Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms

In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate consensus is solvable if and only if the communication graph in each round has a rooted spanning tree, i.e., there is a coordinator at each time. The striking point in this result is that the coordinator is not required to be unique and can change arbitrarily from round to round. Interestingly, the class of averaging algorithms, which are memoryless and require no process identifiers, entirely captures the solvability issue of approximate consensus in that the problem is solvable if and only if it can be solved using any averaging algorithm. Concerning the time complexity of averaging algorithms, we show that approximate consensus can be achieved with precision of $\varepsilon$ in a coordinated network model in $O(n^{n+1} \log\frac{1}{\varepsilon})$ synchronous rounds, and in $O(\Delta n^{n\Delta+1} \log\frac{1}{\varepsilon})$ rounds when the maximum round delay for a message to be delivered is $\Delta$. While in general, an upper bound on the time complexity of averaging algorithms has to be exponential, we investigate various network models in which this exponential bound in the number of nodes reduces to a polynomial bound. We apply our results to networked systems with a fixed topology and classical benign fault models, and deduce both known and new results for approximate consensus in these systems. In particular, we show that for solving approximate consensus, a complete network can tolerate up to 2n-3 arbitrarily located link faults at every round, in contrast with the impossibility result established by Santoro and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1 link faults per round originating from the same node

Sonic Hedgehog Is a Chemoattractant for Midbrain Dopaminergic Axons

Midbrain dopaminergic axons project from the substantia nigra (SN) and the ventral tegmental area (VTA) to rostral target tissues, including the striatum, pallidum, and hypothalamus. The axons from the medially located VTA project primarily to more medial target tissues in the forebrain, whereas the more lateral SN axons project to lateral targets including the dorsolateral striatum. This structural diversity underlies the distinct functions of these pathways. Although a number of guidance cues have been implicated in the formation of the distinct axonal projections of the SN and VTA, the molecular basis of their diversity remains unclear. Here we investigate the molecular basis of structural diversity in mDN axonal projections. We find that Sonic Hedgehog (Shh) is expressed at a choice point in the course of the rostral dopaminergic projections. Furthermore, in midbrain explants, dopaminergic projections are attracted to a Shh source. Finally, in mice in which Shh signaling is inactivated during late neuronal development, the most medial dopaminergic projections are deficient

Morphology and Nanomechanics of Sensory Neurons Growth Cones following Peripheral Nerve Injury

A prior peripheral nerve injury in vivo, promotes a rapid elongated mode of sensory neurons neurite regrowth in vitro. This in vitro model of conditioned axotomy allows analysis of the cellular and molecular mechanisms leading to an improved neurite re-growth. Our differential interference contrast microscopy and immunocytochemistry results show that conditioned axotomy, induced by sciatic nerve injury, did not increase somatic size of adult lumbar sensory neurons from mice dorsal root ganglia sensory neurons but promoted the appearance of larger neurites and growth cones. Using atomic force microscopy on live neurons, we investigated whether membrane mechanical properties of growth cones of axotomized neurons were modified following sciatic nerve injury. Our data revealed that neurons having a regenerative growth were characterized by softer growth cones, compared to control neurons. The increase of the growth cone membrane elasticity suggests a modification in the ratio and the inner framework of the main structural proteins

Proteomic Analysis of S-Acylated Proteins in Human B Cells Reveals Palmitoylation of the Immune Regulators CD20 and CD23

S-palmitoylation is a reversible post-translational modification important for controlling the membrane targeting and function of numerous membrane proteins with diverse roles in signalling, scaffolding, and trafficking. We sought to identify novel palmitoylated proteins in B lymphocytes using acyl-biotin exchange chemistry, coupled with differential analysis by liquid-chromatography tandem mass spectrometry. In total, we identified 57 novel palmitoylated protein candidates from human EBV-transformed lymphoid cells. Two of them, namely CD20 and CD23 (low affinity immunoglobulin epsilon Fc receptor), are immune regulators that are effective/potential therapeutic targets for haematological malignancies, autoimmune diseases and allergic disorders. Palmitoylation of CD20 and CD23 was confirmed by heterologous expression of alanine mutants coupled with bioorthogonal metabolic labeling. This study demonstrates a new subset of palmitoylated proteins in B cells, illustrating the ubiquitous role of protein palmitoylation in immune regulation

Genome-Wide Analysis of Nucleotide-Level Variation in Commonly Used Saccharomyces cerevisiae Strains

Ten years have passed since the genome of Saccharomyces cerevisiae–more precisely, the S288c strain–was completely sequenced. However, experimental work in yeast is commonly performed using strains that are of unknown genetic relationship to S288c. Here, we characterized the nucleotide-level similarity between S288c and seven commonly used lab strains (A364A, W303, FL100, CEN.PK, ∑1278b, SK1 and BY4716) using 25mer oligonucleotide microarrays that provide complete and redundant coverage of the ∼12 Mb Saccharomyces cerevisiae genome. Using these data, we assessed the frequency and distribution of nucleotide variation in comparison to the sequenced reference genome. These data allow us to infer the relationships between experimentally important strains of yeast and provide insight for experimental designs that are sensitive to sequence variation. We propose a rational approach for near complete sequencing of strains related to the reference using these data and directed re-sequencing. These data and new visualization tools are accessible online in a new resource: the Yeast SNPs Browser (YSB; http://gbrowse.princeton.edu/cgi-bin/gbrowse/yeast_strains_snps) that is available to all researchers

