Identificação e caracterização de RNA mensageiros candidatos a alvo das proteínas PUMILHO de Arabidopsis através do sistema triplo-híbrido de levedura

Proteínas PUF regulam a estabilidade e a tradução através da ligação a seqüências específicas nas regiões 3\' não traduzidas (3\' UTR) dos mensageiros. A ligação é mediada por um domínio de ligação conservado constituído por 8 repetições de aproximadamente 36 aminoácidos cada. Experimentos realizados no sistema triplo-híbrido de levedura mostraram que os homólogos PUF de Arabidopsis APUM-1, APUM-2 e APUM-3 são capazes de ligar especificamente à seqüência chamada de Elemento de Resposta a NANOS (NRE) reconhecida pelo homólogo PUF de Drosophila. A utilização de bibliotecas de expressão de RNA em ensaios no sistema triplo-híbrido permitiu a identificação de seqüências de ligação consenso para as três proteínas APUM. Análises computacionais identificaram elementos de ligação a APUM em regiões 3\' UTR de importantes transcritos relacionados ao controle do meristema do caule e à manutenção das células totipotentes. Nós mostramos que os homólogos APUM-l, APUM-2 e APUM-3 reconhecem elementos de ligação a APUM nas regiões 3\' UTR dos transcritos WUSCHEL, CLAVATA-1, ZWILLE e FASCIATA-2. Ensaios de RT-PCR e Western blot semiquantitativos mostraram que a quantidade dos transcritos WUSHEL e CLAVATA-1 é alterada em plantas antisenso induzíveis para APUM-l, APUM-2 e APUM-3. A relevância biológica dessas interações foi observada através de ensaios de coimunoprecipitação, confirmando, portanto, o primeiro caso de regulação traducional descrito para os mensageiros WUSCHEL e CLAVATA-1. Análises computacionais adicionais para a identificação de outros homólogos PUF em Arabidopsis encontraram vinte e cinco proteínas possuindo repetições PUF. Entre elas, os homólogos APUM-4, APUM-S e APUM-6 apresentam alta similaridade com as proteínas APUM-l, APUM-2 e APUM-3, sendo capazes de ligar especificamente à seqüência NRE e aos elementos de ligação a APUM presentes nas regiões 3\' UTR dos transcritos WUSCHEL, CLAVATA-1, ZWILLE e FASCIATA-ts resultados indicam que vários homólogos PUF podem agir como reguladores traducionais em Arabidopsis através de um mecanismo molecular conservado entre as espécies, podendo abrir uma nova área de investigação da regulação de mRNA em plantas.

SUMOylation represses SnRK1 signaling in Arabidopsis

The SnRK1 protein kinase balances cellular energy levels in accordance with extracellular conditions and is thereby key for plant stress tolerance. In addition, SnRK1 has been implicated in numerous growth and developmental processes from seed filling and maturation to flowering and senescence. Despite its importance, the mechanisms that regulate SnRK1 activity are poorly understood. Here, we demonstrate that the SnRK1 complex is SUMOylated on multiple subunits and identify SIZ1 as the E3 Small Ubiquitin-like Modifier (SUMO) ligase responsible for this modification. We further show that SnRK1 is ubiquitinated in a SIZ1-dependent manner, causing its degradation through the proteasome. In consequence, SnRK1 degradation is deficient in siz1-2 mutants, leading to its accumulation and hyperactivation of SnRK1 signaling. Finally, SnRK1 degradation is strictly dependent on its activity, as inactive SnRK1 variants are aberrantly stable but recover normal degradation when expressed as SUMO mimetics. Altogether, our data suggest that active SnRK1 triggers its own SUMOylation and degradation, establishing a negative feedback loop that attenuates SnRK1 signaling and prevents detrimental hyperactivation of stress responses.

