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PubMed2000

Combinatorial explosion in model gene networks.

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such networks are extremely rich and they offer novel ways to think about how mutations can alter dynamics. (c) 2000 American Institute of Physics.

Journal Article↗
PubMed2005

Characterizing the network topology of the energy landscapes of atomic clusters.

By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are characterized in detail for a series of small Lennard-Jones clusters and show behavior characteristic of small-world and scale-free networks. However, unlike many such networks, this topology cannot reflect the rules governing the dynamics of network growth, because they are static spatial networks. Instead, the heterogeneity in the networks stems from differences in the potential energy of the minima, and hence the hyperareas of their associated basins of attraction. The low-energy minima with large basins of attraction act as hubs in the network. Comparisons to randomized networks with the same degree distribution reveals structuring in the networks that reflects their spatial embedding.

Journal Article↗
PubMed2006

Synchronization in complex networks with a modular structure.

Networks with a community (or modular) structure arise in social and biological sciences. In such a network individuals tend to form local communities, each having dense internal connections. The linkage among the communities is, however, much more sparse. The dynamics on modular networks, for instance synchronization, may be of great social or biological interest. (Here by synchronization we mean some synchronous behavior among the nodes in the network, not, for example, partially synchronous behavior in the network or the synchronizability of the network with some external dynamics.) By using a recent theoretical framework, the master-stability approach originally introduced by Pecora and Carroll in the context of synchronization in coupled nonlinear oscillators, we address synchronization in complex modular networks. We use a prototype model and develop scaling relations for the network synchronizability with respect to variations of some key network structural parameters. Our results indicate that random, long-range links among distant modules is the key to synchronization. As an application we suggest a viable strategy to achieve synchronous behavior in social networks.

Action Potentials↗
PubMed1993

The structure of replicating kinetoplast DNA networks.

Kinetoplast DNA (kDNA), the mitochondrial DNA of Crithidia fasciculata and related trypanosomatids, is a network containing approximately 5,000 covalently closed minicircles which are topologically interlocked. kDNA synthesis involves release of covalently closed minicircles from the network, and, after replication of the free minicircles, reattachment of the nicked or gapped progeny minicircles to the network periphery. We have investigated this process by electron microscopy of networks at different stages of replication. The distribution of nicked and closed minicircles is easily detectable either by autoradiography of networks radiolabeled at endogenous nicks by nick translation or by twisting the covalently closed minicircles with intercalating dye. The location of newly synthesized minicircles within the network is determined by autoradiography of network is determined by autoradiography of networks labeled in vivo with a pulse of [3H]thymidine. These studies have clarified structural changes in the network during replication, the timing of repair of nicked minicircles after replication, and the mechanism of division of the network.

Animals↗
PubMed1968

Formation of elaborate networks of T-system tubules in cultured skeletal muscle with special reference to the T-system formation.

Muscle cells, cultured for 1-28 days from 11-day chick embryo breast muscles, often show elaborate, three-dimensional networks of a membranous system. The network consists of tubular units which are quite regularly arranged. The tubular units composing the network are accessible to ferritin particles suspended in the culture medium; this suggests continuity with the extracellular fluid. These networks can be regarded as a special morphological elaboration of the T-system tubules. Such network formations can be seen much more often in well-developed myotubes. The networks usually exhibit a hexagonal pattern, which is formed of tubular units of a constant diameter. However, some early myotubes contain tetragonal networks, which are composed of spherical pockets with channels of lesser diameter connecting the pockets. Networks are also observed which probably represent a transitional form between these two patterns. Myotubes show many inpocketings of the sarcolemma similar to what are commonly referred to as caveolae or micropinocytotic vesicles. The similarity in configuration and dimension of the tubular units of the network to the caveolae leads to the plausible suggestion that repeated caveola-formation from the sarcolemma or T-system tubule may result in formation of these networks. In this connection, a possible mechanism of the T-system tubule formation is discussed.

Animals↗
PubMed2000

Inferring qualitative relations in genetic networks and metabolic pathways.

