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Gene co-expression network topology provides a framework for molecular characterization of cellular state.

MOTIVATION: Gene expression data have become an instrumental resource in describing the molecular state associated with various cellular phenotypes and responses to environmental perturbations. The utility of expression profiling has been demonstrated in partitioning clinical states, predicting the class of unknown samples and in assigning putative functional roles to previously uncharacterized genes based on profile similarity. However, gene expression profiling has had only limited success in identifying therapeutic targets. This is partly due to the fact that current methods based on fold-change focus only on single genes in isolation, and thus cannot convey causal information. In this paper, we present a technique for analysis of expression data in a graph-theoretic framework that relies on associations between genes. We describe the global organization of these networks and biological correlates of their structure. We go on to present a novel technique for the molecular characterization of disparate cellular states that adds a new dimension to the fold-based methods and conclude with an example application to a human medulloblastoma dataset. RESULTS: We have shown that expression networks generated from large model-organism expression datasets are scale-free and that the average clustering coefficient of these networks is several orders of magnitude higher than would be expected for similarly sized scale-free networks, suggesting an inherent hierarchical modularity similar to that previously identified in other biological networks. Furthermore, we have shown that these properties are robust with respect to the parameters of network construction. We have demonstrated an enrichment of genes having lethal knockout phenotypes in the high-degree (i.e. hub) nodes in networks generated from aggregate condition datasets; using process-focused Saccharomyces cerivisiae datasets we have demonstrated additional high-degree enrichments of condition-specific genes encoding proteins known to be involved in or important for the processes interrogated by the microarrays. These results demonstrate the utility of network analysis applied to expression data in identifying genes that are regulated in a state-specific manner. We concluded by showing that a sample application to a human clinical dataset prominently identified a known therapeutic target. AVAILABILITY: Software implementing the methods for network generation presented in this paper is available for academic use by request from the authors in the form of compiled linux binary executables.

Algorithms↗

An empirical Bayes approach to inferring large-scale gene association networks.

MOTIVATION: Genetic networks are often described statistically using graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standard algorithms for graphical models inapplicable, and inferring genetic networks an 'ill-posed' inverse problem. METHODS: We introduce a novel framework for small-sample inference of graphical models from gene expression data. Specifically, we focus on the so-called graphical Gaussian models (GGMs) that are now frequently used to describe gene association networks and to detect conditionally dependent genes. Our new approach is based on (1) improved (regularized) small-sample point estimates of partial correlation, (2) an exact test of edge inclusion with adaptive estimation of the degree of freedom and (3) a heuristic network search based on false discovery rate multiple testing. Steps (2) and (3) correspond to an empirical Bayes estimate of the network topology. RESULTS: Using computer simulations, we investigate the sensitivity (power) and specificity (true negative rate) of the proposed framework to estimate GGMs from microarray data. This shows that it is possible to recover the true network topology with high accuracy even for small-sample datasets. Subsequently, we analyze gene expression data from a breast cancer tumor study and illustrate our approach by inferring a corresponding large-scale gene association network for 3883 genes.

Algorithms↗

Reconstructing biological networks using conditional correlation analysis.

MOTIVATION: One of the present challenges in biological research is the organization of the data originating from high-throughput technologies. One way in which this information can be organized is in the form of networks of influences, physical or statistical, between cellular components. We propose an experimental method for probing biological networks, analyzing the resulting data and reconstructing the network architecture. METHODS: We use networks of known topology consisting of nodes (genes), directed edges (gene-gene interactions) and a dynamics for the genes' mRNA concentrations in terms of the gene-gene interactions. We proposed a network reconstruction algorithm based on the conditional correlation of the mRNA equilibrium concentration between two genes given that one of them was knocked down. Using simulated gene expression data on networks of known connectivity, we investigated how the reconstruction error is affected by noise, network topology, size, sparseness and dynamic parameters. RESULTS: Errors arise from correlation between nodes connected through intermediate nodes (false positives) and when the correlation between two directly connected nodes is obscured by noise, non-linearity or multiple inputs to the target node (false negatives). Two critical components of the method are as follows: (1) the choice of an optimal correlation threshold for predicting connections and (2) the reduction of errors arising from indirect connections (for which a novel algorithm is proposed). With these improvements, we can reconstruct networks with the topology of the transcriptional regulatory network in Escherichia coli with a reasonably low error rate.