Repressor- and activator-type ethylene response factors functioning in jasmonate signaling and disease resistance identified via a genome-wide screen of Arabidopsis transcription factor gene expression

To identify transcription factors (TFs) involved in jasmonate (JA) signaling and plant defense, we screened 1,534 Arabidopsis (Arabidopsis thaliana) TFs by real-time quantitative reverse transcription-PCR for their altered transcript at 6 h following either methyl JA treatment or inoculation with the incompatible pathogen Alternaria brassicicola. We identified 134 TFs that showed a significant change in expression, including many APETALA2/ethylene response factor (AP2/ERF), MYB, WRKY, and NACTF genes with unknown functions. Twenty TF genes were induced by both the pathogen and methyl JA and these included 10 members of the AP2/ERF TF family, primarily from the B1a and B3 subclusters. Functional analysis of the B1a TF AtERF4 revealed that AtERF4 acts as a novel negative regulator of JA-responsive defense gene expression and resistance to the necrotrophic fungal pathogen Fusarium oxysporum and antagonizes JA inhibition of root elongation. In contrast, functional analysis of the B3 TF AtERF2 showed that AtERF2 is a positive regulator of JA-responsive defense genes and resistance to F. oxysporum and enhances JA inhibition of root elongation. Our results suggest that plants coordinately express multiple repressor-and activator-type AP2/ERFs during pathogen challenge to modulate defense gene expression and disease resistance.

Cosuppression of eukaryotic release factor 1-1 in Arabidopsis affects cell elongation and radial cell division

The role of the eukaryotic release factor 1 (eRF1) in translation termination has previously been established in yeast; however, only limited characterization has been performed on any plant homologs. Here, we demonstrate that cosuppression of eRF1-1 in Arabidopsis (Arabidopsis thaliana) has a profound effect on plant morphology, resulting in what we term the broomhead phenotype. These plants primarily exhibit a reduction in internode elongation causing the formation of a broomhead-like cluster of malformed siliques at the top of the inflorescence stem. Histological analysis of broomhead stems revealed that cells are reduced in height and display ectopic lignification of the phloem cap cells, some phloem sieve cells, and regions of the fascicular cambium, as well as enhanced lignification of the interfascicular fibers. We also show that cell division in the fascicular cambial regions is altered, with the majority of vascular bundles containing cambial cells that are disorganized and possess enlarged nuclei. This is the first attempt at functional characterization of a release factor in vivo in plants and demonstrates the importance of eRF1-1 function in Arabidopsis.

Heterotrimeric G proteins facilitate Arabidopsis resistance to necrotrophic pathogens and are involved in jasmonate signaling

Heterotrimeric G proteinshave been previously linked to plant defense; however a role for the G beta gamma dimer in defense signaling has not been described to date. Using available Arabidopsis (Arabidopsis thaliana) mutants lacking functional G alpha or G beta subunits, we show that defense against the necrotrophic pathogens Alternaria brassicicola and Fusarium oxysporum is impaired in G beta- deficient mutants while G alpha-deficient mutants show slightly increased resistance compared to wild-type Columbia ecotype plants. In contrast, responses to virulent (DC3000) and avirulent (JL1065) strains of Pseudomonas syringae appear to be independent of heterotrimeric G proteins. The induction of a number of defense-related genes in G beta-deficient mutants were severely reduced in response to A. brassicicola infection. In addition, G beta-deficient mutants exhibit decreased sensitivity to a number of methyl jasmonate- induced responses such as induction of the plant defensin gene PDF1.2, inhibition of root elongation, seed germination, and growth of plants in sublethal concentrations of methyl jasmonate. In all cases, the behavior of the G alpha- deficient mutants is coherent with the classic heterotrimeric mechanism of action, indicating that jasmonic acid signaling is influenced by the Gbg functional subunit but not by G alpha. We hypothesize that G beta gamma acts as a direct or indirect enhancer of the jasmonate signaling pathway in plants.

The molecular basis of temperature compensation in the Arabidopsis circadian clock

Circadian clocks maintain robust and accurate timing over a broad range of physiological temperatures, a characteristic termed temperature compensation. In Arabidopsis thaliana, ambient temperature affects the rhythmic accumulation of transcripts encoding the clock components TIMING OF CAB EXPRESSION1 (TOC1), GIGANTEA (GI), and the partially redundant genes CIRCADIAN CLOCK ASSOCIATED1 (CCA1) and LATE ELONGATED HYPOCOTYL (LHY). The amplitude and peak levels increase for TOC1 and GI RNA rhythms as the temperature increases (from 17 to 27 degrees C), whereas they decrease for LHY. However, as temperatures decrease ( from 17 to 12 degrees C), CCA1 and LHY RNA rhythms increase in amplitude and peak expression level. At 27 degrees C, a dynamic balance between GI and LHY allows temperature compensation in wild-type plants, but circadian function is impaired in Ihy and gi mutant plants. However, at 12 degrees C, CCA1 has more effect on the buffering mechanism than LHY, as the cca1 and gi mutations impair circadian rhythms more than Ihy at the lower temperature. At 17 degrees C, GI is apparently dispensable for free-running circadian rhythms, although partial GI function can affect circadian period. Numerical simulations using the interlocking-loop model show that balancing LHY/CCA1 function against GI and other evening-expressed genes can largely account for temperature compensation in wild-type plants and the temperature-specific phenotypes of gi mutants.

