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PubMed2002

Random graph models of social networks.

We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of real-world social networks and find that in some cases, the models are in remarkable agreement with the data, whereas in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

Humans↗
PubMed2004

The architecture of complex weighted networks.

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity. Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensity of the connections. These features, however, have mainly not been considered in past studies where links are usually represented as binary states, i.e., either present or absent. Here, we study the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network. We define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices. This information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network. These results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks.

Data Interpretation, Statistical↗
PubMed2004

An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex.

A coarse-grained representation of neuronal network dynamics is developed in terms of kinetic equations, which are derived by a moment closure, directly from the original large-scale integrate-and-fire (I&F) network. This powerful kinetic theory captures the full dynamic range of neuronal networks, from the mean-driven limit (a limit such as the number of neurons N --> infinity, in which the fluctuations vanish) to the fluctuation-dominated limit (such as in small N networks). Comparison with full numerical simulations of the original I&F network establishes that the reduced dynamics is very accurate and numerically efficient over all dynamic ranges. Both analytical insights and scale-up of numerical representation can be achieved by this kinetic approach. Here, the theory is illustrated by a study of the dynamical properties of networks of various architectures, including excitatory and inhibitory neurons of both simple and complex type, which exhibit rich dynamic phenomena, such as, transitions to bistability and hysteresis, even in the presence of large fluctuations. The implication for possible connections between the structure of the bifurcations and the behavior of complex cells is discussed. Finally, I&F networks and kinetic theory are used to discuss orientation selectivity of complex cells for "ring-model" architectures that characterize changes in the response of neurons located from near "orientation pinwheel centers" to far from them.

Computer Simulation↗
PubMed2005

The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles.

We analyze the global structure of the worldwide air transportation network, a critical infrastructure with an enormous impact on local, national, and international economies. We find that the worldwide air transportation network is a scale-free small-world network. In contrast to the prediction of scale-free network models, however, we find that the most connected cities are not necessarily the most central, resulting in anomalous values of the centrality. We demonstrate that these anomalies arise because of the multicommunity structure of the network. We identify the communities in the air transportation network and show that the community structure cannot be explained solely based on geographical constraints and that geopolitical considerations have to be taken into account. We identify each city's global role based on its pattern of intercommunity and intracommunity connections, which enables us to obtain scale-specific representations of the network.

Journal Article↗
PubMed2005

Xenopus as a model system to study transcriptional regulatory networks.

Development is controlled by a complex series of events requiring sequential gene activation. Understanding the logic of gene networks during development is necessary for a complete understanding of how genes contribute to phenotype. Pioneering work initiated in the sea urchin and Drosophila has demonstrated that reasonable transcriptional regulatory network diagrams representing early development in multicellular animals can be generated through use of appropriate genomic, genetic, and biochemical tools. Establishment of similar regulatory network diagrams for vertebrate development is a necessary step. The amphibian Xenopus has long been used as a model for vertebrate early development and has contributed greatly to the elucidation of gene regulation. Because the best and most extensively studied transcriptional regulatory network in Xenopus is that underlying the formation and function of Spemann's organizer, we describe the current status of our understanding of this gene regulatory network and its relationship to mesodermal patterning. Seventy-four transcription factors currently known to be expressed in the mesoendoderm of Xenopus gastrula were characterized according to their modes of action, DNA binding consensus sequences, and target genes. Among them, nineteen transcription factors were characterized sufficiently in detail, allowing us to generate a gene regulatory network diagram. Additionally, we discuss recent amphibian work using a combined DNA microarray and bioinformatics approach that promises to accelerate regulatory network studies.

Animals↗
PubMed2005

Dynamic pattern evolution on scale-free networks.

A general class of dynamic models on scale-free networks is studied by analytical methods and computer simulations. Each network consists of N vertices and is characterized by its degree distribution, P(k), which represents the probability that a randomly chosen vertex is connected to k nearest neighbors. Each vertex can attain two internal states described by binary variables or Ising-like spins that evolve in time according to local majority rules. Scale-free networks, for which the degree distribution has a power law tail P(k) approximately k(-gamma), are shown to exhibit qualitatively different dynamic behavior for gamma < 5/2 and gamma > 5/2, shedding light on the empirical observation that many real-world networks are scale-free with 2 < gamma < 5/2. For 2 < gamma < 5/2, strongly disordered patterns decay within a finite decay time even in the limit of infinite networks. For gamma > 5/2, on the other hand, this decay time diverges as ln(N) with the network size N. An analogous distinction is found for a variety of more complex models including Hopfield models for associative memory networks. In the latter case, the storage capacity is found, within mean field theory, to be independent of N in the limit of large N for gamma > 5/2 but to grow as N(alpha) with alpha = (5 - 2gamma)/(gamma - 1) for 2 < gamma < 5/2.