Algorithms↗

Supervised enzyme network inference from the integration of genomic data and chemical information.

MOTIVATION: The metabolic network is an important biological network which relates enzyme proteins and chemical compounds. A large number of metabolic pathways remain unknown nowadays, and many enzymes are missing even in known metabolic pathways. There is, therefore, an incentive to develop methods to reconstruct the unknown parts of the metabolic network and to identify genes coding for missing enzymes. RESULTS: This paper presents new methods to infer enzyme networks from the integration of multiple genomic data and chemical information, in the framework of supervised graph inference. The originality of the methods is the introduction of chemical compatibility as a constraint for refining the network predicted by the network inference engine. The chemical compatibility between two enzymes is obtained automatically from the information encoded by their Enzyme Commission (EC) numbers. The proposed methods are tested and compared on their ability to infer the enzyme network of the yeast Saccharomyces cerevisiae from four datasets for enzymes with assigned EC numbers: gene expression data, protein localization data, phylogenetic profiles and chemical compatibility information. It is shown that the prediction accuracy of the network reconstruction consistently improves owing to the introduction of chemical constraints, the use of a supervised approach and the weighted integration of multiple datasets. Finally, we conduct a comprehensive prediction of a global enzyme network consisting of all enzyme candidate proteins of the yeast to obtain new biological findings. AVAILABILITY: Softwares are available upon request.

Algorithms↗

Estimating gene regulatory networks and protein-protein interactions of Saccharomyces cerevisiae from multiple genome-wide data.

MOTIVATION: Biological processes in cells are properly performed by gene regulations, signal transductions and interactions between proteins. To understand such molecular networks, we propose a statistical method to estimate gene regulatory networks and protein-protein interaction networks simultaneously from DNA microarray data, protein-protein interaction data and other genome-wide data. RESULTS: We unify Bayesian networks and Markov networks for estimating gene regulatory networks and protein-protein interaction networks according to the reliability of each biological information source. Through the simultaneous construction of gene regulatory networks and protein-protein interaction networks of Saccharomyces cerevisiae cell cycle, we predict the role of several genes whose functions are currently unknown. By using our probabilistic model, we can detect false positives of high-throughput data, such as yeast two-hybrid data. In a genome-wide experiment, we find possible gene regulatory relationships and protein-protein interactions between large protein complexes that underlie complex regulatory mechanisms of biological processes.

Algorithms↗

Intervention in context-sensitive probabilistic Boolean networks.

MOTIVATION: Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean networks in which at any discrete time point the gene state vector transitions according to the rules of one of the constituent networks. For an instantaneously random PBN, the governing Boolean network is randomly chosen at each time point. For a context-sensitive PBN, the governing Boolean network remains fixed for an interval of time until a binary random variable determines a switch. The theory of automatic control has been previously applied to find optimal strategies for manipulating external (control) variables that affect the transition probabilities of an instantaneously random PBN to desirably affect its dynamic evolution over a finite time horizon. This paper extends the methods of external control to context-sensitive PBNs. RESULTS: This paper treats intervention via external control variables in context-sensitive PBNs by extending the results for instantaneously random PBNs in several directions. First, and most importantly, whereas an instantaneously random PBN yields a Markov chain whose state space is composed of gene vectors, each state of the Markov chain corresponding to a context-sensitive PBN is composed of a pair, the current gene vector occupied by the network and the current constituent Boolean network. Second, the analysis is applied to PBNs with perturbation, meaning that random gene perturbation is permitted at each instant with some probability. Third, the (mathematical) influence of genes within the network is used to choose the particular gene with which to intervene. Lastly, PBNs are designed from data using a recently proposed inference procedure that takes steady-state considerations into account. The results are applied to a context-sensitive PBN derived from gene-expression data collected in a study of metastatic melanoma, the intent being to devise a control strategy that reduces the WNT5A gene's action in affecting biological regulation, since the available data suggest that disruption of this influence could reduce the chance of a melanoma metastasizing.

