A General Framework for Weighted Gene Co-Expression Network Analysis

Abstract

Gene co-expression networks are increasingly used to explore the system-level functionality of genes. The network construction is conceptually straightforward: nodes represent genes and nodes are connected if the corresponding genes are significantly co-expressed across appropriately chosen tissue samples. In reality, it is tricky to define the connections between the nodes in such networks. An important question is whether it is biologically meaningful to encode gene co-expression using binary information (connected=1, unconnected=0). We describe a general framework for 'soft' thresholding that assigns a connection weight to each gene pair. This leads us to define the notion of a weighted gene co-expression network. For soft thresholding we propose several adjacency functions that convert the co-expression measure to a connection weight. For determining the parameters of the adjacency function, we propose a biologically motivated criterion (referred to as the scale-free topology criterion).We generalize the following important network concepts to the case of weighted networks. First, we introduce several node connectivity measures and provide empirical evidence that they can be important for predicting the biological significance of a gene. Second, we provide theoretical and empirical evidence that the 'weighted' topological overlap measure (used to define gene modules) leads to more cohesive modules than its 'unweighted' counterpart. Third, we generalize the clustering coefficient to weighted networks. Unlike the unweighted clustering coefficient, the weighted clustering coefficient is not inversely related to the connectivity. We provide a model that shows how an inverse relationship between clustering coefficient and connectivity arises from hard thresholding.We apply our methods to simulated data, a cancer microarray data set, and a yeast microarray data set.

Toxicogenomic module associations with pathogenesis: a network-based approach to understanding drug toxicity

“…Using 654 treatments from DM rat liver and a subset of 9071 liverexpressed genes, 415 co-expression networks were obtained using WGCNA 22 as described in reference. 11 Co-expression modules represent gene sets that show correlated behavior (that is, co-induced or co-repressed) across the DM rat liver database.…”

“…20,21 One such approach, weighted gene co-expression network analysis (WGCNA), uses the property of coexpression to organize genes into gene networks or modules. 22 Here we develop a co-expression framework called the 'toxicogenomic module associations with pathogenesis' (the TXG-MAP) and integrate it with standard pathology evaluation to characterize mechanisms of drug-induced liver injury. We demonstrate the utility of the TXG-MAP for common applications.…”

Population-level expression variability of mitochondrial DNA-encoded genes in humans

“…For each module, we defined eigengene significance by measuring the correlation between the modules and the trait under consideration (ie, the average expression level of mtDNA genes). To ensure the results are robust to the WGCNA parameter settings, 19 we allowed the key parameter, the thresholding power for network construction (or the power), to vary between 5, 6 (the optimal value determined by WGCNA), and 7, where the other parameters were kept fixed (ie, the smallest value of the scale independence ¼ 0.9, the minimum module size ¼ 30, and the maximum joining height ¼ 10). Thus, instead of producing WGCNA modules using one single value for the power, we ran WGCNA three times with three different power values and produced three sets of WGCNA modules.…”

Proteomic Approaches and Identification of Novel Therapeutic Targets for Alcoholism

“…Integrative approaches are thus essential in providing a global picture of the disturbances leading to alcohol addiction or related disorders. As an example, weighted gene coexpression network analysis (WGCNA) is a bioinformatics tool for the study of coexpression patterns from high-throughput data (Langfelder and Horvath, 2008;Zhang and Horvath, 2005). The correlation values between genes indicate expression level similarities or differences, and WGCNA analysis can identify modules of interconnected genes showing overrepresented patterns of coexpression.…”