Journal Article↗
PubMed2005

Targeting c-Myc-activated genes with a correlation method: detection of global changes in large gene expression network dynamics.

This work studies the dynamics of a gene expression time series network. The network, which is obtained from the correlation of gene expressions, exhibits global dynamic properties that emerge after a cell state perturbation. The main features of this network appear to be more robust when compared with those obtained with a network obtained from a linear Markov model. In particular, the network properties strongly depend on the exact time sequence relationships between genes and are destroyed by random temporal data shuffling. We discuss in detail the problem of finding targets of the c-myc protooncogene, which encodes a transcriptional regulator whose inappropriate expression has been correlated with a wide array of malignancies. The data used for network construction are a time series of gene expression, collected by microarray analysis of a rat fibroblast cell line expressing a conditional Myc-estrogen receptor oncoprotein. We show that the correlation-based model can establish a clear relationship between network structure and the cascade of c-myc-activated genes.

Analysis of Variance↗
PubMed2006

A metabolic network in the evolutionary context: multiscale structure and modularity.

The enormous complexity of biological networks has led to the suggestion that networks are built of modules that perform particular functions and are "reused" in evolution in a manner similar to reusable domains in protein structures or modules of electronic circuits. Analysis of known biological networks has revealed several modules, many of which have transparent biological functions. However, it remains to be shown that identified structural modules constitute evolutionary building blocks, independent and easily interchangeable units. An alternative possibility is that evolutionary modules do not match structural modules. To investigate the structure of evolutionary modules and their relationship to functional ones, we integrated a metabolic network with evolutionary associations between genes inferred from comparative genomics. The resulting metabolic-genomic network places metabolic pathways into evolutionary and genomic context, thereby revealing previously unknown components and modules. We analyzed the integrated metabolic-genomic network on three levels: macro-, meso-, and microscale. The macroscale level demonstrates strong associations between neighboring enzymes and between enzymes that are distant on the network but belong to the same linear pathway. At the mesoscale level, we identified evolutionary metabolic modules and compared them with traditional metabolic pathways. Although, in some cases, there is almost exact correspondence, some pathways are split into independent modules. On the microscale level, we observed high association of enzyme subunits and weak association of isoenzymes independently catalyzing the same reaction. This study shows that evolutionary modules, rather than pathways, may be thought of as regulatory and functional units in bacterial genomes.

Biological Evolution↗
PubMed2006

A likelihood approach to analysis of network data.

Biological, sociological, and technological network data are often analyzed by using simple summary statistics, such as the observed degree distribution, and nonparametric bootstrap procedures to provide an adequate null distribution for testing hypotheses about the network. In this article we present a full-likelihood approach that allows us to estimate parameters for general models of network growth that can be expressed in terms of recursion relations. To handle larger networks we have developed an importance sampling scheme that allows us to approximate the likelihood and draw inference about the network and how it has been generated, estimate the parameters in the model, and perform parametric bootstrap analysis of network data. We illustrate the power of this approach by estimating growth parameters for the Caenorhabditis elegans protein interaction network.

Animals↗
PubMed2002

Assigning numbers to the arrows: parameterizing a gene regulation network by using accurate expression kinetics.

A basic challenge in systems biology is to understand the dynamical behavior of gene regulation networks. Current approaches aim at determining the network structure based on genomic-scale data. However, the network connectivity alone is not sufficient to define its dynamics; one needs to also specify the kinetic parameters for the regulation reactions. Here, we ask whether effective kinetic parameters can be assigned to a transcriptional network based on expression data. We present a combined experimental and theoretical approach based on accurate high temporal-resolution measurement of promoter activities from living cells by using green fluorescent protein (GFP) reporter plasmids. We present algorithms that use these data to assign effective kinetic parameters within a mathematical model of the network. To demonstrate this, we employ a well defined network, the SOS DNA repair system of Escherichia coli. We find a strikingly detailed temporal program of expression that correlates with the functional role of the SOS genes and is driven by a hierarchy of effective kinetic parameter strengths for the various promoters. The calculated parameters can be used to determine the kinetics of all SOS genes given the expression profile of just one representative, allowing a significant reduction in complexity. The concentration profile of the master SOS transcriptional repressor can be calculated, demonstrating that relative protein levels may be determined from purely transcriptional data. This finding opens the possibility of assigning kinetic parameters to transcriptional networks on a genomic scale.