Algorithms↗

Identification of biochemical networks by S-tree based genetic programming.

MOTIVATION: Most previous approaches to model biochemical networks have focused either on the characterization of a network structure with a number of components or on the estimation of kinetic parameters of a network with a relatively small number of components. For system-level understanding, however, we should examine both the interactions among the components and the dynamic behaviors of the components. A key obstacle to this simultaneous identification of the structure and parameters is the lack of data compared with the relatively large number of parameters to be estimated. Hence, there are many plausible networks for the given data, but most of them are not likely to exist in the real system. RESULTS: We propose a new representation named S-trees for both the structural and dynamical modeling of a biochemical network within a unified scheme. We further present S-tree based genetic programming to identify the structure of a biochemical network and to estimate the corresponding parameter values at the same time. While other evolutionary algorithms require additional techniques for sparse structure identification, our approach can automatically assemble the sparse primitives of a biochemical network in an efficient way. We evaluate our algorithm on the dynamic profiles of an artificial genetic network. In 20 trials for four settings, we obtain the true structure and their relative squared errors are <5% regardless of releasing constraints about structural sparseness. In addition, we confirm that the proposed algorithm is robust within +/-10% noise ratio. Furthermore, the proposed approach ensures a reasonable estimate of a real yeast fermentation pathway. The comparatively less important connections with non-zero parameters can be detected even though their orders are below 10(-2). To demonstrate the usefulness of the proposed algorithm for real experimental biological data, we provide an additional example on the transcriptional network of SOS response to DNA damage in Escherichia coli. We confirm that the proposed algorithm can successfully identify the true structure except only one relation.

Algorithms↗

Observing local and global properties of metabolic pathways: 'load points' and 'choke points' in the metabolic networks.

MOTIVATION: The local and global aspects of metabolic network analyses allow us to identify enzymes or reactions that are crucial for the survival of the organism(s), therefore directing us towards the discovery of potential drug targets. RESULTS: We demonstrate a new method ('load points') to rank the enzymes/metabolites in the metabolic network and propose a model to determine and rank the biochemical lethality in metabolic networks (enzymes/metabolites) through 'choke points'. Based on an extended form of the graph theory model of metabolic networks, metabolite structural information was used to calculate the k-shortest paths between metabolites (the presence of more than one competing path between substrate and product). On the basis of these paths and connectivity information, load points were calculated and used to empirically rank the importance of metabolites/enzymes in the metabolic network. The load point analysis emphasizes the role that the biochemical structure of a metabolite, rather than its connectivity (hubs), plays in the conversion pathway. In order to identify potential drug targets (based on the biochemical lethality of metabolic networks), the concept of choke points and load points was used to find enzymes (edges) which uniquely consume or produce a particular metabolite (nodes). A non-pathogenic bacterial strain Bacillus subtilis 168 (lactic acid producing bacteria) and a related pathogenic bacterial strain Bacillus anthracis Sterne (avirulent but toxigenic strain, producing the toxin Anthrax) were selected as model organisms. The choke point strategy was implemented on the pathogen bacterial network of B.anthracis Sterne. Potential drug targets are proposed based on the analysis of the top 10 choke points in the bacterial network. A comparative study between the reported top 10 bacterial choke points and the human metabolic network was performed. Further biological inferences were made on results obtained by performing a homology search against the human genome. AVAILABILITY: The load and choke point modules are introduced in the Pathway Hunter Tool (PHT), the basic version of which is available on http://www.pht.uni-koeln.de.