Gene–Environment Interactions at Nucleotide Resolution

Interactions among genes and the environment are a common source of phenotypic variation. To characterize the interplay between genetics and the environment at single nucleotide resolution, we quantified the genetic and environmental interactions of four quantitative trait nucleotides (QTN) that govern yeast sporulation efficiency. We first constructed a panel of strains that together carry all 32 possible combinations of the 4 QTN genotypes in 2 distinct genetic backgrounds. We then measured the sporulation efficiencies of these 32 strains across 8 controlled environments. This dataset shows that variation in sporulation efficiency is shaped largely by genetic and environmental interactions. We find clear examples of QTN:environment, QTN: background, and environment:background interactions. However, we find no QTN:QTN interactions that occur consistently across the entire dataset. Instead, interactions between QTN only occur under specific combinations of environment and genetic background. Thus, what might appear to be a QTN:QTN interaction in one background and environment becomes a more complex QTN:QTN:environment:background interaction when we consider the entire dataset as a whole. As a result, the phenotypic impact of a set of QTN alleles cannot be predicted from genotype alone. Our results instead demonstrate that the effects of QTN and their interactions are inextricably linked both to genetic background and to environmental variation

Global Transcriptome and Deletome Profiles of Yeast Exposed to Transition Metals

A variety of pathologies are associated with exposure to supraphysiological concentrations of essential metals and to non-essential metals and metalloids. The molecular mechanisms linking metal exposure to human pathologies have not been clearly defined. To address these gaps in our understanding of the molecular biology of transition metals, the genomic effects of exposure to Group IB (copper, silver), IIB (zinc, cadmium, mercury), VIA (chromium), and VB (arsenic) elements on the yeast Saccharomyces cerevisiae were examined. Two comprehensive sets of metal-responsive genomic profiles were generated following exposure to equi-toxic concentrations of metal: one that provides information on the transcriptional changes associated with metal exposure (transcriptome), and a second that provides information on the relationship between the expression of ∼4,700 non-essential genes and sensitivity to metal exposure (deletome). Approximately 22% of the genome was affected by exposure to at least one metal. Principal component and cluster analyses suggest that the chemical properties of the metal are major determinants in defining the expression profile. Furthermore, cells may have developed common or convergent regulatory mechanisms to accommodate metal exposure. The transcriptome and deletome had 22 genes in common, however, comparison between Gene Ontology biological processes for the two gene sets revealed that metal stress adaptation and detoxification categories were commonly enriched. Analysis of the transcriptome and deletome identified several evolutionarily conserved, signal transduction pathways that may be involved in regulating the responses to metal exposure. In this study, we identified genes and cognate signaling pathways that respond to exposure to essential and non-essential metals. In addition, genes that are essential for survival in the presence of these metals were identified. This information will contribute to our understanding of the molecular mechanism by which organisms respond to metal stress, and could lead to an understanding of the connection between environmental stress and signal transduction pathways

Virus Adaptation by Manipulation of Host's Gene Expression

Viruses adapt to their hosts by evading defense mechanisms and taking over cellular metabolism for their own benefit. Alterations in cell metabolism as well as side-effects of antiviral responses contribute to symptoms development and virulence. Sometimes, a virus may spill over from its usual host species into a novel one, where usually will fail to successfully infect and further transmit to new host. However, in some cases, the virus transmits and persists after fixing beneficial mutations that allow for a better exploitation of the new host. This situation would represent a case for a new emerging virus. Here we report results from an evolution experiment in which a plant virus was allowed to infect and evolve on a naïve host. After 17 serial passages, the viral genome has accumulated only five changes, three of which were non-synonymous. An amino acid substitution in the viral VPg protein was responsible for the appearance of symptoms, whereas one substitution in the viral P3 protein the epistatically contributed to exacerbate severity. DNA microarray analyses show that the evolved and ancestral viruses affect the global patterns of host gene expression in radically different ways. A major difference is that genes involved in stress and pathogen response are not activated upon infection with the evolved virus, suggesting that selection has favored viral strategies to escape from host defenses

Multiple Translocation of the AVR-Pita Effector Gene among Chromosomes of the Rice Blast Fungus Magnaporthe oryzae and Related Species

Magnaporthe oryzae is the causal agent of rice blast disease, a devastating problem worldwide. This fungus has caused breakdown of resistance conferred by newly developed commercial cultivars. To address how the rice blast fungus adapts itself to new resistance genes so quickly, we examined chromosomal locations of AVR-Pita, a subtelomeric gene family corresponding to the Pita resistance gene, in various isolates of M. oryzae (including wheat and millet pathogens) and its related species. We found that AVR-Pita (AVR-Pita1 and AVR-Pita2) is highly variable in its genome location, occurring in chromosomes 1, 3, 4, 5, 6, 7, and supernumerary chromosomes, particularly in rice-infecting isolates. When expressed in M. oryzae, most of the AVR-Pita homologs could elicit Pita-mediated resistance, even those from non-rice isolates. AVR-Pita was flanked by a retrotransposon, which presumably contributed to its multiple translocation across the genome. On the other hand, family member AVR-Pita3, which lacks avirulence activity, was stably located on chromosome 7 in a vast majority of isolates. These results suggest that the diversification in genome location of AVR-Pita in the rice isolates is a consequence of recognition by Pita in rice. We propose a model that the multiple translocation of AVR-Pita may be associated with its frequent loss and recovery mediated by its transfer among individuals in asexual populations. This model implies that the high mobility of AVR-Pita is a key mechanism accounting for the rapid adaptation toward Pita. Dynamic adaptation of some fungal plant pathogens may be achieved by deletion and recovery of avirulence genes using a population as a unit of adaptation