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.

Defining the role of phytoene synthase in carotenoid accumulation of high provitamin A bananas

Vitamin A deficiency (VAD) is a serious problem in developing countries, affecting approximately 127 million children of preschool age and 7.2 million pregnant women each year. However, this deficiency is readily treated and prevented through adequate nutrition. This can potentially be achieved through genetically engineered biofortification of staple food crops to enhance provitamin A (pVA) carotenoid content. Bananas are the fourth most important food crop with an annual production of 100 million tonnes and are widely consumed in areas affected by VAD. However, the fruit pVA content of most widely consumed banana cultivars is low (~ 0.2 to 0.5 ìg/g dry weight). This includes cultivars such as the East African highland banana (EAHB), the staple crop in countries such as Uganda, where annual banana consumption is approximately 250 kg per person. This fact, in addition to the agronomic properties of staple banana cultivars such as vegetative reproduction and continuous cropping, make bananas an ideal target for pVA enhancement through genetic engineering. Interestingly, there are banana varieties known with high fruit pVA content (up to 27.8 ìg/g dry weight), although they are not widely consumed due to factors such as cultural preference and availability. The genes involved in carotenoid accumulation during banana fruit ripening have not been well studied and an understanding of the molecular basis for the differential capacity of bananas to accumulate carotenoids may impact on the effective production of genetically engineered high pVA bananas. The production of phytoene by the enzyme phytoene synthase (PSY) has been shown to be an important rate limiting determinant of pVA accumulation in crop systems such as maize and rice. Manipulation of this gene in rice has been used successfully to produce Golden Rice, which exhibits higher seed endosperm pVA levels than wild type plants. Therefore, it was hypothesised that differences between high and low pVA accumulating bananas could be due either to differences in PSY enzyme activity or factors regulating the expression of the psy gene. Therefore, the aim of this thesis was to investigate the role of PSY in accumulation of pVA in banana fruit of representative high (Asupina) and low (Cavendish) pVA banana cultivars by comparing the nucleic acid and encoded amino acid sequences of the banana psy genes, in vivo enzyme activity of PSY in rice callus and expression of PSY through analysis of promoter activity and mRNA levels. Initially, partial sequences of the psy coding region from five banana cultivars were obtained using reverse transcriptase (RT)-PCR with degenerate primers designed to conserved amino acids in the coding region of available psy sequences from other plants. Based on phylogenetic analysis and comparison to maize psy sequences, it was found that in banana, psy occurs as a gene family of at least three members (psy1, psy2a and psy2b). Subsequent analysis of the complete coding regions of these genes from Asupina and Cavendish suggested that they were all capable of producing functional proteins due to high conservation in the catalytic domain. However, inability to obtain the complete mRNA sequences of Cavendish psy2a, and isolation of two non-functional Cavendish psy2a coding region variants, suggested that psy2a expression may be impaired in Cavendish. Sequence analysis indicated that these Cavendish psy2a coding region variants may have resulted from alternate splicing. Evidence of alternate splicing was also observed in one Asupina psy1 coding region variant, which was predicted to produce a functional PSY1 isoform. The complete mRNA sequence of the psy2b coding regions could not be isolated from either cultivar. Interestingly, psy1 was cloned predominantly from leaf while psy2 was obtained preferentially from fruit, suggesting some level of tissue-specific expression. The Asupina and Cavendish psy1 and psy2a coding regions were subsequently expressed in rice callus and the activity of the enzymes compared in vivo through visual observation and quantitative measurement of carotenoid accumulation. The maize B73 psy1 coding region was included as a positive control. After several weeks on selection, regenerating calli showed a range of colours from white to dark orange representing various levels of carotenoid accumulation. These results confirmed that the banana psy coding regions were all capable of producing functional enzymes. No statistically significant differences in levels of activity were observed between banana PSYs, suggesting that differences in PSY activity were not responsible for differences in the fruit pVA content of Asupina and Cavendish. The psy1 and psy2a promoter sequences were isolated from Asupina and Cavendish gDNA using a PCR-based genome walking strategy. Interestingly, three Cavendish psy2a promoter clones of different sizes, representing possible allelic variants, were identified while only single promoter sequences were obtained for the other Asupina and Cavendish psy genes. Bioinformatic analysis of these sequences identified motifs that were previously characterised in the Arabidopsis psy promoter. Notably, an ATCTA motif associated with basal expression in Arabidopsis was identified in all promoters with the exception of two of the Cavendish psy2a promoter clones (Cpsy2apr2 and Cpsy2apr3). G1 and G2 motifs, linked to light-regulated responses in Arabidopsis, appeared to be differentially distributed between psy1 and psy2a promoters. In the untranscribed regulatory regions, the G1 motifs were found only in psy1 promoters, while the G2 motifs were found only in psy2a. Interestingly, both ATCTA and G2 motifs were identified in the 5’ UTRs of Asupina and Cavendish psy1. Consistent with other monocot promoters, introns were present in the Asupina and Cavendish psy1 5’ UTRs, while none were observed in the psy2a 5’ UTRs. Promoters were cloned into expression constructs, driving the â-glucuronidase (GUS) reporter gene. Transient expression of the Asupina and Cavendish psy1 and psy2a promoters in both Cavendish embryogenic cells and Cavendish fruit demonstrated that all promoters were active, except Cpsy2apr2 and Cpsy2apr3. The functional Cavendish psy2a promoter (Cpsy2apr1) appeared to have activity similar to the Asupina psy2a promoter. The activities of the Asupina and Cavendish psy1 promoters were similar to each other, and comparable to those of the functional psy2a promoters. Semi-quantitative PCR analysis of Asupina and Cavendish psy1 and psy2a transcripts showed that psy2a levels were high in green fruit and decreased during ripening, reinforcing the hypothesis that fruit pVA levels were largely dependent on levels of psy2a expression. Additionally, semi-quantitative PCR using intron-spanning primers indicated that high levels of unprocessed psy2a and psy2b mRNA were present in the ripe fruit of Cavendish but not in Asupina. This raised the possibility that differences in intron processing may influence pVA accumulation in Asupina and Cavendish. In this study the role of PSY in banana pVA accumulation was analysed at a number of different levels. Both mRNA accumulation and promoter activity of psy genes studied were very similar between Asupina and Cavendish. However, in several experiments there was evidence of cryptic or alternate splicing that differed in Cavendish compared to Asupina, although these differences were not conclusively linked to the differences in fruit pVA accumulation between Asupina and Cavendish. Therefore, other carotenoid biosynthetic genes or regulatory mechanisms may be involved in determining pVA levels in these cultivars. This study has contributed to an increased understanding of the role of PSY in the production of pVA carotenoids in banana fruit, corroborating the importance of this enzyme in regulating carotenoid production. Ultimately, this work may serve to inform future research into pVA accumulation in important crop varieties such as the EAHB and the discovery of avenues to improve such crops through genetic modification.