Algorithms↗
PubMed2002

Formation of geometrically complex lipid nanotube-vesicle networks of higher-order topologies.

We present a microelectrofusion method for construction of fluid-state lipid bilayer networks of high geometrical complexity up to fully connected networks with genus = 3 topology. Within networks, self-organizing branching nanotube architectures could be produced where intersections spontaneously arrange themselves into three-way junctions with an angle of 120 degrees between each nanotube. Formation of branching nanotube networks appears to follow a minimum-bending energy algorithm that solves for pathway minimization. It is also demonstrated that materials can be injected into specific containers within a network by nanotube-mediated transport of satellite vesicles having defined contents. Using a combination of microelectrofusion, spontaneous nanotube pattern formation, and satellite-vesicle injection, complex networks of containers and nanotubes can be produced for a range of applications in, for example, nanofluidics and artificial cell design. In addition, this electrofusion method allows integration of biological cells into lipid nanotube-vesicle networks.

Lipids↗
PubMed2000

Classes of small-world networks.

We study the statistical properties of a variety of diverse real-world networks. We present evidence of the occurrence of three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; (b) broad-scale networks, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and (c) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.

Interpersonal Relations↗
PubMed1986

Sequential state generation by model neural networks.

Sequential patterns of neural output activity form the basis of many biological processes, such as the cyclic pattern of outputs that control locomotion. I show how such sequences can be generated by a class of model neural networks that make defined sets of transitions between selected memory states. Sequence-generating networks depend upon the interplay between two sets of synaptic connections. One set acts to stabilize the network in its current memory state, while the second set, whose action is delayed in time, causes the network to make specified transitions between the memories. The dynamic properties of these networks are described in terms of motion along an energy surface. The performance of the networks, both with intact connections and with noisy or missing connections, is illustrated by numerical examples. In addition, I present a scheme for the recognition of externally generated sequences by these networks.

Artificial Intelligence↗
PubMed1988

Neural networks counting chimes.

It is shown that the ideas that led to neural networks capable of recalling associatively and asynchronously temporal sequences of patterns can be extended to produce a neural network that automatically counts the cardinal number in a sequence of identical external stimuli. The network is explicitly constructed, analyzed, and simulated. Such a network may account for the cognitive effect of the automatic counting of chimes to tell the hour. A more general implication is that different electrophysiological responses to identical stimuli, at certain stages of cortical processing, do not necessarily imply synaptic modification, a la Hebb. Such differences may arise from the fact that consecutive identical inputs find the network in different stages of an active temporal sequence of cognitive states. These types of networks are then situated within a program for the study of cognition, which assigns the detection of meaning as the primary role of attractor neural networks rather than computation, in contrast to the parallel distributed processing attitude to the connectionist project. This interpretation is free of homunculus, as well as from the criticism raised against the cognitive model of symbol manipulation. Computation is then identified as the syntax of temporal sequences of quasi-attractors.

Computer Simulation↗
PubMed2002

Microheterogeneity controls the rate of gelation of actin filament networks.

Rapid sol-gel transitions of the actin cytoskeleton are required for many key cellular processes, including cell spreading and cell locomotion. Actin monomers assemble into semiflexible polymers that rapidly intertwine into a network, a process that in vitro takes approximately 1 min for an actin concentration of 1 mg/ml. The same actin filament network, however, takes approximately 1 h to exhibit a steady-state elasticity. We hypothesize that the slow gelation of F-actin is due to the slow establishment of a homogeneous meshwork. Using a novel method, time-resolved multiple particle tracking, which monitors the range of thermally excited displacements of microspheres imbedded in the network, we show that the increase in elasticity in a polymerizing solution of actin parallels the progressive decline of the network microheterogeneity. The rates of gelation and network homogenization slightly decrease with actin concentration and in the presence of the F-actin cross-linking proteins alpha-actinin and fascin, whereas the rate of actin polymerization increases dramatically with actin concentration. Our measurements show that the slow spatial homogenization of the actin filament network, not actin polymerization or the formation of polymer overlaps, is the rate-limiting step in the establishment of an elastic actin network and suggest that a new activity of F-actin binding proteins may be required for the rapid formation of a homogeneous stiff gel.

Actin Cytoskeleton↗
PubMed2004

Reconstruction and functional characterization of the human mitochondrial metabolic network based on proteomic and biochemical data.

