR and LNCR rasiRNAs is developmentally regulated. Formation of heterochromatin in the genomic region where three copies of the TE-LNCR are embedded was followed by chromatin immunoprecipitation (ChIP) and we observed this chromatin undergo dynamic changes during development. In summary, increased LNCR expression in certain developmental stages is followed by the appearance of a variety of LNCR rasiRNAs which appears to correlate with subsequent accumulation of a heterochromatic histone mark and silencing of the genomic region with TE-LNCR. These results support the notion that a repeat-associated small interfering RNA pathway is linked to heterochromatin formation and/or maintenance during development to establish repression of the TE-LNCR transposable element. This study provides insights into the rasiRNA silencing pathway and its role in the formation of fluctuating heterochromatin during the development of one holocentric organism

Testing the Mid-Holocene Relative Sea-Level Highstand Hypothesis in North Wales, United Kingdom

Accurate Holocene relative sea-level curves are vital for modelling future sea-level changes, particularly in regions where relative sea-level changes are dominated by isostatically induced vertical land movements. In North Wales, various glacial isostatic adjustment (GIA) models predict a mid-Holocene relative sea-level highstand between 4 and 6 ka, which is unsubstantiated by any geological sea-level data but affects the ability of geophysical models to model accurately past and future sea levels. Here, we use a newly developed foraminifera-based sea-level transfer function to produce a 3300-year-long late-Holocene relative sea-level reconstruction from a salt marsh in the Malltraeth estuary on the south Anglesey coast in North Wales. This is the longest continuous late-Holocene relative sea-level reconstruction in Northwest Europe. We combine this record with two new late-Holocene sea-level index points (SLIPs) obtained from a freshwater marsh at Rhoscolyn, Anglesey, and with previously published regional SLIPs, to produce a relative sea-level record for North Wales that spans from ca. 13,000 BP to the present. This record leaves no room for a mid-Holocene relative sea-level highstand in the region. We conclude that GIA models that include a mid-Holocene sea-level highstand for North Wales need revision before they are used in the modelling of past and future relative sea-level changes around the British Isles

PCNA ubiquitylation ensures timely completion of unperturbed DNA replication in fission yeast

PCNA ubiquitylation on lysine 164 is required for DNA damage tolerance. In many organisms PCNA is also ubiquitylated in unchallenged S phase but the significance of this has not been established. Using Schizosaccharomyces pombe, we demonstrate that lysine 164 ubiquitylation of PCNA contributes to efficient DNA replication in the absence of DNA damage. Loss of PCNA ubiquitylation manifests most strongly at late replicating regions and increases the frequency of replication gaps. We show that PCNA ubiquitylation increases the proportion of chromatin associated PCNA and the co-immunoprecipitation of Polymerase δ with PCNA during unperturbed replication and propose that ubiquitylation acts to prolong the chromatin association of these replication proteins to allow the efficient completion of Okazaki fragment synthesis by mediating gap filling

Schizosaccharomyces pombe Ofd2 Is a Nuclear 2-Oxoglutarate and Iron Dependent Dioxygenase Interacting with Histones

2-oxoglutarate (2OG) dependent dioxygenases are ubiquitous iron containing enzymes that couple substrate oxidation to the conversion of 2OG to succinate and carbon dioxide. They participate in a wide range of biological processes including collagen biosynthesis, fatty acid metabolism, hypoxic sensing and demethylation of nucleic acids and histones. Although substantial progress has been made in elucidating their function, the role of many 2OG dioxygenases remains enigmatic. Here we have studied the 2OG and iron (Fe(II)) dependent dioxygenase Ofd2 in Schizosaccharomyces pombe, a member of the AlkB subfamily of dioxygenases. We show that decarboxylation of 2OG by recombinant Ofd2 is dependent on Fe(II) and a histidine residue predicted to be involved in Fe(II) coordination. The decarboxylase activity of Ofd2 is stimulated by histones, and H2A has the strongest effect. Ofd2 interacts with all four core histones, however, only very weakly with H4. Our results define a new subclass of AlkB proteins interacting with histones, which also might comprise some of the human AlkB homologs with unknown function

Novel features of ARS selection in budding yeast Lachancea kluyveri

<p>Abstract</p> <p>Background</p> <p>The characterization of DNA replication origins in yeast has shed much light on the mechanisms of initiation of DNA replication. However, very little is known about the evolution of origins or the evolution of mechanisms through which origins are recognized by the initiation machinery. This lack of understanding is largely due to the vast evolutionary distances between model organisms in which origins have been examined.</p> <p>Results</p> <p>In this study we have isolated and characterized autonomously replicating sequences (ARSs) in <it>Lachancea kluyveri </it>- a pre-whole genome duplication (WGD) budding yeast. Through a combination of experimental work and rigorous computational analysis, we show that <it>L. kluyveri </it>ARSs require a sequence that is similar but much longer than the ARS Consensus Sequence well defined in <it>Saccharomyces cerevisiae</it>. Moreover, compared with <it>S. cerevisiae </it>and <it>K. lactis</it>, the replication licensing machinery in <it>L. kluyveri </it>seems more tolerant to variations in the ARS sequence composition. It is able to initiate replication from almost all <it>S. cerevisiae </it>ARSs tested and most <it>Kluyveromyces lactis </it>ARSs. In contrast, only about half of the <it>L. kluyveri </it>ARSs function in <it>S. cerevisiae </it>and less than 10% function in <it>K. lactis</it>.</p> <p>Conclusions</p> <p>Our findings demonstrate a replication initiation system with novel features and underscore the functional diversity within the budding yeasts. Furthermore, we have developed new approaches for analyzing biologically functional DNA sequences with ill-defined motifs.</p