Dataset Information

Critical effect of dependency groups on the function of networks.

ABSTRACT: Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the nodes to function cooperatively as a network and dependency links that bind the failure of one network element to the failure of other network elements. Here we present an analytical framework for studying the robustness of networks that include both connectivity and dependency links. We show that a synergy exists between the failure of connectivity and dependency links that leads to an iterative process of cascading failures that has a devastating effect on the network stability. We present exact analytical results for the dramatic change in the network behavior when introducing dependency links. For a high density of dependency links, the network disintegrates in a form of a first-order phase transition, whereas for a low density of dependency links, the network disintegrates in a second-order transition. Moreover, opposed to networks containing only connectivity links where a broader degree distribution results in a more robust network, when both types of links are present a broad degree distribution leads to higher vulnerability.

SUBMITTER: Parshani R

PROVIDER: S-EPMC3024657 | biostudies-literature | 2011 Jan

REPOSITORIES: biostudies-literature

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Publications

Critical effect of dependency groups on the function of networks.

Parshani Roni R Buldyrev Sergey V SV Havlin Shlomo S

Proceedings of the National Academy of Sciences of the United States of America 20101229 3

Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the nodes to function cooperatively as a network and dependency links that bind the failure of one network element to the failure of other network elements. Here we present an analytical framework for studying the robustness of networks that include both connectivity ...[more]

PMID: 21191103

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Project description:BackgroundModeling biological networks serves as both a major goal and an effective tool of systems biology in studying mechanisms that orchestrate the activities of gene products in cells. Biological networks are context-specific and dynamic in nature. To systematically characterize the selectively activated regulatory components and mechanisms, modeling tools must be able to effectively distinguish significant rewiring from random background fluctuations. While differential networks cannot be constructed by existing knowledge alone, novel incorporation of prior knowledge into data-driven approaches can improve the robustness and biological relevance of network inference. However, the major unresolved roadblocks include: big solution space but a small sample size; highly complex networks; imperfect prior knowledge; missing significance assessment; and heuristic structural parameter learning.ResultsTo address these challenges, we formulated the inference of differential dependency networks that incorporate both conditional data and prior knowledge as a convex optimization problem, and developed an efficient learning algorithm to jointly infer the conserved biological network and the significant rewiring across different conditions. We used a novel sampling scheme to estimate the expected error rate due to "random" knowledge. Based on that scheme, we developed a strategy that fully exploits the benefit of this data-knowledge integrated approach. We demonstrated and validated the principle and performance of our method using synthetic datasets. We then applied our method to yeast cell line and breast cancer microarray data and obtained biologically plausible results. The open-source R software package and the experimental data are freely available at http://www.cbil.ece.vt.edu/software.htm.ConclusionsExperiments on both synthetic and real data demonstrate the effectiveness of the knowledge-fused differential dependency network in revealing the statistically significant rewiring in biological networks. The method efficiently leverages data-driven evidence and existing biological knowledge while remaining robust to the false positive edges in the prior knowledge. The identified network rewiring events are supported by previous studies in the literature and also provide new mechanistic insight into the biological systems. We expect the knowledge-fused differential dependency network analysis, together with the open-source R package, to be an important and useful bioinformatics tool in biological network analyses.

Project description:MotivationSignificant efforts have been made to acquire data under different conditions and to construct static networks that can explain various gene regulation mechanisms. However, gene regulatory networks are dynamic and condition-specific; under different conditions, networks exhibit different regulation patterns accompanied by different transcriptional network topologies. Thus, an investigation on the topological changes in transcriptional networks can facilitate the understanding of cell development or provide novel insights into the pathophysiology of certain diseases, and help identify the key genetic players that could serve as biomarkers or drug targets.ResultsHere, we report a differential dependency network (DDN) analysis to detect statistically significant topological changes in the transcriptional networks between two biological conditions. We propose a local dependency model to represent the local structures of a network by a set of conditional probabilities. We develop an efficient learning algorithm to learn the local dependency model using the Lasso technique. A permutation test is subsequently performed to estimate the statistical significance of each learned local structure. In testing on a simulation dataset, the proposed algorithm accurately detected all the genes with network topological changes. The method was then applied to the estrogen-dependent T-47D estrogen receptor-positive (ER+) breast cancer cell line datasets and human and mouse embryonic stem cell datasets. In both experiments using real microarray datasets, the proposed method produced biologically meaningful results. We expect DDN to emerge as an important bioinformatics tool in transcriptional network analyses. While we focus specifically on transcriptional networks, the DDN method we introduce here is generally applicable to other biological networks with similar characteristics.AvailabilityThe DDN MATLAB toolbox and experiment data are available at http://www.cbil.ece.vt.edu/software.htm.

Dataset Information

Critical effect of dependency groups on the function of networks.

Publications

Critical effect of dependency groups on the function of networks.

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