Bacillus↗

Two distinct functional networks for successful resolution of proactive interference.

In proactive interference (PI) paradigms, previous learning impairs the acquisition of new, related information. In rats, efficient resolution of PI relies on cholinergic modulation from the basal forebrain (BF). To test whether humans resolve PI using a functional network dependent on the medial septum/diagonal band of Broca (MS/DB) nuclei of the BF, we analyzed functional magnetic resonance imaging signal recorded while human participants learned to respond to baseline color paired associates and then additional pairs that interfered with the baseline pairs. Multivariate, partial least-squares analysis supported a MS/DB-dependent functional network: MS/DB activity covaried with activity in areas important to selective attention, including intraparietal sulcus, and memory that are direct cholinergic efferents of the MS/DB, including the hippocampus, as well as the ventrolateral prefrontal cortex, implicated in PI resolution. This network was associated with effective PI-resolution behavior. A second network also correlated with PI resolution but appearing not to be driven by the MS/DB, included the lateral orbitofrontal cortex. Patients with compromised BF function did not engage the MS/DB-dependent network reliably; instead their PI-resolution behavior was well explained by the second network. Thus, 2 functional networks may underly a single cognitive function; when the MS/DB-dependent attention/memory integration network is compromised, an alternate network is available to maintain normal levels of performance.

Alcoholism↗

Asymmetrical division of the kinetoplast DNA network of the trypanosome.

Trypanosome mitochondrial DNA is a network containing thousands of interlocked minicircles. Silencing of a mitochondrial topoisomerase II by RNA interference (RNAi) causes progressive network shrinking, allowing assessment of the minimal network size compatible with viability. We cloned surviving cells after short-term RNAi and found, as expected, that the number of surviving clones decreased with the duration of RNAi. Unexpectedly, a clonal cell line contained heterogeneously sized networks, some being very small. Several experiments showed that cells survived network shrinkage by asymmetrical division of replicated networks, sacrificing daughters with the small progeny network. Therefore, the average network size gradually increased. During the network shrinkage and early stages of recovery, there were changes in the minicircle repertoire.

Animals↗

Social networks among blacks and whites: the interaction between race and age.

OBJECTIVES: This study examined the main and interactive effects of age and race on the core characteristics of social networks including size, frequency of contact, geographical proximity, and composition of network. METHODS: Respondents were drawn from a stratified probability sample of people aged 20-93 in the greater Detroit metropolitan area. Approximately 30% of the sample were African American, and people aged 60 and older were over-sampled (n = 1.382). The authors used hierarchical regression analysis to estimate the influence of race and age on each component of social network, controlling for marital status, gender, and education. An interaction term (Race x Age) was added to explore the extent to which age moderates any detected race differences. RESULTS: Older age was associated with smaller, less frequently seen, and less proximal networks that had a higher proportion of kin. Blacks and Whites were similar with regard to proximity, but Blacks had smaller networks, more contact with network members, and more family members in their networks. Race differences in frequency of contact and proportion of kin were moderated by age, such that the differences in these variables diminished with increasing age. DISCUSSION: A systematic analysis of how age, race, and their interaction influence the characteristics of social networks furnishes important empirical knowledge about social networks among diverse groups. Such data may provide a context for how, and some explanation for why, support exchanges occur.

Adolescent↗

Social network type and morale in old age.

