Metric Representations Of Networks

The goal of this thesis is to analyze networks by first projecting them onto structured metric-like spaces -- governed by a generalized triangle inequality -- and then leveraging this structure to facilitate the analysis. Networks encode relationships between pairs of nodes, however, the relationship between two nodes can be independent of the other ones and need not be defined for every pair. This is not true for metric spaces, where the triangle inequality imposes conditions that must be satisfied by triads of distances and these must be defined for every pair of nodes. In general terms, this additional structure facilitates the analysis and algorithm design in metric spaces. In deriving metric projections for networks, an axiomatic approach is pursued where we encode as axioms intuitively desirable properties and then seek for admissible projections satisfying these axioms. Although small variations are introduced throughout the thesis, the axioms of projection -- a network that already has the desired metric structure must remain unchanged -- and transformation -- when reducing dissimilarities in a network the projected distances cannot increase -- shape all of the axiomatic constructions considered. Notwithstanding their apparent weakness, the aforementioned axioms serve as a solid foundation for the theory of metric representations of networks. We begin by focusing on hierarchical clustering of asymmetric networks, which can be framed as a network projection problem onto ultrametric spaces. We show that the set of admissible methods is infinite but bounded in a well-defined sense and state additional desirable properties to further winnow the admissibility landscape. Algorithms for the clustering methods developed are also derived and implemented. We then shift focus to projections onto generalized q-metric spaces, a parametric family containing among others the (regular) metric and ultrametric spaces. A uniqueness result is shown for the projection of symmetric networks whereas for asymmetric networks we prove that all admissible projections are contained between two extreme methods. Furthermore, projections are illustrated via their implementation for efficient search and data visualization. Lastly, our analysis is extended to encompass projections of dioid spaces, natural algebraic generalizations of weighted networks

Sampling random graph homomorphisms and applications to network data analysis

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph $F$ into a large network $\mathcal{G}$. We propose two complementary MCMC algorithms for sampling a random graph homomorphisms and establish bounds on their mixing times and concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neigborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also apply our framework for network clustering and classification problems using the Facebook100 dataset and Word Adjacency Networks of a set of classic novels.Comment: 51 pages, 33 figures, 2 table

Evolution of the metabolic and regulatory networks associated with oxygen availability in two phytopathogenic enterobacteria

<p>Abstract</p> <p>Background</p> <p><it>Dickeya dadantii </it>and <it>Pectobacterium atrosepticum </it>are phytopathogenic enterobacteria capable of facultative anaerobic growth in a wide range of O₂concentrations found in plant and natural environments. The transcriptional response to O₂remains under-explored for these and other phytopathogenic enterobacteria although it has been well characterized for animal-associated genera including <it>Escherichia coli </it>and <it>Salmonella enterica</it>. Knowledge of the extent of conservation of the transcriptional response across orthologous genes in more distantly related species is useful to identify rates and patterns of regulon evolution. Evolutionary events such as loss and acquisition of genes by lateral transfer events along each evolutionary branch results in lineage-specific genes, some of which may have been subsequently incorporated into the O₂-responsive stimulon. Here we present a comparison of transcriptional profiles measured using densely tiled oligonucleotide arrays for two phytopathogens, <it>Dickeya dadantii </it>3937 and <it>Pectobacterium atrosepticum </it>SCRI1043, grown to mid-log phase in MOPS minimal medium (0.1% glucose) with and without O₂.</p> <p>Results</p> <p>More than 7% of the genes of each phytopathogen are differentially expressed with greater than 3-fold changes under anaerobic conditions. In addition to anaerobic metabolism genes, the O₂responsive stimulon includes a variety of virulence and pathogenicity-genes. Few of these genes overlap with orthologous genes in the anaerobic stimulon of <it>E. coli</it>. We define these as the conserved core, in which the transcriptional pattern as well as genetic architecture are well preserved. This conserved core includes previously described anaerobic metabolic pathways such as fermentation. Other components of the anaerobic stimulon show variation in genetic content, genome architecture and regulation. Notably formate metabolism, nitrate/nitrite metabolism, and fermentative butanediol production, differ between <it>E. coli </it>and the phytopathogens. Surprisingly, the overlap of the anaerobic stimulon between the phytopathogens is also relatively small considering that they are closely related, occupy similar niches and employ similar strategies to cause disease. There are cases of interesting divergences in the pattern of transcription of genes between <it>Dickeya </it>and <it>Pectobacterium </it>for virulence-associated subsystems including the type VI secretion system (T6SS), suggesting that fine-tuning of the stimulon impacts interaction with plants or competing microbes.</p> <p>Conclusions</p> <p>The small number of genes (an even smaller number if we consider operons) comprising the conserved core transcriptional response to O₂limitation demonstrates the extent of regulatory divergence prevalent in the Enterobacteriaceae. Our orthology-driven comparative transcriptomics approach indicates that the adaptive response in the eneterobacteria is a result of interaction of core (regulators) and lineage-specific (structural and regulatory) genes. Our subsystems based approach reveals that similar phenotypic outcomes are sometimes achieved by each organism using different genes and regulatory strategies.</p