Diverse datasets including genomic, proteomic, isotopomer, and DNA sequence variation are becoming available for human mitochondria. Thus there is a need to integrate these data within an in silico modeling framework where mitochondrial biology and related disorders can be studied and analyzed. This paper reports a reconstruction and characterization of the human mitochondrial metabolic network based on proteomic and biochemical data. The 189 reactions included in this reconstruction are both elementally and charge-balanced and are assigned to their respective cellular compartments (mitochondrial, cytosol, or extracellular). The capabilities of the reconstructed network to fulfill three metabolic functions (ATP production, heme synthesis, and mixed phospholipid synthesis) were determined. Network-based analysis of the mitochondrial energy conversion process showed that the overall ATP yield per glucose is 31.5. Network flexibility, characterized by allowable variation in reaction fluxes, was evaluated using flux variability analysis and analysis of all of the possible optimal flux distributions. Results showed that the network has high flexibility for the biosynthesis of heme and phospholipids but modest flexibility for maximal ATP production. A subset of all of the optimal network flux distributions, computed with respect to the three metabolic functions individually, was found to be highly correlated, suggesting that this set may contain physiological meaningful fluxes. Examinations of optimal flux distributions also identified correlated reaction sets that form functional modules in the network.

Amino Acids↗
PubMed2000

Disruption of the actin filament network affects delivery of endocytic contents marker to phagosomes with early endosome characteristics: the case of phagosomes with pathogenic mycobacteria.

Phagosomes containing live virulent mycobacteria undergo fusion with early endosomes, but they are unable to mature normally. Accordingly, they do not fuse with lysosomes. Although M. avium-containing phagosomes retain fusion and intermingling characteristics of early endosomes indefinitely, fusions with early endosomes are increasingly restricted as bacteria multiply. In addition, when endocytic tracers, such as horseradish peroxidase (HRP), are added to M. avium-infected macrophages at 1 or up to 15 days after infection, an atypical time course of acquisition of the tracer by the phagosomes is observed, i.e., a 10 to 20 min lag, instead of immediate acquisition as is typical for early endosomes (and phagosomes with early endosome characteristics). These events coincide with a marked disorganization of the actin filament network in M. avium-infected macrophages. In the present study, we have therefore addressed the following question: Do actin filaments play a role in fusion and intermingling of contents between early endosomes and immature phagosomes that undergo homotypic fusion with early endosomes? We examined the time course of acquisition of subsequently internalized endocytic marker (HRP) by early endosome-like preexisting phagosomes, i.e. 2 hour-old phagosomes with either hydrophobic latex particles, virulent or avirulent M. avium, after depolymerization of the actin filament network with cytochalasin D or after repolymerization of the actin filament network with jasplakinolide, in cases where the network had been depolymerized (macrophages infected with M. avium, at 1 or up to 7 days after infection). By direct morphological observation at the electron microscope level and by a kinetic approach, we show here that depolymerization of the actin filament network with cytochalasin D delays acquisition of HRP whereas repolymerization restores immediate acquisition of the marker. We conclude that the actin filament network is involved in fusion and intermingling of endocytic contents between early endosomes and early endosome-like phagosomes, and that disruption of this network by M. avium is the cause for the atypical acquisition of content marker by phagosomes containing these pathogenic mycobacteria.

Actins↗
PubMed2003

Evidence for trafficking of PfEMP1 to the surface of P. falciparum-infected erythrocytes via a complex membrane network.

The human malarial parasite Plasmodium falciparum exports virulence determinants, such as the P. falciparum erythrocyte membrane protein 1 (PfEMP1), beyond its own periplasmatic boundaries to the surface of its host erythrocyte. This is remarkable given that erythrocytes lack a secretory pathway. Here we present evidence for a continuous membrane network of parasite origin in the erythrocyte cytoplasm. Co-localizations with antibodies against PfEMP1, PfExp-1, Pf332 and PfSbpl at the light and electron microscopical level indicate that this membrane network is composed of structures that have been previously described as tubovesicular membrane network (TVM), Maurer's clefts and membrane whorls. This membrane network could also be visualized in vivo by vital staining of infected erythrocytes with the fluorescent dye LysoSensor Green DND-153. At sites where the membrane network abuts the erythrocyte plasma membrane we observed small vesicles of 15-25 nm in size, which seem to bud from and/or fuse with the membrane network and the erythrocyte plasma membrane, respectively. On the basis of our data we hypothesize that this membrane network of parasite origin represents a novel secretory organelle that is involved in the trafficking of PfEMP1 across the erythrocyte cytoplasm.

Animals↗