MOTIVATION: Inferring genetic network architecture from time series data of gene expression patterns is an important topic in bioinformatics. Although inference algorithms based on the Boolean network were proposed, the Boolean network was not sufficient as a model of a genetic network. RESULTS: First, a Boolean network model with noise is proposed, together with an inference algorithm for it. Next, a qualitative network model is proposed, in which regulation rules are represented as qualitative rules and embedded in the network structure. Algorithms are also presented for inferring qualitative relations from time series data. Then, an algorithm for inferring S-systems (synergistic and saturable systems) from time series data is presented, where S-systems are based on a particular kind of nonlinear differential equation and have been applied to the analysis of various biological systems. Theoretical results are shown for Boolean networks with noises and simple qualitative networks. Computational results are shown for Boolean networks with noises and S-systems, where real data are not used because the proposed models are still conceptual and the quantity and quality of currently available data are not enough for the application of the proposed methods.

Algorithms↗
PubMed2003

FluxAnalyzer: exploring structure, pathways, and flux distributions in metabolic networks on interactive flux maps.

MOTIVATION: The analysis of structure, pathways and flux distributions in metabolic networks has become an important approach for understanding the functionality of metabolic systems. The need of a user-friendly platform for stoichiometric modeling of metabolic networks in silico is evident. RESULTS: The FluxAnalyzer is a package for MATLAB and facilitates integrated pathway and flux analysis for metabolic networks within a graphical user interface. Arbitrary metabolic network models can be composed by instances of four types of network elements. The abstract network model is linked with network graphics leading to interactive flux maps which allow for user input and display of calculation results within a network visualization. Therein, a large and powerful collection of tools and algorithms can be applied interactively including metabolic flux analysis, flux optimization, detection of topological features and pathway analysis by elementary flux modes or extreme pathways. The FluxAnalyzer has been applied and tested for complex networks with more than 500,000 elementary modes. Some aspects of the combinatorial complexity of pathway analysis in metabolic networks are discussed. AVAILABILITY: Upon request from the corresponding author. Free for academic users (license agreement). Special contracts are available for industrial corporations. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer.

Combinatorial Chemistry Techniques↗
PubMed2003

Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms.

MOTIVATION: Information from fully sequenced genomes makes it possible to reconstruct strain-specific global metabolic network for structural and functional studies. These networks are often very large and complex. To properly understand and analyze the global properties of metabolic networks, methods for rationally representing and quantitatively analyzing their structure are needed. RESULTS: In this work, the metabolic networks of 80 fully sequenced organisms are in silico reconstructed from genome data and an extensively revised bioreaction database. The networks are represented as directed graphs and analyzed by using the 'breadth first searching algorithm to identify the shortest pathway (path length) between any pair of the metabolites. The average path length of the networks are then calculated and compared for all the organisms. Different from previous studies the connections through current metabolites and cofactors are deleted to make the path length analysis physiologically more meaningful. The distribution of the connection degree of these networks is shown to follow the power law, indicating that the overall structure of all the metabolic networks has the characteristics of a small world network. However, clear differences exist in the network structure of the three domains of organisms. Eukaryotes and archaea have a longer average path length than bacteria. AVAILABILITY: The reaction database in excel format and the programs in VBA (Visual Basic for Applications) are available upon request. SUPPLEMENTARY MATERIAL: Bioinformatics Online.

Archaea↗
PubMed2005

Fast protein classification with multiple networks.

MOTIVATION: Support vector machines (SVMs) have been successfully used to classify proteins into functional categories. Recently, to integrate multiple data sources, a semidefinite programming (SDP) based SVM method was introduced. In SDP/SVM, multiple kernel matrices corresponding to each of data sources are combined with weights obtained by solving an SDP. However, when trying to apply SDP/SVM to large problems, the computational cost can become prohibitive, since both converting the data to a kernel matrix for the SVM and solving the SDP are time and memory demanding. Another application-specific drawback arises when some of the data sources are protein networks. A common method of converting the network to a kernel matrix is the diffusion kernel method, which has time complexity of O(n(3)), and produces a dense matrix of size n x n. RESULTS: We propose an efficient method of protein classification using multiple protein networks. Available protein networks, such as a physical interaction network or a metabolic network, can be directly incorporated. Vectorial data can also be incorporated after conversion into a network by means of neighbor point connection. Similar to the SDP/SVM method, the combination weights are obtained by convex optimization. Due to the sparsity of network edges, the computation time is nearly linear in the number of edges of the combined network. Additionally, the combination weights provide information useful for discarding noisy or irrelevant networks. Experiments on function prediction of 3588 yeast proteins show promising results: the computation time is enormously reduced, while the accuracy is still comparable to the SDP/SVM method. AVAILABILITY: Software and data will be available on request.