PURPOSE: The aim of this research was to derive network types among an elderly population and to examine the relationship of network type to morale. DESIGN AND METHODS: Secondary analysis of data compiled by the Israeli Central Bureau of Statistics (n = 2,079) was employed, and network types were derived through K-means cluster analysis. Respondents' morale scores were regressed on network types, controlling for background and health variables. RESULTS: Five network types were derived. Respondents in diverse or friends networks reported the highest morale; those in exclusively family or restricted networks had the lowest. Multivariate regression analysis underscored that certain network types were second among the study variables in predicting respondents' morale, preceded only by disability level (Adjusted R(2) =.41). IMPLICATIONS: Classification of network types allows consideration of the interpersonal environments of older people in relation to outcomes of interest. The relative effects on morale of elective versus obligated social ties, evident in the current analysis, is a case in point.

Activities of Daily Living↗

Effect of social networks on cancer-screening behavior of older Mexican-American women.

BACKGROUND: Previous studies have determined that Hispanic women and, in particular, Mexican-American women have the lowest rates of cancer screening of any race and ethnic group in the United States. In the development of cancer control strategies for this population, little attention has been given to factors that encourage Mexican-American women to seek cancer preventive care. Recent studies suggest that social networks can have a positive influence on cancer-screening participation. PURPOSE: We determined the extent to which differences in social networks account for variations in breast and cervical cancer-screening practices among low-income Mexican-American women. METHODS: The data analyzed in this study were obtained from a baseline survey of knowledge, attitudes, and cancer-screening practices conducted prior to implementation of community interventions designed to improve Pap smear and mammography screening in low-income Mexican-American women 40 years old and older living along the U.S.-Mexican border in El Paso County, Texas. A random selection of 1300 households served as a sampling frame to identify Mexican-American women 40 years old and older for personal interviews. Of the 549 households identified as having at least one eligible female, 450 women completed the personal interviews that provided the data for this study. Personal interviews solicited information on age, income, marital status, place of birth, education, health insurance coverage, Pap smear- and mammogram-screening practices, and six questions relating to social network. A social network score was assigned to each woman by summation of the following six variables: number of confidants, number of close friends, number of close relatives, frequency of contact with these close friends or relatives per month, church membership, and church attendance. Women were grouped into three linear strata of social network (low, medium, high) based on tertiles of the scores. Cancer-screening history was also ascertained during the interview. RESULTS: The 2-year prevalence of Pap smear and mammography use increased with social network. For each gain in social network level (low, medium, high), adjusted for sociodemographic factors, the odds ratio for Pap smear use was 1.33 (95% confidence interval = 1.02-1.73); it was 1.40 (95% confidence interval = 1.02-1.93) for mammogram use. Of the six social network components, the number of close friends was the most important predictor of mammography (P = .002) and Pap smear (P = .025) screening. CONCLUSION: Social networks appear to be an important determinant of cancer-screening behavior among low-income, older Mexican-American women.

Adult↗

Application of phylogenetic networks in evolutionary studies.

The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.

Animals↗

Functional modules by relating protein interaction networks and gene expression.

Genes and proteins are organized on the basis of their particular mutual relations or according to their interactions in cellular and genetic networks. These include metabolic or signaling pathways and protein interaction, regulatory or co-expression networks. Integrating the information from the different types of networks may lead to the notion of a functional network and functional modules. To find these modules, we propose a new technique which is based on collective, multi-body correlations in a genetic network. We calculated the correlation strength of a group of genes (e.g. in the co-expression network) which were identified as members of a module in a different network (e.g. in the protein interaction network) and estimated the probability that this correlation strength was found by chance. Groups of genes with a significant correlation strength in different networks have a high probability that they perform the same function. Here, we propose evaluating the multi-body correlations by applying the superparamagnetic approach. We compare our method to the presently applied mean Pearson correlations and show that our method is more sensitive in revealing functional relationships.

Algorithms↗

Likelihood analysis of phylogenetic networks using directed graphical models.