Isolation of multipotent astroglia form the adult stem cell niche and the injured brain

Adult neural stem cells, as the source of life-long neurogenesis, reside in the subependymal zone (SEZ) in the lateral wall of the lateral ventricles and in the dentate gyrus of the hippocampus. In both neurogenic regions, subsets of glial fibrillary acidic protein (GFAP) expressing astrocytes are found, that have been shown to act as neural stem cells. So far, it is not known how to distinguish these stem cell astrocytes from other astrocyte populations within the SEZ. Towards this end we decided to isolate a subpopulation of adult SEZ astrocytes that expresses the CD133 by FACS. GFP-positive cells in the SEZ from hGFAP/eGFP mice that were also CD133+ve comprised all neurosphere-initiating cells that were self-renewing and multipotent from the SEZ. Moreover, single cell neurosphere analysis showed 70% efficiency in neurosphere formation. Further more Cre-mediated fate mapping of this double-positive population showed their contribution to adult neurogenesis. Transcriptional profiling of the GFP/CD133-double-positive cells allowed us to a) determine their similarity at the transcriptome level to both ependymal cells AND astrocytes and b) to identify their unique molecular neural stem cell signature. We also discovered that astrocytes outside this neurogenic niche could go some way towards dedifferentiation into neural stem cells. We have previously described (Buffo et al., PNAS 2008) a population of astrocytes in the adult cerebral cortex after stab wound injury that dedifferentiates as far to form multipotent and self-renewing neurospheres. Now we succeeded to establish the factor responsible for this dedifferentiation and sufficient to elicit the dedifferentiation response even in cells that were not exposed to injury. These data will be presented. Taken together, our work allows for the first time, the identification and characterization of the astrocyte sub-types acting as neural stem cells

The Role of Rac1 in the Epidermis and in the Hair Follicle

Rac1 is a ubiquitously expressed member of the Rho family of small GTPases, which acts as a molecular switch by shuttling in a highly regulated manner between an active (GTP-bound) and an inactive (GDP-bound) state. Different signalling pathways, which involve integrins, growth factor receptors, cadherins as well as other Rho GTPases, can induce Rac1 activation. Only in the GTP bound form, Rac1 can associate with different effector molecules to initiate cellular responses. Initially described as an important regulator of the actin cytoskeleton, Rac1 was later found to be also involved in the modulation of other processes such as cell adhesion, proliferation, survival, differentiation and migration. In epithelial cells, Rac1 was shown to regulate the formation and maintenance of cadherin dependent cell cell contacts, which are essential for the establishment of the polarized cell morphology. Before this project was initiated, almost all knowledge about the function of Rac1 was based on in vitro studies. As constitutive deletion of the murine rac1 gene leads to early embryonic lethality, mice allowing for a conditional inactivation of the rac1 gene were generated in this study to enable the analysis of the function of Rac1 in selected tissues. To investigate the role of Rac1 in the epidermis and hair follicles and to determine its function in the establishment and maintenance of cell cell contacts between epithelial cells in vivo, mice with a keratinocyte-restricted ablation of the rac1 gene were generated and analyzed. The results obtained in this study showed that the absence of Rac1 in the murine epidermis leads to a progressive hair loss but surprisingly has no effect on the maintenance of the epidermis. The hair loss is caused by the inability of hair follicle keratinocytes to maintain their differentiation state, which leads to the phagocytic removal of the non permanent parts of the hair follicles by infiltrating macrophages. In contrast, differentiation and proliferation of epidermal keratinocytes as well as the formation and maintenance of cell-cell and cell-matrix contacts, and the deposition of the basement membrane in the epidermis are not affected by the loss of Rac1. Biochemical analysis of epidermal lysates demonstrated that the absence of epidermal defects in vivo is not a result of compensatory upregulation of closely related members of the Rho family of GTPases, further indicating that the function of Rac1 in epithelial cells in vivo is limited. Also, the analysis of the formation of the embryoid bodies from Rac1-deficient embryonic stem cells showed that the presence of Rac1 is not required for the establishment of cell cell contacts during differentiation of the polarized primitive ectoderm and for the formation of epithelial sheets, supporting the conclusion that the function of Rac1 in the regulation of cell cell adhesion between epithelial cells is dispensable. However, the re epithelialization after wounding was impaired in the mutant epidermis, demonstrating that Rac1 plays an important role in pathological conditions. The delayed wound closure in the absence of Rac1 is caused by impaired cell migration and proliferation of neo epidermal keratinocytes. Another interesting finding of this study was the observation that, in contrast to the steady state in vivo situation, isolated Rac1 deficent primary keratinocytes display severe defects in cell culture, which lead to their detachment from the matrix. While the initial adhesion is only mildly affected by the lack of Rac1, mutant keratinocytes are unable to spread, show an impaired organization of the actin cytoskeleton and fail to form mature focal adhesions. The differences between in vivo and in vitro effects resulting from the inactivation of the rac1 gene indicate that the function of Rac1 in epithelial cells depends on the complexity of the cellular system and emphasize the importance of performing in vivo studies to fully understand its role. Taken together, the data presented in this study show that Rac1 plays an important role in the maintenance of hair follicles and during epidermal wound healing, but that it is not essential for the homeostasis of the epidermis in physiological conditions and for the formation and maintenance of cell cell contacts between epithelial cells in vivo