Algorithms↗
PubMed2005

Selective integration of multiple biological data for supervised network inference.

MOTIVATION: Inferring networks of proteins from biological data is a central issue of computational biology. Most network inference methods, including Bayesian networks, take unsupervised approaches in which the network is totally unknown in the beginning, and all the edges have to be predicted. A more realistic supervised framework, proposed recently, assumes that a substantial part of the network is known. We propose a new kernel-based method for supervised graph inference based on multiple types of biological datasets such as gene expression, phylogenetic profiles and amino acid sequences. Notably, our method assigns a weight to each type of dataset and thereby selects informative ones. Data selection is useful for reducing data collection costs. For example, when a similar network inference problem must be solved for other organisms, the dataset excluded by our algorithm need not be collected. RESULTS: First, we formulate supervised network inference as a kernel matrix completion problem, where the inference of edges boils down to estimation of missing entries of a kernel matrix. Then, an expectation-maximization algorithm is proposed to simultaneously infer the missing entries of the kernel matrix and the weights of multiple datasets. By introducing the weights, we can integrate multiple datasets selectively and thereby exclude irrelevant and noisy datasets. Our approach is favorably tested in two biological networks: a metabolic network and a protein interaction network. AVAILABILITY: Software is available on request.

Algorithms↗
PubMed1997

A network of tufted layer 5 pyramidal neurons.

Tufted layer 5 (TL5) pyramidal neurons are important projection neurons from the cerebral cortex to subcortical areas. Recent and ongoing experiments aimed at understanding the computational analysis performed by a network of synaptically connected TL5 neurons are reviewed here. The experiments employed dual and triple whole-cell patch clamp recordings from visually identified and preselected neurons in brain slices of somatosensory cortex of young (14- to 16-day-old) rats. These studies suggest that a local network of TL5 neurons within a cortical module of diameter 300 microns consists of a few hundred neurons that are extensively inter-connected with reciprocal feedback from at least first-, second- and third-order target neurons. A statistical analysis of synaptic innervation suggests that this recurrent network is not randomly arranged and hence each neuron could be functionally unique. Synaptic transmission between these neurons is characterized by use-dependent synaptic depression which confers novel properties to this recurrent network of neurons. First, a range of rates of depression for different synaptic connections enable each TL5 neuron to receive a unique mixture of information about the average firing rates and the temporally correlated action potential (AP) activity in the population of presynaptic TL5 neurons. Second, each AP generated by any neuron in the network induces a change (defined as an iteration step) in the functional coupling of the neurons in the network (defined as network configuration). It is proposed that the network configuration is iterated during a stimulus to achieve an optimally orchestrated network response. Hebbian, anti-Hebbian and neuromodulatory-induced modifications of neurotransmitter release probability change the rates of synaptic depression and thereby alter the iteration step size. These data may be important to understand the dynamics of electrical activity within the network.

Animals↗
PubMed2006

Social network typologies and mental health among older adults.

In this study, we test the robustness of previous social network research and extend this work to determine if support quality is one mechanism by which network types predict mental health. Participants included 1,669 adults aged 60 or older from the Americans' Changing Lives study. Using cluster analysis, we found diverse, family, and friends network types, which is consistent with the work by Litwin from 2001. However, we found two types of restricted networks, rather than just one: a nonfamily network and a nonfriends network. Depressive symptomatology was highest for individuals in the nonfriends network and lowest for individuals in the diverse network. Positive support quality partially mediated the association between network type and depressive symptomatology. Results suggest that the absence of family in the context of friends is less detrimental than the absence of friends in the context of family, and that support quality is one mechanism through which network types affect mental health.

Aged↗
PubMed2006

Network type and mortality risk in later life.