Differentiation of isomeric N-glycan structures by normal-phase liquid chromatography-MALDI-TOF/TOF tandem mass spectrometry

The detailed characterization of protein N-glycosylation is very demanding given the many different glycoforms and structural isomers that can exist on glycoproteins. Here we report a fast and sensitive method for the extensive structure elucidation of reducing-end labeled N-glycan mixtures using a combination of capillary normal-phase HPLC coupled off-line to matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and TOF/TOF-MS/MS. Using this method, isobaric N-glycans released from honey bee phospholipase A2 and Arabidopsis thaliana glycoproteins were separated by normal-phase chromatography and subsequently identified by key fragment ions in the MALDI-TOF/TOF tandem mass spectra. In addition, linkage and branching information were provided by abundant cross-ring and "elimination" fragment ions in the MALDI-CID spectra that gave extensive structural information. Furthermore, the fragmentation characteristics of N-glycans reductively aminated with 2-aminobenzoic acid and 2-aminobenzamide were compared. The identification of N-glycans containing 3-linked core fucose was facilitated by distinctive ions present only in the MALDI-CID spectra of 2-aminobenzoic acid-labeled oligosaccharides. To our knowledge, this is the first MS/MS-based technique that allows confident identification of N-glycans containing 3-linked core fucose, which is a major allergenic determinant on insect and plant glycoproteins.

De Novo Transcriptome Sequence Assembly and Analysis of RNA Silencing Genes of Nicotiana benthamiana