Arabidopsis MYC transcription factors are the target of hormonal salicylic acid/jasmonic acid cross talk in response to Pieris brassicae egg extract.

Arabidopsis (Arabidopsis thaliana) plants recognize insect eggs and activate the salicylic acid (SA) pathway. As a consequence, expression of defense genes regulated by the jasmonic acid (JA) pathway is suppressed and larval performance is enhanced. Cross talk between defense signaling pathways is common in plant-pathogen interactions, but the molecular mechanism mediating this phenomenon is poorly understood. Here, we demonstrate that egg-induced SA/JA antagonism works independently of the APETALA2/ETHYLENE RESPONSE FACTOR (AP2/ERF) transcription factor ORA59, which controls the ERF branch of the JA pathway. In addition, treatment with egg extract did not enhance expression or stability of JASMONATE ZIM-domain transcriptional repressors, and SA/JA cross talk did not involve JASMONATE ASSOCIATED MYC2-LIKEs, which are negative regulators of the JA pathway. Investigating the stability of MYC2, MYC3, and MYC4, three basic helix-loop-helix transcription factors that additively control jasmonate-related defense responses, we found that egg extract treatment strongly diminished MYC protein levels in an SA-dependent manner. Furthermore, we identified WRKY75 as a novel and essential factor controlling SA/JA cross talk. These data indicate that insect eggs target the MYC branch of the JA pathway and uncover an unexpected modulation of SA/JA antagonism depending on the biological context in which the SA pathway is activated.

Whole Genome Analysis of Gene Expression Reveals Coordinated Activation of Signaling and Metabolic Pathways during Pollen-Pistil Interactions in Arabidopsis

Plant reproduction depends on the concerted activation of many genes to ensure correct communication between pollen and pistil. Here, we queried the whole transcriptome of Arabidopsis (Arabidopsis thaliana) in order to identify genes with specific reproductive functions. We used the Affymetrix ATH1 whole genome array to profile wild-type unpollinated pistils and unfertilized ovules. By comparing the expression profile of pistils at 0.5, 3.5, and 8.0 h after pollination and applying a number of statistical and bioinformatics criteria, we found 1,373 genes differentially regulated during pollen-pistil interactions. Robust clustering analysis grouped these genes in 16 time-course clusters representing distinct patterns of regulation. Coregulation within each cluster suggests the presence of distinct genetic pathways, which might be under the control of specific transcriptional regulators. A total of 78% of the regulated genes were expressed initially in unpollinated pistil and/or ovules, 15% were initially detected in the pollen data sets as enriched or preferentially expressed, and 7% were induced upon pollination. Among those, we found a particular enrichment for unknown transcripts predicted to encode secreted proteins or representing signaling and cell wall-related proteins, which may function by remodeling the extracellular matrix or as extracellular signaling molecules. A strict regulatory control in various metabolic pathways suggests that fine-tuning of the biochemical and physiological cellular environment is crucial for reproductive success. Our study provides a unique and detailed temporal and spatial gene expression profile of in vivo pollen-pistil interactions, providing a framework to better understand the basis of the molecular mechanisms operating during the reproductive process in higher plants.

Life without complex I: proteome analyses of an Arabidopsis mutant lacking the mitochondrial NADH dehydrogenase complex