PURPOSE: The purpose of this study was to examine the association of baseline network type and 7-year mortality risk in later life. DESIGN AND METHODS: We executed secondary analysis of all-cause mortality in Israel using data from a 1997 national survey of adults aged 60 and older (N=5,055) that was linked to records from the National Death Registry up to 2004. We considered six network types--diverse, friend focused, neighbor focused, family focused, community-clan, and restricted--in the analysis, controlling for population group, sociodemographic background, and health factors. We carried out Cox proportional hazards regressions for the entire sample and separately by age group at baseline: 60-69, 70-79, and 80 and older. RESULTS: Network types were associated with mortality in the 70-79 and 80 and older age groups. Respondents located in diverse and friend-focused network types, and to a lesser degree those located in community-clan network types, had a lower risk of mortality compared to individuals belonging to restricted networks. IMPLICATIONS: Gerontological practitioners should address older adults' social networks in their assessments of clients. The parameters used to derive network types in this study can serve toward the development of practical network type inventories. Moreover, practitioners should tailor the interventions they implement to the different network types in which their elderly clients are embedded.

Aged↗
PubMed1990

The effects of some plasma proteins on fibrin network structure.

Pronounced differences are found between characteristics of networks developed in plasma and those developed in pure fibrinogen solution. Networks in plasma have thicker fibres, are more permeable and have lower tensile strength. In this investigation the role of some plasma proteins as determinants of network structure under physiological conditions of clotting has been examined in an attempt to account for the differences in network structure in plasma and fibrinogen solution. The effect of physiological concentrations of antithrombin III, fibronectin, albumin, alpha globulin and gamma globulin on fibrin network structure was examined using mass-length ratio (muT) from turbidity, bulk network permeability (tau) and kinetics of network development. It was found that differences in fibrin network structure developed in plasma and pure fibrinogen solution could not be accounted for by alterations induced in network properties by albumin, gamma globulin, alpha globulin, fibronectin and antithrombin III. It is concluded that the final network structure is determined by the kinetics of fibrin fibre growth and is highly responsive to the presence of plasma proteins.

Antithrombin III↗
PubMed2006

Analysis of downstream revenue to an academic medical center from a primary care network.

PURPOSE: Many academic medical centers (i.e., teaching hospitals) have established primary care networks for not only assuring a referral base but also for educating students in the primary care setting. Such networks generally are not profitable when analyzed on an individual facility basis. However, revenues generated at the medical center in terms of inpatient admissions, laboratory testing etc., usually are much larger than generated on site. In this study, the downstream revenue from 18 practice sites was evaluated at The Ohio State University Medical Center. METHOD: Revenues in fiscal year July 1, 2003, to June 30, 2004, were broken down into four streams, including inpatient and outpatient charges and collections for both network and specialist physicians. A fifth stream evaluated specialist professional fees. The authors developed a novel conservative weighting system to capture the concept that not all revenues generated from network patients were actually dependent on the use of the network. RESULTS: Findings included that the downstream direct contribution margin of US dollars 14 million just from the admissions and outpatient tests and procedures directly generated by network physicians alone was nearly twice the US dollars 8.3 million network operating loss. The total downstream net revenue of nearly US dollars 115 million was more than 6 times the US dollars 18.9 million net revenue to the network. The downstream direct contribution margin of US dollars 52 million was 6.3 times the network loss. Total downstream gross revenue (charges) to the medical center was over US dollars 250 million and over US dollars 300 million when the specialist gross revenues were included. CONCLUSIONS: This study demonstrates that a primary care network can generate significant financial support for an academic medical center.

Academic Medical Centers↗
PubMed2005

A randomized social network HIV prevention trial with young men who have sex with men in Russia and Bulgaria.