Background: Nicotiana benthamiana has been widely used for transient gene expression assays and as a model plant in the study of plant-microbe interactions, lipid engineering and RNA silencing pathways. Assembling the sequence of its transcriptome provides information that, in conjunction with the genome sequence, will facilitate gaining insight into the plant's capacity for high-level transient transgene expression, generation of mobile gene silencing signals, and hyper-susceptibility to viral infection. Methodology/Results: RNA-seq libraries from 9 different tissues were deep sequenced and assembled, de novo, into a representation of the transcriptome. The assembly, of16GB of sequence, yielded 237,340 contigs, clustering into 119,014 transcripts (unigenes). Between 80 and 85% of reads from all tissues could be mapped back to the full transcriptome. Approximately 63% of the unigenes exhibited a match to the Solgenomics tomato predicted proteins database. Approximately 94% of the Solgenomics N. benthamiana unigene set (16,024 sequences) matched our unigene set (119,014 sequences). Using homology searches we identified 31 homologues that are involved in RNAi-associated pathways in Arabidopsis thaliana, and show that they possess the domains characteristic of these proteins. Of these genes, the RNA dependent RNA polymerase gene, Rdr1, is transcribed but has a 72 nt insertion in exon1 that would cause premature termination of translation. Dicer-like 3 (DCL3) appears to lack both the DEAD helicase motif and second dsRNA binding motif, and DCL2 and AGO4b have unexpectedly high levels of transcription. Conclusions: The assembled and annotated representation of the transcriptome and list of RNAi-associated sequences are accessible at www.benthgenome.com alongside a draft genome assembly. These genomic resources will be very useful for further study of the developmental, metabolic and defense pathways of N. benthamiana and in understanding the mechanisms behind the features which have made it such a well-used model plant. © 2013 Nakasugi et al.

Facile mutant identification via a single parental backcross method and application of whole genome sequencing based mapping pipelines

Forward genetic screens have identified numerous genes involved in development and metabolism, and remain a cornerstone of biological research. However, to locate a causal mutation, the practice of crossing to a polymorphic background to generate a mapping population can be problematic if the mutant phenotype is difficult to recognize in the hybrid F2 progeny, or dependent on parental specific traits. Here in a screen for leaf hyponasty mutants, we have performed a single backcross of an Ethane Methyl Sulphonate (EMS) generated hyponastic mutant to its parent. Whole genome deep sequencing of a bulked homozygous F2 population and analysis via the Next Generation EMS mutation mapping pipeline (NGM) unambiguously determined the causal mutation to be a single nucleotide polymorphisim (SNP) residing in HASTY, a previously characterized gene involved in microRNA biogenesis. We have evaluated the feasibility of this backcross approach using three additional SNP mapping pipelines; SHOREmap, the GATK pipeline, and the samtools pipeline. Although there was variance in the identification of EMS SNPs, all returned the same outcome in clearly identifying the causal mutation in HASTY. The simplicity of performing a single parental backcross and genome sequencing a small pool of segregating mutants has great promise for identifying mutations that may be difficult to map using conventional approaches.

Description of plant tRNA-derived RNA fragments (tRFs) associated with argonaute and identification of their putative targets

tRNA-derived RNA fragments (tRFs) are 19mer small RNAs that associate with Argonaute (AGO) proteins in humans. However, in plants, it is unknown if tRFs bind with AGO proteins. Here, using public deep sequencing libraries of immunoprecipitated Argonaute proteins (AGO-IP) and bioinformatics approaches, we identified the Arabidopsis thaliana AGO-IP tRFs. Moreover, using three degradome deep sequencing libraries, we identified four putative tRF targets. The expression pattern of tRFs, based on deep sequencing data, was also analyzed under abiotic and biotic stresses. The results obtained here represent a useful starting point for future studies on tRFs in plants. © 2013 Loss-Morais et al.; licensee BioMed Central Ltd.

Hairpin RNAs derived from RNA polymerase II and polymerase III promoter-directed transgenes are processed differently in plants

RNA polymerase III (Pol III) as well as Pol II (35S) promoters are able to drive hairpin RNA (hpRNA) expression and induce target gene silencing in plants. siRNAs of 21 nt are the predominant species in a 35S Pol II line, whereas 24- and/or 22-nucleotide (nt) siRNAs are produced by a Pol III line. The 35S line accumulated the loop of the hpRNA, in contrast to full-length hpRNA in the Pol III line. These suggest that Pol II and Pol III-transcribed hpRNAs are processed by different pathways. One Pol III transgene produced only 24-nt siRNAs but silenced the target gene efficiently, indicating that the 24-nt siRNAs can direct mRNA degradation; specific cleavage was confirmed by 59 rapid amplification of cDNA ends (RACE). Both Pol II- and Pol III-directed hpRNA transgenes induced cytosine methylation in the target DNA. The extent of methylation is not correlated with the level of 21-nt siRNAs, suggesting that they are not effective inducers of DNA methylation. The promoter of a U6 transgene was significantly methylated, whereas the promoter of the endogenous U6 gene was almost free of cytosine methylation, suggesting that endogenous sequences are more resistant to de novo DNA methylation than are transgene constructs. Published by Cold Spring Harbor Laboratory Press. Copyright © 2008 RNA Society.