The mitochondrial NADH dehydrogenase complex (complex I) is of particular importance for the respiratory chain in mitochondria. It is the major electron entry site for the mitochondrial electron transport chain (mETC) and therefore of great significance for mitochondrial ATP generation. We recently described an Arabidopsis thaliana double-mutant lacking the genes encoding the carbonic anhydrases CA1 and CA2, which both form part of a plant-specific 'carbonic anhydrase domain' of mitochondrial complex I. The mutant lacks complex I completely. Here we report extended analyses for systematically characterizing the proteome of the ca1ca2 mutant. Using various proteomic tools, we show that lack of complex I causes reorganization of the cellular respiration system. Reduced electron entry into the respiratory chain at the first segment of the mETC leads to induction of complexes II and IV as well as alternative oxidase. Increased electron entry at later segments of the mETC requires an increase in oxidation of organic substrates. This is reflected by higher abundance of proteins involved in glycolysis, the tricarboxylic acid cycle and branched-chain amino acid catabolism. Proteins involved in the light reaction of photosynthesis, the Calvin cycle, tetrapyrrole biosynthesis, and photorespiration are clearly reduced, contributing to the significant delay in growth and development of the double-mutant. Finally, enzymes involved in defense against reactive oxygen species and stress symptoms are much induced. These together with previously reported insights into the function of plant complex I, which were obtained by analysing other complex I mutants, are integrated in order to comprehensively describe 'life without complex I'.

Functional XPB/RAD25 redundancy in Arabidopsis genome: characterization of AtXPB2 and expression analysis

The xeroderma pigmentosum complementation group B (XPB) protein is involved in both DNA repair and transcription in human cells. It is a component of the transcription factor IIH (TFIIH) and is responsible for DNA helicase activity during nucleotide (nt) excision repair (NER). Its high evolutionary conservation has allowed identification of homologous proteins in different organisms, including plants. In contrast to other organisms, Arabidopsis thaliana harbors a duplication of the XPB orthologue (AtXPB1 and AtXPB2), and the proteins encoded by the duplicated genes are very similar (95% amino acid identity). Complementation assays in yeast rad25 mutant strains suggest the involvement of AtXPB2 in DNA repair, as already shown for AtXPB1, indicating that these proteins may be functionally redundant in the removal of DNA lesions in A. thaliana. Although both genes are expressed in a constitutive manner during the plant life cycle, Northern blot analyses suggest that light modulates the expression level of both XPB copies, and transcript levels increase during early stages of development. Considering the high similarity between AtXPB1 and AtXPB2 and that both of predicted proteins may act in DNA repair, it is possible that this duplication may confer more flexibility and resistance to DNA damaging agents in thale cress. (C) 2004 Elsevier B.V. All rights reserved.

The impact of mechanical compression on cortical microtubules in Arabidopsis: a quantitative pipeline

Exogenous mechanical perturbations on living tissues are commonly used to investigate whether cell effectors can respond to mechanical cues. However, in most of these experiments, the applied mechanical stress and/or the biological response are described only qualitatively. We developed a quantitative pipeline based on microindentation and image analysis to investigate the impact of a controlled and prolonged compression on microtubule behaviour in the Arabidopsis shoot apical meristem, using microtubule fluorescent marker lines. We found that a compressive stress, in the order of magnitude of turgor pressure, induced apparent microtubule bundling. Importantly, that response could be reversed several hours after the release of compression. Next, we tested the contribution of microtubule severing to compression-induced bundling: microtubule bundling seemed less pronounced in the katanin mutant, in which microtubule severing is dramatically reduced. Conversely, some microtubule bundles could still be observed 16 hours after the release of compression in the spiral2 mutant, in which severing rate is instead increased. To quantify the impact of mechanical stress on anisotropy and orientation of microtubule arrays, we used the nematic tensor based FibrilTool ImageJ/Fiji plugin. To assess the degree of apparent bundling of the network, we developed several methods, some of which were borrowed from geostatistics. The final microtubule bundling response could notably be related to tissue growth velocity that was recorded by the indenter during compression. Because both input and output are quantified, this pipeline is an initial step towards correlating more precisely the cytoskeleton response to mechanical stress in living tissues.