The role of prophages in Pseudomonas aeruginosa

Pseudomonas aeruginosa is a common opportunistic respiratory pathogen of individuals with cystic fibrosis (CF), capable of establishing chronic infections in which the bacterial population undergoes extensive phenotypic and genetic diversification. The Liverpool Epidemic Strain (LES) is a widespread hypervirulent and transmissible strain that is capable of superinfection and is linked to increased morbidity and mortality, relative to other P. aeruginosa strains. The LES has six prophages (LESφ1-6) within its genome, of which three are essential to the competitiveness of this strain. Temperate bacteriophages are incredibly common in bacterial pathogens and can contribute to bacterial fitness and virulence through the carriage of additional genes or modification of existing bacterial genes, lysis of competitors, or by conferring resistance to phage superinfection. Furthermore, the LES phages are detected at high levels in the CF lungs and have been implicated in controlling bacterial densities. The aims of this study were to (i) further characterise the LES phages and their induction, (ii) determine the extent to which the LES phages contribute to bacterial phenotypic and (iii) genetic diversification and (iv) determine how the LES phages affect host competitiveness, using a variety of in vitro and in vivo infection models. LES phages are continuously produced by spontaneous lysis and this study found that environmental factors that are common to the CF lung, such as oxidative stress, pharmaceutical chelating agents and antibiotics, can alter phage production by clinical LES isolates. Characterisation of the phages highlighted differences between the phages with regards to their lytic cycles and ability to propagate in different environments. P. aeruginosa undergoes extensive phenotypic diversification in an artificial sputum model (ASM) of infection, similar to that observed in chronic CF infections. Hypermutability, loss of motility and auxotrophy were phenotypes observed in bacteria evolved for approximately 240 bacterial generations in ASM in the presence and absence of the LES phages. However, the LES phages accelerated this process; loss of twitching motility occured earlier in populations evolved in the presence of phages. Sequencing of evolved populations revealed a high level of genetic diversification, with genes involved in motility, quorum sensing and genetic regulation experiencing loss of function mutations in parallel populations. In phage treated populations, LESφ4 had disruptively integrated into motility and quorum sensing genes, suggesting that temperate phages can provide an alternative (and quicker) route to adaptation. LES prophage carriage is important for bacterial competitiveness; PAO1 LES Phage Lysogens (PLPLs) successfully invaded a phage-susceptible population in vitro from when initially rare. Strain invasiveness was dependent on the LES prophage; LESφ4 lysogens were more invasive than PLPLφ2 or PLPLφ3, whereas carriage of all three prophages accelerated bacterial invasion. PLPLφtriple could also invade a susceptible competitor population in a rat model of chronic lung infection, although not as successfully as in vitro. These data suggest that prophage carriage is important for LES competitiveness and that phage-mediated lysis of phage-susceptible competitors may explain why LES is adept at superinfection. The study indicates that the LES phages are important drivers of bacterial diversification and evolution and confer a competitive advantage to their bacterial host. This may help explain why the LES is so successful, and the high prevalence of polylysogeny in bacterial pathogens