RNA interference-inducing hairpin RNAs in plants act through the viral defence pathway

RNA interference (RNAi) is widely used to silence genes in plants and animals. It operates through the degradation of target mRNA by endonuclease complexes guided by approximately 21 nucleotide (nt) short interfering RNAs (siRNAs). A similar process regulates the expression of some developmental genes through approximately 21 nt microRNAs. Plants have four types of Dicer-like (DCL) enzyme, each producing small RNAs with different functions. Here, we show that DCL2, DCL3 and DCL4 in Arabidopsis process both replicating viral RNAs and RNAi-inducing hairpin RNAs (hpRNAs) into 22-, 24- and 21 nt siRNAs, respectively, and that loss of both DCL2 and DCL4 activities is required to negate RNAi and to release the plant's repression of viral replication. We also show that hpRNAs, similar to viral infection, can engender long-distance silencing signals and that hpRNA-induced silencing is suppressed by the expression of a virus-derived suppressor protein. These findings indicate that hpRNA-mediated RNAi in plants operates through the viral defence pathway.

RNAi for insect-proof plants

RNA interference induced in insects after ingestion of plant-expressed hairpin RNA offers promise for managing devastating crop pests

Exploring plant genomes by RNA-induced gene silencing

The nucleotide sequences of several animal, plant and bacterial genomes are now known, but the functions of many of the proteins that they are predicted to encode remain unclear. RNA interference is a gene-silencing technology that is being used successfully to investigate gene function in several organisms - for example, Caenorhabditis elegans. We discuss here that RNA-induced gene silencing approaches are also likely to be effective for investigating plant gene function in a high-throughput, genome-wide manner.

Viruses face a double defense by plant small RNAs

Plants fight viral infections with enzymes that digest viral RNA, but viruses retaliate with proteins that suppress these enzymes. To boost their antiviral response plants deploy enzymes with redundant functions.

The Enamovirus P0 protein is a silencing suppressor which inhibits local and systemic RNA silencing through AGO1 degradation

The P0 protein of poleroviruses and P1 protein of sobemoviruses suppress the plant's RNA silencing machinery. Here we identified a silencing suppressor protein (SSP), P0PE, in the Enamovirus Pea enation mosaic virus-1 (PEMV-1) and showed that it and the P0s of poleroviruses Potato leaf roll virus and Cereal yellow dwarf virus have strong local and systemic SSP activity, while the P1 of Sobemovirus Southern bean mosaic virus supresses systemic silencing. The nuclear localized P0PE has no discernable sequence conservation with known SSPs, but proved to be a strong suppressor of local silencing and a moderate suppressor of systemic silencing. Like the P0s from poleroviruses, P0PE destabilizes AGO1 and this action is mediated by an F-box-like domain. Therefore, despite the lack of any sequence similarity, the poleroviral and enamoviral SSPs have a conserved mode of action upon the RNA silencing machinery. © 2012 Elsevier Inc.

Synthesis of complementary RNA by RNA-dependent RNA polymerases in plant extracts is independent of an RNA primer

RNA-dependent RNA polymerase (RDR) activities were readily detected in extracts from cauliflower and broccoli florets, Arabidopsis thaliana (L.) Heynh callus tissue and broccoli nuclei. The synthesis of complementary RNA (cRNA) was independent of a RNA primer, whether or not the primer contained a 3′ terminal 2′-O-methyl group or was phosphorylated at the 5′ terminus. cRNA synthesis in plant extracts was not affected by loss-of-function mutations in the DICER-LIKE (DCL) proteins DCL2, DCL3, and DCL4, indicating that RDRs function independently of these DCL proteins. A loss-of-function mutation in RDR1, RDR2 or RDR6 did not significantly reduce the amount of cRNA synthesis. This indicates that these RDRs did not account for the bulk RDR activities in plant extracts, and suggest that either the individual RDRs each contribute a fraction of polymerase activity or another RDR(s) is predominant in the plant extract. © CSIRO 2008.

The roles of plant dsRNA-binding proteins in RNAi-like pathways

Dicers are associated with double-stranded RNA-binding proteins (dsRBPs) in animals. In the plant, Arabidopsis, there are four dicer-like (DCL) proteins and five potential dsRBPs. These DCLs act redundantly and hierarchically. However, we show there is little or no redundancy or hierarchy amongst the DRBs in their DCL interactions. DCL1 operates exclusively with DRB1 to produce micro (mi)RNAs, DCL4 operates exclusively with DRB4 to produce trans-acting (ta) siRNAs and 21nt siRNAs from viral RNA. DCL2 and DCL3 produce viral siRNAs without requiring assistance from any dsRBP. DRB2, DRB3 and DRB5 appear unnecessary for mi-, tasi-, viral si-, or heterochromatinising siRNA production but act redundantly in a developmental pathway. © 2008 Federation of European Biochemical Societies.