OBJECTIVE: To evaluate the effects of an HIV prevention intervention with social networks of young men who have sex with men (YMSM) in St. Petersburg, Russia and Sofia, Bulgaria. DESIGN: A two-arm randomized trial with a longitudinally-followed community cohort. METHODS: Fifty-two MSM social networks were recruited through access points in high-risk community venues. Network members (n = 276) were assessed to determine risk characteristics, administered sociometric measures to empirically identify the social leader of each network, and counseled in risk reduction. The leaders of 25 experimental condition networks attended a nine-session program that provided training and guidance in delivering ongoing theory-based HIV prevention advice to other network members. Leaders successively targeted network members' AIDS risk-related knowledge and risk reduction norms, attitudes, intentions, and self-efficacy. Participants were re-administered risk assessment measures at 3- and 12-month follow-ups. RESULTS: Among changes produced, the percentage of experimental network members reporting unprotected intercourse (UI) declined from 71.8 to 48.4% at 3-month follow up (P = 0.0001). The percentage who engaged in UI with multiple partners reduced from 31.5 to 12.9% (P = 0.02). After 12 months, the effects became attenuated but remained among participants who had multiple recent sexual partners, the most vulnerable group. Little change was found in control group networks. CONCLUSIONS: Interventions that engage the identified influence leaders of at-risk YMSM social networks to communicate theory-based counseling and advice can produce significant sexual risk behavior change. This model is culturally pertinent for HIV prevention efforts in former socialist countries, as well as elsewhere for other hard-to-reach vulnerable community populations.

Adult↗
PubMed2006

An entropic characterization of protein interaction networks and cellular robustness.

The structure of molecular networks is believed to determine important aspects of their cellular function, such as the organismal resilience against random perturbations. Ultimately, however, cellular behaviour is determined by the dynamical processes, which are constrained by network topology. The present work is based on a fundamental relation from dynamical systems theory, which states that the macroscopic resilience of a steady state is correlated with the uncertainty in the underlying microscopic processes, a property that can be measured by entropy. Here, we use recent network data from large-scale protein interaction screens to characterize the diversity of possible pathways in terms of network entropy. This measure has its origin in statistical mechanics and amounts to a global characterization of both structural and dynamical resilience in terms of microscopic elements. We demonstrate how this approach can be used to rank network elements according to their contribution to network entropy and also investigate how this suggested ranking reflects on the functional data provided by gene knockouts and RNAi experiments in yeast and Caenorhabditis elegans. Our analysis shows that knockouts of proteins with large contribution to network entropy are preferentially lethal. This observation is robust with respect to several possible errors and biases in the experimental data. It underscores the significance of entropy as a fundamental invariant of the dynamical system, and as a measure of structural and dynamical properties of networks. Our analytical approach goes beyond the phenomenological studies of cellular robustness based on local network observables, such as connectivity. One of its principal achievements is to provide a rationale to study proxies of cellular resilience and rank proteins according to their importance within the global network context.

Computer Simulation↗
PubMed2005

Condition-dependent functional connectivity: syntax networks in bilinguals.

This paper introduces a method to study the variation of brain functional connectivity networks with respect to experimental conditions in fMRI data. It is related to the psychophysiological interaction technique introduced by Friston et al. and extends to networks of correlation modulation (CM networks). Extended networks containing several dozens of nodes are determined in which the links correspond to consistent correlation modulation across subjects. In addition, we assess inter-subject variability and determine networks in which the condition-dependent functional interactions can be explained by a subject-dependent variable. We applied the technique to data from a study on syntactical production in bilinguals and analysed functional interactions differentially across tasks (word reading or sentence production) and across languages. We find an extended network of consistent functional interaction modulation across tasks, whereas the network comparing languages shows fewer links. Interestingly, there is evidence for a specific network in which the differences in functional interaction across subjects can be explained by differences in the subjects' syntactical proficiency. Specifically, we find that regions, including ones that have previously been shown to be involved in syntax and in language production, such as the left inferior frontal gyrus, putamen, insula, precentral gyrus, as well as the supplementary motor area, are more functionally linked during sentence production in the second, compared with the first, language in syntactically more proficient bilinguals than in syntactically less proficient ones. Our approach extends conventional activation analyses to the notion of networks, emphasizing functional interactions between regions independently of whether or not they are activated. On the one hand, it gives rise to testable hypotheses and allows an interpretation of the results in terms of the previous literature, and on the other hand, it provides a basis for studying the structure of functional interactions as a whole, and hence represents a further step towards the notion of large-scale networks in functional imaging.

Brain↗