A method for computing the likelihood of a set of sequences assuming a phylogenetic network as an evolutionary hypothesis is presented. The approach applies directed graphical models to sequence evolution on networks and is a natural generalization of earlier work by Felsenstein on evolutionary trees, including it as a special case. The likelihood computation involves several steps. First, the phylogenetic network is rooted to form a directed acyclic graph (DAG). Then, applying standard models for nucleotide/amino acid substitution, the DAG is converted into a Bayesian network from which the joint probability distribution involving all nodes of the network can be directly read. The joint probability is explicitly dependent on branch lengths and on recombination parameters (prior probability of a parent sequence). The likelihood of the data assuming no knowledge of hidden nodes is obtained by marginalization, i.e., by summing over all combinations of unknown states. As the number of terms increases exponentially with the number of hidden nodes, a Markov chain Monte Carlo procedure (Gibbs sampling) is used to accurately approximate the likelihood by summing over the most important states only. Investigating a human T-cell lymphotropic virus (HTLV) data set and optimizing both branch lengths and recombination parameters, we find that the likelihood of a corresponding phylogenetic network outperforms a set of competing evolutionary trees. In general, except for the case of a tree, the likelihood of a network will be dependent on the choice of the root, even if a reversible model of substitution is applied. Thus, the method also provides a way in which to root a phylogenetic network by choosing a node that produces a most likely network.

Computer Graphics↗

Inferring pathways and networks with a Bayesian framework.

Numerous mathematical methods have been adapted and developed to quantitatively reverse engineer biological networks, for example, signal transduction pathways, from experimental micro-array data. Compared with stochastic methods, such as Boolean networks, and deterministic methods, such as thermodynamic or differential equation-based models, Bayesian network analysis has the ability to assess, with scoring metrics, causal relations based on conditional probabilities and thus permit hypothesis testing. The goal of this paper is to illustrate the integration of several Bayesian based techniques into a unified Bayesian framework that can infer hepatocellular networks from metabolic data. Reverse engineering of pathways and networks provides a framework for predictive modeling and hypotheses testing to gain deeper insight into living organisms, disease mechanisms, and targeted therapeutics. Evaluating this methodology initially against the known biochemical network provides confidence in the networks that are uncovered from the experimental data using this framework. From the metabolic data we inferred the known sub-networks, such as the tricarboxylic acid (TCA) and urea cycles. In addition, we combined the relationships learned from the data and our current knowledge of the biological system to postulate several alternative metabolic sub-network models that can predict a particular cellular function, such as intracellular triglyceride accumulation.

Algorithms↗

Trends in HIV seroprevalence among patients with sexually transmitted diseases in 17 European sentinel networks, 1990-1996. European Study Group.

OBJECTIVE: To monitor trends in HIV seroprevalence among sentinel populations of patients with new sexually transmitted disease episodes in 17 networks of 15 European countries. METHODS: Time trends were estimated by logistic regression for homo-/bisexual men, injecting drug users (IDU) and non-IDU heterosexuals. The networks were included as independent variables to account for different prevalence levels across Europe. Socio-demographic and behavioural data were also included in the model. The interactions of time and each factor in the model were evaluated to determine whether trends differed across networks or population subgroups. RESULTS: Overall, more than 150,000 sexually transmitted disease episodes were registered in this study. In the European network as a whole, the prevalence decreased significantly among IDU [n = 2619; odds ratio (OR) for annual change, 0.86; 95% confidence interval (CI), 0.80-0.93]. It also decreased among homo-/bisexual men (n = 11,809; OR, 0.92; 95% CI, 0.89-0.94). In both groups, trends did not differ statistically between networks. Among non-IDU heterosexuals (n = 114,024) the prevalence increased significantly (OR, 1.08; 95% CI, 1.04-1.13), especially among women (OR, 1.13) and the time trends differed statistically across networks. A significant increase was observed in four networks, whereas no specific change was detected in the others. CONCLUSIONS: By applying a standardized protocol, trends in HIV prevalence could be compared across networks and estimated at a more global level. For the validity of HIV trends in such surveys, it is essential to minimize the number of patients not being tested in networks where voluntary testing is required.

Adult↗