Exploring the Function and Regulation of Arabidopsis EIN2 in Ethylene Signaling

Ethylene is an essential plant hormone involved in nearly all stages of plant growth and development. EIN2 (ETHYLENE INSENSITIVE2) is a master positive regulator in the ethylene signaling pathway, consisting of an N-terminal domain and a C-terminal domain. The EIN2 N-terminal domain localizes to the endoplasmic reticulum (ER) membrane and shows sequence similarity to Nramp metal ion transporters. The cytosolic C-terminal domain is unique to plants and signals downstream. There have been several major gaps in our knowledge of EIN2 function. It was unknown how the ethylene signal gets relayed from the known upstream component CTR1 (CONSTITUTIVE RESPONSE1) a Ser/Thr kinase at the ER, to EIN2. How the ethylene signal was transduced from EIN2 to the next downstream component transcription factor EIN3 (ETHYLENE INSENSITIVE3) in the nucleus was also unknown. The N-terminal domain of EIN2 shows homology to Nramp metal ion transporters and whether EIN2 can also function as a metal transporter has been a question plaguing the ethylene field for almost two decades. Here, EIN2 was found to interact with the CTR1 protein kinase, leading to the discovery that CTR1 phosphorylates the C-terminal domain of EIN2 in Arabidopsis thaliana. Using tags at the termini of EIN2, it was deduced that in the presence of ethylene, the EIN2 C-terminal domain is cleaved and translocates into the nucleus, where it could somehow activate downstream ethylene responses. The EIN2 C-terminal domain interacts with nuclear proteins, RTE3 and EER5, which are components of the TREX-2 mRNA export complex, although the role of these interactions remains unclear. The EIN2 N-terminal domain was found to be capable of divalent metal transport when expressed in E. coli and S. cerevisiae leading to the hypothesis that metal transport plays a role in ethylene signaling. This hypothesis was tested using a novel missense allele, ein2 G36E, substituting a highly conserved residue that is required for metal transport in Nramp proteins. This G36E substitution did not disrupt metal ion transport of EIN2, but the ethylene insensitive phenotype of this mutant indicates that the EIN2 N-terminal domain is important for positively regulating the C-terminal domain. The defect of the ein2 G36E mutant does not prevent proper expression or subcellular localization, but might affect protein modifications. The ein2 G36E allele is partially dominant, mostly likely displaying haploinsufficiency. Overexpression of the EIN2 N-terminal domain in the ein2 G36E mutant did not rescue ethylene insensitivity, suggesting the N-terminal domain functions in cis to regulate the C-terminal domain. These findings advance our knowledge of EIN2, which is critical to understanding ethylene signaling.

Interaction of NPR1 with basic leucine zipper protein transcription factors that bind sequences required for salicylic acid induction of the PR–1 gene

The Arabidopsis thaliana NPR1 has been shown to be a key regulator of gene expression during the onset of a plant disease-resistance response known as systemic acquired resistance. The npr1 mutant plants fail to respond to systemic acquired resistance-inducing signals such as salicylic acid (SA), or express SA-induced pathogenesis-related (PR) genes. Using NPR1 as bait in a yeast two-hybrid screen, we identified a subclass of transcription factors in the basic leucine zipper protein family (AHBP-1b and TGA6) and showed that they interact specifically in yeast and in vitro with NPR1. Point mutations that abolish the NPR1 function in A. thaliana also impair the interactions between NPR1 and the transcription factors in the yeast two-hybrid assay. Furthermore, a gel mobility shift assay showed that the purified transcription factor protein, AHBP-1b, binds specifically to an SA-responsive promoter element of the A. thaliana PR-1 gene. These data suggest that NPR1 may regulate PR-1 gene expression by interacting with a subclass of basic leucine zipper protein transcription factors.

A myosin from a higher plant has structural similarities to class V myosins

In plant cells, myosin is believed to be the molecular motor responsible for actin-based motility processes such as cytoplasmic streaming and directed vesicle transport. In an effort to characterize plant myosin, a cDNA encoding a myosin heavy chain was isolated from Arabidopsis thaliana. The predicted product of the MYA1 gene is 173 kDa and is structurally similar to the class V myosins. It is composed of the highly-conserved NH2-terminal "head" domain, a putative calmodulin-binding "neck" domain an alpha-helical coiled-coil domain, and a COOH-terminal domain. Northern blot analysis shows that the Arabidopsis MYA1 gene is expressed in all the major plant tissues (flower, leaf, root, and stem). We suggest that the MYA1 myosin may be involved in a general intracellular transport process in plant cells.

Multifractal characterisation and analysis of complex networks

Complex networks have been studied extensively due to their relevance to many real-world systems such as the world-wide web, the internet, biological and social systems. During the past two decades, studies of such networks in different fields have produced many significant results concerning their structures, topological properties, and dynamics. Three well-known properties of complex networks are scale-free degree distribution, small-world effect and self-similarity. The search for additional meaningful properties and the relationships among these properties is an active area of current research. This thesis investigates a newer aspect of complex networks, namely their multifractality, which is an extension of the concept of selfsimilarity. The first part of the thesis aims to confirm that the study of properties of complex networks can be expanded to a wider field including more complex weighted networks. Those real networks that have been shown to possess the self-similarity property in the existing literature are all unweighted networks. We use the proteinprotein interaction (PPI) networks as a key example to show that their weighted networks inherit the self-similarity from the original unweighted networks. Firstly, we confirm that the random sequential box-covering algorithm is an effective tool to compute the fractal dimension of complex networks. This is demonstrated on the Homo sapiens and E. coli PPI networks as well as their skeletons. Our results verify that the fractal dimension of the skeleton is smaller than that of the original network due to the shortest distance between nodes is larger in the skeleton, hence for a fixed box-size more boxes will be needed to cover the skeleton. Then we adopt the iterative scoring method to generate weighted PPI networks of five species, namely Homo sapiens, E. coli, yeast, C. elegans and Arabidopsis Thaliana. By using the random sequential box-covering algorithm, we calculate the fractal dimensions for both the original unweighted PPI networks and the generated weighted networks. The results show that self-similarity is still present in generated weighted PPI networks. This implication will be useful for our treatment of the networks in the third part of the thesis. The second part of the thesis aims to explore the multifractal behavior of different complex networks. Fractals such as the Cantor set, the Koch curve and the Sierspinski gasket are homogeneous since these fractals consist of a geometrical figure which repeats on an ever-reduced scale. Fractal analysis is a useful method for their study. However, real-world fractals are not homogeneous; there is rarely an identical motif repeated on all scales. Their singularity may vary on different subsets; implying that these objects are multifractal. Multifractal analysis is a useful way to systematically characterize the spatial heterogeneity of both theoretical and experimental fractal patterns. However, the tools for multifractal analysis of objects in Euclidean space are not suitable for complex networks. In this thesis, we propose a new box covering algorithm for multifractal analysis of complex networks. This algorithm is demonstrated in the computation of the generalized fractal dimensions of some theoretical networks, namely scale-free networks, small-world networks, random networks, and a kind of real networks, namely PPI networks of different species. Our main finding is the existence of multifractality in scale-free networks and PPI networks, while the multifractal behaviour is not confirmed for small-world networks and random networks. As another application, we generate gene interactions networks for patients and healthy people using the correlation coefficients between microarrays of different genes. Our results confirm the existence of multifractality in gene interactions networks. This multifractal analysis then provides a potentially useful tool for gene clustering and identification. The third part of the thesis aims to investigate the topological properties of networks constructed from time series. Characterizing complicated dynamics from time series is a fundamental problem of continuing interest in a wide variety of fields. Recent works indicate that complex network theory can be a powerful tool to analyse time series. Many existing methods for transforming time series into complex networks share a common feature: they define the connectivity of a complex network by the mutual proximity of different parts (e.g., individual states, state vectors, or cycles) of a single trajectory. In this thesis, we propose a new method to construct networks of time series: we define nodes by vectors of a certain length in the time series, and weight of edges between any two nodes by the Euclidean distance between the corresponding two vectors. We apply this method to build networks for fractional Brownian motions, whose long-range dependence is characterised by their Hurst exponent. We verify the validity of this method by showing that time series with stronger correlation, hence larger Hurst exponent, tend to have smaller fractal dimension, hence smoother sample paths. We then construct networks via the technique of horizontal visibility graph (HVG), which has been widely used recently. We confirm a known linear relationship between the Hurst exponent of fractional Brownian motion and the fractal dimension of the corresponding HVG network. In the first application, we apply our newly developed box-covering algorithm to calculate the generalized fractal dimensions of the HVG networks of fractional Brownian motions as well as those for binomial cascades and five bacterial genomes. The results confirm the monoscaling of fractional Brownian motion and the multifractality of the rest. As an additional application, we discuss the resilience of networks constructed from time series via two different approaches: visibility graph and horizontal visibility graph. Our finding is that the degree distribution of VG networks of fractional Brownian motions is scale-free (i.e., having a power law) meaning that one needs to destroy a large percentage of nodes before the network collapses into isolated parts; while for HVG networks of fractional Brownian motions, the degree distribution has exponential tails, implying that HVG networks would not survive the same kind of attack.